Finite Group Databasebeta

← #35197462

Subgroups — #35197462

Order 20224.

10986 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099398C211yesmaximal, characteristic, complemented
2C22×#14579208C211yesmaximal, characteristic, complemented
3#23777186C218yesmaximal, complemented
4#23777179C218yesmaximal, complemented
5#23777074C218yesmaximal, complemented
6#23777071C218yesmaximal, complemented
7#23777049C212yesmaximal, complemented
8#23777047C212yesmaximal, complemented
9#23777045C211yesmaximal, characteristic, complemented
10#23777044C211yesmaximal, characteristic, complemented
11#23777041C214yesmaximal, complemented
12#23777040C211yesmaximal, characteristic, complemented
13#23777038C214yesmaximal, complemented
14#23776730C212yesmaximal, complemented
15#23776726C214yesmaximal, complemented
16C2×#19099135C214yesmaximal, complemented
17#536×D79C212yesmaximal, complemented
18#23776598C211yesmaximal, characteristic, complemented
19C79×#3485C211yesmaximal, characteristic, complemented
20#19099398—216no—
21C2×#14579208—216no—
22C2×#14579208C2212yes—
23C2×#14579208C2218yescomplemented
24C2×#14579208C2214yescomplemented
25C2×#14579208C2218yescomplemented
26C2×#14579206C2214yes—
27C2×#14579206C2211yescharacteristic
28C2×#14579206C2214yescomplemented
29C22×#11929624C2212yescomplemented
30C22×#11929624C2211yescharacteristic, complemented
31C22×#11929623C2214yes—
32C22×#11929623C2211yescharacteristic
33C22×#11929623C2211yescharacteristic, complemented
34C22×#11929623C2212yescomplemented
35C22×#11929623C2214yescomplemented
36C22×#11929623C2212yescomplemented
37C2×#41×D79C2212yes—
38C2×#41×D79C2214yescomplemented
39C23×Dic158C2211yescharacteristic, complemented
40C23×Dic158C2212yescomplemented
41C22×Q8×D79C2211yescharacteristic, complemented
42C22×Q8×D79C2211yescharacteristic, complemented
43D4×Dic158C2218yescomplemented
44#19099228C2218yescomplemented
45#19099226C2218yescomplemented
46#19099226C2218yescomplemented
47#19099223C2218yescomplemented
48#19099222C2218yescomplemented
49#19099221C2218yescomplemented
50#19099219C2218yescomplemented
51#19099217C2218yescomplemented
52#19099214C22116yescomplemented
53#19099213C22116yescomplemented
54#19099212C2218yescomplemented
55#19099212C2218yescomplemented
56#19099211C22116yescomplemented
57#19099211C22116yescomplemented
58#19099208C2218yescomplemented
59#19099207C2218yescomplemented
60#19099205C22116yescomplemented
61#19099203C22116yescomplemented
62#19099202C22116yescomplemented
63#19099201C2218yescomplemented
64#19099200C22116yescomplemented
65#19099143C2214yescomplemented
66#19099142C2214yescomplemented
67#19099140C22116yescomplemented
68#19099139C2212yescomplemented
69#19099138C2214yescomplemented
70#19099137C2212yescomplemented
71#19099136C2214yescomplemented
72#19099136C2218yescomplemented
73#19099135C2218yescomplemented
74#19099135C2218yescomplemented
75#19099135C22116yescomplemented
76#19099135C2218yescomplemented
77#19099135C22116yescomplemented
78#19099135C2218yescomplemented
79#19099135C2214yescomplemented
80#19099134C2212yescomplemented
81#19099133C2214yescomplemented
82#19099129C2214yescomplemented
83#19099128C2218yescomplemented
84#19099128C2214yescomplemented
85#19099125C2214yescomplemented
86#19099124C2214yescomplemented
87#19099123C2214yescomplemented
88#19099122C2214yescomplemented
89#19099122C2214yescomplemented
90#19099110C2218yescomplemented
91#19099108C22116yescomplemented
92C2×#14579160C2218yescomplemented
93C4⋊Q8×D79C2214yescomplemented
94C2×#14579147C2218yescomplemented
95#124×D79C2214yescomplemented
96#19099075C2212yescomplemented
97#19099074C2212yescomplemented
98#19099072C2218yescomplemented
99#19099071C2218yescomplemented
100#19099071C2218yescomplemented
101#19099070C2212yescomplemented
102#19099069C2218yescomplemented
103#19099069C2218yescomplemented
104C2×#14579145C2214yescomplemented
105C2×#14579144C2214yescomplemented
106C2×#14579142C2214yescomplemented
107#123×D79C2218yescomplemented
108C2×#14579139C2218yescomplemented
109C2×#14579138C2218yescomplemented
110C22⋊Q8×D79C2218yescomplemented
111#19099042C2218yescomplemented
112#19099040C2212yescomplemented
113#19099038C2211yescharacteristic, complemented
114#19099036C2214yescomplemented
115C4×#11929623C2218yescomplemented
116C2×#14579117C2214yescomplemented
117#117×D79C2212yescomplemented
118C2×H(5,𝔽2)×C79C2211yescharacteristic
119C22×#41×C79C2211yescharacteristic, complemented
120#547×C79C2218yescomplemented
121#546×C79C2218yescomplemented
122#536×C79C2212yescomplemented
123#534×C79C2214yescomplemented
124#525×C79C2212yescomplemented
125C2×#123×C79C2214yescomplemented
126#518×C79C2211yescharacteristic, complemented
127#14579208—264no—
128#14579208—264no—
129#14579208—232no—
130#14579208—216no—
131#14579206—28no—
132#14579206—232no—
133#14579206—232no—
134C2×#11929625C2312yes—
135C2×#11929624—216no—
136C2×#11929624—28no—
137C2×#11929624C2314yes—
138C2×#11929624C2314yes—
139C2×#11929624C2312yes—
140C2×#11929624C2318yes—
141C2×#11929624C2314yes—
142C2×#11929624C2314yes—
143C2×#11929624C23116yes—
144C2×#11929623—28no—
145C2×#11929623—232no—
146C2×#11929623—216no—
147C2×#11929623—216no—
148C2×#11929623—232no—
149C2×#11929623D4116yescomplemented
150C2×#11929623C2318yes—
151C2×#11929623C2318yes—
152C2×#11929623C2314yes—
153C2×#11929623C2314yes—
154C2×#11929623C2318yes—
155C2×#11929623C2318yes—
156C2×#11929623C2318yes—
157C2×#11929623C23116yes—
158C2×#11929623C2318yes—
159C2×#11929623C2318yes—
160C2×#11929623C2312yes—
161C2×#11929623C2314yes—
162C2×#11929623C2314yes—
163C2×#11929623C2314yes—
164#41×D79—232no—
165#41×D79—216no—
166C22×Dic158—28no—
167C22×Dic158—216no—
168C22×Dic158C2311yescharacteristic
169C22×Dic158C2314yes—
170C22×Dic158C2318yes—
171C22×Dic158C2318yes—
172C22×Dic158C2318yes—
173C22×Dic158C2314yes—
174C22×Dic158C2312yes—
175C22×Dic158C2312yes—
176C22×Dic158C2311yescharacteristic
177C22×Dic158C2312yes—
178C22×Dic158C2311yescharacteristic
179C2×Q8×D79—28no—
180C2×Q8×D79—28no—
181C2×Q8×D79C2314yes—
182C2×Q8×D79C2312yes—
183C2×Q8×D79C2314yes—
184C2×Q8×D79C2314yes—
185C2×Q8×D79C2318yes—
186C22×D316C2311yescharacteristic
187C22×C22⋊D79C2314yes—
188C22×C22⋊D79C2318yes—
189C22×C22⋊D79C2314yes—
190C22×C22⋊D79C2312yes—
191C22×C22⋊D79C2311yescharacteristic
192C22×C22⋊D79C2311yescharacteristic
193C22×C22⋊D79C2312yes—
194C2×D4×D79C2314yes—
195C2×D4×D79C2314yes—
196C2×D4×D79C2318yes—
197C2×D4×D79C2312yes—
198C23×Dic79C2314yes—
199C23×Dic79C2312yes—
200C23×Dic79C2312yes—
201C23×Dic79C2312yes—
202C22×C4×D79C2314yes—
203C22×C4×D79C2314yes—
204C22×C4×D79C2312yes—
205C22×C4×D79C2311yescharacteristic
206C22×C4×D79C2312yes—
207C22×C4×D79C2311yescharacteristic
208#14579161C2314yes—
209#14579160C23116yes—
210#14579160C2318yes—
211#14579160C23116yes—
212#14579160C23116yes—
213#14579159C2314yes—
214#14579159C2314yes—
215#14579157C2318yes—
216#14579150C2314yes—
217#14579149C2314yes—
218#14579148C2314yes—
219#14579147C23116yes—
220#14579147C2318yes—
221#14579147C23116yes—
222#14579147C23116yes—
223#14579147C2318yes—
224#14579146C23116yes—
225#14579146C2318yes—
226#14579145C2318yes—
227#14579145C23116yes—
228#14579145C2318yes—
229#14579145C2314yes—
230#14579144C2318yes—
231#14579144C23116yes—
232#14579144C2318yes—
233#14579144C2314yes—
234#14579143C23116yes—
235#14579143C2318yes—
236#14579142C23116yes—
237#14579142C2318yes—
238#14579142C2318yes—
239#14579142C2314yes—
240#14579141C2318yes—
241#14579141C2314yes—
242#14579140C2314yes—
243#14579140C2318yes—
244#14579139C23116yes—
245#14579139C23116yes—
246#14579139C2318yes—
247#14579139C23116yes—
248#14579139C23116yes—
249#14579138C23116yes—
250#14579138C23116yes—
251#14579138C2318yes—
252#14579138C23116yes—
253#14579138C23116yes—
254#14579137C2318yes—
255#14579137C2314yes—
256#14579136C2318yes—
257#14579136C2314yes—
258#14579135C23116yes—
259#14579135C2314yes—
260#14579134C2318yes—
261#14579134C23116yes—
262#14579134C2318yes—
263#14579134C2318yes—
264#14579133C2318yes—
265#14579133C23116yes—
266#14579133C23116yes—
267#14579133C23116yes—
268#14579132C2318yes—
269#14579132C2314yes—
270#14579131C2318yes—
271#14579131C2318yes—
272#14579131C2314yes—
273#14579130C2318yes—
274#14579130C2314yes—
275#14579129C2318yes—
276#14579129C2318yes—
277#14579129C2314yes—
278C4×Dic158C2318yes—
279#14579126C2318yes—
280C4×D316C2318yes—
281D4×Dic79C23116yes—
282D4×Dic79C2318yes—
283#14579123C23116yes—
284C4×C22⋊D79C2318yes—
285C4×C22⋊D79C23116yes—
286C4×C22⋊D79C2318yes—
287(C22⋊D79)⋊C4C23116yes—
288(C22⋊D79)⋊C4C23116yes—
289(C22⋊D79)⋊C4C23116yes—
290#14579120C2312yes—
291#14579119C2314yes—
292#14579118C2314yes—
293#14579117C2314yes—
294#14579117C2318yes—
295#14579117C2318yes—
296#14579117C2318yes—
297C2×C4⋊Dic79C2318yes—
298C2×Dic79⋊C4C2318yes—
299C2×Dic79⋊C4C2318yes—
300C2×Dic79⋊C4C2318yes—
301C4⋊C4×D79C2314yes—
302C4⋊C4×D79C23116yes—
303C2×C22⋊Dic79C2318yes—
304C2×C22⋊Dic79C2314yes—
305C2×(C2×D79)⋊C4C2318yes—
306C2×(C2×D79)⋊C4C2318yes—
307C22⋊C4×D79C23116yes—
308C22⋊C4×D79C2314yes—
309C2×C4×Dic79C2318yes—
310C42×D79C2314yes—
311H(5,𝔽2)×C79—28no—
312C2×#41×C79—28no—
313C2×#41×C79C2312yes—
314C2×#41×C79C2318yes—
315C2×#41×C79C2314yes—
316C22×Q8×C79C2311yescharacteristic
317C22×D4×C79C2314yes—
318C22×D4×C79C2314yes—
319C22×D4×C79C2312yes—
320C22×D4×C79C2311yescharacteristic
321C23×C4×C79C2312yes—
322C23×C4×C79C2311yescharacteristic
323C4⋊Q8×C79C2314yes—
324#124×C79C2314yes—
325#123×C79C23116yes—
326#123×C79C2318yes—
327#123×C79C2314yes—
328#123×C79C2318yes—
329C22⋊Q8×C79C2314yes—
330C22⋊Q8×C79C2318yes—
331#121×C79C23116yes—
332#121×C79C2314yes—
333#120×C79C2318yes—
334#120×C79C2314yes—
335C4×D4×C79C2318yes—
336C4×D4×C79C2318yes—
337#117×C79C2312yes—
338C2×C4⋊C4×C79C2318yes—
339C2×C22⋊C4×C79C2318yes—
340C2×C22⋊C4×C79C2314yes—
341C23×D79C2414yes—
342C23×D79C2414yes—
343C23×D79C2411yescharacteristic
344C23×D79C2411yescharacteristic
345#11929625—28no—
346#11929624—216no—
347#11929624—216no—
348#11929624—216no—
349#11929624—216no—
350#11929624—28no—
351#11929624—232no—
352#11929624—264no—
353#11929623—232no—
354#11929623—216no—
355#11929623—232no—
356#11929623—232no—
357#11929623—232no—
358#11929623—232no—
359#11929623—28no—
360#11929623—216no—
361#11929623—216no—
362#11929623—232no—
363#11929623—232no—
364#11929623—264no—
365#11929623C2×D4132yes—
366#11929623C2×D4132yes—
367C2×Dic158—28no—
368C2×Dic158—28no—
369C2×Dic158—28no—
370C2×Dic158—24no—
371C2×Dic158—232no—
372C2×Dic158—232no—
373C2×Dic158—216no—
374C2×Dic158—232no—
375C2×Dic158—216no—
376C2×Dic158—24no—
377C2×Dic158C2×D418yes—
378C2×Dic158C2414yes—
379C2×Dic158C2418yes—
380C2×Dic158C2414yes—
381C2×Dic158C2414yes—
382C2×Dic158C2418yes—
383C2×Dic158C2412yes—
384C2×Dic158C2414yes—
385C2×Dic158C2412yes—
386C2×Dic158C2418yes—
387C2×Dic158C2412yes—
388C2×Dic158C2414yes—
389Q8×D79—216no—
390Q8×D79—216no—
391Q8×D79—28no—
392Q8×D79—232no—
393Q8×D79—216no—
394C2×D316—24no—
395C2×D316C2414yes—
396C2×D316C2414yes—
397C2×D316C2412yes—
398C2×D316C2418yes—
399C2×C22⋊D79—24no—
400C2×C22⋊D79—216no—
401C2×C22⋊D79—28no—
402C2×C22⋊D79—216no—
403C2×C22⋊D79—24no—
404C2×C22⋊D79—232no—
405C2×C22⋊D79C2×D4116yes—
406C2×C22⋊D79C2414yes—
407C2×C22⋊D79C2418yes—
408C2×C22⋊D79C2412yes—
409C2×C22⋊D79C2412yes—
410C2×C22⋊D79C2414yes—
411C2×C22⋊D79C2414yes—
412C2×C22⋊D79C2418yes—
413C2×C22⋊D79C2418yes—
414C2×C22⋊D79C2414yes—
415C2×C22⋊D79C2418yes—
416C2×C22⋊D79C2418yes—
417C2×C22⋊D79C2418yes—
418D4×D79—28no—
419D4×D79—216no—
420D4×D79—216no—
421D4×D79—232no—
422C22×Dic79—28no—
423C22×Dic79—216no—
424C22×Dic79—28no—
425C22×Dic79C2×D4116yes—
426C22×Dic79C2412yes—
427C22×Dic79C2411yescharacteristic
428C22×Dic79C2418yes—
429C22×Dic79C2418yes—
430C22×Dic79C2414yes—
431C22×Dic79C2418yes—
432C22×Dic79C2414yes—
433C22×Dic79C2418yes—
434C22×Dic79C2414yes—
435C22×Dic79C2412yes—
436C22×Dic79C2411yescharacteristic
437C22×Dic79C2414yes—
438C2×C4×D79—28no—
439C2×C4×D79—216no—
440C2×C4×D79—216no—
441C2×C4×D79—28no—
442C2×C4×D79—24no—
443C2×C4×D79C2×D418yes—
444C2×C4×D79C2418yes—
445C2×C4×D79C2418yes—
446C2×C4×D79C2414yes—
447C2×C4×D79C2414yes—
448C2×C4×D79C2418yes—
449C2×C4×D79C2414yes—
450C2×C4×D79C2414yes—
451C2×C4×D79C2418yes—
452C2×C4×D79C2412yes—
453C2×C4×D79C2412yes—
454C4⋊Dic79C24116yes—
455C4⋊Dic79C2414yes—
456C4⋊Dic79C2418yes—
457Dic79⋊C4C2418yes—
458Dic79⋊C4C24116yes—
459Dic79⋊C4C24116yes—
460Dic79⋊C4C2418yes—
461Dic79⋊C4C2418yes—
462Dic79⋊C4C24116yes—
463C22⋊Dic79C2414yes—
464C22⋊Dic79C24116yes—
465C22⋊Dic79C2418yes—
466C22⋊Dic79C2418yes—
467C22⋊Dic79C2418yes—
468(C2×D79)⋊C4C24116yes—
469(C2×D79)⋊C4C24116yes—
470(C2×D79)⋊C4C2418yes—
471(C2×D79)⋊C4C2418yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2418yes—
475C4×Dic79C2418yes—
476C4×Dic79C2414yes—
477C4×Dic79C24116yes—
478C24×C79C2414yes—
479C24×C79C2411yescharacteristic
480C24×C79C2412yes—
481#41×C79—216no—
482#41×C79—232no—
483#41×C79—28no—
484C2×Q8×C79—24no—
485C2×Q8×C79C2414yes—
486C2×Q8×C79C2412yes—
487C2×D4×C79—28no—
488C2×D4×C79—216no—
489C2×D4×C79—216no—
490C2×D4×C79C2×D418yes—
491C2×D4×C79C2418yes—
492C2×D4×C79C2414yes—
493C2×D4×C79C2418yes—
494C2×D4×C79C2412yes—
495C2×D4×C79C2418yes—
496C2×D4×C79C2414yes—
497C22×C4×C79—28no—
498C22×C4×C79—24no—
499C22×C4×C79C2411yescharacteristic
500C22×C4×C79C2418yes—
501C22×C4×C79C2414yes—
502C22×C4×C79C2412yes—
503C22×C4×C79C2414yes—
504C22×C4×C79C2414yes—
505C22×C4×C79C2418yes—
506C22×C4×C79C2411yescharacteristic
507C4⋊C4×C79C2418yes—
508C4⋊C4×C79C24116yes—
509C4⋊C4×C79C2414yes—
510C22⋊C4×C79C2414yes—
511C22⋊C4×C79C2418yes—
512C22⋊C4×C79C2418yes—
513C22⋊C4×C79C24116yes—
514C22⋊C4×C79C2418yes—
515C42×C79C2414yes—
516C23×C79—22no—
517C23×C79—28no—
518C23×C79—44no—
519C23×C79—42no—
520C23×C79—48no—
521C23×C79C22×D418yes—
522C23×C79C2514yes—
523C23×C79C2512yes—
524C23×C79C2511yescharacteristic
525C23×C79C2514yes—
526C22×D79—22no—
527C22×D79—28no—
528C22×D79—28no—
529C22×D79—42no—
530C22×D79—42no—
531C22×D79—48no—
532C22×D79—48no—
533C22×D79C22×D414yes—
534C22×D79C2514yes—
535C22×D79C2512yes—
536C22×D79C2512yes—
537Q8×C79—28no—
538Q8×C79—24no—
539D4×C79—216no—
540D4×C79—28no—
541D4×C79—216no—
542D4×C79—24no—
543D4×C79—48no—
544D4×C79C22×D4116yes—
545C2×C4×C79—24no—
546C2×C4×C79—28no—
547C2×C4×C79—22no—
548C2×C4×C79—216no—
549C2×C4×C79—28no—
550C2×C4×C79—28no—
551C2×C4×C79—48no—
552C2×C4×C79C22×D414yes—
553C2×C4×C79C2518yes—
554C2×C4×C79C2514yes—
555C2×C4×C79C2512yes—
556C2×C4×C79C2514yes—
557C2×C4×C79C2512yes—
558C22⋊D79—216no—
559C22⋊D79—28no—
560C22⋊D79—216no—
561C22⋊D79—28no—
562C22⋊D79—28no—
563C22⋊D79—28no—
564C22⋊D79—216no—
565C22⋊D79—24no—
566C22⋊D79—24no—
567C22⋊D79—48no—
568C22⋊D79—48no—
569C22⋊D79C22×D4132yes—
570C2×Dic79—24no—
571C2×Dic79—22no—
572C2×Dic79—28no—
573C2×Dic79—216no—
574C2×Dic79—28no—
575C2×Dic79—216no—
576C2×Dic79—216no—
577C2×Dic79—48no—
578C2×Dic79C22×D418yes—
579C2×Dic79C22×D4116yes—
580C2×Dic79C22×D414yes—
581C2×Dic79C22×D4116yes—
582C2×Dic79C2518yes—
583C2×Dic79C2514yes—
584C2×Dic79C2512yes—
585C2×Dic79C2514yes—
586C2×Dic79C2511yescharacteristic
587C2×Dic79C2514yes—
588C2×Dic79C2511yescharacteristic
589D316—28no—
590D316—28no—
591D316—24no—
592D316—48no—
593C4×D79—28no—
594C4×D79—216no—
595C4×D79—28no—
596C4×D79—28no—
597C4×D79—28no—
598C4×D79—216no—
599C4×D79—216no—
600C4×D79—48no—
601C4×D79C22×D418yes—
602C4×D79C22×D418yes—
603Dic158—28no—
604Dic158—24no—
605Dic158—28no—
606Dic158—216no—
607Dic158—28no—
608Dic158—28no—
609Dic158—216no—
610Dic158—24no—
611Dic158—216no—
612Dic158—24no—
613Dic158C22×D4116yes—
614C22×C79—28no—
615C22×C79—22no—
616C22×C79—22no—
617C22×C79—24no—
618C22×C79—24no—
619C22×C79—28no—
620C22×C79—48no—
621C22×C79—44no—
622C22×C79—88no—
623C22×C79C23×D418yes—
624C22×C79C23×D412yes—
625C22×C79C2611yescharacteristic
626C2×D79—24no—
627C2×D79—24no—
628C2×D79—22no—
629C2×D79—24no—
630C2×D79—28no—
631C2×D79—44no—
632C2×D79—44no—
633C2×D79—88no—
634C2×D79—88no—
635C2×D79C23×D414yes—
636C4×C79—22no—
637C4×C79—24no—
638C4×C79—24no—
639C4×C79—28no—
640C4×C79C23×D414yes—
641Dic79—24no—
642Dic79—24no—
643Dic79—22no—
644Dic79—28no—
645Dic79C23×D412yes—
646Dic79C23×D418yes—
647Dic79C23×D412yes—
648#62859—791nomaximal, Sylow
649C2×C79—22no—
650C2×C79—28no—
651C2×C79—44no—
652C2×C79—42no—
653C2×C79C24×D411yescharacteristic
654C2×C792−1+612yes—
655D79—24no—
656D79—42no—
657D79—44no—
658C2×#585—791no—
659C22×2−1+4—791no—
660#3500—798no—
661#3499—798no—
662#3489—798no—
663#3489—798no—
664#3486—792no—
665#3486—792no—
666#3485—791no—
667#3485—791no—
668#3485—794no—
669#3485—794no—
670#3485—791no—
671#3485D7911yescharacteristic, complemented
672#3449—794no—
673#3449—792no—
674C2×#536—792no—
675C2×#536—794no—
676#3428—791no—
677C79#6285911yescharacteristic, complemented, Sylow
678#585—15816no—
679C2×2−1+4—792no—
680C2×2−1+4—798no—
681C2×2−1+4—798no—
682C2×2−1+4—794no—
683C2×2−1+4—15816no—
684C2×H(5,𝔽2)—794no—
685C2×H(5,𝔽2)—791no—
686C2×H(5,𝔽2)—794no—
687C2×H(5,𝔽2)C2×D7911yescharacteristic
688C22×#41—792no—
689C22×#41—794no—
690C22×#41—791no—
691C22×#41—792no—
692C22×#41—791no—
693C22×#41—792no—
694C22×#41—794no—
695C22×#41—794no—
696C22×#41—791no—
697C22×#41—792no—
698C22×#41C2×D7911yescharacteristic, complemented
699C23×Q8—791no—
700C23×Q8—791no—
701C23×Q8—792no—
702C23×Q8—791no—
703D4×Q8—798no—
704D4×Q8—798no—
705D4×Q8—798no—
706D4×Q8—798no—
707#548—798no—
708#548—798no—
709#548—798no—
710#548—798no—
711#547—798no—
712#547—798no—
713#547—7916no—
714#547—7916no—
715#547—7916no—
716#547—798no—
717#547—7916no—
718#547C2×D7918yescomplemented
719#546—798no—
720#546—798no—
721#546—7916no—
722#546—7916no—
723#546—7916no—
724#546—798no—
725#546—7916no—
726#546C2×D7918yescomplemented
727#537—794no—
728#537—7916no—
729#537—794no—
730#536—792no—
731#536—792no—
732#536—794no—
733#536—794no—
734#536—798no—
735#536—794no—
736#536—798no—
737#536—798no—
738#536—7916no—
739#536—7916no—
740#536—798no—
741#536—798no—
742#536—794no—
743#536—792no—
744#536C2×D7912yescomplemented
745#535—794no—
746#535—794no—
747#535—798no—
748#534—794no—
749#534—794no—
750#534—794no—
751#534—794no—
752#534—794no—
753#534C2×D7914yescomplemented
754#532—7916no—
755#532—798no—
756C2×C4⋊Q8—794no—
757C2×C4⋊Q8—798no—
758C2×#124—794no—
759C2×#124—798no—
760#525—792no—
761#525—792no—
762#525—798no—
763#525—798no—
764#525—798no—
765#525—798no—
766#525—798no—
767#525—792no—
768#525C2×D7912yescomplemented
769C2×#123—794no—
770C2×#123—794no—
771C2×#123—798no—
772C2×#123—794no—
773C2×#123C2×D7914yescomplemented
774C2×C22⋊Q8—798no—
775C2×C22⋊Q8—798no—
776C2×C22⋊Q8—798no—
777#520—798no—
778#519—792no—
779#518—791no—
780#518—794no—
781#518C2×D7911yescharacteristic, complemented
782C4×#41—798no—
783C2×#117—792no—
784C2×#117—794no—
7852−1+4—15816no—
7862−1+4—15864no—
7872−1+4—15864no—
7882−1+4—15832no—
789H(5,𝔽2)—28no—
790H(5,𝔽2)—15832no—
791H(5,𝔽2)—15832no—
792H(5,𝔽2)—1588no—
793C2×#41—28no—
794C2×#41—792no—
795C2×#41—7916no—
796C2×#41—794no—
797C2×#41—794no—
798C2×#41—798no—
799C2×#41—798no—
800C2×#41—798no—
801C2×#41—798no—
802C2×#41—794no—
803C2×#41—798no—
804C2×#41—792no—
805C2×#41—798no—
806C2×#41—7916no—
807C2×#41—794no—
808C2×#41—798no—
809C2×#41—794no—
810C2×#41—792no—
811C2×#41—794no—
812C2×#41—794no—
813C2×#41—794no—
814C2×#41—7916no—
815C2×#41—798no—
816C2×#41—794no—
817C2×#41—1588no—
818C2×#41—15816no—
819C2×#41—15816no—
820C2×#41—15832no—
821C2×#41—15816no—
822C2×#41—15816no—
823C2×#41—15832no—
824C2×#41—15832no—
825C2×#41—1588no—
826C2×#41C22×D7912yes—
827C2×#41C22×D7918yes—
828C2×#41C22×D7914yes—
829C22×Q8—794no—
830C22×Q8—794no—
831C22×Q8—792no—
832C22×Q8—798no—
833C22×Q8—794no—
834C22×Q8—791no—
835C22×Q8—798no—
836C22×Q8—798no—
837C22×Q8—794no—
838C22×Q8—792no—
839C22×Q8—792no—
840C22×Q8—791no—
841C22×Q8—792no—
842C22×Q8—791no—
843C22×Q8—798no—
844C22×Q8—794no—
845C22×Q8—15816no—
846C22×Q8—1588no—
847C22×Q8—1588no—
848C22×Q8—1588no—
849C22×Q8C22×D7911yescharacteristic
850C22×D4—792no—
851C22×D4—794no—
852C22×D4—794no—
853C22×D4—791no—
854C22×D4—792no—
855C22×D4—791no—
856C22×D4—798no—
857C22×D4—794no—
858C22×D4—792no—
859C22×D4—798no—
860C22×D4—794no—
861C22×D4—791no—
862C22×D4C22×D7914yes—
863C22×D4C22×D7912yes—
864C22×D4C22×D7914yes—
865C22×D4C22×D7911yescharacteristic
866C23×C4—792no—
867C23×C4—791no—
868C23×C4—794no—
869C23×C4—792no—
870C23×C4—792no—
871C23×C4—794no—
872C23×C4—794no—
873C23×C4—792no—
874C23×C4—792no—
875C23×C4—791no—
876C23×C4C22×D7912yes—
877C23×C4C22×D7911yescharacteristic
878C4⋊Q8—794no—
879C4⋊Q8—794no—
880C4⋊Q8—7916no—
881C4⋊Q8—798no—
882C4⋊Q8—7916no—
883C4⋊Q8—7916no—
884C4⋊Q8—794no—
885C4⋊Q8C22×D7914yes—
886#127—798no—
887#124—794no—
888#124—794no—
889#124—7916no—
890#124—798no—
891#124—7916no—
892#124—7916no—
893#124—798no—
894#124—794no—
895#124C22×D7914yes—
896#123—794no—
897#123—798no—
898#123—7916no—
899#123—798no—
900#123—798no—
901#123—794no—
902#123—7916no—
903#123—798no—
904#123—7916no—
905#123—798no—
906#123—798no—
907#123—794no—
908#123—7916no—
909#123—7916no—
910#123—798no—
911#123—798no—
912#123C22×D7918yes—
913#123C22×D7914yes—
914#123C22×D79116yes—
915#123C22×D7918yes—
916C22⋊Q8—798no—
917C22⋊Q8—794no—
918C22⋊Q8—798no—
919C22⋊Q8—794no—
920C22⋊Q8—7916no—
921C22⋊Q8—798no—
922C22⋊Q8—7916no—
923C22⋊Q8—7916no—
924C22⋊Q8—798no—
925C22⋊Q8—7916no—
926C22⋊Q8—794no—
927C22⋊Q8—7916no—
928C22⋊Q8—798no—
929C22⋊Q8—7916no—
930C22⋊Q8—7916no—
931C22⋊Q8—7916no—
932C22⋊Q8C22×D7918yes—
933C22⋊Q8C22×D7914yes—
934#121—798no—
935#121—794no—
936#121—7916no—
937#121—798no—
938#121—7916no—
939#121—7916no—
940#121—794no—
941#121—7916no—
942#121—794no—
943#121—798no—
944#121—798no—
945#121—7916no—
946#121—798no—
947#121—798no—
948#121C22×D7914yes—
949#121C22×D79116yes—
950#120—794no—
951#120—798no—
952#120—794no—
953#120—798no—
954#120—798no—
955#120—794no—
956#120—798no—
957#120—798no—
958#120C22×D7914yes—
959#120C22×D7918yes—
960C4×Q8—798no—
961C4×Q8—798no—
962C4×D4—798no—
963C4×D4—7916no—
964C4×D4—7916no—
965C4×D4—798no—
966C4×D4—798no—
967C4×D4—7916no—
968C4×D4—7916no—
969C4×D4—7916no—
970C4×D4—7916no—
971C4×D4—798no—
972C4×D4C22×D7918yes—
973C4×D4C22×D7918yes—
974#117—792no—
975#117—794no—
976#117—794no—
977#117—798no—
978#117—798no—
979#117—798no—
980#117—794no—
981#117C22×D7912yes—
982C2×C4⋊C4—798no—
983C2×C4⋊C4—798no—
984C2×C4⋊C4—798no—
985C2×C4⋊C4—798no—
986C2×C4⋊C4—794no—
987C2×C4⋊C4—7916no—
988C2×C4⋊C4C22×D7918yes—
989C2×C22⋊C4—794no—
990C2×C22⋊C4—798no—
991C2×C22⋊C4—798no—
992C2×C22⋊C4—798no—
993C2×C22⋊C4—794no—
994C2×C22⋊C4—7916no—
995C2×C22⋊C4C22×D7914yes—
996C2×C22⋊C4C22×D7918yes—
997C2×C42—798no—
998C2×C42—794no—
999C24—791no—
1000C24—794no—
1001C24—794no—
1002C24—791no—
1003C24C23×D7914yes—
1004C24C23×D7911yescharacteristic
1005C24C23×D7912yes—
1006#41—232no—
1007#41—216no—
1008#41—28no—
1009#41—7932no—
1010#41—7932no—
1011#41—15816no—
1012#41—15816no—
1013#41—15816no—
1014#41—15832no—
1015#41—15864no—
1016#41—15816no—
1017#41—15816no—
1018#41—15832no—
1019#41—1588no—
1020#41—15832no—
1021#41—15832no—
1022#41—15832no—
1023#41—15832no—
1024#41—1588no—
1025#41—15832no—
1026#41—15864no—
1027#41—15816no—
1028#41—15816no—
1029#41—15832no—
1030#41—1588no—
1031C2×Q8—24no—
1032C2×Q8—794no—
1033C2×Q8—794no—
1034C2×Q8—792no—
1035C2×Q8—798no—
1036C2×Q8—798no—
1037C2×Q8—794no—
1038C2×Q8—798no—
1039C2×Q8—792no—
1040C2×Q8—794no—
1041C2×Q8—792no—
1042C2×Q8—794no—
1043C2×Q8—798no—
1044C2×Q8—1584no—
1045C2×Q8—1588no—
1046C2×Q8—1588no—
1047C2×Q8—1588no—
1048C2×Q8—15832no—
1049C2×Q8—15832no—
1050C2×Q8—15816no—
1051C2×Q8—15832no—
1052C2×Q8—15816no—
1053C2×Q8—15816no—
1054C2×Q8—15816no—
1055C2×Q8—1588no—
1056C2×Q8—15832no—
1057C2×Q8—15816no—
1058C2×Q8—1584no—
1059C2×Q8C23×D7914yes—
1060C2×Q8C23×D7912yes—
1061C2×D4—28no—
1062C2×D4—216no—
1063C2×D4—216no—
1064C2×D4—798no—
1065C2×D4—798no—
1066C2×D4—798no—
1067C2×D4—7916no—
1068C2×D4—794no—
1069C2×D4—798no—
1070C2×D4—794no—
1071C2×D4—792no—
1072C2×D4—794no—
1073C2×D4—798no—
1074C2×D4—798no—
1075C2×D4—794no—
1076C2×D4—792no—
1077C2×D4—798no—
1078C2×D4—794no—
1079C2×D4—794no—
1080C2×D4—792no—
1081C2×D4—1584no—
1082C2×D4—1588no—
1083C2×D4—1584no—
1084C2×D4—15816no—
1085C2×D4—15832no—
1086C2×D4—15816no—
1087C2×D4—15832no—
1088C2×D4—1584no—
1089C2×D4—1588no—
1090C2×D4—15816no—
1091C2×D4—15816no—
1092C2×D4D4×D7918yes—
1093C2×D4C23×D7918yes—
1094C2×D4C23×D7914yes—
1095C2×D4C23×D7918yes—
1096C2×D4C23×D7912yes—
1097C2×D4C23×D7918yes—
1098C2×D4C23×D7914yes—
1099C22×C4—28no—
1100C22×C4—24no—
1101C22×C4—798no—
1102C22×C4—798no—
1103C22×C4—794no—
1104C22×C4—794no—
1105C22×C4—791no—
1106C22×C4—792no—
1107C22×C4—7916no—
1108C22×C4—792no—
1109C22×C4—792no—
1110C22×C4—798no—
1111C22×C4—798no—
1112C22×C4—794no—
1113C22×C4—798no—
1114C22×C4—798no—
1115C22×C4—794no—
1116C22×C4—791no—
1117C22×C4—792no—
1118C22×C4—798no—
1119C22×C4—794no—
1120C22×C4—798no—
1121C22×C4—794no—
1122C22×C4—798no—
1123C22×C4—794no—
1124C22×C4—794no—
1125C22×C4—1588no—
1126C22×C4—15816no—
1127C22×C4—15816no—
1128C22×C4—1588no—
1129C22×C4—1588no—
1130C22×C4—15816no—
1131C22×C4—1588no—
1132C22×C4—1584no—
1133C22×C4C23×D7918yes—
1134C22×C4C23×D7914yes—
1135C22×C4C23×D7914yes—
1136C22×C4C23×D7914yes—
1137C22×C4C23×D7912yes—
1138C22×C4C23×D7911yescharacteristic
1139C22×C4C23×D7918yes—
1140C22×C4C23×D7911yescharacteristic
1141C4⋊C4—798no—
1142C4⋊C4—7916no—
1143C4⋊C4—798no—
1144C4⋊C4—7916no—
1145C4⋊C4—798no—
1146C4⋊C4—7916no—
1147C4⋊C4—7916no—
1148C4⋊C4—798no—
1149C4⋊C4—794no—
1150C4⋊C4C23×D79116yes—
1151C4⋊C4C23×D7914yes—
1152C4⋊C4C23×D7918yes—
1153C22⋊C4—794no—
1154C22⋊C4—7916no—
1155C22⋊C4—798no—
1156C22⋊C4—798no—
1157C22⋊C4—798no—
1158C22⋊C4—7916no—
1159C22⋊C4—798no—
1160C22⋊C4—7916no—
1161C22⋊C4—798no—
1162C22⋊C4—798no—
1163C22⋊C4—798no—
1164C22⋊C4—798no—
1165C22⋊C4C23×D7914yes—
1166C22⋊C4C23×D79116yes—
1167C22⋊C4C23×D7918yes—
1168C22⋊C4C23×D7918yes—
1169C22⋊C4C23×D7918yes—
1170C42—798no—
1171C42—7916no—
1172C42—794no—
1173C42C23×D7914yes—
1174C23—22no—
1175C23—28no—
1176C23—44no—
1177C23—42no—
1178C23—48no—
1179C23—3162no—
1180C23—3162no—
1181C23—3168no—
1182C23—3168no—
1183C23—794no—
1184C23—792no—
1185C23—794no—
1186C23—792no—
1187C23—1588no—
1188C23—1582no—
1189C23—1588no—
1190C23C2×D4×D7918yes—
1191C23C24×D7914yes—
1192C23C24×D7912yes—
1193C23C24×D7911yescharacteristic
1194C23C24×D7914yes—
1195Q8—28no—
1196Q8—24no—
1197Q8—7916no—
1198Q8—1584no—
1199Q8—1584no—
1200Q8—15816no—
1201Q8—1588no—
1202Q8—1588no—
1203Q8—15816no—
1204Q8—1588no—
1205Q8—15816no—
1206Q8—1588no—
1207Q8—1584no—
1208D4—28no—
1209D4—216no—
1210D4—216no—
1211D4—24no—
1212D4—48no—
1213D4—3168no—
1214D4—3168no—
1215D4—3168no—
1216D4—7932no—
1217D4—1588no—
1218D4—1588no—
1219D4—1588no—
1220D4—15816no—
1221D4—1584no—
1222D4—1584no—
1223D4—1588no—
1224D4—1588no—
1225D4—1588no—
1226D4—15816no—
1227D4—15816no—
1228D4—1584no—
1229D4C2×D4×D79116yes—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—216no—
1233C2×C4—28no—
1234C2×C4—28no—
1235C2×C4—28no—
1236C2×C4—48no—
1237C2×C4—3168no—
1238C2×C4—3168no—
1239C2×C4—791no—
1240C2×C4—794no—
1241C2×C4—791no—
1242C2×C4—794no—
1243C2×C4—798no—
1244C2×C4—7916no—
1245C2×C4—7916no—
1246C2×C4—798no—
1247C2×C4—798no—
1248C2×C4—798no—
1249C2×C4—792no—
1250C2×C4—794no—
1251C2×C4—794no—
1252C2×C4—1588no—
1253C2×C4—15816no—
1254C2×C4—15816no—
1255C2×C4—1588no—
1256C2×C4—15816no—
1257C2×C4—1588no—
1258C2×C4—15816no—
1259C2×C4—15816no—
1260C2×C4—1584no—
1261C2×C4—1582no—
1262C2×C4—1588no—
1263C2×C4—15816no—
1264C2×C4—1588no—
1265C2×C4—1588no—
1266C2×C4C2×D4×D7914yes—
1267C2×C4C24×D7918yes—
1268C2×C4C24×D7914yes—
1269C2×C4C24×D7912yes—
1270C2×C4C24×D7914yes—
1271C2×C4C24×D7912yes—
1272C22—28no—
1273C22—22no—
1274C22—22no—
1275C22—24no—
1276C22—24no—
1277C22—28no—
1278C22—48no—
1279C22—44no—
1280C22—88no—
1281C22—3164no—
1282C22—3164no—
1283C22—794no—
1284C22—6328no—
1285C22—6328no—
1286C22—1582no—
1287C22—1584no—
1288C22—1584no—
1289C22—1588no—
1290C22—1584no—
1291C22C22×D4×D7912yes—
1292C22C22×D4×D7918yes—
1293C22C25×D7911yescharacteristic
1294C4—22no—
1295C4—24no—
1296C4—24no—
1297C4—28no—
1298C4—792no—
1299C4—792no—
1300C4—798no—
1301C4—1584no—
1302C4—1584no—
1303C4—1582no—
1304C4—1588no—
1305C4C22×D4×D7914yes—
1306C2—22no—
1307C2—28no—
1308C2—42no—
1309C2—44no—
1310C2—3162no—
1311C2—3164no—
1312C2—1584no—
1313C2C23×D4×D7911yescharacteristic
1314C2#2377821312yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3485C2
hypercenter#3485D79
hypocenterC79#62859
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. C2×#19099398C2semidirect
2. C22×#14579208C2semidirect
3. #23777186C2semidirect
4. #23777179C2semidirect
5. #23777074C2semidirect
6. #23777071C2semidirect
7. #23777049C2semidirect
8. #23777047C2semidirect
9. #23777045C2semidirect
10. #23777044C2semidirect
11. #23777041C2semidirect
12. #23777040C2semidirect
13. #23777038C2semidirect
14. #23776730C2semidirect
15. #23776726C2semidirect
16. C2×#19099135C2semidirect
17. #536×D79C2semidirect
18. #23776598C2semidirect
19. C79×#3485C2semidirect
23. C2×#14579208C22semidirect
24. C2×#14579208C22semidirect
25. C2×#14579208C22semidirect
28. C2×#14579206C22semidirect
29. C22×#11929624C22semidirect
30. C22×#11929624C22semidirect
33. C22×#11929623C22semidirect
34. C22×#11929623C22semidirect
35. C22×#11929623C22semidirect
36. C22×#11929623C22semidirect
38. C2×#41×D79C22semidirect
39. C23×Dic158C22semidirect
40. C23×Dic158C22semidirect
41. C22×Q8×D79C22semidirect
42. C22×Q8×D79C22semidirect
43. D4×Dic158C22semidirect
44. #19099228C22semidirect
45. #19099226C22semidirect
46. #19099226C22semidirect
47. #19099223C22semidirect
48. #19099222C22semidirect
49. #19099221C22semidirect
50. #19099219C22semidirect
51. #19099217C22semidirect
52. #19099214C22semidirect
53. #19099213C22semidirect
54. #19099212C22semidirect
55. #19099212C22semidirect
56. #19099211C22semidirect
57. #19099211C22semidirect
58. #19099208C22semidirect
59. #19099207C22semidirect
60. #19099205C22semidirect
61. #19099203C22semidirect
62. #19099202C22semidirect
63. #19099201C22semidirect
64. #19099200C22semidirect
65. #19099143C22semidirect
66. #19099142C22semidirect
67. #19099140C22semidirect
68. #19099139C22semidirect
69. #19099138C22semidirect
70. #19099137C22semidirect
71. #19099136C22semidirect
72. #19099136C22semidirect
73. #19099135C22semidirect
74. #19099135C22semidirect
75. #19099135C22semidirect
76. #19099135C22semidirect
77. #19099135C22semidirect
78. #19099135C22semidirect
79. #19099135C22semidirect
80. #19099134C22semidirect
81. #19099133C22semidirect
82. #19099129C22semidirect
83. #19099128C22semidirect
84. #19099128C22semidirect
85. #19099125C22semidirect
86. #19099124C22semidirect
87. #19099123C22semidirect
88. #19099122C22semidirect
89. #19099122C22semidirect
90. #19099110C22semidirect
91. #19099108C22semidirect
92. C2×#14579160C22semidirect
93. C4⋊Q8×D79C22semidirect
94. C2×#14579147C22semidirect
95. #124×D79C22semidirect
96. #19099075C22semidirect
97. #19099074C22semidirect
98. #19099072C22semidirect
99. #19099071C22semidirect
100. #19099071C22semidirect
101. #19099070C22semidirect
102. #19099069C22semidirect
103. #19099069C22semidirect
104. C2×#14579145C22semidirect
105. C2×#14579144C22semidirect
106. C2×#14579142C22semidirect
107. #123×D79C22semidirect
108. C2×#14579139C22semidirect
109. C2×#14579138C22semidirect
110. C22⋊Q8×D79C22semidirect
111. #19099042C22semidirect
112. #19099040C22semidirect
113. #19099038C22semidirect
114. #19099036C22semidirect
115. C4×#11929623C22semidirect
116. C2×#14579117C22semidirect
117. #117×D79C22semidirect
119. C22×#41×C79C22semidirect
120. #547×C79C22semidirect
121. #546×C79C22semidirect
122. #536×C79C22semidirect
123. #534×C79C22semidirect
124. #525×C79C22semidirect
125. C2×#123×C79C22semidirect
126. #518×C79C22semidirect
149. C2×#11929623D4semidirect
671. #3485D79semidirect
677. C79#62859semidirect
698. C22×#41C2×D79semidirect
718. #547C2×D79semidirect
726. #546C2×D79semidirect
744. #536C2×D79semidirect
753. #534C2×D79semidirect
768. #525C2×D79semidirect
773. C2×#123C2×D79semidirect
781. #518C2×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190993982
C22×#145792082
#237771862
#237771792
#237770742
#237770712
#237770492
#237770472
#237770452
#237770442
#237770412
#237770402
#237770382
#237767302
#237767262
C2×#190991352
#536×D792
#237765982
C79×#34852
#6285979