Finite Group Databasebeta

← #11909913

Subgroups — #11909913

Order 1152.

2124 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5721C211yesmaximal, characteristic, complemented
4#10595379C212yesmaximal, complemented
5#10595361C212yesmaximal, complemented
6#10595354C212yesmaximal, complemented
7#10595339C212yesmaximal, complemented
8#10594453C212yesmaximal
9#10594408C214yesmaximal, complemented
10#10594385C212yesmaximal, complemented
11#10594350C212yesmaximal, complemented
12#10594323C214yesmaximal, complemented
13#10594322C212yesmaximal, complemented
14C4×D3×Dic6C211yesmaximal, characteristic, complemented
15#10593870C211yesmaximal, characteristic
16#10593865C211yesmaximal, characteristic, complemented
17#10593864C211yesmaximal, characteristic, complemented
18#87025—31nomaximal
19#86266—31nomaximal
20C2×Q8×C3⋊D3C2212yes—
21C2×D3×Dic6C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23#64155C2212yes—
24#64105C2214yes—
25#64102C2212yes—
26#64097C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C3×#946C2212yes—
30C3×Q8×Dic3C2212yes—
31C3×Q8×Dic3C2212yes—
32C3×#944C2212yes—
33C3×#897C2212yes—
34C3×#892C2212yes—
35C3×#890C2212yes—
36C3×#890C2212yes—
37C3×#889C2214yes—
38C3×#887C2212yes—
39C3×#887C2212yes—
40C3×C42×D3C2211yescharacteristic
41C3×#869C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C4×#627C2212yes—
45#63909C2211yescharacteristic
46C4×#626C2212yes—
47#63896C2214yes—
48#63890C2214yes—
49D3×C4⋊Dic3C2211yescharacteristic
50#63881C2214yes—
51#63877C2214yes—
52D3×Dic3⋊C4C2212yes—
53C4×D3×Dic3C2212yes—
54#63874C2212yes—
55#63874C2214yes—
56#63873C2212yes—
57#63871C2212yes—
58#63869C2211yescharacteristic
59#63869C2212yes—
60#63868C2212yes—
61#63868C2214yes—
62#63868C2214yes—
63#63867C2214yes—
64#63865C2214yes—
65#63864C2211yescharacteristic
66#63864C2212yes—
67#63856C2211yescharacteristic
68#63850C2212yes—
69#63849C2214yes—
70#63849C2212yes—
71#63848C2214yes—
72#63848C2214yes—
73#63847C2214yes—
74#63847C2214yes—
75#63846C2214yes—
76#63844C2211yescharacteristic
77#63844C2214yes—
78#63844C2214yes—
79#63844C2212yes—
80#63843C2212yes—
81Dic3×Dic6C2212yes—
82Dic3×Dic6C2211yescharacteristic
83#63840C2214yes—
84#63837C2212yes—
85C3×#557—31no—
86C3×#533—31no—
87#5732—31no—
88#5731—32no—
89#5728D311yescharacteristic, complemented
90#5727—31no—
91#5727—31no—
92#5727—32no—
93#5727—61no—
94#5721—31no—
95#5721D311yescharacteristic, complemented
96#5696—34no—
97#5696—34no—
98#5693—34no—
99#5691—32no—
100#5685—32no—
101#5642—32no—
102#5632—32no—
103#5624—32no—
104#5622—32no—
105#5584—31no—
106#5583—32no—
107#5581—32no—
108#5580—31no—
109#5578—32no—
110#5572—32no—
111#5572—32no—
112C4×D3×Q8—31no—
113#5569—32no—
114#5568—32no—
115#5568—32no—
116#5567—31no—
117#5531—34no—
118#5479—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121Q8×C3⋊D3—28no—
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2314yes—
126C2×#634C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×Dic6C2311yescharacteristic
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2312yes—
134C2×#626C2312yes—
135C2×D3×Dic3C2312yes—
136C2×D3×Dic3C2312yes—
137D3×Dic6—24no—
138C32×C4⋊C4C2312yes—
139C32×C4⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141#3752C2312yes—
142#3752C2314yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144C4⋊(C3⋊Dic3)C2311yescharacteristic
145#3750C2312yes—
146#3750C2314yes—
147C4×C3⋊Dic3C2312yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×C4⋊Dic3C2314yes—
150C3×C4⋊Dic3C2311yescharacteristic
151C3×C4⋊Dic3C2312yes—
152C3×C4⋊Dic3C2314yes—
153C3×C4⋊Dic3C2311yescharacteristic
154C3×C4⋊Dic3C2312yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2312yes—
158C3×Dic3⋊C4C2312yes—
159C3×Dic3⋊C4C2314yes—
160C3×C4×Dic3C2311yescharacteristic
161C3×C4×Dic3C2314yes—
162C3×C4×Dic3C2312yes—
163C3×C4×Dic3C2314yes—
164C3×C4×Dic3C2311yescharacteristic
165C3×C4×Dic3C2312yes—
166C3×C4×Dic3C2311yescharacteristic
167#3724C2312yes—
168#3724C2312yes—
169#3724C2314yes—
170#3724C2312yes—
171#3724C2314yes—
172Dic3⋊Dic3C2312yes—
173Dic3⋊Dic3C2312yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2314yes—
177#3722C2312yes—
178#3722C2314yes—
179#3722C2314yes—
180#3722C2312yes—
181#3722C2312yes—
182(C2×D3)⋊Dic3C2312yes—
183Dic32C2312yes—
184Dic32C2312yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C2×D3×Q8—32no—
189C2×D3×Q8—32no—
190C2×D3×Q8—31no—
191C2×D3×Q8—62no—
192C22×Dic6—31no—
193C3×C4⋊Q8—21no—
194C3×C4⋊Q8—32no—
195C3×C4⋊Q8—31no—
196C3×C4⋊Q8C2×D311yescharacteristic
197C3×C4⋊Q8C2×D311yescharacteristic
198C3×#125—34no—
199C3×#125—32no—
200C3×#125—32no—
201C3×C22⋊Q8—32no—
202C3×C22⋊Q8—32no—
203C3×C4×Q8—32no—
204C3×C4×Q8—32no—
205C3×C4×Q8—32no—
206C3×C4×Q8—32no—
207C3×C4×Q8—31no—
208C3×C4×Q8—31no—
209C3×#117—32no—
210C2×C3×C42—31no—
211#947—32no—
212#947—31no—
213#946—32no—
214#946—32no—
215#946—31no—
216#946—32no—
217#946—62no—
218#946C2×D312yes—
219Q8×Dic3—32no—
220Q8×Dic3—31no—
221Q8×Dic3—32no—
222Q8×Dic3C2×D312yes—
223Q8×Dic3C2×D312yes—
224#944—32no—
225#944—32no—
226#944C2×D312yes—
227#930—31no—
228#929—32no—
229C4×#67—32no—
230C2×C4⋊Dic3—31no—
231#924—31no—
232C2×Dic3⋊C4—32no—
233C2×C4×Dic3—32no—
234#898—34no—
235#898—34no—
236#898—34no—
237#898—34no—
238#898—34no—
239#898—34no—
240#898—32no—
241#897—32no—
242#897C2×D312yes—
243#896—34no—
244#896—34no—
245#896—34no—
246#896—34no—
247#896—34no—
248#896—64no—
249#895—31no—
250#894—32no—
251#894—34no—
252#893—32no—
253#893—32no—
254#893—34no—
255#893—62no—
256#892—32no—
257#892—34no—
258#892—34no—
259#892—32no—
260#892C2×D312yes—
261D3×C4⋊C4—32no—
262D3×C4⋊C4—31no—
263#890—34no—
264#890—32no—
265#890—31no—
266#890C2×D312yes—
267#890C2×D312yes—
268#889—34no—
269#889—34no—
270#889—34no—
271#889—34no—
272#889—34no—
273#889—34no—
274#889C2×D314yes—
275#888—32no—
276#888—32no—
277#888—34no—
278#888—34no—
279#888—62no—
280#887—32no—
281#887—32no—
282#887—34no—
283#887—32no—
284#887—34no—
285#887—31no—
286#887C2×D312yes—
287#887C2×D312yes—
288#886—34no—
289#67⋊C4—34no—
290#878—34no—
291#877—34no—
292#876—32no—
293#876—34no—
294#876—34no—
295#875—32no—
296#875—31no—
297C4×D12—32no—
298C4×D12—31no—
299C4×D12—31no—
300C4×D12—61no—
301#872—34no—
302#872—34no—
303#872—32no—
304#872—32no—
305#872—34no—
306C42×D3—32no—
307C42×D3C2×D311yescharacteristic
308#870—32no—
309#870—31no—
310#870—34no—
311#869C2×D311yescharacteristic
312C4×Dic6—32no—
313C4×Dic6—31no—
314C4×Dic6—31no—
315C4×Dic6—31no—
316C4×Dic6—34no—
317C4×Dic6—31no—
318C4×Dic6—32no—
319C4×Dic6—34no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—61no—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D311yescharacteristic
326C22×C3⋊D3C2412yes—
327C22×C3×D3C2411yescharacteristic
328C32×Q8—24no—
329C2×C32×C4C2414yes—
330C2×C32×C4C2411yescharacteristic
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C4⋊(C3⋊D3)—22no—
337C4×C3⋊D3—24no—
338C4×C3⋊D3—28no—
339#634—28no—
340#634#4114yes—
341C2×C3×Dic3C2411yescharacteristic
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2414yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2411yescharacteristic
349C3×C4×D3—22no—
350C3×C4×D3—22no—
351C3×C4×D3—22no—
352C3×Dic6—22no—
353C3×Dic6—22no—
354C3×Dic6—24no—
355#627—24no—
356#626—24no—
357D3×Dic3—24no—
358D3×Dic3—24no—
359#557—31no—
360#557—92no—
361#557—91no—
362#556—92no—
363#556—91no—
364#552—94no—
365#552—92no—
366D4×Q8—92no—
367D4×Q8—91no—
368#541—92no—
369#541—94no—
370#533—31no—
371#533—92no—
372#529—91no—
373#529—92no—
374#519—92no—
375C2×C4×Q8—91no—
376C2×C3×Q8—22no—
377C2×C3×Q8—31no—
378C2×C3×Q8—32no—
379C2×C3×Q8—31no—
380C2×C3×Q8C22×D312yes—
381C2×C3×Q8C22×D312yes—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C2×#67—32no—
386C22×Dic3—32no—
387C22×Dic3—32no—
388D3×Q8—64no—
389D3×Q8—68no—
390D3×Q8—68no—
391D3×Q8—128no—
392C2×D12—32no—
393C2×D12—31no—
394C2×D12—31no—
395C2×D12—61no—
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3—32no—
399C2×C4×D3—32no—
400C2×C4×D3—34no—
401C2×C4×D3—34no—
402C2×C4×D3—62no—
403C2×C4×D3—64no—
404C2×C4×D3C22×D311yescharacteristic
405C2×C4×D3C22×D311yescharacteristic
406C2×C4×D3C22×D311yescharacteristic
407C2×Dic6—31no—
408C2×Dic6—31no—
409C2×Dic6—34no—
410C2×Dic6—34no—
411C2×Dic6—32no—
412C2×Dic6—32no—
413C2×Dic6—61no—
414C2×Dic6—64no—
415C2×Dic6—64no—
416C2×Dic6C22×D311yescharacteristic
417C2×Dic6C22×D312yes—
418C2×Dic6C22×D311yescharacteristic
419C3×C4⋊C4—22no—
420C3×C4⋊C4—22no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—34no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4—34no—
428C3×C4⋊C4—34no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4—32no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4C22×D312yes—
433C3×C4⋊C4C22×D312yes—
434C3×C4⋊C4C22×D312yes—
435C3×C4⋊C4C22×D312yes—
436C3×C22⋊C4—34no—
437C3×C42—21no—
438C3×C42—31no—
439C3×C42—32no—
440C3×C42—31no—
441C3×C42—31no—
442C3×C42—32no—
443C3×C42—34no—
444C3×C42—34no—
445C3×C42C22×D311yescharacteristic
446C3×C42C22×D311yescharacteristic
447#217—32no—
448(C2×D3)⋊C4—32no—
449(C2×D3)⋊C4—32no—
450(C2×D3)⋊C4—32no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—32no—
454(C2×D3)⋊C4—32no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—32no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—32no—
459(C2×D3)⋊C4—32no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—62no—
464(C2×D3)⋊C4—64no—
465(C2×D3)⋊C4C22×D314yes—
466C4⋊Dic3—31no—
467C4⋊Dic3—31no—
468C4⋊Dic3—31no—
469C4⋊Dic3—31no—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—34no—
473C4⋊Dic3—34no—
474C4⋊Dic3—32no—
475C4⋊Dic3—61no—
476C4⋊Dic3—61no—
477C4⋊Dic3C22×D311yescharacteristic
478C4⋊Dic3C22×D312yes—
479C4⋊Dic3C22×D314yes—
480C4⋊Dic3C22×D314yes—
481C4⋊Dic3C22×D311yescharacteristic
482C4⋊Dic3C22×D312yes—
483Dic3⋊C4—32no—
484Dic3⋊C4—32no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—32no—
488Dic3⋊C4—32no—
489Dic3⋊C4—32no—
490Dic3⋊C4—32no—
491Dic3⋊C4—34no—
492Dic3⋊C4—32no—
493Dic3⋊C4—32no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—32no—
497Dic3⋊C4—34no—
498Dic3⋊C4—32no—
499Dic3⋊C4—34no—
500Dic3⋊C4—32no—
501Dic3⋊C4—34no—
502Dic3⋊C4—62no—
503Dic3⋊C4—64no—
504Dic3⋊C4C22×D312yes—
505Dic3⋊C4C22×D312yes—
506Dic3⋊C4C22×D314yes—
507Dic3⋊C4C22×D314yes—
508Dic3⋊C4C22×D314yes—
509C4×Dic3—32no—
510C4×Dic3—32no—
511C4×Dic3—32no—
512C4×Dic3—34no—
513C4×Dic3—32no—
514C4×Dic3—32no—
515C4×Dic3—34no—
516C4×Dic3—34no—
517C4×Dic3—34no—
518C4×Dic3—32no—
519C4×Dic3—62no—
520C4×Dic3C22×D311yescharacteristic
521C4×Dic3C22×D312yes—
522C4×Dic3C22×D312yes—
523C4×Dic3C22×D311yescharacteristic
524C4×Dic3C22×D311yescharacteristic
525C4×Dic3C22×D314yes—
526C4×Dic3C22×D314yes—
527C22×C32C2511yescharacteristic
528C2×C3⋊D3—22no—
529C2×C3⋊D3—22no—
530C2×C3⋊D3—22no—
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D32−1+412yes—
534C32×C4—24no—
535C32×C4—21no—
536C32×C4C2×#4112yes—
537C32×C42−1+412yes—
538C3⋊Dic3—22no—
539C3⋊Dic3—22no—
540C3⋊Dic3C2×#4114yes—
541C3×Dic3—22no—
542C3×Dic3—21no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—24no—
547C3×Dic3—21no—
548C3×Dic3—21no—
549C22×Q8—91no—
550C22×Q8—92no—
551C4⋊Q8—32no—
552C4⋊Q8—31no—
553C4⋊Q8—94no—
554C4⋊Q8—92no—
555C4⋊Q8—92no—
556C4⋊Q8D3211yescharacteristic
557#126—92no—
558#126—94no—
559#126—94no—
560#126—94no—
561#126—94no—
562#125—32no—
563#125—32no—
564#125—34no—
565#125—91no—
566#125—94no—
567#125—92no—
568#125—94no—
569#125—94no—
570#125—94no—
571#124—91no—
572#124—92no—
573#123—94no—
574#123—92no—
575C22⋊Q8—32no—
576C22⋊Q8—32no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—92no—
580C22⋊Q8—91no—
581C22⋊Q8—92no—
582C22⋊Q8—94no—
583#121—91no—
584C4×Q8—32no—
585C4×Q8—32no—
586C4×Q8—32no—
587C4×Q8—32no—
588C4×Q8—31no—
589C4×Q8—31no—
590C4×Q8—92no—
591C4×Q8—91no—
592C4×Q8—92no—
593C4×Q8—94no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—91no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×Q8—91no—
600C4×D4—92no—
601C4×D4—94no—
602C4×D4—92no—
603C4×D4—91no—
604#117—32no—
605#117—92no—
606#117—94no—
607#117—94no—
608#117—94no—
609#117—92no—
610C2×C4⋊C4—92no—
611C2×C4⋊C4—91no—
612C2×C42—31no—
613C2×C42—92no—
614C23×C3—31no—
615C22×D3—32no—
616C22×D3—32no—
617C22×D3—62no—
618C22×D3C23×D311yescharacteristic
619C3×Q8—24no—
620C3×Q8—24no—
621C3×Q8—44no—
622C3×Q8—64no—
623C3×Q8—62no—
624C3×Q8—62no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—24no—
629C2×C3×C4—31no—
630C2×C3×C4—32no—
631C2×C3×C4—32no—
632C2×C3×C4—34no—
633C2×C3×C4—32no—
634C2×C3×C4—31no—
635C2×C3×C4—32no—
636C2×C3×C4—31no—
637C2×C3×C4—62no—
638C2×C3×C4—62no—
639C2×C3×C4—62no—
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D314yes—
642C2×C3×C4C23×D314yes—
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647C2×C3×C4C23×D311yescharacteristic
648#67—64no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—64no—
659C2×Dic3—64no—
660C2×Dic3C23×D311yescharacteristic
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D314yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D311yescharacteristic
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D311yescharacteristic
668D12—64no—
669D12—64no—
670D12—62no—
671D12—62no—
672C4×D3—22no—
673C4×D3—22no—
674C4×D3—22no—
675C4×D3—68no—
676C4×D3—68no—
677C4×D3—64no—
678C4×D3—64no—
679C4×D3—64no—
680C4×D3—64no—
681C4×D3—128no—
682C4×D3—124no—
683Dic6—22no—
684Dic6—22no—
685Dic6—24no—
686Dic6—34no—
687Dic6—34no—
688Dic6—64no—
689Dic6—64no—
690Dic6—64no—
691Dic6—68no—
692Dic6—68no—
693Dic6—128no—
694C2×C32C22×#4111yescharacteristic
695C2×C32C2×2−1+411yescharacteristic
696C2×C32C2×2−1+411yescharacteristic
697C3⋊D3—42no—
698C3×D3—22no—
699C2×Q8—31no—
700C2×Q8—32no—
701C2×Q8—31no—
702C2×Q8—92no—
703C2×Q8—91no—
704C2×Q8—94no—
705C2×Q8—184no—
706C2×Q8—188no—
707C2×Q8C2×D3212yes—
708C2×D4—92no—
709C2×D4—91no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—92no—
714C22×C4—92no—
715C22×C4—94no—
716C22×C4—92no—
717C4⋊C4—31no—
718C4⋊C4—32no—
719C4⋊C4—32no—
720C4⋊C4—32no—
721C4⋊C4—34no—
722C4⋊C4—34no—
723C4⋊C4—34no—
724C4⋊C4—31no—
725C4⋊C4—34no—
726C4⋊C4—34no—
727C4⋊C4—32no—
728C4⋊C4—92no—
729C4⋊C4—92no—
730C4⋊C4—92no—
731C4⋊C4—94no—
732C4⋊C4—92no—
733C4⋊C4—92no—
734C4⋊C4—94no—
735C4⋊C4—92no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—92no—
739C4⋊C4—91no—
740C4⋊C4—94no—
741C4⋊C4—91no—
742C4⋊C4C2×D3212yes—
743C4⋊C4C2×D3212yes—
744C22⋊C4—34no—
745C22⋊C4—92no—
746C22⋊C4—92no—
747C22⋊C4—94no—
748C22⋊C4—92no—
749C22⋊C4—94no—
750C22⋊C4—92no—
751C22⋊C4—94no—
752C22⋊C4—92no—
753C42—31no—
754C42—31no—
755C42—31no—
756C42—32no—
757C42—34no—
758C42—34no—
759C42—32no—
760C42—92no—
761C42—92no—
762C42—94no—
763C42—94no—
764C42—92no—
765C42C2×D3211yescharacteristic
766C22×C3—21no—
767C22×C3—32no—
768C22×C3—61no—
769C22×C3—61no—
770C22×C3C24×D311yescharacteristic
771C22×C3C24×D311yescharacteristic
772C2×D3—21no—
773C2×D3—21no—
774C2×D3—64no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—62no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—62no—
781C2×D3—122no—
782C2×D3—122no—
783C2×D3#100712yes—
784C3×C4—21no—
785C3×C4—24no—
786C3×C4—24no—
787C3×C4—21no—
788C3×C4—22no—
789C3×C4—22no—
790C3×C4—44no—
791C3×C4—41no—
792C3×C4—62no—
793C3×C4—62no—
794C3×C4—61no—
795C3×C4—64no—
796C3×C4—61no—
797C3×C4—62no—
798C3×C4—62no—
799C3×C4—61no—
800C3×C4#100712yes—
801C3×C4D3×#4112yes—
802C3×C4D3×#4112yes—
803C3×C4#101012yes—
804Dic3—22no—
805Dic3—21no—
806Dic3—22no—
807Dic3—21no—
808Dic3—24no—
809Dic3—21no—
810Dic3—22no—
811Dic3—22no—
812Dic3—34no—
813Dic3—34no—
814Dic3—64no—
815Dic3—62no—
816Dic3—62no—
817Dic3—62no—
818Dic3—62no—
819Dic3—122no—
820Dic3—122no—
821C32#352311yescharacteristic, complemented, Sylow
822C23—31no—
823C23—92no—
824Q8—24no—
825Q8—62no—
826Q8—62no—
827Q8—64no—
828Q8—94no—
829Q8—188no—
830Q8—184no—
831D4—184no—
832D4—182no—
833C2×C4—31no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—31no—
837C2×C4—31no—
838C2×C4—34no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—62no—
844C2×C4—92no—
845C2×C4—92no—
846C2×C4—92no—
847C2×C4—188no—
848C2×C4—184no—
849C2×C4—184no—
850C2×C4—184no—
851C2×C4C22×D3214yes—
852C2×C4C22×D3211yescharacteristic
853C2×C4C22×D3211yescharacteristic
854C2×C4C22×D3211yescharacteristic
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—62no—
859C2×C3C2×#100711yescharacteristic
860C2×C3C2×#100711yescharacteristic
861C2×C3C2×D3×#4111yescharacteristic
862C2×C3C2×D3×#4111yescharacteristic
863C2×C3C2×#101011yescharacteristic
864C2×C3D3×2−1+411yescharacteristic
865D3—22no—
866D3—124no—
867D3—122no—
868D3—122no—
869C22—32no—
870C22—61no—
871C22—61no—
872C22—182no—
873C22—182no—
874C22—182no—
875C22C23×D3211yescharacteristic
876C4—24no—
877C4—21no—
878C4—61no—
879C4—62no—
880C4—61no—
881C4—62no—
882C4—64no—
883C4—61no—
884C4—62no—
885C4—62no—
886C4—94no—
887C4—182no—
888C4—182no—
889C4#6431212yes—
890C4#6431512yes—
891C3—21no—
892C3#8626611yescharacteristic, complemented
893C3#8702511yescharacteristic, complemented
894C2—62no—
895C2—362no—
896C2C2×#6431211yescharacteristic
897C2C2×#6431511yescharacteristic
898C2D3×#100711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radical#63909C22
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
1. #10596198C2semidirect
2. C3×#5728C2semidirect
3. C3×#5721C2semidirect
4. #10595379C2semidirect
5. #10595361C2semidirect
6. #10595354C2semidirect
7. #10595339C2semidirect
9. #10594408C2semidirect
10. #10594385C2semidirect
11. #10594350C2semidirect
12. #10594323C2semidirect
13. #10594322C2semidirect
14. C4×D3×Dic6C2semidirect
16. #10593865C2semidirect
17. #10593864C2semidirect
89. #5728D3semidirect
95. #5721D3semidirect
821. C32#3523semidirect
892. C3#86266semidirect
893. C3#87025semidirect

Maximal subgroups

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

subgroupindex
#105961982
C3×#57282
C3×#57212
#105953792
#105953612
#105953542
#105953392
#105944532
#105944082
#105943852
#105943502
#105943232
#105943222
C4×D3×Dic62
#105938702
#105938652
#105938642
#870253
#862663