Finite Group Databasebeta

← #35197465

Subgroups — #35197465

Order 20224.

10986 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099400C211yesmaximal, characteristic, complemented
2C2×2−1+4×D79C211yesmaximal, characteristic, complemented
3#23777194C211yesmaximal, characteristic, complemented
4#23777193C211yesmaximal, characteristic, complemented
5#23777189C213yesmaximal, complemented
6#23777187C213yesmaximal, complemented
7#23777183C213yesmaximal, complemented
8#23777182C213yesmaximal, complemented
9#23777181C211yesmaximal, characteristic, complemented
10#23777077C214yesmaximal, complemented
11#23777074C2112yesmaximal, complemented
12#23777050C214yesmaximal, complemented
13#23777039C2112yesmaximal, complemented
14#23776732C213yesmaximal, complemented
15#23776727C213yesmaximal, complemented
16C2×#19099138C213yesmaximal, complemented
17#536×D79C213yesmaximal, complemented
18#23776599C211yesmaximal, characteristic, complemented
19C79×#3499C211yesmaximal, characteristic, complemented
20#19099400—216no—
21C2×#14579209C2212yes—
22C2×#14579209C2212yescomplemented
23C2×#14579209C2213yescomplemented
24C2×#14579209C2213yescomplemented
25C2×#14579208C2216yescomplemented
26C2×#14579208C2211yescharacteristic, complemented
27C2×#14579208C2213yescomplemented
282−1+4×D79—216no—
29C2×#14579207C2216yes—
30C2×#14579207C2213yescomplemented
31C2×#14579207C2211yescharacteristic, complemented
32C22×#11929625C2213yes—
33C22×#11929625C2212yescomplemented
34C2×#41×D79C2213yes—
35C2×#41×D79C2211yescharacteristic
36C2×#41×D79C2216yescomplemented
37C2×#41×D79C2216yescomplemented
38C2×#41×D79C2213yescomplemented
39C22×Q8×D79C2212yescomplemented
40C22×Q8×D79C2213yescomplemented
41#19099228C22112yescomplemented
42Q8×C22⋊D79C2214yescomplemented
43#19099226C22112yescomplemented
44#19099225C2214yescomplemented
45#19099224C2214yescomplemented
46#19099223C22112yescomplemented
47#19099222C22112yescomplemented
48#19099216C22112yescomplemented
49#19099215C22112yescomplemented
50#19099214C22124yescomplemented
51#19099212C22112yescomplemented
52#19099211C22124yescomplemented
53#19099209C22112yescomplemented
54#19099208C22112yescomplemented
55#19099205C22124yescomplemented
56#19099204C22112yescomplemented
57#19099202C22124yescomplemented
58#19099201C22112yescomplemented
59#19099143C22112yescomplemented
60#19099140C22112yescomplemented
61#19099139C2213yescomplemented
62#19099138C22112yescomplemented
63#19099138C22112yescomplemented
64#19099138C2216yescomplemented
65#19099138C2213yescomplemented
66#19099138C2216yescomplemented
67#19099138C2216yescomplemented
68#19099138C2213yescomplemented
69#19099137C2213yescomplemented
70#19099137C2213yescomplemented
71#19099136C22112yescomplemented
72#19099135C22112yescomplemented
73#19099134C2213yescomplemented
74#19099133C2213yescomplemented
75#19099133C2213yescomplemented
76#19099132C2213yescomplemented
77#19099131C2213yescomplemented
78#19099131C2213yescomplemented
79#19099127C2213yescomplemented
80#19099126C2213yescomplemented
81#19099126C2211yescharacteristic, complemented
82#19099124C22112yescomplemented
83#19099121C22112yescomplemented
84#19099114C2216yescomplemented
85#19099113C2213yescomplemented
86#19099112C2216yescomplemented
87#19099109C2213yescomplemented
88#19099109C2213yescomplemented
89C2×#14579159C2213yescomplemented
90C4⋊Q8×D79C2216yescomplemented
91C2×#14579150C2213yescomplemented
92C2×#14579149C2213yescomplemented
93#124×D79C2216yescomplemented
94#19099076C22112yescomplemented
95#19099072C22112yescomplemented
96#19099072C22112yescomplemented
97#19099071C22112yescomplemented
98C2×#14579146C22112yescomplemented
99#123×D79C22112yescomplemented
100C2×#14579139C22112yescomplemented
101C22⋊Q8×D79C22112yescomplemented
102#19099045C2212yescomplemented
103#19099042C2216yescomplemented
104#19099039C2212yescomplemented
105#19099035C2216yescomplemented
106#41×Dic79C2211yescharacteristic, complemented
107C4×#11929624C2213yescomplemented
108#19099031C2213yescomplemented
109C2×#14579118C2213yescomplemented
110#117×D79C2213yescomplemented
111C2×2−1+4×C79C2211yescharacteristic, complemented
112C2×2−1+4×C79C2211yescharacteristic, complemented
113D4×Q8×C79C2214yescomplemented
114#547×C79C22112yescomplemented
115#536×C79C2213yescomplemented
116#536×C79C2213yescomplemented
117#532×C79C2213yescomplemented
118C2×C4⋊Q8×C79C2213yescomplemented
119C4×#41×C79C2211yescharacteristic, complemented
120#14579209—216no—
121#14579209—224no—
122#14579209—224no—
123#14579209—216no—
124#14579208—28no—
125#14579208—224no—
126#14579208—248no—
127#14579207—28no—
128#14579207—224no—
129#14579207—248no—
130C2×#11929625—216no—
131C2×#11929625—224no—
132C2×#11929625C2313yes—
133C2×#11929625C2316yes—
134C2×#11929625C2316yes—
135C2×#11929625C2316yes—
136C2×#11929625C2313yes—
137C2×#11929625C2316yes—
138C2×#11929625C2312yes—
139C2×#11929625C2316yes—
140C2×#11929625C2311yescharacteristic
141C2×#11929624C2316yes—
142C2×#11929624C2313yes—
143C2×#11929624C2313yes—
144C2×#11929624C23112yes—
145C2×#11929624C2316yes—
146C2×#11929624C2316yes—
147C2×#11929624C23112yes—
148C2×#11929624C2316yes—
149C2×#11929624C2313yes—
150C2×#11929623C2316yes—
151C2×#11929623C2316yes—
152C2×#11929623C23112yes—
153C2×#11929623C2316yes—
154C2×#11929623C2313yes—
155C2×#11929623C2311yescharacteristic
156C2×#11929623C2313yes—
157#41×D79—248no—
158#41×D79—248no—
159#41×D79—224no—
160#41×D79—224no—
161#41×D79D4116yescomplemented
162C22×Dic158C2313yes—
163C22×Dic158C2316yes—
164C22×Dic158C2316yes—
165C2×Q8×D79—216no—
166C2×Q8×D79—224no—
167C2×Q8×D79C2316yes—
168C2×Q8×D79C2313yes—
169C2×Q8×D79C2316yes—
170C2×Q8×D79C2316yes—
171C2×Q8×D79C2313yes—
172C2×Q8×D79C2316yes—
173C2×Q8×D79C2312yes—
174C2×Q8×D79C2316yes—
175C2×Q8×D79C2311yescharacteristic
176C22×D316C2316yes—
177C22×D316C2316yes—
178C22×D316C2313yes—
179C2×D4×D79C2316yes—
180C2×D4×D79C2316yes—
181C2×D4×D79C23112yes—
182C2×D4×D79C2313yes—
183C2×D4×D79C2316yes—
184C2×D4×D79C2311yescharacteristic
185C2×D4×D79C2313yes—
186C22×C4×D79C2316yes—
187C22×C4×D79C2316yes—
188C22×C4×D79C2316yes—
189C22×C4×D79C2316yes—
190C22×C4×D79C2313yes—
191#14579161C2313yes—
192#14579160C23124yes—
193#14579159C2313yes—
194#14579159C2316yes—
195#14579159C2313yes—
196#14579159C23112yes—
197#14579158C2313yes—
198#14579157C2311yescharacteristic
199#14579157C2313yes—
200#14579150C2313yes—
201#14579150C2316yes—
202#14579150C2313yes—
203#14579150C23112yes—
204#14579149C2313yes—
205#14579149C2311yescharacteristic
206#14579149C2316yes—
207#14579149C23112yes—
208#14579148C2313yes—
209#14579148C2311yescharacteristic
210#14579147C23124yes—
211#14579146C23124yes—
212#14579146C23112yes—
213#14579146C23124yes—
214#14579146C23124yes—
215#14579146C23112yes—
216#14579145C23112yes—
217#14579144C23112yes—
218#14579144C23112yes—
219#14579143C23112yes—
220#14579143C23112yes—
221#14579142C23112yes—
222#14579141C23112yes—
223#14579140C23112yes—
224#14579139C23112yes—
225#14579139C23124yes—
226#14579139C23124yes—
227#14579139C23124yes—
228#14579139C23112yes—
229#14579138C23112yes—
230#14579138C23112yes—
231#14579137C23112yes—
232#14579137C23112yes—
233#14579136C23124yes—
234#14579136C23112yes—
235#14579135C23112yes—
236#14579135C23112yes—
237#14579134C23112yes—
238#14579134C23112yes—
239#14579134C23124yes—
240#14579133C2314yes—
241#14579133C23112yes—
242#14579133C23112yes—
243#14579133C23112yes—
244#14579131C23112yes—
245#14579131C23112yes—
246#14579131C23112yes—
247#14579129C23112yes—
248#14579129C23112yes—
249#14579129C2314yes—
250Q8×Dic79C2312yes—
251C4×Dic158C2316yes—
252#14579126C2316yes—
253C4×D316C23112yes—
254C4×D316C2316yes—
255D4×Dic79C2316yes—
256#14579123C2316yes—
257#14579123C23124yes—
258C4×C22⋊D79C23112yes—
259C4×C22⋊D79C23112yes—
260C4×C22⋊D79C23112yes—
261(C22⋊D79)⋊C4C23124yes—
262(C22⋊D79)⋊C4C23112yes—
263#14579120C2313yes—
264#14579119C2316yes—
265#14579118C2311yescharacteristic
266#14579118C2313yes—
267#14579118C2313yes—
268#14579118C2313yes—
269#14579118C2316yes—
270#14579118C2316yes—
271#14579117C2316yes—
272C2×Dic79⋊C4C2316yes—
273C2×Dic79⋊C4C23112yes—
274C4⋊C4×D79C2316yes—
275C4⋊C4×D79C23124yes—
276C2×(C2×D79)⋊C4C23112yes—
277C2×(C2×D79)⋊C4C23112yes—
278C2×(C2×D79)⋊C4C2316yes—
279C22⋊C4×D79C23124yes—
280C22⋊C4×D79C2316yes—
281C2×C4×Dic79C2313yes—
282C42×D79C2316yes—
2832−1+4×C79—28no—
2842−1+4×C79—28no—
285C2×#41×C79C2316yes—
286C2×#41×C79C2313yes—
287C2×#41×C79C2316yes—
288C2×#41×C79C2313yes—
289C2×#41×C79C2311yescharacteristic
290C22×Q8×C79C2313yes—
291C22×Q8×C79C2313yes—
292C22×Q8×C79C2312yes—
293C22×Q8×C79C2312yes—
294C4⋊Q8×C79C2313yes—
295C4⋊Q8×C79C23112yes—
296C4⋊Q8×C79C2316yes—
297#127×C79C2311yescharacteristic
298#124×C79C2313yes—
299#124×C79C2313yes—
300#123×C79C23112yes—
301#123×C79C23112yes—
302C22⋊Q8×C79C23112yes—
303C22⋊Q8×C79C23112yes—
304#121×C79C23112yes—
305C4×Q8×C79C2312yes—
306C4×D4×C79C2316yes—
307C4×D4×C79C23112yes—
308#117×C79C2313yes—
309C2×C4⋊C4×C79C23112yes—
310C2×C42×C79C2313yes—
311C23×D79C2416yes—
312C23×D79C2416yes—
313C23×D79C2412yes—
314C23×D79C2413yes—
315#11929625—224no—
316#11929625—224no—
317#11929625—224no—
318#11929625—212no—
319#11929625—212no—
320#11929625—224no—
321#11929625—224no—
322#11929625—28no—
323#11929625C2×D418yes—
324#11929624—224no—
325#11929624—224no—
326#11929624—224no—
327#11929624—224no—
328#11929624—212no—
329#11929624—212no—
330#11929624—248no—
331#11929624—248no—
332#11929624C2×D4124yes—
333#11929623—224no—
334#11929623—224no—
335#11929623—24no—
336#11929623—212no—
337#11929623—224no—
338#11929623—248no—
339#11929623C2×D4124yes—
340C2×Dic158—224no—
341C2×Dic158—224no—
342C2×Dic158—212no—
343C2×Dic158C2416yes—
344C2×Dic158C24112yes—
345C2×Dic158C2416yes—
346C2×Dic158C2413yes—
347C2×Dic158C2416yes—
348C2×Dic158C2411yescharacteristic
349C2×Dic158C2413yes—
350Q8×D79—224no—
351Q8×D79—212no—
352Q8×D79—224no—
353Q8×D79—224no—
354Q8×D79—212no—
355Q8×D79—224no—
356Q8×D79—224no—
357Q8×D79—28no—
358Q8×D79C2×D418yes—
359C2×D316—224no—
360C2×D316—224no—
361C2×D316—212no—
362C2×D316C2416yes—
363C2×D316C2411yescharacteristic
364C2×D316C2416yes—
365C2×D316C24112yes—
366C2×D316C2416yes—
367C2×D316C2413yes—
368C2×D316C24112yes—
369C2×D316C2413yes—
370C2×C22⋊D79C2416yes—
371C2×C22⋊D79C2416yes—
372C2×C22⋊D79C2412yes—
373C2×C22⋊D79C2412yes—
374C2×C22⋊D79C2416yes—
375C2×C22⋊D79C2416yes—
376C2×C22⋊D79C24112yes—
377C2×C22⋊D79C2414yes—
378C2×C22⋊D79C2416yes—
379D4×D79—24no—
380D4×D79—212no—
381D4×D79—224no—
382D4×D79—224no—
383D4×D79—224no—
384D4×D79—248no—
385D4×D79C2×D4124yes—
386C22×Dic79C2416yes—
387C22×Dic79C2416yes—
388C22×Dic79C2412yes—
389C22×Dic79C2416yes—
390C22×Dic79C2413yes—
391C2×C4×D79—224no—
392C2×C4×D79—224no—
393C2×C4×D79—224no—
394C2×C4×D79—224no—
395C2×C4×D79C2×D4124yes—
396C2×C4×D79C2416yes—
397C2×C4×D79C24112yes—
398C2×C4×D79C2416yes—
399C2×C4×D79C2416yes—
400C2×C4×D79C2416yes—
401C2×C4×D79C24112yes—
402C2×C4×D79C2416yes—
403C2×C4×D79C2416yes—
404C2×C4×D79C24112yes—
405C2×C4×D79C2413yes—
406C2×C4×D79C2411yescharacteristic
407C2×C4×D79C2413yes—
408C2×C4×D79C2413yes—
409C4⋊Dic79C24112yes—
410C4⋊Dic79C2416yes—
411Dic79⋊C4C2416yes—
412Dic79⋊C4C24112yes—
413Dic79⋊C4C24124yes—
414Dic79⋊C4C2412yes—
415Dic79⋊C4C24112yes—
416Dic79⋊C4C2416yes—
417Dic79⋊C4C2416yes—
418C22⋊Dic79C24112yes—
419C22⋊Dic79C2416yes—
420C22⋊Dic79C2414yes—
421(C2×D79)⋊C4C2416yes—
422(C2×D79)⋊C4C24124yes—
423(C2×D79)⋊C4C24124yes—
424(C2×D79)⋊C4C2412yes—
425(C2×D79)⋊C4C24112yes—
426(C2×D79)⋊C4C24112yes—
427(C2×D79)⋊C4C2416yes—
428(C2×D79)⋊C4C2416yes—
429(C2×D79)⋊C4C24112yes—
430(C2×D79)⋊C4C2414yes—
431C4×Dic79C2413yes—
432C4×Dic79C24112yes—
433C4×Dic79C2411yescharacteristic
434C4×Dic79C2416yes—
435#41×C79—224no—
436#41×C79—224no—
437#41×C79—212no—
438#41×C79—212no—
439#41×C79C2×D418yes—
440C2×Q8×C79—28no—
441C2×Q8×C79—28no—
442C2×Q8×C79—212no—
443C2×Q8×C79—212no—
444C2×Q8×C79C2416yes—
445C2×Q8×C79C2413yes—
446C2×Q8×C79C2416yes—
447C2×Q8×C79C2413yes—
448C2×Q8×C79C2411yescharacteristic
449C2×D4×C79C2416yes—
450C2×D4×C79C2411yescharacteristic
451C2×D4×C79C2416yes—
452C2×D4×C79C2411yescharacteristic
453C2×D4×C79C2414yes—
454C2×D4×C79C2413yes—
455C22×C4×C79C2416yes—
456C22×C4×C79C2416yes—
457C22×C4×C79C2416yes—
458C22×C4×C79C2416yes—
459C22×C4×C79C2416yes—
460C22×C4×C79C2413yes—
461C4⋊C4×C79C24112yes—
462C4⋊C4×C79C24124yes—
463C4⋊C4×C79C2416yes—
464C22⋊C4×C79C2416yes—
465C22⋊C4×C79C24112yes—
466C22⋊C4×C79C24112yes—
467C42×C79C2411yescharacteristic
468C42×C79C2413yes—
469C42×C79C2416yes—
470C23×C79C2512yes—
471C23×C79C2512yes—
472C23×C79C2513yes—
473C22×D79—212no—
474C22×D79—24no—
475C22×D79—212no—
476C22×D79—46no—
477C22×D79—44no—
478C22×D79—412no—
479C22×D79—412no—
480C22×D79C22×D4112yes—
481C22×D79C2516yes—
482C22×D79C2512yes—
483C22×D79C2511yescharacteristic
484C22×D79C2513yes—
485Q8×C79—212no—
486Q8×C79—26no—
487Q8×C79—212no—
488Q8×C79—26no—
489Q8×C79C22×D414yes—
490D4×C79—212no—
491D4×C79—212no—
492D4×C79—22no—
493D4×C79—22no—
494D4×C79—44no—
495D4×C79C22×D4112yes—
496C2×C4×C79—212no—
497C2×C4×C79—212no—
498C2×C4×C79—212no—
499C2×C4×C79—212no—
500C2×C4×C79—46no—
501C2×C4×C79C22×D4112yes—
502C2×C4×C79C2516yes—
503C2×C4×C79C2512yes—
504C2×C4×C79C2516yes—
505C2×C4×C79C2516yes—
506C2×C4×C79C2511yescharacteristic
507C2×C4×C79C2513yes—
508C22⋊D79—212no—
509C22⋊D79—212no—
510C22⋊D79—24no—
511C22⋊D79—212no—
512C22⋊D79—212no—
513C22⋊D79—24no—
514C22⋊D79—412no—
515C22⋊D79—44no—
516C22⋊D79C22×D4124yes—
517C2×Dic79—212no—
518C2×Dic79—24no—
519C2×Dic79—212no—
520C2×Dic79—46no—
521C2×Dic79C22×D4112yes—
522C2×Dic79C2512yes—
523C2×Dic79C2516yes—
524C2×Dic79C2516yes—
525C2×Dic79C2512yes—
526C2×Dic79C2513yes—
527C2×Dic79C2511yescharacteristic
528D316—224no—
529D316—212no—
530D316—212no—
531D316—212no—
532D316—26no—
533D316—22no—
534D316—412no—
535D316C22×D4112yes—
536C4×D79—212no—
537C4×D79—212no—
538C4×D79—224no—
539C4×D79—212no—
540C4×D79—212no—
541C4×D79—212no—
542C4×D79—224no—
543C4×D79—212no—
544C4×D79—412no—
545C4×D79C22×D4112yes—
546C4×D79C22×D4112yes—
547C4×D79C22×D414yes—
548C4×D79C22×D4112yes—
549Dic158—212no—
550Dic158—26no—
551Dic158—22no—
552Dic158—224no—
553Dic158—212no—
554Dic158—212no—
555Dic158C22×D4112yes—
556C22×C79—26no—
557C22×C79—22no—
558C22×C79—22no—
559C22×C79—24no—
560C22×C79—24no—
561C22×C79C23×D416yes—
562C22×C79C2611yescharacteristic
563C2×D79—22no—
564C2×D79—26no—
565C2×D79—22no—
566C2×D79—26no—
567C2×D79—212no—
568C2×D79—24no—
569C2×D79—412no—
570C2×D79—48no—
571C2×D79—812no—
572C2×D79—812no—
573C2×D79C23×D416yes—
574C2×D79C23×D412yes—
575C4×C79—26no—
576C4×C79—26no—
577C4×C79—22no—
578C4×C79—26no—
579C4×C79C23×D416yes—
580C4×C79C23×D412yes—
581Dic79—22no—
582Dic79—26no—
583Dic79—26no—
584Dic79—22no—
585Dic79C23×D416yes—
586Dic79C23×D412yes—
587#62859—791nomaximal, Sylow
588C2×C79—26no—
589C2×C79—42no—
590C2×C79—42no—
591C2×C79C24×D411yescharacteristic
592C2×C792−1+612yes—
593D79—22no—
594D79—26no—
595D79—42no—
596D79—46no—
597C2×#585—791no—
598C22×2−1+4—791no—
599#3500—791no—
600#3500—793no—
601#3500—793no—
602#3500—791no—
603#3499—791no—
604#3499—793no—
605#3499—793no—
606#3499D7911yescharacteristic, complemented
607#3489—794no—
608#3489—7912no—
609#3486—794no—
610#3485—7912no—
611#3449—793no—
612#3449—793no—
613C2×#536—793no—
614C2×#536—793no—
615#3428—791no—
616C79#6285911yescharacteristic, complemented, Sylow
617#585—15816no—
618C2×2−1+4—796no—
619C2×2−1+4—793no—
620C2×2−1+4—791no—
621C2×2−1+4—792no—
622C2×2−1+4—792no—
623C2×2−1+4—793no—
624C2×2−1+4—793no—
625C2×2−1+4—15816no—
626C2×2−1+4C2×D7911yescharacteristic, complemented
627C2×2−1+4C2×D7911yescharacteristic, complemented
628C2×H(5,𝔽2)—796no—
629C2×H(5,𝔽2)—793no—
630C2×H(5,𝔽2)—791no—
631C22×#41—791no—
632C22×#41—793no—
633C22×#41—796no—
634C22×#41—793no—
635C22×#41—796no—
636C22×#41—793no—
637C22×#41—792no—
638C23×Q8—793no—
639C23×Q8—792no—
640D4×Q8—794no—
641D4×Q8—7912no—
642D4×Q8—7912no—
643D4×Q8C2×D7914yescomplemented
644#548—794no—
645#548—7912no—
646#548—794no—
647#548—7912no—
648#547—7912no—
649#547—7912no—
650#547—7924no—
651#547—7912no—
652#547—7924no—
653#547C2×D79112yescomplemented
654#546—7912no—
655#546—7924no—
656#546—7912no—
657#546—7924no—
658#546—7912no—
659#546—7912no—
660#537—7912no—
661#537—7912no—
662#536—793no—
663#536—793no—
664#536—793no—
665#536—796no—
666#536—793no—
667#536—7912no—
668#536—7912no—
669#536—796no—
670#536—796no—
671#536—793no—
672#536—793no—
673#536—793no—
674#536—7912no—
675#536—7912no—
676#536—793no—
677#536C2×D7913yescomplemented
678#536C2×D7913yescomplemented
679#535—793no—
680#535—791no—
681#535—793no—
682#535—793no—
683#535—793no—
684#535—793no—
685#534—7912no—
686#534—7912no—
687#532—793no—
688#532—793no—
689#532—796no—
690#532—796no—
691#532—793no—
692#532C2×D7913yescomplemented
693C2×C4⋊Q8—793no—
694C2×C4⋊Q8—796no—
695C2×C4⋊Q8C2×D7913yescomplemented
696C2×#124—793no—
697C2×#124—796no—
698C2×#124—793no—
699#525—7912no—
700#525—7912no—
701#525—7912no—
702#525—7912no—
703C2×#123—7912no—
704C2×#123—7912no—
705C2×C22⋊Q8—7912no—
706C2×C22⋊Q8—7912no—
707#520—792no—
708#520—796no—
709#519—792no—
710#518—796no—
711C4×#41—791no—
712C4×#41—793no—
713C4×#41—793no—
714C4×#41C2×D7911yescharacteristic, complemented
715C2×#117—793no—
716C2×#117—793no—
7172−1+4—28no—
7182−1+4—28no—
7192−1+4—15816no—
7202−1+4—15816no—
7212−1+4—15824no—
7222−1+4—15824no—
7232−1+4—15848no—
7242−1+4—15824no—
7252−1+4—1588no—
726H(5,𝔽2)—15848no—
727H(5,𝔽2)—15824no—
728H(5,𝔽2)—1588no—
729C2×#41—7916no—
730C2×#41—791no—
731C2×#41—796no—
732C2×#41—793no—
733C2×#41—796no—
734C2×#41—793no—
735C2×#41—796no—
736C2×#41—796no—
737C2×#41—796no—
738C2×#41—792no—
739C2×#41—793no—
740C2×#41—796no—
741C2×#41—793no—
742C2×#41—791no—
743C2×#41—796no—
744C2×#41—796no—
745C2×#41—7912no—
746C2×#41—793no—
747C2×#41—796no—
748C2×#41—796no—
749C2×#41—793no—
750C2×#41—793no—
751C2×#41—796no—
752C2×#41—7912no—
753C2×#41—7912no—
754C2×#41—796no—
755C2×#41—15824no—
756C2×#41—15824no—
757C2×#41—15824no—
758C2×#41—15848no—
759C2×#41—15816no—
760C2×#41—15848no—
761C2×#41C22×D7913yes—
762C2×#41C22×D7913yes—
763C2×#41C22×D7916yes—
764C2×#41C22×D7916yes—
765C2×#41C22×D7911yescharacteristic
766C22×Q8—791no—
767C22×Q8—796no—
768C22×Q8—796no—
769C22×Q8—793no—
770C22×Q8—793no—
771C22×Q8—796no—
772C22×Q8—796no—
773C22×Q8—792no—
774C22×Q8—796no—
775C22×Q8—796no—
776C22×Q8—793no—
777C22×Q8—796no—
778C22×Q8—15824no—
779C22×Q8—15816no—
780C22×Q8C22×D7913yes—
781C22×Q8C22×D7913yes—
782C22×Q8C22×D7912yes—
783C22×Q8C22×D7912yes—
784C22×D4—793no—
785C22×D4—796no—
786C22×D4—793no—
787C22×D4—796no—
788C22×D4—791no—
789C22×D4—7912no—
790C22×D4—796no—
791C22×D4—796no—
792C22×D4—793no—
793C22×D4—796no—
794C23×C4—793no—
795C23×C4—796no—
796C23×C4—796no—
797C23×C4—796no—
798C23×C4—796no—
799C4⋊Q8—793no—
800C4⋊Q8—796no—
801C4⋊Q8—793no—
802C4⋊Q8—7912no—
803C4⋊Q8—7924no—
804C4⋊Q8—793no—
805C4⋊Q8C22×D7916yes—
806C4⋊Q8C22×D7913yes—
807C4⋊Q8C22×D79112yes—
808#127—793no—
809#127—791no—
810#127—793no—
811#127C22×D7911yescharacteristic
812#124—793no—
813#124—796no—
814#124—7912no—
815#124—793no—
816#124—793no—
817#124—791no—
818#124—7924no—
819#124—796no—
820#124—793no—
821#124—7912no—
822#124—791no—
823#124C22×D7913yes—
824#124C22×D7913yes—
825#123—7912no—
826#123—7912no—
827#123—7912no—
828#123—7924no—
829#123—7912no—
830#123—7924no—
831#123—7924no—
832#123—7912no—
833#123—7912no—
834#123—7912no—
835#123—7912no—
836#123C22×D79112yes—
837#123C22×D79112yes—
838C22⋊Q8—7912no—
839C22⋊Q8—7912no—
840C22⋊Q8—7912no—
841C22⋊Q8—7924no—
842C22⋊Q8—7912no—
843C22⋊Q8—7924no—
844C22⋊Q8—7924no—
845C22⋊Q8—7912no—
846C22⋊Q8—7912no—
847C22⋊Q8—7912no—
848C22⋊Q8—7912no—
849C22⋊Q8C22×D79112yes—
850C22⋊Q8C22×D79112yes—
851#121—794no—
852#121—7912no—
853#121—7912no—
854#121—7912no—
855#121—7912no—
856#121—7912no—
857#121—7912no—
858#121—7924no—
859#121—7912no—
860#121—7912no—
861#121—7924no—
862#121C22×D79112yes—
863#120—794no—
864#120—7912no—
865#120—7912no—
866#120—7912no—
867#120—7912no—
868#120—7912no—
869C4×Q8—792no—
870C4×Q8—796no—
871C4×Q8—796no—
872C4×Q8C22×D7912yes—
873C4×D4—796no—
874C4×D4—7912no—
875C4×D4—7912no—
876C4×D4—7912no—
877C4×D4—796no—
878C4×D4—7924no—
879C4×D4—7912no—
880C4×D4—7924no—
881C4×D4—796no—
882C4×D4—7912no—
883C4×D4C22×D7916yes—
884C4×D4C22×D79112yes—
885#117—793no—
886#117—796no—
887#117—796no—
888#117—793no—
889#117—791no—
890#117—793no—
891#117—793no—
892#117—796no—
893#117—796no—
894#117C22×D7913yes—
895C2×C4⋊C4—796no—
896C2×C4⋊C4—7912no—
897C2×C4⋊C4—796no—
898C2×C4⋊C4—7924no—
899C2×C4⋊C4C22×D79112yes—
900C2×C22⋊C4—796no—
901C2×C22⋊C4—7912no—
902C2×C22⋊C4—7912no—
903C2×C22⋊C4—796no—
904C2×C22⋊C4—7924no—
905C2×C42—793no—
906C2×C42—796no—
907C2×C42C22×D7913yes—
908C24—793no—
909C24—796no—
910C24—796no—
911C24—792no—
912#41—224no—
913#41—224no—
914#41—212no—
915#41—212no—
916#41—798no—
917#41—7924no—
918#41—7924no—
919#41—15824no—
920#41—15824no—
921#41—15848no—
922#41—15848no—
923#41—15824no—
924#41—15824no—
925#41—15824no—
926#41—1584no—
927#41—15824no—
928#41—15812no—
929#41—15812no—
930#41—15824no—
931#41—15824no—
932#41—15824no—
933#41—15812no—
934#41—15848no—
935#41—15824no—
936#41—15824no—
937#41—1588no—
938#41—15824no—
939#41—15812no—
940#41—15812no—
941#41D4×D7918yes—
942C2×Q8—28no—
943C2×Q8—28no—
944C2×Q8—212no—
945C2×Q8—212no—
946C2×Q8—798no—
947C2×Q8—793no—
948C2×Q8—796no—
949C2×Q8—7912no—
950C2×Q8—796no—
951C2×Q8—796no—
952C2×Q8—793no—
953C2×Q8—791no—
954C2×Q8—15824no—
955C2×Q8—15824no—
956C2×Q8—15812no—
957C2×Q8—15824no—
958C2×Q8—15824no—
959C2×Q8—15824no—
960C2×Q8—15812no—
961C2×Q8—15824no—
962C2×Q8—15824no—
963C2×Q8—1588no—
964C2×Q8—15812no—
965C2×Q8C23×D7916yes—
966C2×Q8C23×D7916yes—
967C2×Q8C23×D7913yes—
968C2×Q8C23×D7913yes—
969C2×Q8C23×D7911yescharacteristic
970C2×D4—7912no—
971C2×D4—794no—
972C2×D4—796no—
973C2×D4—7924no—
974C2×D4—796no—
975C2×D4—796no—
976C2×D4—792no—
977C2×D4—792no—
978C2×D4—796no—
979C2×D4—796no—
980C2×D4—7912no—
981C2×D4—793no—
982C2×D4—796no—
983C2×D4—796no—
984C2×D4—7912no—
985C2×D4—796no—
986C2×D4—793no—
987C2×D4—791no—
988C2×D4—15824no—
989C2×D4—15824no—
990C2×D4—1584no—
991C2×D4—15812no—
992C2×D4—15848no—
993C2×D4—15824no—
994C2×D4—15824no—
995C2×D4—15824no—
996C2×D4—15812no—
997C2×D4C23×D7916yes—
998C2×D4C23×D7916yes—
999C2×D4C23×D7911yescharacteristic
1000C2×D4C23×D7911yescharacteristic
1001C2×D4C23×D7914yes—
1002C2×D4C23×D7913yes—
1003C22×C4—796no—
1004C22×C4—7912no—
1005C22×C4—793no—
1006C22×C4—793no—
1007C22×C4—793no—
1008C22×C4—793no—
1009C22×C4—791no—
1010C22×C4—7924no—
1011C22×C4—796no—
1012C22×C4—796no—
1013C22×C4—792no—
1014C22×C4—7912no—
1015C22×C4—796no—
1016C22×C4—796no—
1017C22×C4—796no—
1018C22×C4—7912no—
1019C22×C4—796no—
1020C22×C4—796no—
1021C22×C4—796no—
1022C22×C4—15824no—
1023C22×C4—15824no—
1024C22×C4—15824no—
1025C22×C4—15824no—
1026C22×C4C23×D7916yes—
1027C22×C4C23×D7916yes—
1028C22×C4C23×D7916yes—
1029C22×C4C23×D7916yes—
1030C22×C4C23×D7916yes—
1031C22×C4C23×D7913yes—
1032C4⋊C4—796no—
1033C4⋊C4—792no—
1034C4⋊C4—7924no—
1035C4⋊C4—7912no—
1036C4⋊C4—7912no—
1037C4⋊C4—796no—
1038C4⋊C4—796no—
1039C4⋊C4—7912no—
1040C4⋊C4—796no—
1041C4⋊C4C23×D79124yes—
1042C4⋊C4C23×D7916yes—
1043C4⋊C4C23×D79112yes—
1044C22⋊C4—7912no—
1045C22⋊C4—796no—
1046C22⋊C4—794no—
1047C22⋊C4—796no—
1048C22⋊C4—792no—
1049C22⋊C4—7924no—
1050C22⋊C4—7912no—
1051C22⋊C4—7924no—
1052C22⋊C4—7912no—
1053C22⋊C4—796no—
1054C22⋊C4—796no—
1055C22⋊C4—7912no—
1056C22⋊C4—794no—
1057C22⋊C4C23×D79112yes—
1058C22⋊C4C23×D7916yes—
1059C22⋊C4C23×D79112yes—
1060C42—793no—
1061C42—791no—
1062C42—7912no—
1063C42—796no—
1064C42C23×D7913yes—
1065C42C23×D7911yescharacteristic
1066C42C23×D7916yes—
1067C23—3166no—
1068C23—3164no—
1069C23—31612no—
1070C23—31612no—
1071C23—7912no—
1072C23—791no—
1073C23—793no—
1074C23—796no—
1075C23—792no—
1076C23—1584no—
1077C23—15812no—
1078C23—15812no—
1079C23C24×D7912yes—
1080C23C24×D7912yes—
1081C23C24×D7913yes—
1082Q8—212no—
1083Q8—26no—
1084Q8—212no—
1085Q8—26no—
1086Q8—7912no—
1087Q8—15812no—
1088Q8—15824no—
1089Q8—15812no—
1090Q8—15812no—
1091Q8—1586no—
1092Q8—1582no—
1093Q8C2×D4×D7914yes—
1094D4—212no—
1095D4—212no—
1096D4—22no—
1097D4—22no—
1098D4—44no—
1099D4—31612no—
1100D4—31612no—
1101D4—3164no—
1102D4—7924no—
1103D4—7912no—
1104D4—15812no—
1105D4—15824no—
1106D4—15812no—
1107D4—15812no—
1108D4—1584no—
1109D4—1584no—
1110D4—15812no—
1111D4—15812no—
1112D4—15812no—
1113D4—15812no—
1114D4—1586no—
1115D4—1582no—
1116D4C2×D4×D79112yes—
1117C2×C4—212no—
1118C2×C4—212no—
1119C2×C4—212no—
1120C2×C4—212no—
1121C2×C4—46no—
1122C2×C4—31612no—
1123C2×C4—3166no—
1124C2×C4—793no—
1125C2×C4—791no—
1126C2×C4—7912no—
1127C2×C4—794no—
1128C2×C4—7912no—
1129C2×C4—7912no—
1130C2×C4—7912no—
1131C2×C4—796no—
1132C2×C4—792no—
1133C2×C4—796no—
1134C2×C4—792no—
1135C2×C4—15812no—
1136C2×C4—15824no—
1137C2×C4—15812no—
1138C2×C4—15812no—
1139C2×C4—15812no—
1140C2×C4—15824no—
1141C2×C4—1584no—
1142C2×C4—15812no—
1143C2×C4—15812no—
1144C2×C4—15812no—
1145C2×C4—15812no—
1146C2×C4C2×D4×D79112yes—
1147C2×C4C24×D7916yes—
1148C2×C4C24×D7912yes—
1149C2×C4C24×D7916yes—
1150C2×C4C24×D7916yes—
1151C2×C4C24×D7911yescharacteristic
1152C2×C4C24×D7913yes—
1153C22—26no—
1154C22—22no—
1155C22—22no—
1156C22—24no—
1157C22—24no—
1158C22—31612no—
1159C22—3168no—
1160C22—792no—
1161C22—796no—
1162C22—63212no—
1163C22—63212no—
1164C22—1582no—
1165C22—1586no—
1166C22—1584no—
1167C22—15812no—
1168C22—1586no—
1169C22—1582no—
1170C22C22×D4×D7916yes—
1171C22C25×D7911yescharacteristic
1172C4—26no—
1173C4—26no—
1174C4—22no—
1175C4—26no—
1176C4—792no—
1177C4—796no—
1178C4—1582no—
1179C4—1586no—
1180C4—1586no—
1181C4—1582no—
1182C4C22×D4×D7916yes—
1183C4C22×D4×D7912yes—
1184C2—26no—
1185C2—42no—
1186C2—42no—
1187C2—3162no—
1188C2—3166no—
1189C2—1582no—
1190C2—1586no—
1191C2C23×D4×D7911yescharacteristic
1192C2#2377821212yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3499C2
hypercenter#3499D79
hypocenterC79#62859
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×#19099400C2semidirect
2. C2×2−1+4×D79C2semidirect
3. #23777194C2semidirect
4. #23777193C2semidirect
5. #23777189C2semidirect
6. #23777187C2semidirect
7. #23777183C2semidirect
8. #23777182C2semidirect
9. #23777181C2semidirect
10. #23777077C2semidirect
11. #23777074C2semidirect
12. #23777050C2semidirect
13. #23777039C2semidirect
14. #23776732C2semidirect
15. #23776727C2semidirect
16. C2×#19099138C2semidirect
17. #536×D79C2semidirect
18. #23776599C2semidirect
19. C79×#3499C2semidirect
22. C2×#14579209C22semidirect
23. C2×#14579209C22semidirect
24. C2×#14579209C22semidirect
25. C2×#14579208C22semidirect
26. C2×#14579208C22semidirect
27. C2×#14579208C22semidirect
30. C2×#14579207C22semidirect
31. C2×#14579207C22semidirect
33. C22×#11929625C22semidirect
36. C2×#41×D79C22semidirect
37. C2×#41×D79C22semidirect
38. C2×#41×D79C22semidirect
39. C22×Q8×D79C22semidirect
40. C22×Q8×D79C22semidirect
41. #19099228C22semidirect
42. Q8×C22⋊D79C22semidirect
43. #19099226C22semidirect
44. #19099225C22semidirect
45. #19099224C22semidirect
46. #19099223C22semidirect
47. #19099222C22semidirect
48. #19099216C22semidirect
49. #19099215C22semidirect
50. #19099214C22semidirect
51. #19099212C22semidirect
52. #19099211C22semidirect
53. #19099209C22semidirect
54. #19099208C22semidirect
55. #19099205C22semidirect
56. #19099204C22semidirect
57. #19099202C22semidirect
58. #19099201C22semidirect
59. #19099143C22semidirect
60. #19099140C22semidirect
61. #19099139C22semidirect
62. #19099138C22semidirect
63. #19099138C22semidirect
64. #19099138C22semidirect
65. #19099138C22semidirect
66. #19099138C22semidirect
67. #19099138C22semidirect
68. #19099138C22semidirect
69. #19099137C22semidirect
70. #19099137C22semidirect
71. #19099136C22semidirect
72. #19099135C22semidirect
73. #19099134C22semidirect
74. #19099133C22semidirect
75. #19099133C22semidirect
76. #19099132C22semidirect
77. #19099131C22semidirect
78. #19099131C22semidirect
79. #19099127C22semidirect
80. #19099126C22semidirect
81. #19099126C22semidirect
82. #19099124C22semidirect
83. #19099121C22semidirect
84. #19099114C22semidirect
85. #19099113C22semidirect
86. #19099112C22semidirect
87. #19099109C22semidirect
88. #19099109C22semidirect
89. C2×#14579159C22semidirect
90. C4⋊Q8×D79C22semidirect
91. C2×#14579150C22semidirect
92. C2×#14579149C22semidirect
93. #124×D79C22semidirect
94. #19099076C22semidirect
95. #19099072C22semidirect
96. #19099072C22semidirect
97. #19099071C22semidirect
98. C2×#14579146C22semidirect
99. #123×D79C22semidirect
100. C2×#14579139C22semidirect
101. C22⋊Q8×D79C22semidirect
102. #19099045C22semidirect
103. #19099042C22semidirect
104. #19099039C22semidirect
105. #19099035C22semidirect
106. #41×Dic79C22semidirect
107. C4×#11929624C22semidirect
108. #19099031C22semidirect
109. C2×#14579118C22semidirect
110. #117×D79C22semidirect
111. C2×2−1+4×C79C22semidirect
112. C2×2−1+4×C79C22semidirect
113. D4×Q8×C79C22semidirect
114. #547×C79C22semidirect
115. #536×C79C22semidirect
116. #536×C79C22semidirect
117. #532×C79C22semidirect
118. C2×C4⋊Q8×C79C22semidirect
119. C4×#41×C79C22semidirect
161. #41×D79D4semidirect
606. #3499D79semidirect
616. C79#62859semidirect
626. C2×2−1+4C2×D79semidirect
627. C2×2−1+4C2×D79semidirect
643. D4×Q8C2×D79semidirect
653. #547C2×D79semidirect
677. #536C2×D79semidirect
678. #536C2×D79semidirect
692. #532C2×D79semidirect
695. C2×C4⋊Q8C2×D79semidirect
714. C4×#41C2×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190994002
C2×2−1+4×D792
#237771942
#237771932
#237771892
#237771872
#237771832
#237771822
#237771812
#237770772
#237770742
#237770502
#237770392
#237767322
#237767272
C2×#190991382
#536×D792
#237765992
C79×#34992
#6285979