Finite Group Databasebeta

← #35197413

Subgroups — #35197413

Order 20224.

7086 conjugacy classes of subgroups.

The subgroup lattice has 1582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777318C214yesmaximal, complemented
2#23777314C214yesmaximal, complemented
3#23777310C214yesmaximal, complemented
4#23777308C214yesmaximal, complemented
5#23777232C214yesmaximal, complemented
6#23777228C214yesmaximal, complemented
7#23777151C214yesmaximal, complemented
8#23777148C214yesmaximal, complemented
9#23777128C214yesmaximal, complemented
10#23777124C214yesmaximal, complemented
11#23777121C211yesmaximal, characteristic, complemented
12#23777119C211yesmaximal, characteristic, complemented
13#23777117C212yesmaximal, complemented
14#23777109C211yesmaximal, characteristic, complemented
15#23777103C212yesmaximal, complemented
16#23776830C214yesmaximal, complemented
17#23776818C214yesmaximal, complemented
18#544×D79C211yesmaximal, characteristic, complemented
19#23776730C212yesmaximal, complemented
20#537×D79C211yesmaximal, characteristic, complemented
21#23776600C212yesmaximal, complemented
22C2×#19099044C211yesmaximal, characteristic, complemented
23C79×#3492C211yesmaximal, characteristic, complemented
24C22×#11929624C2211yescharacteristic
25C2×#41×D79C2212yes—
26#19099287C2214yescomplemented
27#19099284C2214yescomplemented
28#19099284C2214yescomplemented
29#19099283C2214yescomplemented
30#19099279C2214yescomplemented
31#19099278C2214yescomplemented
32#19099277C2214yescomplemented
33#19099277C2214yescomplemented
34#19099273C2214yescomplemented
35#19099268C2214yescomplemented
36#19099268C2214yescomplemented
37#19099266C2218yescomplemented
38#19099266C2214yescomplemented
39#19099265C2214yescomplemented
40#19099264C2218yescomplemented
41#19099263C2218yescomplemented
42#19099263C2214yescomplemented
43#19099261C2214yescomplemented
44#19099260C2214yescomplemented
45#19099260C2214yescomplemented
46#19099259C2214yescomplemented
47#19099258C2218yescomplemented
48#19099258C2218yescomplemented
49#19099257C2214yescomplemented
50#19099257C2214yescomplemented
51#19099255C2214yescomplemented
52#19099254C2214yescomplemented
53#19099253C2214yescomplemented
54#19099252C2214yescomplemented
55#19099252C2214yescomplemented
56#19099251C2214yescomplemented
57#19099248C2214yescomplemented
58#19099247C2214yescomplemented
59#19099247C2214yescomplemented
60#19099245C2218yescomplemented
61#19099242C2218yescomplemented
62#19099241C2218yescomplemented
63#19099240C2218yescomplemented
64#19099238C2218yescomplemented
65#19099223C2214yescomplemented
66#19099223C2218yescomplemented
67#19099220C2214yescomplemented
68#19099218C2214yescomplemented
69#19099214C2214yescomplemented
70#19099214C2214yescomplemented
71#19099210C2214yescomplemented
72#19099205C2218yescomplemented
73#19099201C2214yescomplemented
74#19099194C2211yescharacteristic, complemented
75#19099193C2214yescomplemented
76#19099192C2214yescomplemented
77#19099191C2212yescomplemented
78#19099190C2214yescomplemented
79#19099183C2218yescomplemented
80#19099183C2218yescomplemented
81#19099181C2218yescomplemented
82#19099181C2218yescomplemented
83#19099172C2218yescomplemented
84#19099170C2218yescomplemented
85#19099165C2218yescomplemented
86#19099163C2218yescomplemented
87#19099160C2214yescomplemented
88#19099155C2218yescomplemented
89#19099153C2214yescomplemented
90#19099150C2214yescomplemented
91#19099148C2218yescomplemented
92#19099144C2211yescharacteristic
93#19099143C2212yescomplemented
94#19099143C2214yescomplemented
95#19099143C2212yescomplemented
96#19099142C2212yescomplemented
97#19099142C2214yescomplemented
98#19099142C2212yescomplemented
99#19099141C2212yes—
100#19099140C2214yes—
101#19099136C2212yes—
102#19099136C2212yes—
103#19099135C2214yescomplemented
104#19099129C2212yes—
105#19099129C2212yes—
106#19099128C2214yescomplemented
107#19099124C2214yes—
108#19099123C2214yes—
109#19099119C2218yescomplemented
110#19099115C2218yescomplemented
111#19099110C2214yescomplemented
112#19099110C2218yescomplemented
113#19099110C2214yescomplemented
114#19099109C2218yescomplemented
115C4⋊Q8×D79C2214yescomplemented
116#19099099C2214yescomplemented
117#19099096C2218yescomplemented
118#19099094C2214yescomplemented
119#19099093C2218yescomplemented
120#19099091C2218yescomplemented
121#19099090C2218yescomplemented
122#19099090C2218yescomplemented
123#125×D79C2214yescomplemented
124#19099075C2212yescomplemented
125#19099074C2214yescomplemented
126#19099074C2212yescomplemented
127#19099072C2214yes—
128#19099072C2214yes—
129#19099072C2218yescomplemented
130#19099070C2212yescomplemented
131C22⋊Q8×D79C2214yes—
132C22⋊Q8×D79C2214yescomplemented
133#121×D79C2214yes—
134#121×D79C2214yescomplemented
135#19099046C2212yescomplemented
136#19099044C2214yes—
137#19099044C2214yes—
138#19099044C2214yescomplemented
139#19099044C2214yescomplemented
140#19099044C2214yescomplemented
141#19099044C2212yescomplemented
142#19099043C2214yescomplemented
143#19099043C2212yescomplemented
144#19099039C2214yescomplemented
145#19099035C2218yes—
146#19099035C2214yescomplemented
147C4×#11929625C2214yescomplemented
148C4×#11929623C2214yescomplemented
149C4×#11929623C2218yescomplemented
150C2×#14579126C2212yescomplemented
151C2×#14579123C2212yes—
152C2×C4×C22⋊D79C2212yes—
153C2×C4×C22⋊D79C2212yescomplemented
154C2×#14579120C2211yescharacteristic, complemented
155C2×#14579119C2211yescharacteristic
156C2×#14579119C2211yescharacteristic, complemented
157C2×#14579119C2214yescomplemented
158#117×D79C2212yes—
159#117×D79C2214yescomplemented
160C2×C4⋊C4×D79C2211yescharacteristic
161C2×C4⋊C4×D79C2211yescharacteristic, complemented
162#554×C79C2214yescomplemented
163#553×C79C2214yescomplemented
164#552×C79C2214yescomplemented
165#547×C79C2214yescomplemented
166#544×C79C2211yescharacteristic, complemented
167#539×C79C2214yescomplemented
168#537×C79C2211yescharacteristic
169#525×C79C2214yescomplemented
170#525×C79C2212yescomplemented
171#520×C79C2212yescomplemented
172C22×C4⋊C4×C79C2211yescharacteristic, complemented
173C2×#11929625C2312yes—
174C2×#11929624—28no—
175C2×#11929624C2312yes—
176C2×#11929624C2312yes—
177C2×#11929624C2312yes—
178C2×#11929624C2314yes—
179C2×#11929624C2312yes—
180C2×#11929624C2312yes—
181C2×#11929624C2318yes—
182C2×#11929624C2314yes—
183C2×#11929623C2314yes—
184C2×#11929623C2312yes—
185#41×D79—216no—
186C22×Dic158C2311yescharacteristic
187C2×Q8×D79C2312yes—
188C2×Q8×D79C2314yes—
189C22×D316C2311yescharacteristic
190C22×C22⋊D79C2311yescharacteristic
191C22×C22⋊D79C2311yescharacteristic
192C2×D4×D79C2314yes—
193C2×D4×D79C2312yes—
194C2×D4×D79C2314yes—
195C22×C4×D79C2311yescharacteristic
196C22×C4×D79C2314yes—
197C22×C4×D79C2312yes—
198C22×C4×D79C2312yes—
199C22×C4×D79C2311yescharacteristic
200#14579161C2314yes—
201#14579160C2314yes—
202#14579160C2314yes—
203#14579160C2318yes—
204#14579160C2314yes—
205#14579160C2314yes—
206#14579159C2318yes—
207#14579157C2314yes—
208#14579157C2314yes—
209#14579156C2318yes—
210#14579156C2318yes—
211#14579156C2318yes—
212#14579156C2318yes—
213#14579156C2318yes—
214#14579155C2318yes—
215#14579154C2318yes—
216#14579154C2318yes—
217#14579154C2318yes—
218#14579154C2318yes—
219#14579154C2318yes—
220#14579153C2318yes—
221#14579153C2314yes—
222#14579152C2314yes—
223#14579152C2314yes—
224#14579152C2314yes—
225#14579152C2314yes—
226#14579151C2318yes—
227#14579151C2318yes—
228#14579151C2318yes—
229#14579151C2318yes—
230#14579151C2318yes—
231#14579150C2318yes—
232#14579150C2314yes—
233#14579148C2318yes—
234#14579148C2314yes—
235#14579147C2314yes—
236#14579147C2314yes—
237#14579147C2318yes—
238#14579147C2318yes—
239#14579147C2314yes—
240#14579147C2318yes—
241#14579147C2314yes—
242#14579146C2314yes—
243#14579146C2314yes—
244#14579146C2318yes—
245#14579146C2318yes—
246#14579146C2318yes—
247#14579145C2318yes—
248#14579145C2314yes—
249#14579144C2318yes—
250#14579144C2314yes—
251#14579144C2318yes—
252#14579143C2314yes—
253#14579143C2314yes—
254#14579143C2318yes—
255#14579143C2318yes—
256#14579143C2318yes—
257#14579142C2318yes—
258#14579142C2314yes—
259#14579141C2312yes—
260#14579141C2312yes—
261#14579141C2314yes—
262#14579141C2314yes—
263#14579140C2312yes—
264#14579140C2312yes—
265#14579140C2314yes—
266#14579140C2314yes—
267#14579140C2318yes—
268#14579140C2314yes—
269#14579139C2318yes—
270#14579139C2314yes—
271#14579139C2314yes—
272#14579139C2318yes—
273#14579139C2318yes—
274#14579139C2318yes—
275#14579139C2318yes—
276#14579138C2318yes—
277#14579138C2314yes—
278#14579138C2314yes—
279#14579138C2318yes—
280#14579137C2312yes—
281#14579137C2312yes—
282#14579137C2314yes—
283#14579137C2314yes—
284#14579136C2314yes—
285#14579136C2314yes—
286#14579136C2312yes—
287#14579136C2314yes—
288#14579136C2312yes—
289#14579136C2314yes—
290#14579136C2318yes—
291#14579135C2314yes—
292#14579135C2314yes—
293#14579135C2312yes—
294#14579135C2312yes—
295#14579135C2314yes—
296#14579134C2318yes—
297#14579134C2318yes—
298#14579134C2314yes—
299#14579134C2314yes—
300#14579134C2314yes—
301#14579134C2314yes—
302#14579134C2314yes—
303#14579134C2314yes—
304#14579134C2318yes—
305#14579133C2318yes—
306#14579133C2318yes—
307#14579133C2314yes—
308#14579133C2314yes—
309#14579133C2318yes—
310#14579133C2318yes—
311#14579132C2314yes—
312#14579132C2314yes—
313#14579132C2312yes—
314#14579132C2314yes—
315#14579132C2314yes—
316#14579132C2312yes—
317#14579132C2318yes—
318#14579131C2314yes—
319#14579131C2314yes—
320#14579131C2314yes—
321#14579130C2314yes—
322#14579129C2314yes—
323#14579129C2314yes—
324#14579129C2314yes—
325Q8×Dic79C2314yes—
326Q8×Dic79C2314yes—
327C4×Dic158C2318yes—
328C4×Dic158C2314yes—
329#14579126C2318yes—
330#14579126C2318yes—
331#14579126C2318yes—
332#14579126C2318yes—
333#14579126C2314yes—
334#14579126C2314yes—
335C4×D316C2314yes—
336C4×D316C2318yes—
337C4×D316C2314yes—
338C4×D316C2318yes—
339C4×D316C2314yes—
340D4×Dic79C2318yes—
341D4×Dic79C2314yes—
342D4×Dic79C2314yes—
343#14579123C2318yes—
344#14579123C2314yes—
345#14579123C2314yes—
346#14579123C2318yes—
347#14579123C2318yes—
348C4×C22⋊D79C2318yes—
349C4×C22⋊D79C2318yes—
350C4×C22⋊D79C2318yes—
351C4×C22⋊D79C2318yes—
352C4×C22⋊D79C2314yes—
353C4×C22⋊D79C2314yes—
354C4×C22⋊D79C2314yes—
355C4×C22⋊D79C2314yes—
356C4×C22⋊D79C2318yes—
357C4×C22⋊D79C2314yes—
358C4×C22⋊D79C2314yes—
359C4×C22⋊D79C2318yes—
360C4×C22⋊D79C2318yes—
361C4×C22⋊D79C2314yes—
362C4×C22⋊D79C2314yes—
363(C22⋊D79)⋊C4C2318yes—
364(C22⋊D79)⋊C4C2318yes—
365(C22⋊D79)⋊C4C2318yes—
366(C22⋊D79)⋊C4C2318yes—
367#14579120C2312yes—
368#14579120C2314yes—
369#14579120C2314yes—
370#14579120C2314yes—
371#14579120C2314yes—
372#14579119C2312yes—
373#14579119C2312yes—
374#14579119C2318yes—
375#14579119C2318yes—
376#14579119C2318yes—
377#14579119C2318yes—
378#14579119C2314yes—
379#14579119C2314yes—
380#14579119C2314yes—
381#14579119C2314yes—
382#14579119C2314yes—
383#14579119C2314yes—
384#14579118C2314yes—
385#14579118C2318yes—
386#14579118C2318yes—
387#14579117C2318yes—
388#14579117C2314yes—
389#14579117C2318yes—
390#14579117C2318yes—
391C2×C4⋊Dic79C2311yescharacteristic
392C2×C4⋊Dic79C2314yes—
393C2×C4⋊Dic79C2311yescharacteristic
394C2×Dic79⋊C4C2312yes—
395C2×Dic79⋊C4C2312yes—
396C4⋊C4×D79C2314yes—
397C4⋊C4×D79C2312yes—
398C4⋊C4×D79C2312yes—
399C4⋊C4×D79C2314yes—
400C4⋊C4×D79C2314yes—
401C4⋊C4×D79C2314yes—
402C4⋊C4×D79C2314yes—
403C4⋊C4×D79C2314yes—
404C4⋊C4×D79C2314yes—
405C4⋊C4×D79C2314yes—
406C4⋊C4×D79C2318yes—
407C2×C22⋊Dic79C2312yes—
408C2×(C2×D79)⋊C4C2312yes—
409C2×(C2×D79)⋊C4C2318yes—
410C2×(C2×D79)⋊C4C2312yes—
411C22⋊C4×D79C2318yes—
412C22⋊C4×D79C2318yes—
413C22⋊C4×D79C2314yes—
414C2×C4×Dic79C2312yes—
415C2×C4×Dic79C2312yes—
416C2×C4×Dic79C2318yes—
417C2×C4×Dic79C2312yes—
418C42×D79C2314yes—
419C42×D79C2318yes—
420C2×#41×C79C2312yes—
421C2×#41×C79C2314yes—
422C23×C4×C79C2311yescharacteristic
423C23×C4×C79C2312yes—
424C4⋊Q8×C79C2314yes—
425#126×C79C2318yes—
426#125×C79C2318yes—
427#125×C79C2314yes—
428#123×C79C2318yes—
429#123×C79C2318yes—
430#123×C79C2314yes—
431C22⋊Q8×C79C2312yes—
432C22⋊Q8×C79C2312yes—
433C22⋊Q8×C79C2314yes—
434C22⋊Q8×C79C2314yes—
435C22⋊Q8×C79C2314yes—
436C22⋊Q8×C79C2318yes—
437#121×C79C2314yes—
438#121×C79C2312yes—
439#121×C79C2312yes—
440#121×C79C2314yes—
441#121×C79C2314yes—
442#120×C79C2314yes—
443C4×Q8×C79C2314yes—
444C4×D4×C79C2318yes—
445C4×D4×C79C2314yes—
446C4×D4×C79C2318yes—
447C4×D4×C79C2314yes—
448C4×D4×C79C2314yes—
449#117×C79C2312yes—
450#117×C79C2314yes—
451#117×C79C2314yes—
452C2×C4⋊C4×C79C2311yescharacteristic
453C2×C4⋊C4×C79C2312yes—
454C2×C4⋊C4×C79C2314yes—
455C2×C4⋊C4×C79C2314yes—
456C2×C4⋊C4×C79C2311yescharacteristic
457C2×C4⋊C4×C79C2314yes—
458C23×D79C2414yes—
459C23×D79C2411yescharacteristic
460C23×D79C2411yescharacteristic
461#11929625—28no—
462#11929624—216no—
463#11929624—28no—
464#11929624—28no—
465#11929624—28no—
466#11929624—28no—
467#11929624—28no—
468#11929624—88no—
469#11929624—84no—
470#11929623—216no—
471#11929623—28no—
472C2×Dic158—24no—
473C2×Dic158C2414yes—
474C2×Dic158C2412yes—
475C2×Dic158C2412yes—
476C2×Dic158C2412yes—
477C2×Dic158C2418yes—
478C2×Dic158C2414yes—
479Q8×D79—28no—
480Q8×D79—84no—
481C2×D316—24no—
482C2×D316C2412yes—
483C2×D316C2412yes—
484C2×D316C2414yes—
485C2×D316C2412yes—
486C2×D316C2414yes—
487C2×D316C2414yes—
488C2×D316C2414yes—
489C2×C22⋊D79—24no—
490C2×C22⋊D79—24no—
491C2×C22⋊D79C2414yes—
492C2×C22⋊D79C2414yes—
493C2×C22⋊D79C2414yes—
494C2×C22⋊D79C2411yescharacteristic
495C2×C22⋊D79C2411yescharacteristic
496C2×C22⋊D79C2411yescharacteristic
497C2×C22⋊D79C2411yescharacteristic
498C2×C22⋊D79C2412yes—
499C2×C22⋊D79C2412yes—
500C2×C22⋊D79C2414yes—
501C2×C22⋊D79C2414yes—
502C2×C22⋊D79C2418yes—
503C2×C22⋊D79C2414yes—
504C2×C22⋊D79C2414yes—
505D4×D79—28no—
506D4×D79—216no—
507D4×D79—84no—
508C22×Dic79C2411yescharacteristic
509C22×Dic79C2414yes—
510C22×Dic79C2412yes—
511C22×Dic79C2418yes—
512C22×Dic79C2412yes—
513C22×Dic79C2411yescharacteristic
514C2×C4×D79—216no—
515C2×C4×D79—24no—
516C2×C4×D79—82no—
517C2×C4×D79—82no—
518C2×C4×D79#4118yescomplemented
519C2×C4×D79C2414yes—
520C2×C4×D79C2414yes—
521C2×C4×D79C2412yes—
522C2×C4×D79C2412yes—
523C2×C4×D79C2414yes—
524C2×C4×D79C2414yes—
525C2×C4×D79C2414yes—
526C2×C4×D79C2418yes—
527C2×C4×D79C2418yes—
528C2×C4×D79C2414yes—
529C2×C4×D79C2418yes—
530C2×C4×D79C2414yes—
531C2×C4×D79C2412yes—
532C2×C4×D79C2412yes—
533C4⋊Dic79C2414yes—
534C4⋊Dic79C2412yes—
535C4⋊Dic79C2414yes—
536C4⋊Dic79C2412yes—
537C4⋊Dic79C2418yes—
538C4⋊Dic79C2414yes—
539C4⋊Dic79C2414yes—
540C4⋊Dic79C2418yes—
541C4⋊Dic79C2414yes—
542C4⋊Dic79C2414yes—
543Dic79⋊C4C2418yes—
544Dic79⋊C4C2414yes—
545Dic79⋊C4C2414yes—
546Dic79⋊C4C2414yes—
547Dic79⋊C4C2418yes—
548Dic79⋊C4C2414yes—
549Dic79⋊C4C2418yes—
550Dic79⋊C4C2418yes—
551Dic79⋊C4C2418yes—
552Dic79⋊C4C2418yes—
553Dic79⋊C4C2418yes—
554Dic79⋊C4C2414yes—
555Dic79⋊C4C2414yes—
556Dic79⋊C4C2414yes—
557Dic79⋊C4C2414yes—
558C22⋊Dic79C2414yes—
559C22⋊Dic79C2418yes—
560C22⋊Dic79C2418yes—
561C22⋊Dic79C2414yes—
562C22⋊Dic79C2414yes—
563C22⋊Dic79C2414yes—
564C22⋊Dic79C2414yes—
565C22⋊Dic79C2414yes—
566C22⋊Dic79C2414yes—
567(C2×D79)⋊C4C2414yes—
568(C2×D79)⋊C4C2414yes—
569(C2×D79)⋊C4C2414yes—
570(C2×D79)⋊C4C2418yes—
571(C2×D79)⋊C4C2418yes—
572(C2×D79)⋊C4C2414yes—
573(C2×D79)⋊C4C2418yes—
574(C2×D79)⋊C4C2418yes—
575(C2×D79)⋊C4C2418yes—
576(C2×D79)⋊C4C2414yes—
577(C2×D79)⋊C4C2414yes—
578(C2×D79)⋊C4C2414yes—
579(C2×D79)⋊C4C2414yes—
580(C2×D79)⋊C4C2414yes—
581(C2×D79)⋊C4C2414yes—
582(C2×D79)⋊C4C2414yes—
583(C2×D79)⋊C4C2414yes—
584C4×Dic79C2414yes—
585C4×Dic79C2418yes—
586C4×Dic79C2414yes—
587C4×Dic79C2418yes—
588C4×Dic79C2414yes—
589C4×Dic79C2414yes—
590C4×Dic79C2418yes—
591C4×Dic79C2418yes—
592C4×Dic79C2418yes—
593C4×Dic79C2414yes—
594C24×C79C2411yescharacteristic
595#41×C79—28no—
596#41×C79—84no—
597C2×Q8×C79C2412yes—
598C2×Q8×C79C2414yes—
599C2×D4×C79C2414yes—
600C2×D4×C79C2412yes—
601C2×D4×C79C2414yes—
602C2×D4×C79C2414yes—
603C2×D4×C79C2414yes—
604C22×C4×C79—24no—
605C22×C4×C79—82no—
606C22×C4×C79C2411yescharacteristic
607C22×C4×C79C2412yes—
608C22×C4×C79C2412yes—
609C22×C4×C79C2414yes—
610C22×C4×C79C2414yes—
611C22×C4×C79C2418yes—
612C22×C4×C79C2414yes—
613C22×C4×C79C2412yes—
614C22×C4×C79C2412yes—
615C22×C4×C79C2411yescharacteristic
616C4⋊C4×C79C2414yes—
617C4⋊C4×C79C2414yes—
618C4⋊C4×C79C2418yes—
619C4⋊C4×C79C2412yes—
620C4⋊C4×C79C2418yes—
621C4⋊C4×C79C2412yes—
622C4⋊C4×C79C2414yes—
623C4⋊C4×C79C2414yes—
624C4⋊C4×C79C2414yes—
625C4⋊C4×C79C2418yes—
626C4⋊C4×C79C2414yes—
627C22⋊C4×C79C2414yes—
628C22⋊C4×C79C2414yes—
629C22⋊C4×C79C2418yes—
630C22⋊C4×C79C2414yes—
631C22⋊C4×C79C2418yes—
632C22⋊C4×C79C2414yes—
633C22⋊C4×C79C2414yes—
634C42×C79C2418yes—
635C42×C79C2414yes—
636C23×C79—22no—
637C23×C79—41no—
638C23×C79—41no—
639C23×C79C2511yescharacteristic
640C23×C79C2511yescharacteristic
641C23×C79C2514yes—
642C23×C79C2511yescharacteristic
643C22×D79—22no—
644C22×D79—28no—
645C22×D79—41no—
646C22×D79—41no—
647C22×D79—41no—
648C22×D79—41no—
649C22×D79—44no—
650C22×D79—44no—
651C22×D79C2×#4114yes—
652C22×D79C2514yes—
653C22×D79C2512yes—
654C22×D79C2511yescharacteristic
655C22×D79C2511yescharacteristic
656Q8×C79—24no—
657Q8×C79—44no—
658D4×C79—28no—
659D4×C79—24no—
660D4×C79—44no—
661D4×C79—44no—
662D4×C79—44no—
663C2×C4×C79—22no—
664C2×C4×C79—28no—
665C2×C4×C79—24no—
666C2×C4×C79—24no—
667C2×C4×C79—42no—
668C2×C4×C79—42no—
669C2×C4×C79—44no—
670C2×C4×C79—48no—
671C2×C4×C79—44no—
672C2×C4×C79C2×#4114yes—
673C2×C4×C79C2514yes—
674C2×C4×C79C2512yes—
675C2×C4×C79C2514yes—
676C2×C4×C79C2514yes—
677C2×C4×C79C2514yes—
678C2×C4×C79C2514yes—
679C2×C4×C79C2512yes—
680C22⋊D79—28no—
681C22⋊D79—28no—
682C22⋊D79—22no—
683C22⋊D79—22no—
684C22⋊D79—22no—
685C22⋊D79—22no—
686C22⋊D79—28no—
687C22⋊D79—24no—
688C22⋊D79—24no—
689C22⋊D79—48no—
690C22⋊D79—44no—
691C22⋊D79—44no—
692C22⋊D79—44no—
693C22⋊D79—44no—
694C2×Dic79—22no—
695C2×Dic79—28no—
696C2×Dic79—42no—
697C2×Dic79—48no—
698C2×Dic79—42no—
699C2×Dic79C2×#4114yes—
700C2×Dic79C2514yes—
701C2×Dic79C2514yes—
702C2×Dic79C2511yescharacteristic
703C2×Dic79C2514yes—
704C2×Dic79C2511yescharacteristic
705C2×Dic79C2514yes—
706C2×Dic79C2514yes—
707C2×Dic79C2512yes—
708D316—28no—
709D316—24no—
710D316—24no—
711D316—24no—
712D316—44no—
713D316—44no—
714D316—44no—
715C4×D79—28no—
716C4×D79—28no—
717C4×D79—24no—
718C4×D79—24no—
719C4×D79—28no—
720C4×D79—44no—
721C4×D79—44no—
722C4×D79—48no—
723C4×D79—44no—
724C4×D79—48no—
725C4×D79—44no—
726C4×D79—48no—
727C4×D79C2×#4118yes—
728C4×D79C2×#4118yes—
729Dic158—24no—
730Dic158—28no—
731Dic158—24no—
732Dic158—24no—
733Dic158—44no—
734Dic158—48no—
735C22×C79—21no—
736C22×C79—21no—
737C22×C79—21no—
738C22×C79—21no—
739C22×C79—24no—
740C22×C79—21no—
741C22×C79—24no—
742C22×C79—21no—
743C22×C79—21no—
744C22×C79—24no—
745C22×C79—21no—
746C22×C79—44no—
747C22×C79C22×#4112yes—
748C22×C79C2611yescharacteristic
749C2×D79—21no—
750C2×D79—21no—
751C2×D79—21no—
752C2×D79—21no—
753C2×D79—22no—
754C2×D79—24no—
755C2×D79—24no—
756C2×D79—22no—
757C2×D79—22no—
758C2×D79—24no—
759C2×D79—44no—
760C2×D79—44no—
761C2×D79—88no—
762C2×D79C22×#4112yes—
763C2×D79C22×#4112yes—
764C4×C79—22no—
765C4×C79—24no—
766C4×C79—24no—
767C4×C79—24no—
768C4×C79—24no—
769C4×C79—24no—
770C4×C79C22×#4114yes—
771Dic79—24no—
772Dic79—21no—
773Dic79—21no—
774Dic79—24no—
775Dic79—24no—
776Dic79—24no—
777Dic79—24no—
778Dic79C22×#4114yes—
779#62856—791nomaximal, Sylow
780C2×C79—22no—
781C2×C79—44no—
782C2×C79—41no—
783C2×C79—41no—
784C2×C79C23×#4111yescharacteristic
785C2×C79H(7,𝔽2)11yescharacteristic
786C2×C792−1+611yescharacteristic
787D79—22no—
788D79—22no—
789D79—42no—
790D79—44no—
791#3512—794no—
792#3512—794no—
793#3511—794no—
794#3511—794no—
795#3505—794no—
796#3505—794no—
797#3495—794no—
798#3495—794no—
799#3494—794no—
800#3494—794no—
801#3493—791no—
802#3493—791no—
803#3493—792no—
804#3492—792no—
805#3492—791no—
806#3492D7911yescharacteristic, complemented
807#3461—794no—
808#3460—794no—
809C2×#544—791no—
810#3449—792no—
811C2×#537—791no—
812#3428—792no—
813C2×#520—791no—
814C79#6285611yescharacteristic, complemented, Sylow
815C22×#41—792no—
816C22×#41—791no—
817#556—794no—
818#556—794no—
819#556—794no—
820#556—794no—
821#555—794no—
822#555—794no—
823#555—794no—
824#555—794no—
825#554—794no—
826#554—794no—
827#554—794no—
828#554C2×D7914yescomplemented
829#553—798no—
830#553—794no—
831#553—798no—
832#553—798no—
833#553—798no—
834#553—794no—
835#553—794no—
836#553—794no—
837#553—794no—
838#553—794no—
839#553—798no—
840#553—794no—
841#553—794no—
842#553—794no—
843#553C2×D7914yescomplemented
844#552—798no—
845#552—794no—
846#552—794no—
847#552—794no—
848#552—794no—
849#552—794no—
850#552—794no—
851#552—794no—
852#552—794no—
853#552—794no—
854#552C2×D7914yescomplemented
855#551—798no—
856#551—798no—
857#551—798no—
858#551—798no—
859#548—794no—
860#548—794no—
861#548—798no—
862#547—794no—
863#547—794no—
864#547—794no—
865#547C2×D7914yescomplemented
866#546—794no—
867#546—798no—
868#546—794no—
869#544—794no—
870#544—794no—
871#544—794no—
872#544—792no—
873#544—791no—
874#544C2×D7911yescharacteristic, complemented
875#542—798no—
876#542—798no—
877#542—798no—
878#542—798no—
879#541—798no—
880#541—798no—
881#540—798no—
882#540—798no—
883#539—798no—
884#539—794no—
885#539C2×D7914yescomplemented
886#538—794no—
887#538—794no—
888#538—798no—
889#537—792no—
890#537—794no—
891#537—792no—
892#537—792no—
893#537—794no—
894#537—794no—
895#537—792no—
896#537—792no—
897#537—791no—
898#537C2×D7911yescharacteristic
899#536—794no—
900#536—792no—
901#536—792no—
902#535—792no—
903#535—792no—
904#535—794no—
905#534—794no—
906#534—794no—
907#533—798no—
908#533—798no—
909#532—798no—
910#532—794no—
911#532—794no—
912#532—798no—
913C2×C4⋊Q8—794no—
914#529—798no—
915#529—798no—
916#529—798no—
917#529—794no—
918#529—794no—
919#529—798no—
920#529—798no—
921C2×#125—794no—
922#525—792no—
923#525—792no—
924#525—794no—
925#525—794no—
926#525—794no—
927#525—798no—
928#525—792no—
929#525C2×D7912yescomplemented
930#525C2×D7914yescomplemented
931C2×C22⋊Q8—794no—
932C2×C22⋊Q8—794no—
933C2×#121—794no—
934C2×#121—794no—
935#520—792no—
936#520—792no—
937#520—794no—
938#520—794no—
939#520—794no—
940#520—794no—
941#520—794no—
942#520—792no—
943#520—794no—
944#520C2×D7912yescomplemented
945#519—794no—
946#518—798no—
947#518—794no—
948C4×#41—794no—
949C4×#41—798no—
950C4×#41—794no—
951C2×C4×Q8—792no—
952C2×C4×D4—792no—
953C2×C4×D4—792no—
954C2×C4×D4—792no—
955C2×#117—791no—
956C2×#117—792no—
957C2×#117—794no—
958C2×#117—791no—
959C2×#117—791no—
960C2×#117—794no—
961C22×C4⋊C4—791no—
962C22×C4⋊C4—791no—
963C22×C4⋊C4C2×D7911yescharacteristic, complemented
964C2×#41—792no—
965C2×#41—794no—
966C2×#41—792no—
967C2×#41—794no—
968C2×#41—798no—
969C2×#41—792no—
970C2×#41—792no—
971C2×#41—792no—
972C2×#41—794no—
973C2×#41—792no—
974C2×#41—792no—
975C2×#41—1588no—
976C2×#41—15816no—
977C2×#41C22×D7912yes—
978C2×#41C22×D7914yes—
979C22×Q8—794no—
980C22×Q8—792no—
981C22×Q8—791no—
982C22×D4—791no—
983C22×D4—791no—
984C22×D4—794no—
985C22×D4—794no—
986C22×D4—792no—
987C22×D4—791no—
988C23×C4—791no—
989C23×C4—792no—
990C23×C4—792no—
991C23×C4—791no—
992C23×C4—794no—
993C23×C4C22×D7911yescharacteristic
994C23×C4C22×D7912yes—
995C4⋊Q8—798no—
996C4⋊Q8—798no—
997C4⋊Q8—794no—
998C4⋊Q8—794no—
999C4⋊Q8—794no—
1000C4⋊Q8—794no—
1001C4⋊Q8—794no—
1002C4⋊Q8C22×D7914yes—
1003#127—794no—
1004#127—794no—
1005#126—798no—
1006#126—798no—
1007#126—798no—
1008#126—798no—
1009#126—798no—
1010#126—798no—
1011#126—798no—
1012#126—798no—
1013#126—798no—
1014#126—798no—
1015#126—798no—
1016#126C22×D7918yes—
1017#125—798no—
1018#125—798no—
1019#125—794no—
1020#125—794no—
1021#125—798no—
1022#125—794no—
1023#125—794no—
1024#125—798no—
1025#125—798no—
1026#125—794no—
1027#125—798no—
1028#125C22×D7914yes—
1029#125C22×D7918yes—
1030#124—794no—
1031#124—798no—
1032#124—794no—
1033#124—798no—
1034#124—794no—
1035#124—794no—
1036#124—794no—
1037#124—794no—
1038#124—798no—
1039#124—798no—
1040#124—798no—
1041#123—794no—
1042#123—798no—
1043#123—794no—
1044#123—798no—
1045#123—798no—
1046#123—794no—
1047#123—794no—
1048#123—798no—
1049#123—798no—
1050#123—798no—
1051#123—794no—
1052#123—794no—
1053#123—794no—
1054#123—798no—
1055#123—798no—
1056#123—798no—
1057#123—798no—
1058#123C22×D7914yes—
1059#123C22×D7918yes—
1060#123C22×D7918yes—
1061C22⋊Q8—794no—
1062C22⋊Q8—794no—
1063C22⋊Q8—792no—
1064C22⋊Q8—792no—
1065C22⋊Q8—794no—
1066C22⋊Q8—794no—
1067C22⋊Q8—792no—
1068C22⋊Q8—792no—
1069C22⋊Q8—794no—
1070C22⋊Q8—798no—
1071C22⋊Q8—798no—
1072C22⋊Q8—794no—
1073C22⋊Q8—798no—
1074C22⋊Q8—794no—
1075C22⋊Q8—794no—
1076C22⋊Q8—794no—
1077C22⋊Q8—792no—
1078C22⋊Q8—792no—
1079C22⋊Q8—798no—
1080C22⋊Q8—798no—
1081C22⋊Q8—798no—
1082C22⋊Q8—798no—
1083C22⋊Q8—798no—
1084C22⋊Q8—794no—
1085C22⋊Q8—794no—
1086C22⋊Q8C22×D7914yes—
1087C22⋊Q8C22×D7914yes—
1088C22⋊Q8C22×D7912yes—
1089C22⋊Q8C22×D7912yes—
1090C22⋊Q8C22×D7914yes—
1091C22⋊Q8C22×D7918yes—
1092#121—798no—
1093#121—798no—
1094#121—794no—
1095#121—794no—
1096#121—794no—
1097#121—794no—
1098#121—792no—
1099#121—792no—
1100#121—794no—
1101#121—794no—
1102#121—798no—
1103#121—798no—
1104#121—798no—
1105#121—794no—
1106#121—794no—
1107#121—792no—
1108#121—792no—
1109#121—794no—
1110#121—794no—
1111#121—794no—
1112#121—792no—
1113#121—792no—
1114#121—794no—
1115#121—794no—
1116#121—798no—
1117#121—798no—
1118#121—798no—
1119#121—794no—
1120#121—794no—
1121#121—798no—
1122#121—794no—
1123#121—794no—
1124#121—794no—
1125#121—794no—
1126#121C22×D7914yes—
1127#121C22×D7914yes—
1128#121C22×D7912yes—
1129#121C22×D7912yes—
1130#121C22×D7914yes—
1131#120—794no—
1132#120—794no—
1133#120—794no—
1134#120—794no—
1135#120—794no—
1136#120—794no—
1137#120—794no—
1138#120C22×D7914yes—
1139C4×Q8—794no—
1140C4×Q8—794no—
1141C4×Q8—798no—
1142C4×Q8—798no—
1143C4×Q8—798no—
1144C4×Q8—794no—
1145C4×Q8—798no—
1146C4×Q8—794no—
1147C4×Q8—798no—
1148C4×Q8—794no—
1149C4×Q8C22×D7914yes—
1150C4×D4—798no—
1151C4×D4—794no—
1152C4×D4—794no—
1153C4×D4—798no—
1154C4×D4—798no—
1155C4×D4—794no—
1156C4×D4—794no—
1157C4×D4—794no—
1158C4×D4—794no—
1159C4×D4—798no—
1160C4×D4—798no—
1161C4×D4—798no—
1162C4×D4—794no—
1163C4×D4—794no—
1164C4×D4—794no—
1165C4×D4—794no—
1166C4×D4—798no—
1167C4×D4—798no—
1168C4×D4—798no—
1169C4×D4—798no—
1170C4×D4—794no—
1171C4×D4—798no—
1172C4×D4—794no—
1173C4×D4—798no—
1174C4×D4—798no—
1175C4×D4—798no—
1176C4×D4—798no—
1177C4×D4—798no—
1178C4×D4—794no—
1179C4×D4—794no—
1180C4×D4—794no—
1181C4×D4—798no—
1182C4×D4C22×D7918yes—
1183C4×D4C22×D7914yes—
1184C4×D4C22×D7914yes—
1185C4×D4C22×D7914yes—
1186C4×D4C22×D7918yes—
1187#117—792no—
1188#117—794no—
1189#117—794no—
1190#117—794no—
1191#117—794no—
1192#117—794no—
1193#117—792no—
1194#117—792no—
1195#117—794no—
1196#117—798no—
1197#117—798no—
1198#117—794no—
1199#117—794no—
1200#117—794no—
1201#117—794no—
1202#117—798no—
1203#117—798no—
1204#117—794no—
1205#117—798no—
1206#117—798no—
1207#117—798no—
1208#117—794no—
1209#117—798no—
1210#117—798no—
1211#117C22×D7912yes—
1212#117C22×D7914yes—
1213#117C22×D7914yes—
1214C2×C4⋊C4—791no—
1215C2×C4⋊C4—792no—
1216C2×C4⋊C4—792no—
1217C2×C4⋊C4—791no—
1218C2×C4⋊C4—794no—
1219C2×C4⋊C4—794no—
1220C2×C4⋊C4—794no—
1221C2×C4⋊C4—794no—
1222C2×C4⋊C4—794no—
1223C2×C4⋊C4—792no—
1224C2×C4⋊C4—792no—
1225C2×C4⋊C4—794no—
1226C2×C4⋊C4—794no—
1227C2×C4⋊C4—794no—
1228C2×C4⋊C4—794no—
1229C2×C4⋊C4—798no—
1230C2×C4⋊C4C22×D7911yescharacteristic
1231C2×C4⋊C4C22×D7911yescharacteristic
1232C2×C4⋊C4C22×D7912yes—
1233C2×C4⋊C4C22×D7914yes—
1234C2×C4⋊C4C22×D7914yes—
1235C2×C4⋊C4C22×D7914yes—
1236C2×C22⋊C4—792no—
1237C2×C22⋊C4—792no—
1238C2×C22⋊C4—792no—
1239C2×C22⋊C4—798no—
1240C2×C22⋊C4—794no—
1241C2×C22⋊C4—798no—
1242C2×C22⋊C4—798no—
1243C2×C42—792no—
1244C2×C42—792no—
1245C2×C42—792no—
1246C2×C42—798no—
1247C2×C42—794no—
1248C2×C42—798no—
1249C24—791no—
1250C24—794no—
1251C24—791no—
1252C24C23×D7911yescharacteristic
1253#41—28no—
1254#41—84no—
1255#41—6324no—
1256#41—6328no—
1257#41—1588no—
1258#41—1588no—
1259#41—1588no—
1260#41—1588no—
1261#41—15816no—
1262#41—15816no—
1263#41—1588no—
1264#41—1588no—
1265#41—1588no—
1266C2×Q8—794no—
1267C2×Q8—798no—
1268C2×Q8—792no—
1269C2×Q8—792no—
1270C2×Q8—792no—
1271C2×Q8—794no—
1272C2×Q8—6324no—
1273C2×Q8—1584no—
1274C2×Q8—1588no—
1275C2×Q8C23×D7912yes—
1276C2×Q8C23×D7914yes—
1277C2×D4—794no—
1278C2×D4—794no—
1279C2×D4—794no—
1280C2×D4—794no—
1281C2×D4—798no—
1282C2×D4—791no—
1283C2×D4—791no—
1284C2×D4—794no—
1285C2×D4—791no—
1286C2×D4—791no—
1287C2×D4—794no—
1288C2×D4—792no—
1289C2×D4—792no—
1290C2×D4—794no—
1291C2×D4—794no—
1292C2×D4—794no—
1293C2×D4—794no—
1294C2×D4—792no—
1295C2×D4—792no—
1296C2×D4—794no—
1297C2×D4—792no—
1298C2×D4—6324no—
1299C2×D4—1584no—
1300C2×D4—1588no—
1301C2×D4—1584no—
1302C2×D4—15816no—
1303C2×D4—1584no—
1304C2×D4C23×D7914yes—
1305C2×D4C23×D7912yes—
1306C2×D4C23×D7914yes—
1307C2×D4C23×D7914yes—
1308C2×D4C23×D7914yes—
1309C22×C4—24no—
1310C22×C4—82no—
1311C22×C4—792no—
1312C22×C4—792no—
1313C22×C4—798no—
1314C22×C4—794no—
1315C22×C4—794no—
1316C22×C4—798no—
1317C22×C4—798no—
1318C22×C4—794no—
1319C22×C4—794no—
1320C22×C4—798no—
1321C22×C4—791no—
1322C22×C4—798no—
1323C22×C4—792no—
1324C22×C4—792no—
1325C22×C4—791no—
1326C22×C4—794no—
1327C22×C4—794no—
1328C22×C4—794no—
1329C22×C4—792no—
1330C22×C4—792no—
1331C22×C4—794no—
1332C22×C4—6322no—
1333C22×C4—6322no—
1334C22×C4—15816no—
1335C22×C4—1584no—
1336C22×C4C23×D7911yescharacteristic
1337C22×C4C23×D7914yes—
1338C22×C4C23×D7912yes—
1339C22×C4C23×D7912yes—
1340C22×C4C23×D7912yes—
1341C22×C4C23×D7912yes—
1342C22×C4C23×D7918yes—
1343C22×C4C23×D7914yes—
1344C22×C4C23×D7914yes—
1345C22×C4C23×D7911yescharacteristic
1346C4⋊C4—798no—
1347C4⋊C4—794no—
1348C4⋊C4—794no—
1349C4⋊C4—794no—
1350C4⋊C4—794no—
1351C4⋊C4—798no—
1352C4⋊C4—798no—
1353C4⋊C4—798no—
1354C4⋊C4—798no—
1355C4⋊C4—798no—
1356C4⋊C4—798no—
1357C4⋊C4—794no—
1358C4⋊C4—794no—
1359C4⋊C4—794no—
1360C4⋊C4—794no—
1361C4⋊C4—794no—
1362C4⋊C4—794no—
1363C4⋊C4—792no—
1364C4⋊C4—792no—
1365C4⋊C4—798no—
1366C4⋊C4—794no—
1367C4⋊C4—798no—
1368C4⋊C4—794no—
1369C4⋊C4—794no—
1370C4⋊C4—794no—
1371C4⋊C4C23×D7914yes—
1372C4⋊C4C23×D7912yes—
1373C4⋊C4C23×D7914yes—
1374C4⋊C4C23×D7912yes—
1375C4⋊C4C23×D7918yes—
1376C4⋊C4C23×D7914yes—
1377C4⋊C4C23×D7914yes—
1378C4⋊C4C23×D7918yes—
1379C4⋊C4C23×D7918yes—
1380C4⋊C4C23×D7914yes—
1381C4⋊C4C23×D7914yes—
1382C22⋊C4—794no—
1383C22⋊C4—794no—
1384C22⋊C4—794no—
1385C22⋊C4—798no—
1386C22⋊C4—798no—
1387C22⋊C4—794no—
1388C22⋊C4—794no—
1389C22⋊C4—794no—
1390C22⋊C4—794no—
1391C22⋊C4—794no—
1392C22⋊C4—794no—
1393C22⋊C4—794no—
1394C22⋊C4—794no—
1395C22⋊C4—798no—
1396C22⋊C4—798no—
1397C22⋊C4—798no—
1398C22⋊C4—798no—
1399C22⋊C4—798no—
1400C22⋊C4—794no—
1401C22⋊C4—794no—
1402C22⋊C4—794no—
1403C22⋊C4—794no—
1404C22⋊C4—794no—
1405C22⋊C4—794no—
1406C22⋊C4—794no—
1407C22⋊C4—794no—
1408C22⋊C4C23×D7914yes—
1409C22⋊C4C23×D7918yes—
1410C22⋊C4C23×D7918yes—
1411C22⋊C4C23×D7914yes—
1412C22⋊C4C23×D7914yes—
1413C22⋊C4C23×D7914yes—
1414C22⋊C4C23×D7914yes—
1415C42—798no—
1416C42—794no—
1417C42—794no—
1418C42—798no—
1419C42—794no—
1420C42—794no—
1421C42—798no—
1422C42—798no—
1423C42—798no—
1424C42—794no—
1425C42C23×D7918yes—
1426C42C23×D7914yes—
1427C23—22no—
1428C23—41no—
1429C23—41no—
1430C23—3161no—
1431C23—3161no—
1432C23—3161no—
1433C23—3161no—
1434C23—3164no—
1435C23—3164no—
1436C23—794no—
1437C23—791no—
1438C23—791no—
1439C23—792no—
1440C23—794no—
1441C23—1588no—
1442C23—1582no—
1443C23C24×D7911yescharacteristic
1444C23C24×D7911yescharacteristic
1445C23C24×D7914yes—
1446C23C24×D7911yescharacteristic
1447Q8—24no—
1448Q8—44no—
1449Q8—3164no—
1450Q8—3168no—
1451Q8—1584no—
1452Q8—1584no—
1453Q8—1588no—
1454Q8—1584no—
1455D4—28no—
1456D4—24no—
1457D4—44no—
1458D4—44no—
1459D4—44no—
1460D4—3164no—
1461D4—3164no—
1462D4—3164no—
1463D4—3164no—
1464D4—3164no—
1465D4—3168no—
1466D4—3164no—
1467D4—3164no—
1468D4—1584no—
1469D4—1584no—
1470D4—1588no—
1471D4—1584no—
1472D4—1584no—
1473D4—1588no—
1474D4—1582no—
1475D4—1582no—
1476D4—1582no—
1477D4—1582no—
1478D4—1588no—
1479D4—1588no—
1480D4—1584no—
1481C2×C4—22no—
1482C2×C4—24no—
1483C2×C4—24no—
1484C2×C4—28no—
1485C2×C4—42no—
1486C2×C4—42no—
1487C2×C4—44no—
1488C2×C4—44no—
1489C2×C4—48no—
1490C2×C4—3164no—
1491C2×C4—3164no—
1492C2×C4—3168no—
1493C2×C4—3164no—
1494C2×C4—3168no—
1495C2×C4—3168no—
1496C2×C4—3164no—
1497C2×C4—3162no—
1498C2×C4—3162no—
1499C2×C4—3168no—
1500C2×C4—792no—
1501C2×C4—794no—
1502C2×C4—798no—
1503C2×C4—798no—
1504C2×C4—794no—
1505C2×C4—794no—
1506C2×C4—794no—
1507C2×C4—791no—
1508C2×C4—791no—
1509C2×C4—794no—
1510C2×C4—794no—
1511C2×C4—1588no—
1512C2×C4—1588no—
1513C2×C4—1588no—
1514C2×C4—1582no—
1515C2×C4—1588no—
1516C2×C4—1584no—
1517C2×C4—1584no—
1518C2×C4#41×D7914yes—
1519C2×C4C24×D7914yes—
1520C2×C4C24×D7912yes—
1521C2×C4C24×D7914yes—
1522C2×C4C24×D7914yes—
1523C2×C4C24×D7914yes—
1524C2×C4C24×D7914yes—
1525C2×C4C24×D7912yes—
1526C22—21no—
1527C22—21no—
1528C22—21no—
1529C22—21no—
1530C22—24no—
1531C22—21no—
1532C22—21no—
1533C22—24no—
1534C22—24no—
1535C22—21no—
1536C22—21no—
1537C22—44no—
1538C22—3164no—
1539C22—3164no—
1540C22—792no—
1541C22—792no—
1542C22—6328no—
1543C22—1582no—
1544C22—1584no—
1545C22—1582no—
1546C22—1584no—
1547C22—1584no—
1548C22—1582no—
1549C22—1581no—
1550C22—1581no—
1551C22—1581no—
1552C22—1581no—
1553C22C2×#41×D7912yes—
1554C22C25×D7911yescharacteristic
1555C4—22no—
1556C4—24no—
1557C4—24no—
1558C4—24no—
1559C4—24no—
1560C4—24no—
1561C4—794no—
1562C4—1584no—
1563C4—1581no—
1564C4—1581no—
1565C4—1584no—
1566C4—1584no—
1567C4—1584no—
1568C4—1584no—
1569C4C2×#41×D7914yes—
1570C2—22no—
1571C2—41no—
1572C2—41no—
1573C2—44no—
1574C2—3162no—
1575C2—3164no—
1576C2—1582no—
1577C2—1582no—
1578C2C22×#41×D7911yescharacteristic
1579C2#2377821011yescharacteristic
1580C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3492C2
hypercenter#3492D79
hypocenterC79#62856
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3492

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777318C2semidirect
2. #23777314C2semidirect
3. #23777310C2semidirect
4. #23777308C2semidirect
5. #23777232C2semidirect
6. #23777228C2semidirect
7. #23777151C2semidirect
8. #23777148C2semidirect
9. #23777128C2semidirect
10. #23777124C2semidirect
11. #23777121C2semidirect
12. #23777119C2semidirect
13. #23777117C2semidirect
14. #23777109C2semidirect
15. #23777103C2semidirect
16. #23776830C2semidirect
17. #23776818C2semidirect
18. #544×D79C2semidirect
19. #23776730C2semidirect
20. #537×D79C2semidirect
21. #23776600C2semidirect
22. C2×#19099044C2semidirect
23. C79×#3492C2semidirect
26. #19099287C22semidirect
27. #19099284C22semidirect
28. #19099284C22semidirect
29. #19099283C22semidirect
30. #19099279C22semidirect
31. #19099278C22semidirect
32. #19099277C22semidirect
33. #19099277C22semidirect
34. #19099273C22semidirect
35. #19099268C22semidirect
36. #19099268C22semidirect
37. #19099266C22semidirect
38. #19099266C22semidirect
39. #19099265C22semidirect
40. #19099264C22semidirect
41. #19099263C22semidirect
42. #19099263C22semidirect
43. #19099261C22semidirect
44. #19099260C22semidirect
45. #19099260C22semidirect
46. #19099259C22semidirect
47. #19099258C22semidirect
48. #19099258C22semidirect
49. #19099257C22semidirect
50. #19099257C22semidirect
51. #19099255C22semidirect
52. #19099254C22semidirect
53. #19099253C22semidirect
54. #19099252C22semidirect
55. #19099252C22semidirect
56. #19099251C22semidirect
57. #19099248C22semidirect
58. #19099247C22semidirect
59. #19099247C22semidirect
60. #19099245C22semidirect
61. #19099242C22semidirect
62. #19099241C22semidirect
63. #19099240C22semidirect
64. #19099238C22semidirect
65. #19099223C22semidirect
66. #19099223C22semidirect
67. #19099220C22semidirect
68. #19099218C22semidirect
69. #19099214C22semidirect
70. #19099214C22semidirect
71. #19099210C22semidirect
72. #19099205C22semidirect
73. #19099201C22semidirect
74. #19099194C22semidirect
75. #19099193C22semidirect
76. #19099192C22semidirect
77. #19099191C22semidirect
78. #19099190C22semidirect
79. #19099183C22semidirect
80. #19099183C22semidirect
81. #19099181C22semidirect
82. #19099181C22semidirect
83. #19099172C22semidirect
84. #19099170C22semidirect
85. #19099165C22semidirect
86. #19099163C22semidirect
87. #19099160C22semidirect
88. #19099155C22semidirect
89. #19099153C22semidirect
90. #19099150C22semidirect
91. #19099148C22semidirect
93. #19099143C22semidirect
94. #19099143C22semidirect
95. #19099143C22semidirect
96. #19099142C22semidirect
97. #19099142C22semidirect
98. #19099142C22semidirect
103. #19099135C22semidirect
106. #19099128C22semidirect
109. #19099119C22semidirect
110. #19099115C22semidirect
111. #19099110C22semidirect
112. #19099110C22semidirect
113. #19099110C22semidirect
114. #19099109C22semidirect
115. C4⋊Q8×D79C22semidirect
116. #19099099C22semidirect
117. #19099096C22semidirect
118. #19099094C22semidirect
119. #19099093C22semidirect
120. #19099091C22semidirect
121. #19099090C22semidirect
122. #19099090C22semidirect
123. #125×D79C22semidirect
124. #19099075C22semidirect
125. #19099074C22semidirect
126. #19099074C22semidirect
129. #19099072C22semidirect
130. #19099070C22semidirect
132. C22⋊Q8×D79C22semidirect
134. #121×D79C22semidirect
135. #19099046C22semidirect
138. #19099044C22semidirect
139. #19099044C22semidirect
140. #19099044C22semidirect
141. #19099044C22semidirect
142. #19099043C22semidirect
143. #19099043C22semidirect
144. #19099039C22semidirect
146. #19099035C22semidirect
147. C4×#11929625C22semidirect
148. C4×#11929623C22semidirect
149. C4×#11929623C22semidirect
150. C2×#14579126C22semidirect
153. C2×C4×C22⋊D79C22semidirect
154. C2×#14579120C22semidirect
156. C2×#14579119C22semidirect
157. C2×#14579119C22semidirect
159. #117×D79C22semidirect
161. C2×C4⋊C4×D79C22semidirect
162. #554×C79C22semidirect
163. #553×C79C22semidirect
164. #552×C79C22semidirect
165. #547×C79C22semidirect
166. #544×C79C22semidirect
167. #539×C79C22semidirect
169. #525×C79C22semidirect
170. #525×C79C22semidirect
171. #520×C79C22semidirect
172. C22×C4⋊C4×C79C22semidirect
518. C2×C4×D79#41semidirect
806. #3492D79semidirect
814. C79#62856semidirect
828. #554C2×D79semidirect
843. #553C2×D79semidirect
854. #552C2×D79semidirect
865. #547C2×D79semidirect
874. #544C2×D79semidirect
885. #539C2×D79semidirect
929. #525C2×D79semidirect
930. #525C2×D79semidirect
944. #520C2×D79semidirect
963. C22×C4⋊C4C2×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237773182
#237773142
#237773102
#237773082
#237772322
#237772282
#237771512
#237771482
#237771282
#237771242
#237771212
#237771192
#237771172
#237771092
#237771032
#237768302
#237768182
#544×D792
#237767302
#537×D792
#237766002
C2×#190990442
C79×#34922
#6285679