Finite Group Databasebeta

← #11909924

Subgroups — #11909924

Order 1152.

2090 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5721C211yesmaximal, characteristic, complemented
4#10595422C212yesmaximal, complemented
5#10595387C212yesmaximal, complemented
6#10595376C212yesmaximal
7#10595368C212yesmaximal, complemented
8#10594457C212yesmaximal, complemented
9#10594412C214yesmaximal, complemented
10#10594383C212yesmaximal, complemented
11#10594355C212yesmaximal, complemented
12#10594347C212yesmaximal, complemented
13#10594320C214yesmaximal, complemented
14#10593903C211yesmaximal, characteristic, complemented
15C4×D3×Dic6C211yesmaximal, characteristic, complemented
16#10593870C211yesmaximal, characteristic
17#10593861C211yesmaximal, characteristic, complemented
18#87024—31nomaximal
19#86266—31nomaximal
20C2×#3797C2212yes—
21C2×D3×Dic6C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23#64156C2212yes—
24Q8×C3⋊Dic3C2212yes—
25#64107C2214yes—
26#64106C2212yes—
27#64101C2212yes—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C3×#946C2212yes—
31C3×Q8×Dic3C2212yes—
32C3×Q8×Dic3C2212yes—
33C3×#944C2212yes—
34C3×#897C2212yes—
35C3×#892C2212yes—
36C3×#890C2212yes—
37C3×#890C2212yes—
38C3×#889C2214yes—
39C3×#887C2212yes—
40C3×#887C2212yes—
41C3×C42×D3C2211yescharacteristic
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63918C2214yes—
46#63918C2212yes—
47C4×#627C2214yes—
48C4×#627C2212yes—
49#63909C2211yescharacteristic
50C4×#626C2212yes—
51#63895C2214yes—
52#63895C2214yes—
53#63894C2212yes—
54#63893C2214yes—
55#63890C2214yes—
56D3×C4⋊Dic3C2211yescharacteristic
57#63880C2214yes—
58#63878C2214yes—
59D3×Dic3⋊C4C2212yes—
60C4×D3×Dic3C2212yes—
61#63874C2212yes—
62#63872C2214yes—
63#63872C2212yes—
64#63871C2212yes—
65#63869C2214yes—
66#63869C2211yescharacteristic
67#63868C2212yes—
68#63868C2214yes—
69#63866C2212yes—
70#63864C2211yescharacteristic
71#63856C2211yescharacteristic
72#63850C2212yes—
73#63848C2214yes—
74#63848C2214yes—
75#63846C2214yes—
76#63845C2214yes—
77#63844C2211yescharacteristic
78#63843C2212yes—
79Dic3×Dic6C2211yescharacteristic
80Dic3×Dic6C2212yes—
81#63838C2214yes—
82#63837C2212yes—
83#63836C2214yes—
84#63836C2214yes—
85C3×#557—31no—
86C3×#533—31no—
87#5732—31no—
88#5732—31no—
89#5732—32no—
90#5732—61no—
91#5728—32no—
92#5728D311yescharacteristic, complemented
93#5727—31no—
94#5721—31no—
95#5721D311yescharacteristic, complemented
96#5698—34no—
97#5698—32no—
98#5696—34no—
99#5694—32no—
100#5694—34no—
101#5642—32no—
102#5632—32no—
103#5624—32no—
104#5622—32no—
105#5583—32no—
106#5580—32no—
107#5580—31no—
108Q8×D12—32no—
109Q8×D12—31no—
110#5572—32no—
111#5572—32no—
112C4×D3×Q8—31no—
113#5570—32no—
114#5570—31no—
115#5569—32no—
116#5568—32no—
117#5531—34no—
118#5479—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121C2×C4⋊(C3⋊D3)C2311yescharacteristic
122C2×C4×C3⋊D3C2312yes—
123C2×#634C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×Dic6C2312yes—
128C2×C3×Dic6C2311yescharacteristic
129C2×C3×Dic6C2311yescharacteristic
130C2×#627C2312yes—
131C2×#627C2314yes—
132C2×#626C2312yes—
133C2×#624C2314yes—
134C2×D3×Dic3C2312yes—
135C2×D3×Dic3C2312yes—
136#3797—28no—
137D3×Dic6—24no—
138C32×C4⋊C4C2312yes—
139C32×C4⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141#3752C2312yes—
142#3752C2314yes—
143#3752C2314yes—
144C4⋊(C3⋊Dic3)C2311yescharacteristic
145C4⋊(C3⋊Dic3)C2311yescharacteristic
146C4⋊(C3⋊Dic3)C2314yes—
147#3750C2312yes—
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×C4⋊Dic3C2314yes—
152C3×C4⋊Dic3C2311yescharacteristic
153C3×C4⋊Dic3C2312yes—
154C3×C4⋊Dic3C2314yes—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4⋊Dic3C2312yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2312yes—
160C3×Dic3⋊C4C2312yes—
161C3×Dic3⋊C4C2314yes—
162C3×C4×Dic3C2311yescharacteristic
163C3×C4×Dic3C2314yes—
164C3×C4×Dic3C2312yes—
165C3×C4×Dic3C2314yes—
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2311yescharacteristic
169#3724C2312yes—
170#3724C2312yes—
171#3724C2312yes—
172Dic3⋊Dic3C2312yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179#3722C2312yes—
180#3722C2312yes—
181#3722C2312yes—
182#3722C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184Dic32C2312yes—
185Dic32C2314yes—
186Dic32C2312yes—
187#3523—91noSylow
188C2×D3×Q8—31no—
189C2×D3×Q8—32no—
190C2×D3×Q8—32no—
191C22×Dic6—31no—
192C3×C4⋊Q8—21no—
193C3×C4⋊Q8—32no—
194C3×C4⋊Q8—31no—
195C3×C4⋊Q8C2×D311yescharacteristic
196C3×C4⋊Q8C2×D311yescharacteristic
197C3×#125—34no—
198C3×#125—32no—
199C3×#125—32no—
200C3×C22⋊Q8—32no—
201C3×C22⋊Q8—32no—
202C3×C4×Q8—32no—
203C3×C4×Q8—32no—
204C3×C4×Q8—32no—
205C3×C4×Q8—32no—
206C3×C4×Q8—31no—
207C3×C4×Q8—31no—
208C3×#117—32no—
209C2×C3×C42—31no—
210#947—32no—
211#947—32no—
212#947—31no—
213#947—62no—
214#946—31no—
215#946—32no—
216#946C2×D312yes—
217Q8×Dic3—32no—
218Q8×Dic3—32no—
219Q8×Dic3—32no—
220Q8×Dic3—32no—
221Q8×Dic3—31no—
222Q8×Dic3—62no—
223Q8×Dic3C2×D312yes—
224Q8×Dic3C2×D312yes—
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—34no—
241#898—32no—
242#898—64no—
243#897—32no—
244#897—32no—
245#897—32no—
246#897—34no—
247#897—34no—
248#897—34no—
249#897—62no—
250#897C2×D312yes—
251#896—34no—
252#896—34no—
253#895—31no—
254#894—32no—
255#894—34no—
256#893—32no—
257#892—32no—
258#892—32no—
259#892—34no—
260#892—34no—
261#892—34no—
262#892—62no—
263#892C2×D312yes—
264D3×C4⋊C4—32no—
265D3×C4⋊C4—31no—
266#890—34no—
267#890—34no—
268#890—34no—
269#890—32no—
270#890—32no—
271#890—34no—
272#890—34no—
273#890—31no—
274#890C2×D312yes—
275#890C2×D312yes—
276#889—34no—
277#889—34no—
278#889C2×D314yes—
279#888—34no—
280#888—32no—
281#887—32no—
282#887—34no—
283#887—34no—
284#887—32no—
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#875—31no—
295C4×D12—32no—
296C4×D12—31no—
297C4×D12—31no—
298C4×D12—34no—
299C4×D12—32no—
300C4×D12—61no—
301#872—34no—
302#872—34no—
303#872—32no—
304#872—32no—
305C42×D3—32no—
306C42×D3C2×D311yescharacteristic
307#870—31no—
308#870—34no—
309#869—32no—
310#869—34no—
311#869—32no—
312#869C2×D311yescharacteristic
313C4×Dic6—32no—
314C4×Dic6—31no—
315C4×Dic6—31no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—32no—
319C4×Dic6—34no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—34no—
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—
338#634—22no—
339C2×C3×Dic3C2411yescharacteristic
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2414yes—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C3×C4×D3—22no—
348C3×C4×D3—22no—
349C3×C4×D3—22no—
350C3×Dic6—24no—
351C3×Dic6—22no—
352C3×Dic6#4114yes—
353#627—24no—
354#627—28no—
355#626—24no—
356#624—28no—
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—68no—
389D3×Q8—64no—
390D3×Q8—68no—
391C2×D12—32no—
392C2×D12—31no—
393C2×D12—31no—
394C2×D12—61no—
395C2×C4×D3—32no—
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3—32no—
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—62no—
402C2×C4×D3C22×D311yescharacteristic
403C2×C4×D3C22×D311yescharacteristic
404C2×C4×D3C22×D311yescharacteristic
405C2×Dic6—31no—
406C2×Dic6—31no—
407C2×Dic6—32no—
408C2×Dic6—34no—
409C2×Dic6—32no—
410C2×Dic6—34no—
411C2×Dic6—61no—
412C2×Dic6—64no—
413C2×Dic6C22×D312yes—
414C2×Dic6C22×D311yescharacteristic
415C2×Dic6C22×D311yescharacteristic
416C3×C4⋊C4—22no—
417C3×C4⋊C4—22no—
418C3×C4⋊C4—32no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4—32no—
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⋊C4C22×D312yes—
430C3×C4⋊C4C22×D312yes—
431C3×C4⋊C4C22×D312yes—
432C3×C4⋊C4C22×D312yes—
433C3×C22⋊C4—34no—
434C3×C42—21no—
435C3×C42—31no—
436C3×C42—31no—
437C3×C42—31no—
438C3×C42—32no—
439C3×C42—34no—
440C3×C42—32no—
441C3×C42—34no—
442C3×C42C22×D311yescharacteristic
443C3×C42C22×D311yescharacteristic
444#217—32no—
445(C2×D3)⋊C4—32no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—32no—
449(C2×D3)⋊C4—32no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—32no—
453(C2×D3)⋊C4—32no—
454(C2×D3)⋊C4—32no—
455(C2×D3)⋊C4—32no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—32no—
458(C2×D3)⋊C4—32no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—62no—
461(C2×D3)⋊C4—64no—
462(C2×D3)⋊C4—64no—
463(C2×D3)⋊C4C22×D314yes—
464C4⋊Dic3—31no—
465C4⋊Dic3—31no—
466C4⋊Dic3—31no—
467C4⋊Dic3—34no—
468C4⋊Dic3—31no—
469C4⋊Dic3—34no—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—34no—
473C4⋊Dic3—34no—
474C4⋊Dic3—32no—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477C4⋊Dic3—61no—
478C4⋊Dic3—61no—
479C4⋊Dic3—64no—
480C4⋊Dic3C22×D311yescharacteristic
481C4⋊Dic3C22×D311yescharacteristic
482C4⋊Dic3C22×D312yes—
483C4⋊Dic3C22×D314yes—
484C4⋊Dic3C22×D312yes—
485C4⋊Dic3C22×D314yes—
486Dic3⋊C4—32no—
487Dic3⋊C4—32no—
488Dic3⋊C4—32no—
489Dic3⋊C4—32no—
490Dic3⋊C4—32no—
491Dic3⋊C4—34no—
492Dic3⋊C4—32no—
493Dic3⋊C4—32no—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—34no—
501Dic3⋊C4—62no—
502Dic3⋊C4C22×D312yes—
503Dic3⋊C4C22×D312yes—
504Dic3⋊C4C22×D314yes—
505Dic3⋊C4C22×D314yes—
506Dic3⋊C4C22×D314yes—
507C4×Dic3—32no—
508C4×Dic3—32no—
509C4×Dic3—34no—
510C4×Dic3—34no—
511C4×Dic3—32no—
512C4×Dic3—32no—
513C4×Dic3—34no—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—34no—
517C4×Dic3—62no—
518C4×Dic3—64no—
519C4×Dic3C22×D311yescharacteristic
520C4×Dic3C22×D312yes—
521C4×Dic3C22×D314yes—
522C4×Dic3C22×D314yes—
523C4×Dic3C22×D312yes—
524C4×Dic3C22×D311yescharacteristic
525C4×Dic3C22×D311yescharacteristic
526C22×C32C2511yescharacteristic
527C2×C3⋊D3—22no—
528C2×C3⋊D3—22no—
529C2×C3⋊D3—22no—
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D32−1+412yes—
533C32×C4—21no—
534C32×C4—24no—
535C32×C4C2×#4112yes—
536C32×C42−1+412yes—
537C3⋊Dic3—22no—
538C3⋊Dic3—22no—
539C3⋊Dic3—22no—
540C3×Dic3—24no—
541C3×Dic3—21no—
542C3×Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3C2×#4114yes—
548C22×Q8—91no—
549C22×Q8—92no—
550C4⋊Q8—32no—
551C4⋊Q8—31no—
552C4⋊Q8—92no—
553C4⋊Q8—94no—
554C4⋊Q8—92no—
555C4⋊Q8D3211yescharacteristic
556#126—92no—
557#126—94no—
558#126—94no—
559#126—94no—
560#126—94no—
561#125—32no—
562#125—34no—
563#125—32no—
564#125—91no—
565#125—94no—
566#125—92no—
567#125—94no—
568#125—94no—
569#125—94no—
570#124—91no—
571#124—92no—
572#123—94no—
573#123—92no—
574C22⋊Q8—32no—
575C22⋊Q8—32no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—92no—
580C22⋊Q8—91no—
581C22⋊Q8—92no—
582#121—91no—
583C4×Q8—32no—
584C4×Q8—32no—
585C4×Q8—32no—
586C4×Q8—32no—
587C4×Q8—31no—
588C4×Q8—31no—
589C4×Q8—92no—
590C4×Q8—94no—
591C4×Q8—91no—
592C4×Q8—92no—
593C4×Q8—91no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—91no—
599C4×D4—94no—
600C4×D4—92no—
601C4×D4—92no—
602C4×D4—91no—
603#117—32no—
604#117—92no—
605#117—94no—
606#117—94no—
607#117—94no—
608#117—92no—
609C2×C4⋊C4—92no—
610C2×C4⋊C4—91no—
611C2×C42—31no—
612C2×C42—92no—
613C23×C3—31no—
614C22×D3—32no—
615C22×D3—32no—
616C22×D3—62no—
617C22×D3C23×D311yescharacteristic
618C3×Q8—24no—
619C3×Q8—24no—
620C3×Q8—34no—
621C3×Q8—44no—
622C3×Q8—64no—
623C3×Q8—62no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—24no—
627C2×C3×C4—21no—
628C2×C3×C4—32no—
629C2×C3×C4—31no—
630C2×C3×C4—32no—
631C2×C3×C4—34no—
632C2×C3×C4—32no—
633C2×C3×C4—31no—
634C2×C3×C4—32no—
635C2×C3×C4—31no—
636C2×C3×C4—62no—
637C2×C3×C4—62no—
638C2×C3×C4—62no—
639C2×C3×C4C23×D314yes—
640C2×C3×C4C23×D314yes—
641C2×C3×C4C23×D311yescharacteristic
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647#67—64no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—64no—
658C2×Dic3—64no—
659C2×Dic3C23×D311yescharacteristic
660C2×Dic3C23×D312yes—
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D314yes—
663C2×Dic3C23×D311yescharacteristic
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D311yescharacteristic
666C2×Dic3C23×D312yes—
667D12—64no—
668D12—62no—
669D12—62no—
670D12—122no—
671C4×D3—22no—
672C4×D3—22no—
673C4×D3—22no—
674C4×D3—68no—
675C4×D3—64no—
676C4×D3—64no—
677C4×D3—64no—
678C4×D3—64no—
679C4×D3—68no—
680C4×D3—124no—
681Dic6—24no—
682Dic6—22no—
683Dic6—68no—
684Dic6—64no—
685Dic6—62no—
686Dic6—62no—
687Dic6—64no—
688Dic6—68no—
689Dic6—122no—
690Dic6#23914yes—
691C2×C32C22×#4111yescharacteristic
692C2×C32C2×2−1+411yescharacteristic
693C2×C32C2×2−1+411yescharacteristic
694C3⋊D3—42no—
695C3×D3—22no—
696C2×Q8—31no—
697C2×Q8—31no—
698C2×Q8—32no—
699C2×Q8—92no—
700C2×Q8—94no—
701C2×Q8—91no—
702C2×Q8—184no—
703C2×Q8—188no—
704C2×Q8C2×D3212yes—
705C2×D4—92no—
706C2×D4—91no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—94no—
711C22×C4—92no—
712C22×C4—92no—
713C22×C4—92no—
714C4⋊C4—32no—
715C4⋊C4—31no—
716C4⋊C4—32no—
717C4⋊C4—34no—
718C4⋊C4—34no—
719C4⋊C4—34no—
720C4⋊C4—32no—
721C4⋊C4—31no—
722C4⋊C4—34no—
723C4⋊C4—32no—
724C4⋊C4—34no—
725C4⋊C4—92no—
726C4⋊C4—92no—
727C4⋊C4—92no—
728C4⋊C4—92no—
729C4⋊C4—92no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C4⋊C4—92no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—91no—
736C4⋊C4—92no—
737C4⋊C4—91no—
738C4⋊C4—94no—
739C4⋊C4C2×D3212yes—
740C4⋊C4C2×D3212yes—
741C22⋊C4—34no—
742C22⋊C4—92no—
743C22⋊C4—92no—
744C22⋊C4—94no—
745C22⋊C4—92no—
746C22⋊C4—92no—
747C22⋊C4—94no—
748C22⋊C4—92no—
749C22⋊C4—94no—
750C42—31no—
751C42—31no—
752C42—31no—
753C42—32no—
754C42—34no—
755C42—34no—
756C42—32no—
757C42—92no—
758C42—92no—
759C42—94no—
760C42—92no—
761C42—94no—
762C42C2×D3211yescharacteristic
763C22×C3—21no—
764C22×C3—32no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3C24×D311yescharacteristic
768C22×C3C24×D311yescharacteristic
769C2×D3—21no—
770C2×D3—21no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—122no—
778C2×D3—122no—
779C2×D3—122no—
780C2×D3#100712yes—
781C3×C4—21no—
782C3×C4—24no—
783C3×C4—24no—
784C3×C4—21no—
785C3×C4—22no—
786C3×C4—22no—
787C3×C4—34no—
788C3×C4—44no—
789C3×C4—41no—
790C3×C4—61no—
791C3×C4—64no—
792C3×C4—62no—
793C3×C4—62no—
794C3×C4—61no—
795C3×C4—62no—
796C3×C4—61no—
797C3×C4C2×#23912yes—
798C3×C4D3×#4112yes—
799C3×C4#101012yes—
800C3×C4#101012yes—
801Dic3—21no—
802Dic3—24no—
803Dic3—21no—
804Dic3—22no—
805Dic3—21no—
806Dic3—22no—
807Dic3—22no—
808Dic3—62no—
809Dic3—62no—
810Dic3—62no—
811Dic3—62no—
812Dic3—62no—
813Dic3—62no—
814Dic3—122no—
815Dic3—122no—
816Dic3—122no—
817Dic3C2×#23914yes—
818C32#352311yescharacteristic, complemented, Sylow
819C23—31no—
820C23—92no—
821Q8—24no—
822Q8—34no—
823Q8—62no—
824Q8—64no—
825Q8—184no—
826Q8—188no—
827Q8—182no—
828D4—184no—
829D4—182no—
830C2×C4—32no—
831C2×C4—31no—
832C2×C4—32no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—32no—
836C2×C4—34no—
837C2×C4—32no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—92no—
842C2×C4—92no—
843C2×C4—92no—
844C2×C4—188no—
845C2×C4—184no—
846C2×C4—184no—
847C2×C4—184no—
848C2×C4C22×D3214yes—
849C2×C4C22×D3211yescharacteristic
850C2×C4C22×D3211yescharacteristic
851C2×C4C22×D3211yescharacteristic
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—62no—
856C2×C3C22×#23911yescharacteristic
857C2×C3C2×#100711yescharacteristic
858C2×C3C2×D3×#4111yescharacteristic
859C2×C3C2×#101011yescharacteristic
860C2×C3C2×#101011yescharacteristic
861C2×C3D3×2−1+411yescharacteristic
862D3—22no—
863D3—122no—
864D3—122no—
865D3—242no—
866C22—32no—
867C22—61no—
868C22—61no—
869C22—182no—
870C22—182no—
871C22—182no—
872C22C23×D3211yescharacteristic
873C4—24no—
874C4—21no—
875C4—34no—
876C4—61no—
877C4—62no—
878C4—61no—
879C4—64no—
880C4—61no—
881C4—62no—
882C4—62no—
883C4—182no—
884C4—182no—
885C4—182no—
886C4#6430912yes—
887C4D3×#23912yes—
888C3—21no—
889C3#8626611yescharacteristic, complemented
890C3#8702411yescharacteristic, complemented
891C2—62no—
892C2—362no—
893C2C2×#6430911yescharacteristic
894C2C2×D3×#23911yescharacteristic
895C2D3×#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. #10596203C2semidirect
2. C3×#5728C2semidirect
3. C3×#5721C2semidirect
4. #10595422C2semidirect
5. #10595387C2semidirect
7. #10595368C2semidirect
8. #10594457C2semidirect
9. #10594412C2semidirect
10. #10594383C2semidirect
11. #10594355C2semidirect
12. #10594347C2semidirect
13. #10594320C2semidirect
14. #10593903C2semidirect
15. C4×D3×Dic6C2semidirect
17. #10593861C2semidirect
92. #5728D3semidirect
95. #5721D3semidirect
818. C32#3523semidirect
889. C3#86266semidirect
890. C3#87024semidirect

Maximal subgroups

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

subgroupindex
#105962032
C3×#57282
C3×#57212
#105954222
#105953872
#105953762
#105953682
#105944572
#105944122
#105943832
#105943552
#105943472
#105943202
#105939032
C4×D3×Dic62
#105938702
#105938612
#870243
#862663