Finite Group Databasebeta

← #35197383

Subgroups — #35197383

Order 20224.

11222 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099398C212yesmaximal, complemented
2#23777169C212yesmaximal, complemented
3#23777166C212yesmaximal, complemented
4#23777164C211yesmaximal, characteristic, complemented
5#23777161C214yesmaximal, complemented
6#23777159C212yesmaximal, complemented
7#23777157C214yesmaximal, complemented
8#23777074C218yesmaximal, complemented
9#23777071C218yesmaximal, complemented
10#23777063C218yesmaximal, complemented
11#23777060C218yesmaximal, complemented
12#23776727C212yesmaximal, complemented
13#23776726C214yesmaximal, complemented
14C2×#19099140C214yesmaximal, complemented
15#537×D79C212yesmaximal, complemented
16C2×#19099042C211yesmaximal, characteristic, complemented
17C79×#3496C211yesmaximal, characteristic, complemented
18#19099398—232no—
19C2×#14579208C2218yescomplemented
20C2×#14579208C2214yescomplemented
21C2×#14579206C2218yescomplemented
22C2×#14579206C2218yescomplemented
23C2×#14579206C2212yescomplemented
24C22×#11929623C2211yescharacteristic
25C22×#11929623C2218yescomplemented
26C22×#11929623C2218yescomplemented
27C2×#41×D79C2218yescomplemented
28C2×#41×D79C2214yescomplemented
29#19099234C2214yescomplemented
30#19099233C2214yescomplemented
31#19099231C2218yescomplemented
32D4×Dic158C2214yescomplemented
33#19099228C2214yescomplemented
34#19099226C2218yescomplemented
35#19099223C2218yescomplemented
36#19099222C2218yescomplemented
37#19099221C2218yescomplemented
38#19099219C2218yescomplemented
39#19099217C2214yescomplemented
40#19099214C2218yescomplemented
41#19099213C2218yescomplemented
42#19099212C2218yescomplemented
43#19099211C22116yescomplemented
44#19099208C2218yescomplemented
45#19099207C2218yescomplemented
46#19099205C22116yescomplemented
47#19099203C22116yescomplemented
48#19099202C22116yescomplemented
49#19099201C2218yescomplemented
50#19099200C22116yescomplemented
51D4×D316C2214yescomplemented
52#19099197C2218yescomplemented
53D4×C22⋊D79C2218yescomplemented
54D4×C22⋊D79C2218yescomplemented
55#19099195C22116yescomplemented
56#19099144C2212yescomplemented
57#19099143C2218yescomplemented
58#19099142C2218yescomplemented
59#19099141C2214yescomplemented
60#19099140C22116yescomplemented
61#19099140C22116yescomplemented
62#19099140C2218yescomplemented
63#19099140C2218yescomplemented
64#19099140C2218yescomplemented
65#19099140C2214yescomplemented
66#19099140C2214yescomplemented
67#19099138C2214yescomplemented
68#19099135C22116yescomplemented
69#19099133C2214yescomplemented
70#19099131C2214yescomplemented
71#19099128C22116yescomplemented
72#19099126C2214yescomplemented
73#19099125C2214yescomplemented
74#19099122C2218yescomplemented
75#19099121C2214yescomplemented
76#19099121C2214yescomplemented
77#19099113C2212yescomplemented
78#19099109C2214yescomplemented
79#19099108C2218yescomplemented
80#19099108C2218yescomplemented
81#19099072C2218yescomplemented
82#19099072C2218yescomplemented
83#19099071C22116yescomplemented
84#19099069C22116yescomplemented
85C2×#14579139C2218yescomplemented
86C2×#14579138C2218yescomplemented
87C22⋊Q8×D79C2218yescomplemented
88C2×#14579135C2214yescomplemented
89C2×#14579134C2218yescomplemented
90C2×#14579133C2218yescomplemented
91C2×#14579133C2218yescomplemented
92#121×D79C2218yescomplemented
93#121×D79C2218yescomplemented
94#19099042C2218yescomplemented
95#19099042C2218yescomplemented
96C2×C4×Dic158C2211yescharacteristic, complemented
97C2×#14579126C2211yescharacteristic, complemented
98C2×D4×Dic79C2211yescharacteristic, complemented
99C2×C4×C22⋊D79C2212yescomplemented
100C2×(C22⋊D79)⋊C4C2212yescomplemented
101C2×#14579118C2211yescharacteristic, complemented
102C2×#14579117C2212yescomplemented
103C22×Dic79⋊C4C2212yescomplemented
104C2×C4⋊C4×D79C2211yescharacteristic, complemented
105C2×H(5,𝔽2)×C79C2212yescomplemented
106#547×C79C2214yescomplemented
107#546×C79C2218yescomplemented
108D42×C79C2214yescomplemented
109#537×C79C2212yescomplemented
110#534×C79C2214yescomplemented
111#532×C79C2212yescomplemented
112C2×#121×C79C2214yescomplemented
113C2×C4×D4×C79C2211yescharacteristic, complemented
114#14579208—264no—
115#14579208—232no—
116#14579206—216no—
117#14579206—264no—
118#14579206—264no—
119C2×#11929625C2314yes—
120C2×#11929624C2314yes—
121C2×#11929624C2318yes—
122C2×#11929624C23116yes—
123C2×#11929624C2318yes—
124C2×#11929623—264no—
125C2×#11929623—264no—
126C2×#11929623D4116yescomplemented
127C2×#11929623C23116yes—
128C2×#11929623C23116yes—
129C2×#11929623C23116yes—
130C2×#11929623C2318yes—
131C2×#11929623C2318yes—
132C2×#11929623C2318yes—
133C2×#11929623C23116yes—
134C2×#11929623C2314yes—
135C2×#11929623C2318yes—
136#41×D79—264no—
137#41×D79—232no—
138C22×Dic158C2318yes—
139C22×Dic158C2318yes—
140C22×Dic158C2311yescharacteristic
141C2×Q8×D79C2314yes—
142C2×Q8×D79C2318yes—
143C22×D316C2314yes—
144C22×C22⋊D79C23116yes—
145C22×C22⋊D79C2318yes—
146C22×C22⋊D79C2318yes—
147C22×C22⋊D79C2318yes—
148C22×C22⋊D79C2312yes—
149C2×D4×D79C23116yes—
150C2×D4×D79C2318yes—
151C2×D4×D79C2318yes—
152C2×D4×D79C2314yes—
153C2×D4×D79C2318yes—
154C23×Dic79C2318yes—
155C23×Dic79C2312yes—
156C23×Dic79C2312yes—
157C22×C4×D79C2318yes—
158C22×C4×D79C2318yes—
159C22×C4×D79C2312yes—
160C22×C4×D79C2311yescharacteristic
161#14579161C2312yes—
162#14579160C2318yes—
163#14579160C2318yes—
164#14579159C2314yes—
165#14579158C2312yes—
166#14579157C2318yes—
167#14579157C2314yes—
168#14579157C2318yes—
169#14579150C2314yes—
170#14579149C2314yes—
171#14579148C2314yes—
172#14579147C23116yes—
173#14579147C23116yes—
174#14579146C2318yes—
175#14579146C2318yes—
176#14579145C23116yes—
177#14579144C23116yes—
178#14579143C2318yes—
179#14579143C2318yes—
180#14579142C23116yes—
181#14579141C2318yes—
182#14579140C2318yes—
183#14579139C2318yes—
184#14579139C2318yes—
185#14579139C23116yes—
186#14579139C23116yes—
187#14579139C23116yes—
188#14579138C2318yes—
189#14579138C23116yes—
190#14579138C23116yes—
191#14579138C23116yes—
192#14579138C2318yes—
193#14579137C2318yes—
194#14579136C2318yes—
195#14579136C2318yes—
196#14579135C2314yes—
197#14579135C2318yes—
198#14579135C2318yes—
199#14579135C2318yes—
200#14579135C2314yes—
201#14579135C2318yes—
202#14579134C2318yes—
203#14579134C23116yes—
204#14579134C23116yes—
205#14579134C23116yes—
206#14579134C2318yes—
207#14579134C23116yes—
208#14579133C2318yes—
209#14579133C2318yes—
210#14579133C23116yes—
211#14579133C23116yes—
212#14579133C23116yes—
213#14579133C23116yes—
214#14579133C23116yes—
215#14579133C23116yes—
216#14579133C2318yes—
217#14579133C2318yes—
218#14579132C2318yes—
219#14579132C2318yes—
220#14579131C2318yes—
221#14579131C23116yes—
222#14579131C2318yes—
223#14579130C23116yes—
224#14579129C2318yes—
225#14579129C2318yes—
226#14579129C23116yes—
227C4×Dic158C2314yes—
228C4×Dic158C2314yes—
229#14579126C2318yes—
230C4×D316C2314yes—
231C4×D316C2314yes—
232D4×Dic79C2318yes—
233D4×Dic79C2318yes—
234D4×Dic79C2318yes—
235#14579123C2318yes—
236#14579123C2318yes—
237C4×C22⋊D79C2318yes—
238C4×C22⋊D79C2318yes—
239C4×C22⋊D79C2318yes—
240C4×C22⋊D79C2318yes—
241(C22⋊D79)⋊C4C23116yes—
242(C22⋊D79)⋊C4C23116yes—
243(C22⋊D79)⋊C4C23116yes—
244#14579118C2314yes—
245#14579118C2314yes—
246#14579117C23116yes—
247C2×C4⋊Dic79C2311yescharacteristic
248C2×C4⋊Dic79C2314yes—
249C2×Dic79⋊C4C2312yes—
250C2×Dic79⋊C4C2311yescharacteristic
251C2×Dic79⋊C4C2312yes—
252C2×Dic79⋊C4C2312yes—
253C2×Dic79⋊C4C2311yescharacteristic
254C2×Dic79⋊C4C2318yes—
255C2×Dic79⋊C4C2318yes—
256C2×Dic79⋊C4C2318yes—
257C4⋊C4×D79C2318yes—
258C4⋊C4×D79C2318yes—
259C2×C22⋊Dic79C2318yes—
260C2×C22⋊Dic79C2312yes—
261C2×(C2×D79)⋊C4C2318yes—
262C2×(C2×D79)⋊C4C2318yes—
263C2×(C2×D79)⋊C4C2311yescharacteristic
264C2×(C2×D79)⋊C4C2311yescharacteristic
265C22⋊C4×D79C23116yes—
266C2×C4×Dic79C2312yes—
267C2×C4×Dic79C2312yes—
268C2×C4×Dic79C2311yescharacteristic
269H(5,𝔽2)×C79—216no—
270C2×#41×C79C2314yes—
271C2×#41×C79C2318yes—
272C22×D4×C79C2318yes—
273C22×D4×C79C2318yes—
274C22×D4×C79C2314yes—
275C22×D4×C79C2311yescharacteristic
276C23×C4×C79C2312yes—
277C4⋊Q8×C79C2312yes—
278#127×C79C2312yes—
279#124×C79C2314yes—
280#123×C79C23116yes—
281C22⋊Q8×C79C2318yes—
282#121×C79C2314yes—
283#121×C79C2318yes—
284#121×C79C2318yes—
285#121×C79C2318yes—
286#121×C79C2314yes—
287#121×C79C2318yes—
288#120×C79C23116yes—
289C4×D4×C79C2314yes—
290C4×D4×C79C2314yes—
291C4×D4×C79C2314yes—
292C4×D4×C79C2314yes—
293C2×C4⋊C4×C79C2311yescharacteristic
294C2×C4⋊C4×C79C2314yes—
295C2×C22⋊C4×C79C2318yes—
296C2×C22⋊C4×C79C2312yes—
297C2×C42×C79C2311yescharacteristic
298C23×D79C2418yes—
299C23×D79C2418yes—
300C23×D79C2411yescharacteristic
301#11929625—216no—
302#11929624—232no—
303#11929624—232no—
304#11929624—216no—
305#11929624—264no—
306#11929623—264no—
307#11929623—232no—
308#11929623—264no—
309#11929623—264no—
310#11929623—216no—
311#11929623—232no—
312#11929623—232no—
313#11929623—264no—
314#11929623C2×D4164yescomplemented
315C2×Dic158—232no—
316C2×Dic158—232no—
317C2×Dic158C2×D418yescomplemented
318C2×Dic158C2418yes—
319C2×Dic158C24116yes—
320C2×Dic158C2414yes—
321C2×Dic158C2414yes—
322Q8×D79—216no—
323Q8×D79—232no—
324C2×D316—84no—
325C2×D316C2418yes—
326C2×D316C2414yes—
327C2×D316C2414yes—
328C2×D316C2418yes—
329C2×D316C2414yes—
330C2×C22⋊D79—232no—
331C2×C22⋊D79—232no—
332C2×C22⋊D79—264no—
333C2×C22⋊D79—88no—
334C2×C22⋊D79C2×D4116yescomplemented
335C2×C22⋊D79C2418yes—
336C2×C22⋊D79C24116yes—
337C2×C22⋊D79C2418yes—
338C2×C22⋊D79C2418yes—
339C2×C22⋊D79C24116yes—
340C2×C22⋊D79C2418yes—
341C2×C22⋊D79C24116yes—
342C2×C22⋊D79C2418yes—
343C2×C22⋊D79C2418yes—
344D4×D79—216no—
345D4×D79—232no—
346D4×D79—232no—
347D4×D79—264no—
348D4×D79—88no—
349C22×Dic79—232no—
350C22×Dic79—82no—
351C22×Dic79C2×D4116yescomplemented
352C22×Dic79C2418yes—
353C22×Dic79C24116yes—
354C22×Dic79C2418yes—
355C22×Dic79C2411yescharacteristic
356C22×Dic79C2411yescharacteristic
357C22×Dic79C2412yes—
358C22×Dic79C2418yes—
359C22×Dic79C2412yes—
360C22×Dic79C2418yes—
361C22×Dic79C2411yescharacteristic
362C2×C4×D79—232no—
363C2×C4×D79—232no—
364C2×C4×D79—82no—
365C2×C4×D79C2×D418yescomplemented
366C2×C4×D79C2418yes—
367C2×C4×D79C24116yes—
368C2×C4×D79C2418yes—
369C2×C4×D79C2418yes—
370C2×C4×D79C2418yes—
371C2×C4×D79C2414yes—
372C4⋊Dic79C2414yes—
373C4⋊Dic79C2418yes—
374C4⋊Dic79C2414yes—
375C4⋊Dic79C2414yes—
376Dic79⋊C4C2418yes—
377Dic79⋊C4C24116yes—
378Dic79⋊C4C2412yes—
379Dic79⋊C4C2412yes—
380Dic79⋊C4C2418yes—
381Dic79⋊C4C2414yes—
382Dic79⋊C4C2414yes—
383Dic79⋊C4C2418yes—
384Dic79⋊C4C2414yes—
385Dic79⋊C4C2418yes—
386C22⋊Dic79C24116yes—
387C22⋊Dic79C2418yes—
388C22⋊Dic79C2418yes—
389C22⋊Dic79C2418yes—
390(C2×D79)⋊C4C24116yes—
391(C2×D79)⋊C4C24116yes—
392(C2×D79)⋊C4C2418yes—
393(C2×D79)⋊C4C2418yes—
394(C2×D79)⋊C4C2414yes—
395(C2×D79)⋊C4C2412yes—
396(C2×D79)⋊C4C2412yes—
397(C2×D79)⋊C4C2418yes—
398(C2×D79)⋊C4C2418yes—
399C4×Dic79C2418yes—
400C4×Dic79C2418yes—
401C4×Dic79C2414yes—
402C24×C79C2418yes—
403C24×C79C2412yes—
404#41×C79—232no—
405#41×C79—216no—
406C2×Q8×C79C2414yes—
407C2×D4×C79—232no—
408C2×D4×C79—232no—
409C2×D4×C79—84no—
410C2×D4×C79C2×D418yescomplemented
411C2×D4×C79C24116yes—
412C2×D4×C79C2418yes—
413C2×D4×C79C2414yes—
414C2×D4×C79C2414yes—
415C2×D4×C79C2414yes—
416C2×D4×C79C2418yes—
417C2×D4×C79C2414yes—
418C22×C4×C79—82no—
419C22×C4×C79C2418yes—
420C22×C4×C79C2418yes—
421C22×C4×C79C2411yescharacteristic
422C22×C4×C79C2411yescharacteristic
423C22×C4×C79C2414yes—
424C22×C4×C79C2412yes—
425C22×C4×C79C2414yes—
426C22×C4×C79C2411yescharacteristic
427C4⋊C4×C79C2414yes—
428C4⋊C4×C79C2414yes—
429C4⋊C4×C79C2418yes—
430C4⋊C4×C79C2414yes—
431C22⋊C4×C79C2418yes—
432C22⋊C4×C79C2418yes—
433C22⋊C4×C79C24116yes—
434C22⋊C4×C79C2418yes—
435C42×C79C2412yes—
436C42×C79C2412yes—
437C23×C79—216no—
438C23×C79—42no—
439C23×C79—42no—
440C23×C79—48no—
441C23×C79—48no—
442C23×C79C22×D418yes—
443C23×C79C2518yes—
444C23×C79C2514yes—
445C23×C79C2511yescharacteristic
446C22×D79—216no—
447C22×D79—216no—
448C22×D79—41no—
449C22×D79—41no—
450C22×D79—48no—
451C22×D79—48no—
452C22×D79—48no—
453C22×D79—48no—
454C22×D79C22×D414yes—
455C22×D79C2518yes—
456C22×D79C2512yes—
457Q8×C79—28no—
458D4×C79—216no—
459D4×C79—232no—
460D4×C79—28no—
461D4×C79—48no—
462D4×C79—44no—
463D4×C79—44no—
464D4×C79C22×D4116yes—
465C2×C4×C79—216no—
466C2×C4×C79—216no—
467C2×C4×C79—42no—
468C2×C4×C79—44no—
469C2×C4×C79—41no—
470C2×C4×C79—44no—
471C2×C4×C79—41no—
472C2×C4×C79C22×D414yes—
473C2×C4×C79C2512yes—
474C2×C4×C79C2514yes—
475C2×C4×C79C2511yescharacteristic
476C2×C4×C79C2518yes—
477C2×C4×C79C2511yescharacteristic
478C2×C4×C79C2512yes—
479C22⋊D79—216no—
480C22⋊D79—232no—
481C22⋊D79—216no—
482C22⋊D79—232no—
483C22⋊D79—216no—
484C22⋊D79—416no—
485C22⋊D79—48no—
486C22⋊D79—48no—
487C22⋊D79C22×D4132yes—
488C2×Dic79—216no—
489C2×Dic79—216no—
490C2×Dic79—232no—
491C2×Dic79—42no—
492C2×Dic79—41no—
493C2×Dic79—48no—
494C2×Dic79—41no—
495C2×Dic79C22×D4132yes—
496C2×Dic79C22×D414yes—
497C2×Dic79C22×D418yes—
498C2×Dic79C2512yes—
499C2×Dic79C2512yes—
500C2×Dic79C2514yes—
501C2×Dic79C2518yes—
502C2×Dic79C2514yes—
503C2×Dic79C2512yes—
504D316—216no—
505D316—28no—
506D316—48no—
507D316—44no—
508D316—44no—
509C4×D79—216no—
510C4×D79—216no—
511C4×D79—216no—
512C4×D79—232no—
513C4×D79—48no—
514C4×D79C22×D4116yes—
515Dic158—28no—
516Dic158—232no—
517Dic158—216no—
518Dic158C22×D4116yes—
519C22×C79—21no—
520C22×C79—24no—
521C22×C79—21no—
522C22×C79—24no—
523C22×C79—28no—
524C22×C79—28no—
525C22×C79—28no—
526C22×C79—48no—
527C22×C79—816no—
528C22×C79C23×D412yes—
529C22×C79C23×D418yes—
530C22×C79C2611yescharacteristic
531C2×D79—22no—
532C2×D79—22no—
533C2×D79—28no—
534C2×D79—28no—
535C2×D79—28no—
536C2×D79—44no—
537C2×D79—816no—
538C2×D79—816no—
539C2×D79C23×D414yes—
540C4×C79—28no—
541C4×C79—21no—
542C4×C79—21no—
543C4×C79—24no—
544C4×C79—22no—
545C4×C79C23×D414yes—
546Dic79—28no—
547Dic79—24no—
548Dic79—22no—
549Dic79—22no—
550Dic79C23×D418yes—
551Dic79C23×D414yes—
552#62853—791nomaximal, Sylow
553C2×C79—22no—
554C2×C79—28no—
555C2×C79—48no—
556C2×C79C24×D411yescharacteristic
557C2×C79H(7,𝔽2)11yescharacteristic
558C2×C792−1+611yescharacteristic
559D79—24no—
560D79—48no—
561C2×#585—792no—
562#3497—792no—
563#3497—792no—
564#3496—792no—
565#3496—794no—
566#3496—794no—
567#3496—791no—
568#3496D7911yescharacteristic, complemented
569#3489—798no—
570#3489—798no—
571#3488—798no—
572#3488—798no—
573#3449—794no—
574#3449—792no—
575C2×#537—792no—
576C2×#537—794no—
577C2×#520—791no—
578C79#6285311yescharacteristic, complemented, Sylow
579#585—15832no—
580C2×2−1+4—798no—
581C2×2−1+4—794no—
582C2×H(5,𝔽2)—798no—
583C2×H(5,𝔽2)—798no—
584C2×H(5,𝔽2)—792no—
585C2×H(5,𝔽2)C2×D7912yescomplemented
586C22×#41—794no—
587C22×#41—798no—
588C22×#41—791no—
589C22×#41—798no—
590C22×#41—798no—
591#550—794no—
592#550—798no—
593#550—794no—
594D4×Q8—794no—
595D4×Q8—798no—
596D4×Q8—794no—
597#548—798no—
598#548—798no—
599#548—798no—
600#548—798no—
601#547—798no—
602#547—7916no—
603#547—798no—
604#547—794no—
605#547—798no—
606#547C2×D7914yescomplemented
607#546—798no—
608#546—798no—
609#546—7916no—
610#546—7916no—
611#546—7916no—
612#546—798no—
613#546—7916no—
614#546C2×D7918yescomplemented
615D42—798no—
616D42—798no—
617D42—798no—
618D42—7916no—
619D42—794no—
620D42C2×D7914yescomplemented
621#537—794no—
622#537—798no—
623#537—798no—
624#537—794no—
625#537—7916no—
626#537—7916no—
627#537—798no—
628#537—798no—
629#537—794no—
630#537—798no—
631#537—792no—
632#537C2×D7912yescomplemented
633#536—794no—
634#536—794no—
635#536—7916no—
636#535—794no—
637#535—794no—
638#535—7916no—
639#534—798no—
640#534—794no—
641#534—794no—
642#534—794no—
643#534C2×D7914yescomplemented
644#532—794no—
645#532—798no—
646#532—798no—
647#532—792no—
648#532C2×D7912yescomplemented
649#525—7916no—
650#525—7916no—
651#525—798no—
652#525—798no—
653C2×C22⋊Q8—798no—
654C2×C22⋊Q8—798no—
655C2×C22⋊Q8—798no—
656C2×#121—798no—
657C2×#121—798no—
658C2×#121—794no—
659C2×#121—798no—
660C2×#121—798no—
661C2×#121—798no—
662C2×#121C2×D7914yescomplemented
663#520—798no—
664#520—798no—
665C2×C4×Q8—791no—
666C2×C4×Q8—791no—
667C2×C4×D4—791no—
668C2×C4×D4—792no—
669C2×C4×D4—792no—
670C2×C4×D4C2×D7911yescharacteristic, complemented
671C2×#117—792no—
672C2×#117—791no—
673C22×C4⋊C4—792no—
674C22×C4⋊C4—791no—
6752−1+4—15832no—
6762−1+4—15864no—
677H(5,𝔽2)—216no—
678H(5,𝔽2)—15864no—
679H(5,𝔽2)—15864no—
680H(5,𝔽2)—15816no—
681C2×#41—794no—
682C2×#41—7916no—
683C2×#41—798no—
684C2×#41—7916no—
685C2×#41—7916no—
686C2×#41—7916no—
687C2×#41—794no—
688C2×#41—798no—
689C2×#41—798no—
690C2×#41—7916no—
691C2×#41—798no—
692C2×#41—798no—
693C2×#41—794no—
694C2×#41—7916no—
695C2×#41—798no—
696C2×#41—15864no—
697C2×#41—15832no—
698C2×#41—15864no—
699C2×#41—15864no—
700C2×#41C22×D7914yes—
701C2×#41C22×D7918yes—
702C22×Q8—794no—
703C22×Q8—798no—
704C22×Q8—791no—
705C22×Q8—798no—
706C22×Q8—798no—
707C22×D4—792no—
708C22×D4—798no—
709C22×D4—798no—
710C22×D4—798no—
711C22×D4—7916no—
712C22×D4—798no—
713C22×D4—798no—
714C22×D4—794no—
715C22×D4—7916no—
716C22×D4—798no—
717C22×D4—794no—
718C22×D4C22×D7918yes—
719C22×D4C22×D7918yes—
720C22×D4C22×D7914yes—
721C22×D4C22×D7911yescharacteristic
722C23×C4—792no—
723C23×C4—791no—
724C23×C4—792no—
725C23×C4—798no—
726C23×C4—792no—
727C23×C4—798no—
728C23×C4—798no—
729C23×C4C22×D7912yes—
730C4⋊Q8—794no—
731C4⋊Q8—798no—
732C4⋊Q8—798no—
733C4⋊Q8—792no—
734C4⋊Q8C22×D7912yes—
735#127—794no—
736#127—798no—
737#127—798no—
738#127—792no—
739#127C22×D7912yes—
740#124—794no—
741#124—794no—
742#124—7916no—
743#124—7916no—
744#124—794no—
745#124C22×D7914yes—
746#123—7916no—
747#123—7916no—
748#123—798no—
749#123—798no—
750#123—798no—
751#123—798no—
752#123—7916no—
753#123C22×D79116yes—
754C22⋊Q8—798no—
755C22⋊Q8—798no—
756C22⋊Q8—7916no—
757C22⋊Q8—798no—
758C22⋊Q8—7916no—
759C22⋊Q8—7916no—
760C22⋊Q8—798no—
761C22⋊Q8—798no—
762C22⋊Q8—7916no—
763C22⋊Q8—798no—
764C22⋊Q8—7916no—
765C22⋊Q8—7916no—
766C22⋊Q8—798no—
767C22⋊Q8C22×D7918yes—
768#121—7916no—
769#121—798no—
770#121—798no—
771#121—7916no—
772#121—798no—
773#121—7916no—
774#121—7916no—
775#121—798no—
776#121—7916no—
777#121—7916no—
778#121—798no—
779#121—798no—
780#121—798no—
781#121—794no—
782#121—798no—
783#121—798no—
784#121—798no—
785#121—794no—
786#121—798no—
787#121—798no—
788#121—7916no—
789#121—798no—
790#121—7916no—
791#121—7916no—
792#121—7916no—
793#121—798no—
794#121C22×D7918yes—
795#121C22×D7918yes—
796#121C22×D7914yes—
797#121C22×D7918yes—
798#121C22×D7918yes—
799#121C22×D7914yes—
800#120—7916no—
801#120—798no—
802#120—7916no—
803#120—798no—
804#120—798no—
805#120—7916no—
806#120—798no—
807#120C22×D79116yes—
808C4×Q8—798no—
809C4×Q8—794no—
810C4×Q8—794no—
811C4×D4—798no—
812C4×D4—798no—
813C4×D4—798no—
814C4×D4—798no—
815C4×D4—798no—
816C4×D4—798no—
817C4×D4—798no—
818C4×D4—798no—
819C4×D4—798no—
820C4×D4—7916no—
821C4×D4—7916no—
822C4×D4—7916no—
823C4×D4—794no—
824C4×D4—794no—
825C4×D4C22×D7914yes—
826C4×D4C22×D7914yes—
827C4×D4C22×D7914yes—
828C4×D4C22×D7914yes—
829#117—7916no—
830#117—794no—
831#117—794no—
832C2×C4⋊C4—792no—
833C2×C4⋊C4—791no—
834C2×C4⋊C4—792no—
835C2×C4⋊C4—792no—
836C2×C4⋊C4—791no—
837C2×C4⋊C4—798no—
838C2×C4⋊C4—798no—
839C2×C4⋊C4—791no—
840C2×C4⋊C4—798no—
841C2×C4⋊C4—794no—
842C2×C4⋊C4—798no—
843C2×C4⋊C4—798no—
844C2×C4⋊C4C22×D7911yescharacteristic
845C2×C4⋊C4C22×D7914yes—
846C2×C22⋊C4—792no—
847C2×C22⋊C4—798no—
848C2×C22⋊C4—791no—
849C2×C22⋊C4—791no—
850C2×C22⋊C4—798no—
851C2×C22⋊C4—798no—
852C2×C22⋊C4—7916no—
853C2×C22⋊C4C22×D7912yes—
854C2×C22⋊C4C22×D7918yes—
855C2×C42—791no—
856C2×C42—792no—
857C2×C42—792no—
858C2×C42C22×D7911yescharacteristic
859C24—791no—
860C24—798no—
861C24—798no—
862C24C23×D7918yes—
863C24C23×D7912yes—
864#41—232no—
865#41—216no—
866#41—7964no—
867#41—15832no—
868#41—15864no—
869#41—15832no—
870#41—15832no—
871#41—15864no—
872#41—15816no—
873#41—15864no—
874#41—15864no—
875#41—15816no—
876#41—15864no—
877#41—15832no—
878#41—15832no—
879#41—15816no—
880C2×Q8—794no—
881C2×Q8—798no—
882C2×Q8—7916no—
883C2×Q8—794no—
884C2×Q8—798no—
885C2×Q8—15832no—
886C2×Q8—15832no—
887C2×Q8—15816no—
888C2×Q8—15832no—
889C2×Q8C23×D7914yes—
890C2×D4—232no—
891C2×D4—232no—
892C2×D4—84no—
893C2×D4—798no—
894C2×D4—7916no—
895C2×D4—798no—
896C2×D4—798no—
897C2×D4—7916no—
898C2×D4—798no—
899C2×D4—7916no—
900C2×D4—798no—
901C2×D4—798no—
902C2×D4—7916no—
903C2×D4—794no—
904C2×D4—798no—
905C2×D4—794no—
906C2×D4—798no—
907C2×D4—794no—
908C2×D4—6324no—
909C2×D4—6328no—
910C2×D4—6328no—
911C2×D4—15816no—
912C2×D4—15832no—
913C2×D4—15864no—
914C2×D4—15832no—
915C2×D4—15864no—
916C2×D4—15832no—
917C2×D4—15832no—
918C2×D4D4×D7918yescomplemented
919C2×D4C23×D79116yes—
920C2×D4C23×D7918yes—
921C2×D4C23×D7914yes—
922C2×D4C23×D7914yes—
923C2×D4C23×D7918yes—
924C2×D4C23×D7914yes—
925C2×D4C23×D7914yes—
926C22×C4—82no—
927C22×C4—791no—
928C22×C4—791no—
929C22×C4—792no—
930C22×C4—798no—
931C22×C4—798no—
932C22×C4—792no—
933C22×C4—791no—
934C22×C4—798no—
935C22×C4—7916no—
936C22×C4—794no—
937C22×C4—798no—
938C22×C4—798no—
939C22×C4—7916no—
940C22×C4—798no—
941C22×C4—798no—
942C22×C4—7916no—
943C22×C4—798no—
944C22×C4—798no—
945C22×C4—6322no—
946C22×C4—6322no—
947C22×C4—15832no—
948C22×C4—15832no—
949C22×C4—15832no—
950C22×C4C23×D7918yes—
951C22×C4C23×D7918yes—
952C22×C4C23×D7911yescharacteristic
953C22×C4C23×D7912yes—
954C22×C4C23×D7911yescharacteristic
955C22×C4C23×D7914yes—
956C22×C4C23×D7914yes—
957C22×C4C23×D7911yescharacteristic
958C4⋊C4—798no—
959C4⋊C4—792no—
960C4⋊C4—792no—
961C4⋊C4—798no—
962C4⋊C4—794no—
963C4⋊C4—794no—
964C4⋊C4—7916no—
965C4⋊C4—798no—
966C4⋊C4—794no—
967C4⋊C4—798no—
968C4⋊C4—794no—
969C4⋊C4—798no—
970C4⋊C4—794no—
971C4⋊C4—794no—
972C4⋊C4C23×D7914yes—
973C4⋊C4C23×D7918yes—
974C4⋊C4C23×D7914yes—
975C4⋊C4C23×D7914yes—
976C22⋊C4—7916no—
977C22⋊C4—798no—
978C22⋊C4—798no—
979C22⋊C4—798no—
980C22⋊C4—7916no—
981C22⋊C4—798no—
982C22⋊C4—7916no—
983C22⋊C4—798no—
984C22⋊C4—792no—
985C22⋊C4—792no—
986C22⋊C4—794no—
987C22⋊C4—798no—
988C22⋊C4—798no—
989C22⋊C4C23×D79116yes—
990C22⋊C4C23×D7918yes—
991C22⋊C4C23×D7918yes—
992C22⋊C4C23×D7918yes—
993C42—798no—
994C42—798no—
995C42—794no—
996C42C23×D7912yes—
997C42C23×D7912yes—
998C23—216no—
999C23—42no—
1000C23—42no—
1001C23—48no—
1002C23—48no—
1003C23—3161no—
1004C23—3161no—
1005C23—3168no—
1006C23—3168no—
1007C23—3168no—
1008C23—3168no—
1009C23—794no—
1010C23—792no—
1011C23—798no—
1012C23—15816no—
1013C23—15816no—
1014C23C2×D4×D7918yes—
1015C23C24×D7918yes—
1016C23C24×D7914yes—
1017C23C24×D7911yescharacteristic
1018Q8—28no—
1019Q8—7916no—
1020Q8—15816no—
1021Q8—15832no—
1022Q8—1588no—
1023D4—232no—
1024D4—216no—
1025D4—28no—
1026D4—44no—
1027D4—48no—
1028D4—44no—
1029D4—3164no—
1030D4—3168no—
1031D4—3164no—
1032D4—3168no—
1033D4—31616no—
1034D4—3168no—
1035D4—7932no—
1036D4—15816no—
1037D4—15816no—
1038D4—15832no—
1039D4—15816no—
1040D4—15832no—
1041D4—15816no—
1042D4—1588no—
1043D4C2×D4×D79116yes—
1044C2×C4—216no—
1045C2×C4—216no—
1046C2×C4—41no—
1047C2×C4—42no—
1048C2×C4—44no—
1049C2×C4—44no—
1050C2×C4—41no—
1051C2×C4—3168no—
1052C2×C4—3162no—
1053C2×C4—3161no—
1054C2×C4—3168no—
1055C2×C4—3161no—
1056C2×C4—794no—
1057C2×C4—792no—
1058C2×C4—794no—
1059C2×C4—7932no—
1060C2×C4—798no—
1061C2×C4—7916no—
1062C2×C4—792no—
1063C2×C4—794no—
1064C2×C4—792no—
1065C2×C4—798no—
1066C2×C4—15816no—
1067C2×C4—15832no—
1068C2×C4—15816no—
1069C2×C4—15816no—
1070C2×C4—15832no—
1071C2×C4—15816no—
1072C2×C4—15816no—
1073C2×C4C2×D4×D7914yes—
1074C2×C4C24×D7912yes—
1075C2×C4C24×D7914yes—
1076C2×C4C24×D7911yescharacteristic
1077C2×C4C24×D7911yescharacteristic
1078C2×C4C24×D7918yes—
1079C2×C4C24×D7912yes—
1080C22—21no—
1081C22—24no—
1082C22—21no—
1083C22—24no—
1084C22—28no—
1085C22—28no—
1086C22—28no—
1087C22—48no—
1088C22—816no—
1089C22—3164no—
1090C22—794no—
1091C22—63216no—
1092C22—63216no—
1093C22—1588no—
1094C22—1588no—
1095C22—1588no—
1096C22—1582no—
1097C22—1582no—
1098C22C22×D4×D7918yes—
1099C22C22×D4×D7912yes—
1100C22C25×D7911yescharacteristic
1101C4—28no—
1102C4—21no—
1103C4—21no—
1104C4—24no—
1105C4—22no—
1106C4—794no—
1107C4—798no—
1108C4—1588no—
1109C4—1584no—
1110C4—1582no—
1111C4—1582no—
1112C4C22×D4×D7914yes—
1113C2—22no—
1114C2—28no—
1115C2—48no—
1116C2—3168no—
1117C2—1584no—
1118C2C23×D4×D7911yescharacteristic
1119C2#2377821011yescharacteristic
1120C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3496C2
hypercenter#3496D79
hypocenterC79#62853
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. C2×#19099398C2semidirect
2. #23777169C2semidirect
3. #23777166C2semidirect
4. #23777164C2semidirect
5. #23777161C2semidirect
6. #23777159C2semidirect
7. #23777157C2semidirect
8. #23777074C2semidirect
9. #23777071C2semidirect
10. #23777063C2semidirect
11. #23777060C2semidirect
12. #23776727C2semidirect
13. #23776726C2semidirect
14. C2×#19099140C2semidirect
15. #537×D79C2semidirect
16. C2×#19099042C2semidirect
17. C79×#3496C2semidirect
19. C2×#14579208C22semidirect
20. C2×#14579208C22semidirect
21. C2×#14579206C22semidirect
22. C2×#14579206C22semidirect
23. C2×#14579206C22semidirect
25. C22×#11929623C22semidirect
26. C22×#11929623C22semidirect
27. C2×#41×D79C22semidirect
28. C2×#41×D79C22semidirect
29. #19099234C22semidirect
30. #19099233C22semidirect
31. #19099231C22semidirect
32. D4×Dic158C22semidirect
33. #19099228C22semidirect
34. #19099226C22semidirect
35. #19099223C22semidirect
36. #19099222C22semidirect
37. #19099221C22semidirect
38. #19099219C22semidirect
39. #19099217C22semidirect
40. #19099214C22semidirect
41. #19099213C22semidirect
42. #19099212C22semidirect
43. #19099211C22semidirect
44. #19099208C22semidirect
45. #19099207C22semidirect
46. #19099205C22semidirect
47. #19099203C22semidirect
48. #19099202C22semidirect
49. #19099201C22semidirect
50. #19099200C22semidirect
51. D4×D316C22semidirect
52. #19099197C22semidirect
53. D4×C22⋊D79C22semidirect
54. D4×C22⋊D79C22semidirect
55. #19099195C22semidirect
56. #19099144C22semidirect
57. #19099143C22semidirect
58. #19099142C22semidirect
59. #19099141C22semidirect
60. #19099140C22semidirect
61. #19099140C22semidirect
62. #19099140C22semidirect
63. #19099140C22semidirect
64. #19099140C22semidirect
65. #19099140C22semidirect
66. #19099140C22semidirect
67. #19099138C22semidirect
68. #19099135C22semidirect
69. #19099133C22semidirect
70. #19099131C22semidirect
71. #19099128C22semidirect
72. #19099126C22semidirect
73. #19099125C22semidirect
74. #19099122C22semidirect
75. #19099121C22semidirect
76. #19099121C22semidirect
77. #19099113C22semidirect
78. #19099109C22semidirect
79. #19099108C22semidirect
80. #19099108C22semidirect
81. #19099072C22semidirect
82. #19099072C22semidirect
83. #19099071C22semidirect
84. #19099069C22semidirect
85. C2×#14579139C22semidirect
86. C2×#14579138C22semidirect
87. C22⋊Q8×D79C22semidirect
88. C2×#14579135C22semidirect
89. C2×#14579134C22semidirect
90. C2×#14579133C22semidirect
91. C2×#14579133C22semidirect
92. #121×D79C22semidirect
93. #121×D79C22semidirect
94. #19099042C22semidirect
95. #19099042C22semidirect
96. C2×C4×Dic158C22semidirect
97. C2×#14579126C22semidirect
98. C2×D4×Dic79C22semidirect
99. C2×C4×C22⋊D79C22semidirect
100. C2×(C22⋊D79)⋊C4C22semidirect
101. C2×#14579118C22semidirect
102. C2×#14579117C22semidirect
103. C22×Dic79⋊C4C22semidirect
104. C2×C4⋊C4×D79C22semidirect
105. C2×H(5,𝔽2)×C79C22semidirect
106. #547×C79C22semidirect
107. #546×C79C22semidirect
108. D42×C79C22semidirect
109. #537×C79C22semidirect
110. #534×C79C22semidirect
111. #532×C79C22semidirect
112. C2×#121×C79C22semidirect
113. C2×C4×D4×C79C22semidirect
126. C2×#11929623D4semidirect
314. #11929623C2×D4semidirect
317. C2×Dic158C2×D4semidirect
334. C2×C22⋊D79C2×D4semidirect
351. C22×Dic79C2×D4semidirect
365. C2×C4×D79C2×D4semidirect
410. C2×D4×C79C2×D4semidirect
568. #3496D79semidirect
578. C79#62853semidirect
585. C2×H(5,𝔽2)C2×D79semidirect
606. #547C2×D79semidirect
614. #546C2×D79semidirect
620. D42C2×D79semidirect
632. #537C2×D79semidirect
643. #534C2×D79semidirect
648. #532C2×D79semidirect
662. C2×#121C2×D79semidirect
670. C2×C4×D4C2×D79semidirect
918. C2×D4D4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190993982
#237771692
#237771662
#237771642
#237771612
#237771592
#237771572
#237770742
#237770712
#237770632
#237770602
#237767272
#237767262
C2×#190991402
#537×D792
C2×#190990422
C79×#34962
#6285379