Finite Group Databasebeta

← #11909917

Subgroups — #11909917

Order 1152.

2101 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596051C211yesmaximal, characteristic
2C3×#5570C211yesmaximal, characteristic, complemented
3C3×#5567C211yesmaximal, characteristic, complemented
4#10595387C212yesmaximal, complemented
5#10595374C212yesmaximal, complemented
6#10594469C214yesmaximal, complemented
7#10594464C212yesmaximal
8#10594321C212yesmaximal, complemented
9#10594320C214yesmaximal, complemented
10#10593947C212yesmaximal, complemented
11#10593903C211yesmaximal, characteristic, complemented
12#10593903C212yesmaximal, complemented
13C4×#3797C211yesmaximal, characteristic, complemented
14#10593867C212yesmaximal, complemented
15#10593866C211yesmaximal, characteristic, complemented
16#10593865C211yesmaximal, characteristic, complemented
17#10593848C212yesmaximal, complemented
18#87025—31nomaximal
19#87024—31nomaximal
20C2×#3797C2212yes—
21C2×#3797C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23#64156C2211yescharacteristic
24#64155C2211yescharacteristic
25#64107C2212yes—
26#64104C2211yescharacteristic
27#64103C2212yes—
28#64099C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2212yes—
31#64081C2212yes—
32C42×C3⋊D3C2211yescharacteristic
33C3×Q8×Dic3C2212yes—
34C3×#944C2212yes—
35C3×#890C2214yes—
36C3×#890C2212yes—
37C3×#889C2214yes—
38C3×#887C2212yes—
39C3×#870C2212yes—
40C3×#869C2211yescharacteristic
41C3×#869C2211yescharacteristic
42C3×#869C2212yes—
43C3×C4×Dic6C2212yes—
44C3×C4×Dic6C2212yes—
45C3×C4×Dic6C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47#63918C2214yes—
48#63918C2212yes—
49C4×#627C2212yes—
50#63900C2211yescharacteristic
51#63897C2214yes—
52#63895C2214yes—
53#63895C2214yes—
54#63895C2214yes—
55#63894C2212yes—
56#63894C2214yes—
57#63883C2212yes—
58C4×#624C2212yes—
59#63872C2212yes—
60#63871C2212yes—
61#63871C2212yes—
62#63871C2212yes—
63#63871C2212yes—
64#63868C2214yes—
65#63864C2212yes—
66#63849C2212yes—
67#63849C2212yes—
68#63848C2214yes—
69#63848C2214yes—
70#63848C2214yes—
71#63846C2214yes—
72#63846C2214yes—
73#63845C2214yes—
74#63843C2212yes—
75#63843C2211yescharacteristic
76#63843C2212yes—
77#63843C2211yescharacteristic
78Dic3×Dic6C2212yes—
79#63838C2212yes—
80#63837C2214yes—
81#63837C2214yes—
82#63836C2214yes—
83#63836C2214yes—
84#63836C2214yes—
85C3×#557—31no—
86C3×#557—31no—
87#5732—32no—
88#5732—31no—
89#5731—32no—
90#5728—32no—
91#5728—31no—
92#5728—31no—
93#5727—31no—
94#5727—32no—
95#5698—34no—
96#5698—32no—
97#5696—34no—
98#5694—34no—
99#5694—32no—
100#5693—34no—
101#5691—32no—
102#5685—32no—
103#5584—31no—
104#5581—32no—
105#5580—31no—
106#5580—31no—
107#5580—32no—
108#5580—61no—
109#5578—32no—
110Q8×D12—32no—
111Q8×D12—31no—
112#5572—32no—
113#5572—32no—
114C4×D3×Q8—31no—
115C4×D3×Q8—31no—
116#5570—32no—
117#5570D311yescharacteristic, complemented
118#5568—32no—
119#5567D311yescharacteristic, complemented
120C2×C32×Q8C2311yescharacteristic
121C2×C4⋊(C3⋊D3)C2312yes—
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2312yes—
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×C3×Dic6C2312yes—
128C2×C3×Dic6C2312yes—
129C2×C3×Dic6C2311yescharacteristic
130C2×C3×Dic6C2311yescharacteristic
131C2×#627C2314yes—
132C2×#627C2312yes—
133C2×#624C2314yes—
134C2×#624C2312yes—
135C2×#624C2312yes—
136#3797—28no—
137#3797—24no—
138C32×C4⋊C4C2311yescharacteristic
139C32×C4⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141C32×C42C2312yes—
142#3752C2312yes—
143#3752C2312yes—
144#3752C2312yes—
145#3752C2312yes—
146#3752C2312yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2312yes—
149#3750C2312yes—
150#3750C2312yes—
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2311yescharacteristic
153C4×C3⋊Dic3C2311yescharacteristic
154C3×C4⋊Dic3C2312yes—
155C3×C4⋊Dic3C2314yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2314yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2312yes—
168C3×C4×Dic3C2314yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2314yes—
171C3×C4×Dic3C2312yes—
172#3724C2312yes—
173Dic3⋊Dic3C2312yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179#3722C2314yes—
180#3722C2314yes—
181#3722C2314yes—
182#3722C2314yes—
183Dic32C2312yes—
184Dic32C2314yes—
185Dic32C2314yes—
186Dic32C2312yes—
187#3523—91noSylow
188C2×D3×Q8—31no—
189C2×D3×Q8—32no—
190C2×D3×Q8—31no—
191C2×D3×Q8—32no—
192C3×C4⋊Q8—32no—
193C3×C4⋊Q8—31no—
194C3×C4⋊Q8—32no—
195C3×C4⋊Q8—31no—
196C3×#125—34no—
197C3×#125—32no—
198C3×#125—34no—
199C3×#125—32no—
200C3×C4×Q8—21no—
201C3×C4×Q8—32no—
202C3×C4×Q8—32no—
203C3×C4×Q8—31no—
204C3×C4×Q8—31no—
205C3×C4×Q8—32no—
206C3×C4×Q8—32no—
207C3×C4×Q8C2×D311yescharacteristic
208C3×C4×Q8C2×D311yescharacteristic
209#947—31no—
210#947—31no—
211#947—32no—
212#947—61no—
213#946—31no—
214#946—31no—
215#946—32no—
216#946—32no—
217#946—32no—
218#946—32no—
219#946—61no—
220Q8×Dic3—32no—
221Q8×Dic3—32no—
222Q8×Dic3—31no—
223Q8×Dic3—31no—
224Q8×Dic3—32no—
225Q8×Dic3C2×D312yes—
226#944C2×D312yes—
227#898—32no—
228#898—32no—
229#898—34no—
230#898—34no—
231#898—34no—
232#898—34no—
233#898—34no—
234#898—34no—
235#898—34no—
236#898—62no—
237#897—32no—
238#897—32no—
239#897—32no—
240#897—32no—
241#897—34no—
242#897—34no—
243#897—34no—
244#896—34no—
245#896—34no—
246#896—34no—
247#895—31no—
248#895—31no—
249#895—61no—
250#894—32no—
251#894—32no—
252#894—34no—
253#894—34no—
254#894—62no—
255#893—34no—
256#893—32no—
257#892—32no—
258#892—32no—
259#892—32no—
260#892—32no—
261#892—34no—
262#892—34no—
263#892—34no—
264D3×C4⋊C4—31no—
265D3×C4⋊C4—31no—
266D3×C4⋊C4—32no—
267D3×C4⋊C4—32no—
268#890—31no—
269#890—31no—
270#890—34no—
271#890—32no—
272#890—34no—
273#890—32no—
274#890—34no—
275#890—61no—
276#890C2×D314yes—
277#890C2×D312yes—
278#889—34no—
279#889—34no—
280#889—34no—
281#889C2×D314yes—
282#888—34no—
283#888—32no—
284#887—32no—
285#887—31no—
286#887—32no—
287#887—31no—
288#887—32no—
289#887—32no—
290#887—34no—
291#887—34no—
292#887C2×D312yes—
293#876—34no—
294#875—32no—
295C4×D12—32no—
296C4×D12—32no—
297C4×D12—31no—
298C4×D12—31no—
299C4×D12—34no—
300C4×D12—32no—
301C4×D12—62no—
302C4×D12—61no—
303#872—32no—
304#872—32no—
305#872—34no—
306#872—34no—
307#872—34no—
308#872—62no—
309C42×D3—31no—
310C42×D3—31no—
311C42×D3—32no—
312C42×D3—32no—
313C42×D3—61no—
314#870C2×D312yes—
315#869—34no—
316#869—32no—
317#869C2×D312yes—
318#869C2×D311yescharacteristic
319#869C2×D311yescharacteristic
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—34no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6C2×D312yes—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D312yes—
328C4×Dic6C2×D311yescharacteristic
329C22×C3⋊D3C2412yes—
330C22×C3⋊D3C2411yescharacteristic
331C32×Q8—22no—
332C2×C32×C4C2412yes—
333C2×C32×C4C2412yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3C2411yescharacteristic
338C2×C3⋊Dic3C2411yescharacteristic
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2411yescharacteristic
341C4⋊(C3⋊D3)—24no—
342C4⋊(C3⋊D3)—22no—
343C4×C3⋊D3—22no—
344C4×C3⋊D3—22no—
345C4×C3⋊D3—24no—
346C4×C3⋊D3—22no—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2414yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C3×Dic6—24no—
354C3×Dic6—22no—
355C3×Dic6—24no—
356C3×Dic6#4114yes—
357#627—28no—
358#627—24no—
359#624—24no—
360#624—24no—
361#624—28no—
362#557—31no—
363#557—31no—
364#557—92no—
365#556—92no—
366#556—91no—
367#552—92no—
368#552—94no—
369D4×Q8—92no—
370D4×Q8—91no—
371#541—94no—
372#541—92no—
373#533—92no—
374#533—91no—
375#529—92no—
376#529—91no—
377#519—92no—
378C2×C4×Q8—91no—
379C2×C3×Q8—21no—
380C2×C3×Q8—31no—
381C2×C3×Q8—32no—
382C2×C3×Q8—32no—
383C2×C3×Q8—31no—
384C2×C3×Q8C22×D311yescharacteristic
385C2×C3×Q8C22×D311yescharacteristic
386D3×Q8—64no—
387D3×Q8—68no—
388D3×Q8—64no—
389D3×Q8—68no—
390C2×D12—32no—
391C2×D12—31no—
392C2×D12—31no—
393C2×D12—32no—
394C2×D12—62no—
395C2×D12—61no—
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—32no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—61no—
411C2×C4×D3—61no—
412C2×C4×D3—61no—
413C2×C4×D3—62no—
414C2×Dic6—34no—
415C2×Dic6—32no—
416C2×Dic6—34no—
417C2×Dic6—32no—
418C2×Dic6C22×D312yes—
419C2×Dic6C22×D312yes—
420C2×Dic6C22×D311yescharacteristic
421C2×Dic6C22×D311yescharacteristic
422C3×C4⋊C4—21no—
423C3×C4⋊C4—22no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4—32no—
428C3×C4⋊C4—31no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—32no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—34no—
435C3×C4⋊C4—32no—
436C3×C4⋊C4—34no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4C22×D311yescharacteristic
439C3×C4⋊C4C22×D312yes—
440C3×C4⋊C4C22×D311yescharacteristic
441C3×C4⋊C4C22×D312yes—
442C3×C42—21no—
443C3×C42—22no—
444C3×C42—32no—
445C3×C42—32no—
446C3×C42—34no—
447C3×C42—34no—
448C3×C42C22×D311yescharacteristic
449C3×C42C22×D311yescharacteristic
450C3×C42C22×D312yes—
451C3×C42C22×D312yes—
452(C2×D3)⋊C4—32no—
453(C2×D3)⋊C4—32no—
454(C2×D3)⋊C4—32no—
455(C2×D3)⋊C4—32no—
456(C2×D3)⋊C4—32no—
457(C2×D3)⋊C4—32no—
458(C2×D3)⋊C4—32no—
459(C2×D3)⋊C4—32no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—32no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—62no—
473(C2×D3)⋊C4—62no—
474(C2×D3)⋊C4—62no—
475C4⋊Dic3—31no—
476C4⋊Dic3—32no—
477C4⋊Dic3—31no—
478C4⋊Dic3—32no—
479C4⋊Dic3—32no—
480C4⋊Dic3—32no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—62no—
486C4⋊Dic3—61no—
487C4⋊Dic3C22×D311yescharacteristic
488C4⋊Dic3C22×D312yes—
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D314yes—
491C4⋊Dic3C22×D312yes—
492C4⋊Dic3C22×D312yes—
493C4⋊Dic3C22×D312yes—
494C4⋊Dic3C22×D314yes—
495Dic3⋊C4—32no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—62no—
508Dic3⋊C4—62no—
509Dic3⋊C4C22×D314yes—
510Dic3⋊C4C22×D314yes—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D312yes—
513Dic3⋊C4C22×D314yes—
514Dic3⋊C4C22×D314yes—
515C4×Dic3—31no—
516C4×Dic3—31no—
517C4×Dic3—31no—
518C4×Dic3—31no—
519C4×Dic3—31no—
520C4×Dic3—31no—
521C4×Dic3—32no—
522C4×Dic3—34no—
523C4×Dic3—34no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—34no—
529C4×Dic3—61no—
530C4×Dic3—61no—
531C4×Dic3—61no—
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D312yes—
534C4×Dic3C22×D314yes—
535C4×Dic3C22×D314yes—
536C22×C32C2511yescharacteristic
537C2×C3⋊D3—21no—
538C2×C3⋊D3—21no—
539C2×C3⋊D3—22no—
540C2×C3⋊D3—22no—
541C2×C3⋊D3—22no—
542C2×C3⋊D32−1+412yes—
543C32×C4—21no—
544C32×C4—22no—
545C32×C4—22no—
546C32×C4C2×#4112yes—
547C32×C42−1+412yes—
548C3⋊Dic3—22no—
549C3⋊Dic3—21no—
550C3⋊Dic3—21no—
551C3⋊Dic3—21no—
552C3×Dic3—22no—
553C3×Dic3—24no—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—24no—
557C3×Dic3C2×#4114yes—
558C22×Q8—91no—
559C22×Q8—92no—
560C4⋊Q8—32no—
561C4⋊Q8—31no—
562C4⋊Q8—31no—
563C4⋊Q8—32no—
564C4⋊Q8—92no—
565C4⋊Q8—94no—
566#126—94no—
567#126—94no—
568#126—94no—
569#126—94no—
570#126—92no—
571#125—32no—
572#125—34no—
573#125—34no—
574#125—32no—
575#125—94no—
576#125—92no—
577#125—94no—
578#125—94no—
579#125—91no—
580#124—92no—
581#124—91no—
582#123—94no—
583#123—92no—
584C22⋊Q8—94no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—92no—
588C22⋊Q8—92no—
589C22⋊Q8—92no—
590C22⋊Q8—92no—
591C22⋊Q8—91no—
592#121—91no—
593C4×Q8—32no—
594C4×Q8—32no—
595C4×Q8—31no—
596C4×Q8—31no—
597C4×Q8—32no—
598C4×Q8—32no—
599C4×Q8—92no—
600C4×Q8—94no—
601C4×Q8—94no—
602C4×Q8—92no—
603C4×Q8—92no—
604C4×Q8—91no—
605C4×Q8—91no—
606C4×Q8—92no—
607C4×Q8—92no—
608C4×Q8D3211yescharacteristic
609C4×D4—94no—
610C4×D4—92no—
611C4×D4—92no—
612C4×D4—91no—
613#117—94no—
614#117—94no—
615#117—94no—
616#117—92no—
617#117—92no—
618#117—92no—
619C2×C4⋊C4—91no—
620C2×C4⋊C4—92no—
621C2×C42—92no—
622C2×C42—91no—
623C22×D3—31no—
624C22×D3—31no—
625C22×D3—32no—
626C22×D3—32no—
627C22×D3—61no—
628C22×D3—62no—
629C3×Q8—22no—
630C3×Q8—22no—
631C3×Q8—34no—
632C3×Q8—42no—
633C3×Q8—62no—
634C3×Q8—64no—
635C3×Q8—64no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—34no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—34no—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D312yes—
650C2×C3×C4C23×D312yes—
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—31no—
660C2×Dic3—31no—
661C2×Dic3—32no—
662C2×Dic3—31no—
663C2×Dic3—32no—
664C2×Dic3—31no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—62no—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D314yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D314yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675D12—64no—
676D12—64no—
677D12—62no—
678D12—62no—
679D12—122no—
680D12—124no—
681C4×D3—64no—
682C4×D3—68no—
683C4×D3—64no—
684C4×D3—64no—
685C4×D3—62no—
686C4×D3—62no—
687C4×D3—62no—
688C4×D3—64no—
689C4×D3—62no—
690C4×D3—62no—
691C4×D3—64no—
692C4×D3—62no—
693C4×D3—64no—
694C4×D3—68no—
695C4×D3—122no—
696C4×D3—122no—
697C4×D3—124no—
698C4×D3—122no—
699Dic6—24no—
700Dic6—22no—
701Dic6—24no—
702Dic6—68no—
703Dic6—64no—
704Dic6—68no—
705Dic6—64no—
706Dic6#23914yes—
707C2×C32C22×#4111yescharacteristic
708C2×C32C2×2−1+411yescharacteristic
709C2×C32C2×2−1+411yescharacteristic
710C3⋊D3—22no—
711C3⋊D3—42no—
712C2×Q8—31no—
713C2×Q8—32no—
714C2×Q8—31no—
715C2×Q8—32no—
716C2×Q8—92no—
717C2×Q8—94no—
718C2×Q8—184no—
719C2×Q8—188no—
720C2×Q8C2×D3211yescharacteristic
721C2×D4—92no—
722C2×D4—91no—
723C22×C4—92no—
724C22×C4—92no—
725C22×C4—94no—
726C22×C4—91no—
727C22×C4—91no—
728C22×C4—91no—
729C22×C4—92no—
730C4⋊C4—31no—
731C4⋊C4—32no—
732C4⋊C4—31no—
733C4⋊C4—32no—
734C4⋊C4—34no—
735C4⋊C4—32no—
736C4⋊C4—34no—
737C4⋊C4—32no—
738C4⋊C4—34no—
739C4⋊C4—32no—
740C4⋊C4—32no—
741C4⋊C4—34no—
742C4⋊C4—34no—
743C4⋊C4—34no—
744C4⋊C4—92no—
745C4⋊C4—92no—
746C4⋊C4—92no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—92no—
752C4⋊C4—92no—
753C4⋊C4—91no—
754C4⋊C4—92no—
755C4⋊C4C2×D3211yescharacteristic
756C4⋊C4C2×D3212yes—
757C22⋊C4—94no—
758C22⋊C4—94no—
759C22⋊C4—94no—
760C22⋊C4—94no—
761C22⋊C4—92no—
762C22⋊C4—92no—
763C22⋊C4—92no—
764C22⋊C4—92no—
765C22⋊C4—92no—
766C42—32no—
767C42—32no—
768C42—34no—
769C42—34no—
770C42—92no—
771C42—92no—
772C42—94no—
773C42—94no—
774C42—91no—
775C42—91no—
776C42—91no—
777C42C2×D3211yescharacteristic
778C42C2×D3212yes—
779C22×C3—21no—
780C22×C3C24×D311yescharacteristic
781C22×C3C24×D311yescharacteristic
782C2×D3—32no—
783C2×D3—32no—
784C2×D3—62no—
785C2×D3—61no—
786C2×D3—61no—
787C2×D3—61no—
788C2×D3—61no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—122no—
798C2×D3—122no—
799C2×D3—122no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—34no—
809C3×C4—41no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4—62no—
813C3×C4—64no—
814C3×C4—64no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4C2×#23912yes—
818C3×C4#100712yes—
819C3×C4D3×#4112yes—
820C3×C4#101012yes—
821Dic3—22no—
822Dic3—24no—
823Dic3—24no—
824Dic3—22no—
825Dic3—22no—
826Dic3—61no—
827Dic3—62no—
828Dic3—61no—
829Dic3—61no—
830Dic3—62no—
831Dic3—61no—
832Dic3—61no—
833Dic3—61no—
834Dic3—121no—
835Dic3—121no—
836Dic3—122no—
837Dic3—121no—
838Dic3C2×#23914yes—
839C32#352311yescharacteristic, complemented, Sylow
840C23—91no—
841C23—92no—
842Q8—22no—
843Q8—34no—
844Q8—64no—
845Q8—62no—
846Q8—64no—
847Q8—184no—
848Q8—188no—
849D4—184no—
850D4—182no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—34no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—34no—
857C2×C4—91no—
858C2×C4—91no—
859C2×C4—92no—
860C2×C4—91no—
861C2×C4—182no—
862C2×C4—184no—
863C2×C4—188no—
864C2×C4—184no—
865C2×C4—182no—
866C2×C4—182no—
867C2×C4—184no—
868C2×C4C22×D3212yes—
869C2×C4C22×D3212yes—
870C2×C4C22×D3211yescharacteristic
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3211yescharacteristic
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3C22×#23911yescharacteristic
877C2×C3C2×#100711yescharacteristic
878C2×C3C2×D3×#4111yescharacteristic
879C2×C3C2×#101011yescharacteristic
880C2×C3D3×2−1+411yescharacteristic
881C2×C3D3×2−1+411yescharacteristic
882D3—62no—
883D3—62no—
884D3—122no—
885D3—122no—
886D3—122no—
887D3—242no—
888C22—92no—
889C22—181no—
890C22—181no—
891C22—182no—
892C22—182no—
893C22—182no—
894C22C23×D3211yescharacteristic
895C4—22no—
896C4—21no—
897C4—22no—
898C4—34no—
899C4—64no—
900C4—62no—
901C4—64no—
902C4—62no—
903C4—62no—
904C4—181no—
905C4—182no—
906C4—181no—
907C4—181no—
908C4#6429712yes—
909C4D3×#23912yes—
910C3—21no—
911C3#8702411yescharacteristic, complemented
912C3#8702511yescharacteristic, complemented
913C2—182no—
914C2—362no—
915C2C2×#6429711yescharacteristic
916C2C2×D3×#23911yescharacteristic
917C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radical#64104C22
hypercenterC4×Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5570C2semidirect
3. C3×#5567C2semidirect
4. #10595387C2semidirect
5. #10595374C2semidirect
6. #10594469C2semidirect
8. #10594321C2semidirect
9. #10594320C2semidirect
10. #10593947C2semidirect
11. #10593903C2semidirect
12. #10593903C2semidirect
13. C4×#3797C2semidirect
14. #10593867C2semidirect
15. #10593866C2semidirect
16. #10593865C2semidirect
17. #10593848C2semidirect
117. #5570D3semidirect
119. #5567D3semidirect
839. C32#3523semidirect
911. C3#87024semidirect
912. C3#87025semidirect

Maximal subgroups

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

subgroupindex
#105960512
C3×#55702
C3×#55672
#105953872
#105953742
#105944692
#105944642
#105943212
#105943202
#105939472
#105939032
C4×#37972
#105938672
#105938662
#105938652
#105938482
#870253
#870243