Finite Group Databasebeta

← #11906273

Subgroups — #11906273

Order 1152.

2034 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#634C211yesmaximal, characteristic, complemented
2C3×#5578C211yesmaximal, characteristic
3C3×#5567C211yesmaximal, characteristic, complemented
4#10595368C212yesmaximal
5#10595338C212yesmaximal, complemented
6#10594390C214yesmaximal
7#10594385C212yesmaximal
8#10594315C214yesmaximal, complemented
9#10594312C212yesmaximal, complemented
10#10593959C212yesmaximal
11#10593885C212yesmaximal
12C4×D3×Dic6C211yesmaximal, characteristic
13#10593864C211yesmaximal, characteristic, complemented
14#10593860C212yesmaximal, complemented
15#10593859C211yesmaximal, characteristic
16Dic62C211yesmaximal, characteristic, complemented
17#10593852C212yesmaximal, complemented
18#87031—31nomaximal
19#86258—31nomaximal
20C2×D3×Dic6C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22Q8×C3⋊Dic3C2212yes—
23#64097C2212yes—
24#64097C2214yes—
25#64078C2211yescharacteristic
26#64078C2212yes—
27C4×#634C2212yes—
28C4×#634C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C3×#944C2211yescharacteristic
31C3×#944C2212yes—
32C3×#897C2211yescharacteristic
33C3×#896C2212yes—
34C3×#889C2212yes—
35C3×#889C2214yes—
36C3×#888C2211yescharacteristic
37C3×#887C2212yes—
38C3×#872C2212yes—
39C3×C42×D3C2211yescharacteristic
40C3×#870C2212yes—
41C3×#869C2211yescharacteristic
42C3×C4×Dic6C2212yes—
43C3×C4×Dic6C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2212yes—
46#63918C2212yes—
47#63918C2212yes—
48C4×#627C2212yes—
49#63896C2214yes—
50#63893C2214yes—
51D3×C4⋊Dic3C2211yescharacteristic
52#63878C2214yes—
53#63877C2214yes—
54D3×Dic3⋊C4C2212yes—
55C4×D3×Dic3C2212yes—
56#63873C2212yes—
57#63870C2214yes—
58#63869C2212yes—
59#63869C2212yes—
60#63866C2214yes—
61#63857C2212yes—
62#63856C2212yes—
63#63847C2214yes—
64#63847C2214yes—
65#63845C2214yes—
66#63845C2214yes—
67#63845C2214yes—
68#63844C2212yes—
69#63844C2214yes—
70#63844C2211yescharacteristic
71#63844C2212yes—
72#63843C2212yes—
73Dic3×Dic6C2212yes—
74Dic3×Dic6C2212yes—
75Dic3×Dic6C2212yes—
76Dic3×Dic6C2211yescharacteristic
77#63841C2212yes—
78#63840C2214yes—
79#63840C2214yes—
80#63839C2214yes—
81#63838C2214yes—
82#63838C2214yes—
83#63837C2214yes—
84#63837C2212yes—
85C3×#557—31no—
86C3×#533—31no—
87#5728—32no—
88#5728—31no—
89#5722—32no—
90#5721—32no—
91#5721—32no—
92#5721—31no—
93#5689—34no—
94#5689—32no—
95#5685—34no—
96#5685—34no—
97#5685—32no—
98#5623—34no—
99#5622—32no—
100#5622—32no—
101#5578—32no—
102#5578D311yescharacteristic
103#5572—32no—
104C4×D3×Q8—31no—
105#5570—32no—
106#5567—32no—
107#5567—31no—
108#5567—32no—
109#5567D311yescharacteristic, complemented
110Q8×Dic6—31no—
111Q8×Dic6—31no—
112Q8×Dic6—32no—
113Q8×Dic6—31no—
114Q8×Dic6—31no—
115Q8×Dic6—61no—
116#5519—32no—
117#5516—32no—
118#5470—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×#634C2312yes—
122C2×#634C2314yes—
123C2×#634C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×Dic6C2312yes—
128C2×C3×Dic6C2311yescharacteristic
129C2×C3×Dic6C2312yes—
130C2×C3×Dic6C2311yescharacteristic
131C2×#627C2314yes—
132C2×#627C2312yes—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2312yes—
135D3×Dic6Q818yescomplemented
136C32×C4⋊C4C2311yescharacteristic
137C32×C4⋊C4C2312yes—
138C32×C42C2311yescharacteristic
139C32×C42C2312yes—
140C4⋊(C3⋊Dic3)C2312yes—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2314yes—
144#3750C2314yes—
145#3750C2312yes—
146C4×C3⋊Dic3C2314yes—
147C4×C3⋊Dic3C2312yes—
148C3×(C2×D3)⋊C4C2312yes—
149C3×(C2×D3)⋊C4C2312yes—
150C3×C4⋊Dic3C2311yescharacteristic
151C3×C4⋊Dic3C2312yes—
152C3×C4⋊Dic3C2312yes—
153C3×C4⋊Dic3C2312yes—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2312yes—
157C3×Dic3⋊C4C2312yes—
158C3×Dic3⋊C4C2312yes—
159C3×Dic3⋊C4C2312yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2312yes—
164C3×C4×Dic3C2314yes—
165C3×C4×Dic3C2312yes—
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2312yes—
170#3724C2314yes—
171#3724C2314yes—
172#3724C2312yes—
173#3724C2314yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180(C2×D3)⋊Dic3C2314yes—
181Dic32C2312yes—
182Dic32C2314yes—
183Dic32C2314yes—
184Dic32C2312yes—
185Dic32C2314yes—
186#3502—91noSylow
187C2×D3×Q8—31no—
188C22×Dic6—31no—
189C3×C4⋊Q8—31no—
190C3×C4⋊Q8—32no—
191C3×C4⋊Q8—31no—
192C3×C4⋊Q8—31no—
193C3×#125—32no—
194C3×#125—34no—
195C3×#125—32no—
196C3×C22⋊Q8—31no—
197C3×C22⋊Q8—32no—
198C3×C22⋊Q8—31no—
199C3×C4×Q8—21no—
200C3×C4×Q8—32no—
201C3×C4×Q8—31no—
202C3×C4×Q8—31no—
203C3×C4×Q8—32no—
204C3×C4×Q8—32no—
205C3×C4×Q8C2×D311yescharacteristic
206C3×C4×Q8C2×D311yescharacteristic
207C3×#117—32no—
208C2×C3×C42—31no—
209#946—32no—
210#946C2×D311yescharacteristic
211Q8×Dic3—32no—
212Q8×Dic3—32no—
213Q8×Dic3—32no—
214Q8×Dic3—32no—
215Q8×Dic3—32no—
216Q8×Dic3—32no—
217Q8×Dic3—31no—
218Q8×Dic3—62no—
219#944—32no—
220#944—32no—
221#944—34no—
222#944—34no—
223#944C2×D311yescharacteristic
224#944C2×D312yes—
225#926—32no—
226C2×C4⋊Dic3—31no—
227#924—32no—
228#924—32no—
229C2×Dic3⋊C4—32no—
230C2×C4×Dic3—32no—
231#897—32no—
232#897—34no—
233#897C2×D311yescharacteristic
234#896—34no—
235#896C2×D312yes—
236#892—32no—
237#892—34no—
238D3×C4⋊C4—32no—
239D3×C4⋊C4—31no—
240#890—34no—
241#890—34no—
242#890—34no—
243#890—32no—
244#890—32no—
245#889—34no—
246#889—34no—
247#889—34no—
248#889—34no—
249#889—34no—
250#889—34no—
251#889—34no—
252#889—34no—
253#889—34no—
254#889C2×D312yes—
255#889C2×D314yes—
256#888—34no—
257#888—34no—
258#888—34no—
259#888—32no—
260#888—32no—
261#888—34no—
262#888—34no—
263#888—34no—
264#888—34no—
265#888—32no—
266#888—32no—
267#888—62no—
268#888—64no—
269#888C2×D311yescharacteristic
270#887—32no—
271#887—34no—
272#887—34no—
273#887—34no—
274#887—34no—
275#887—32no—
276#887—32no—
277#887—31no—
278#887—32no—
279#887—34no—
280#887—34no—
281#887C2×D312yes—
282#878—34no—
283#878—34no—
284#877—34no—
285#877—34no—
286#872—34no—
287#872C2×D312yes—
288C42×D3—32no—
289C42×D3C2×D311yescharacteristic
290#870—32no—
291#870—32no—
292#870C2×D312yes—
293#869—34no—
294#869—32no—
295#869—31no—
296#869—31no—
297#869—32no—
298#869—32no—
299#869—32no—
300#869—61no—
301#869—62no—
302#869C2×D311yescharacteristic
303C4×Dic6—32no—
304C4×Dic6—32no—
305C4×Dic6—31no—
306C4×Dic6—32no—
307C4×Dic6—32no—
308C4×Dic6—31no—
309C4×Dic6—31no—
310C4×Dic6—32no—
311C4×Dic6—32no—
312C4×Dic6—34no—
313C4×Dic6—31no—
314C4×Dic6—32no—
315C4×Dic6—32no—
316C4×Dic6—34no—
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—61no—
320C4×Dic6—62no—
321C4×Dic6C2×D312yes—
322C4×Dic6C2×D311yescharacteristic
323C4×Dic6C2×D311yescharacteristic
324C4×Dic6C2×D312yes—
325C22×C3×D3C2411yescharacteristic
326C32×Q8—22no—
327C2×C32×C4C2412yes—
328C2×C32×C4C2411yescharacteristic
329C2×C32×C4C2412yes—
330C2×C32×C4C2411yescharacteristic
331C2×C32×C4C2411yescharacteristic
332C2×C3⋊Dic3C2414yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335#634—44no—
336#634—42no—
337#634C2×Q814yes—
338C2×C3×Dic3C2411yescharacteristic
339C2×C3×Dic3C2414yes—
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2412yes—
346C3×C4×D3—22no—
347C3×C4×D3—41no—
348C3×C4×D3C2×Q814yes—
349C3×Dic6—24no—
350C3×Dic6—22no—
351C3×Dic6—42no—
352C3×Dic6C2×Q814yes—
353#627—44no—
354#627C2×Q818yes—
355D3×Dic3—42no—
356D3×Dic3C2×Q818yes—
357Q82—91no—
358Q82—92no—
359Q82—91no—
360#557—31no—
361#557—92no—
362#557—92no—
363#557—91no—
364#557—94no—
365#557—92no—
366#544—92no—
367#544—94no—
368#533—31no—
369#533—91no—
370#533—92no—
371#533—92no—
372#519—92no—
373C2×C4×Q8—91no—
374C2×C3×Q8—21no—
375C2×C3×Q8—31no—
376C2×C3×Q8—31no—
377C2×C3×Q8—32no—
378C2×C3×Q8—32no—
379C2×C3×Q8C22×D311yescharacteristic
380C2×C3×Q8C22×D311yescharacteristic
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×Dic3—32no—
385C22×Dic3—32no—
386D3×Q8—38no—
387C2×C4×D3—32no—
388C2×C4×D3—32no—
389C2×C4×D3C22×D311yescharacteristic
390C2×C4×D3C22×D311yescharacteristic
391C2×C4×D3C22×D311yescharacteristic
392C2×Dic6—31no—
393C2×Dic6—31no—
394C2×Dic6—32no—
395C2×Dic6—32no—
396C2×Dic6—38no—
397C2×Dic6—34no—
398C2×Dic6—32no—
399C2×Dic6—34no—
400C2×Dic6—32no—
401C2×Dic6—34no—
402C2×Dic6—34no—
403C2×Dic6—61no—
404C2×Dic6—62no—
405C2×Dic6—64no—
406C2×Dic6C22×D311yescharacteristic
407C2×Dic6C22×D312yes—
408C2×Dic6C22×D312yes—
409C2×Dic6C22×D311yescharacteristic
410C3×C4⋊C4—21no—
411C3×C4⋊C4—22no—
412C3×C4⋊C4—32no—
413C3×C4⋊C4—31no—
414C3×C4⋊C4—32no—
415C3×C4⋊C4—32no—
416C3×C4⋊C4—32no—
417C3×C4⋊C4—32no—
418C3×C4⋊C4—31no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—34no—
422C3×C4⋊C4—32no—
423C3×C4⋊C4—32no—
424C3×C4⋊C4—34no—
425C3×C4⋊C4—32no—
426C3×C4⋊C4C22×D311yescharacteristic
427C3×C4⋊C4C22×D311yescharacteristic
428C3×C4⋊C4C22×D312yes—
429C3×C4⋊C4C22×D312yes—
430C3×C22⋊C4—32no—
431C3×C22⋊C4—32no—
432C3×C42—21no—
433C3×C42—22no—
434C3×C42—31no—
435C3×C42—31no—
436C3×C42—32no—
437C3×C42—32no—
438C3×C42—34no—
439C3×C42—31no—
440C3×C42C22×D311yescharacteristic
441C3×C42C22×D312yes—
442C3×C42C22×D311yescharacteristic
443C3×C42C22×D312yes—
444#217—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4C22×D312yes—
447(C2×D3)⋊C4C22×D312yes—
448C4⋊Dic3—32no—
449C4⋊Dic3—31no—
450C4⋊Dic3—32no—
451C4⋊Dic3—32no—
452C4⋊Dic3—31no—
453C4⋊Dic3—32no—
454C4⋊Dic3—34no—
455C4⋊Dic3—34no—
456C4⋊Dic3—32no—
457C4⋊Dic3—34no—
458C4⋊Dic3—32no—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—61no—
463C4⋊Dic3—62no—
464C4⋊Dic3—62no—
465C4⋊Dic3—64no—
466C4⋊Dic3C22×D312yes—
467C4⋊Dic3C22×D311yescharacteristic
468C4⋊Dic3C22×D312yes—
469C4⋊Dic3C22×D312yes—
470C4⋊Dic3C22×D311yescharacteristic
471Dic3⋊C4—34no—
472Dic3⋊C4—32no—
473Dic3⋊C4—34no—
474Dic3⋊C4—32no—
475Dic3⋊C4—32no—
476Dic3⋊C4—32no—
477Dic3⋊C4—34no—
478Dic3⋊C4—34no—
479Dic3⋊C4—34no—
480Dic3⋊C4—34no—
481Dic3⋊C4—34no—
482Dic3⋊C4—32no—
483Dic3⋊C4—32no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—62no—
490Dic3⋊C4—64no—
491Dic3⋊C4C22×D312yes—
492Dic3⋊C4C22×D312yes—
493Dic3⋊C4C22×D314yes—
494Dic3⋊C4C22×D312yes—
495Dic3⋊C4C22×D312yes—
496Dic3⋊C4C22×D312yes—
497Dic3⋊C4C22×D314yes—
498Dic3⋊C4C22×D314yes—
499Dic3⋊C4C22×D312yes—
500C4×Dic3—32no—
501C4×Dic3—32no—
502C4×Dic3—34no—
503C4×Dic3—34no—
504C4×Dic3—32no—
505C4×Dic3—34no—
506C4×Dic3—34no—
507C4×Dic3—32no—
508C4×Dic3—32no—
509C4×Dic3—34no—
510C4×Dic3—34no—
511C4×Dic3—34no—
512C4×Dic3—34no—
513C4×Dic3—32no—
514C4×Dic3—62no—
515C4×Dic3—64no—
516C4×Dic3C22×D311yescharacteristic
517C4×Dic3C22×D312yes—
518C4×Dic3C22×D311yescharacteristic
519C4×Dic3C22×D312yes—
520C4×Dic3C22×D314yes—
521C4×Dic3C22×D311yescharacteristic
522C22×C32C2511yescharacteristic
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3C22×Q812yes—
526C32×C4—22no—
527C32×C4—22no—
528C32×C4—21no—
529C32×C4C22×Q812yes—
530C32×C42−1+412yes—
531C3⋊Dic3—22no—
532C3⋊Dic3—24no—
533C3⋊Dic3C22×Q814yes—
534C3×Dic3—24no—
535C3×Dic3—22no—
536C3×Dic3—21no—
537C3×Dic3—22no—
538C3×Dic3—22no—
539C3×Dic3—21no—
540C3×Dic3C22×Q814yes—
541C3×Dic3C22×Q812yes—
542C22×Q8—91no—
543C4⋊Q8—31no—
544C4⋊Q8—32no—
545C4⋊Q8—31no—
546C4⋊Q8—31no—
547C4⋊Q8—92no—
548C4⋊Q8—92no—
549C4⋊Q8—94no—
550C4⋊Q8—94no—
551C4⋊Q8—94no—
552C4⋊Q8—94no—
553C4⋊Q8—92no—
554C4⋊Q8—92no—
555C4⋊Q8—94no—
556C4⋊Q8—91no—
557C4⋊Q8—92no—
558#125—32no—
559#125—34no—
560#125—32no—
561#125—92no—
562#125—92no—
563#125—94no—
564#125—94no—
565#125—94no—
566#125—94no—
567#125—94no—
568#125—94no—
569C22⋊Q8—31no—
570C22⋊Q8—31no—
571C22⋊Q8—32no—
572C22⋊Q8—94no—
573C22⋊Q8—94no—
574C22⋊Q8—92no—
575C22⋊Q8—92no—
576C4×Q8—32no—
577C4×Q8—31no—
578C4×Q8—32no—
579C4×Q8—32no—
580C4×Q8—31no—
581C4×Q8—92no—
582C4×Q8—91no—
583C4×Q8—92no—
584C4×Q8—92no—
585C4×Q8—94no—
586C4×Q8—92no—
587C4×Q8—94no—
588C4×Q8—91no—
589C4×Q8—92no—
590C4×Q8—92no—
591C4×Q8—92no—
592C4×Q8—94no—
593C4×Q8—94no—
594C4×Q8—92no—
595C4×Q8—92no—
596C4×Q8—91no—
597C4×Q8—92no—
598C4×Q8D3211yescharacteristic
599#117—32no—
600#117—94no—
601#117—94no—
602#117—92no—
603C2×C4⋊C4—92no—
604C2×C4⋊C4—91no—
605C2×C42—31no—
606C2×C42—92no—
607C23×C3—31no—
608C22×D3C23×D311yescharacteristic
609C3×Q8—24no—
610C3×Q8—22no—
611C3×Q8—22no—
612C3×Q8—34no—
613C3×Q8—62no—
614C3×Q8—64no—
615C3×Q8—122no—
616C2×C3×C4—22no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—22no—
620C2×C3×C4—21no—
621C2×C3×C4—31no—
622C2×C3×C4—32no—
623C2×C3×C4—34no—
624C2×C3×C4—31no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—34no—
628C2×C3×C4—32no—
629C2×C3×C4—31no—
630C2×C3×C4—62no—
631C2×C3×C4—121no—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D312yes—
634C2×C3×C4C23×D312yes—
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D312yes—
638C2×C3×C4C23×D311yescharacteristic
639C2×C3×C4C23×D311yescharacteristic
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D311yescharacteristic
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—38no—
645C2×Dic3—34no—
646C2×Dic3—34no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—62no—
650C2×Dic3—64no—
651C2×Dic3—62no—
652C2×Dic3—122no—
653C2×Dic3C23×D311yescharacteristic
654C2×Dic3C23×D312yes—
655C2×Dic3C23×D314yes—
656C2×Dic3C23×D312yes—
657C2×Dic3C23×D312yes—
658C2×Dic3C23×D311yescharacteristic
659C2×Dic3C23×D311yescharacteristic
660C2×Dic3C23×D312yes—
661C4×D3—22no—
662C4×D3—38no—
663C4×D3—41no—
664C4×D3—122no—
665C4×D3D3×Q814yes—
666Dic6—24no—
667Dic6—22no—
668Dic6—34no—
669Dic6—34no—
670Dic6—38no—
671Dic6—38no—
672Dic6—42no—
673Dic6—64no—
674Dic6—124no—
675Dic6—124no—
676Dic6—122no—
677Dic6—124no—
678Dic6—122no—
679Dic6—124no—
680Dic6—242no—
681Dic6—244no—
682Dic6D3×Q814yes—
683C2×C32C23×Q811yescharacteristic
684C2×C32C2×2−1+411yescharacteristic
685C2×C32#58511yescharacteristic
686C3×D3—22no—
687C2×Q8—31no—
688C2×Q8—31no—
689C2×Q8—32no—
690C2×Q8—32no—
691C2×Q8—92no—
692C2×Q8—94no—
693C2×Q8—98no—
694C2×Q8—91no—
695C2×Q8—92no—
696C2×Q8—94no—
697C2×Q8C2×D3211yescharacteristic
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—92no—
702C22×C4—92no—
703C4⋊C4—32no—
704C4⋊C4—31no—
705C4⋊C4—32no—
706C4⋊C4—32no—
707C4⋊C4—34no—
708C4⋊C4—32no—
709C4⋊C4—32no—
710C4⋊C4—32no—
711C4⋊C4—31no—
712C4⋊C4—32no—
713C4⋊C4—32no—
714C4⋊C4—34no—
715C4⋊C4—34no—
716C4⋊C4—32no—
717C4⋊C4—92no—
718C4⋊C4—92no—
719C4⋊C4—92no—
720C4⋊C4—94no—
721C4⋊C4—94no—
722C4⋊C4—94no—
723C4⋊C4—94no—
724C4⋊C4—94no—
725C4⋊C4—94no—
726C4⋊C4—94no—
727C4⋊C4—92no—
728C4⋊C4—91no—
729C4⋊C4—94no—
730C4⋊C4—92no—
731C4⋊C4—92no—
732C4⋊C4—94no—
733C4⋊C4C2×D3211yescharacteristic
734C4⋊C4C2×D3212yes—
735C22⋊C4—32no—
736C22⋊C4—32no—
737C22⋊C4—94no—
738C42—31no—
739C42—31no—
740C42—31no—
741C42—32no—
742C42—32no—
743C42—34no—
744C42—92no—
745C42—92no—
746C42—94no—
747C42—94no—
748C42—94no—
749C42—92no—
750C42—94no—
751C42C2×D3211yescharacteristic
752C42C2×D3212yes—
753C22×C3—21no—
754C22×C3—32no—
755C22×C3—61no—
756C22×C3—61no—
757C22×C3C24×D311yescharacteristic
758C22×C3C24×D311yescharacteristic
759C2×D3—21no—
760C2×D3—21no—
761C2×D3C2×D3×Q812yes—
762C3×C4—24no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—32no—
772C3×C4—34no—
773C3×C4—41no—
774C3×C4—42no—
775C3×C4—61no—
776C3×C4—64no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—62no—
780C3×C4—61no—
781C3×C4C2×D3×Q812yes—
782C3×C4C2×D3×Q812yes—
783C3×C4#101012yes—
784C3×C4#101012yes—
785Dic3—22no—
786Dic3—24no—
787Dic3—21no—
788Dic3—21no—
789Dic3—22no—
790Dic3—22no—
791Dic3—34no—
792Dic3—34no—
793Dic3—64no—
794Dic3—64no—
795Dic3—62no—
796Dic3—64no—
797Dic3—62no—
798Dic3—122no—
799Dic3—124no—
800Dic3C2×D3×Q812yes—
801Dic3C2×D3×Q814yes—
802C32#350211yescharacteristic, complemented, Sylow
803C23—31no—
804Q8—22no—
805Q8—34no—
806Q8—62no—
807Q8—64no—
808Q8—98no—
809Q8—94no—
810Q8—122no—
811Q8—362no—
812Q8—364no—
813Q8—364no—
814C2×C4—32no—
815C2×C4—31no—
816C2×C4—34no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—34no—
822C2×C4—32no—
823C2×C4—62no—
824C2×C4—98no—
825C2×C4—92no—
826C2×C4—94no—
827C2×C4—92no—
828C2×C4—121no—
829C2×C4—362no—
830C2×C4C22×D3212yes—
831C2×C4C22×D3211yescharacteristic
832C2×C4C22×D3212yes—
833C2×C4C22×D3211yescharacteristic
834C2×C4C22×D3211yescharacteristic
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—62no—
839C2×C3C22×D3×Q811yescharacteristic
840C2×C3C22×D3×Q811yescharacteristic
841C2×C3C2×#101011yescharacteristic
842C2×C3C2×#101011yescharacteristic
843C2×C3#596411yescharacteristic
844C2×C3#596811yescharacteristic
845D3—22no—
846C22—32no—
847C22—61no—
848C22—61no—
849C22C23×D3211yescharacteristic
850C4—22no—
851C4—21no—
852C4—22no—
853C4—32no—
854C4—34no—
855C4—61no—
856C4—62no—
857C4—64no—
858C4—61no—
859C4—62no—
860C4—62no—
861C4—94no—
862C4—182no—
863C4—184no—
864C4#6429812yes—
865C4D32×Q812yes—
866C3—21no—
867C3#8625811yescharacteristic, complemented
868C3#8703111yescharacteristic, complemented
869C2—62no—
870C2C2×#6429811yescharacteristic
871C2C2×D32×Q811yescharacteristic
872C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC22×C3×D3C24
hypercenterC4×Q8D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#634C2semidirect
3. C3×#5567C2semidirect
5. #10595338C2semidirect
8. #10594315C2semidirect
9. #10594312C2semidirect
13. #10593864C2semidirect
14. #10593860C2semidirect
16. Dic62C2semidirect
17. #10593852C2semidirect
109. #5567D3semidirect
135. D3×Dic6Q8semidirect
802. C32#3502semidirect
867. C3#86258semidirect
868. C3#87031semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
C3×#55782
C3×#55672
#105953682
#105953382
#105943902
#105943852
#105943152
#105943122
#105939592
#105938852
C4×D3×Dic62
#105938642
#105938602
#105938592
Dic622
#105938522
#870313
#862583