Finite Group Databasebeta

← #11909909

Subgroups — #11909909

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#10596013C211yesmaximal, characteristic, complemented
2C3×#5557C211yesmaximal, characteristic
3C3×D4×Dic6C211yesmaximal, characteristic, complemented
4#10595273C212yesmaximal, complemented
5#10595172C212yesmaximal
6#10594942C212yesmaximal, complemented
7Dic6×#67C212yesmaximal, complemented
8#10594824C212yesmaximal, complemented
9#10594818C212yesmaximal, complemented
10#10594387C212yesmaximal, complemented
11#10594318C212yesmaximal, complemented
12#10594118C214yesmaximal, complemented
13#10594027C214yesmaximal, complemented
14C4×D3×Dic6C211yesmaximal, characteristic, complemented
15#10593861C211yesmaximal, characteristic, complemented
16#10593860C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86753—31nomaximal
19#86129—31nomaximal
20C22×C3×Dic6C2212yes—
21C2×D3×Dic6C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23#64145C2212yes—
24#64135C2212yes—
25#64133C2212yes—
26#64096C2212yes—
27#64088C2214yes—
28#64078C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C3×#938C2211yescharacteristic
31C3×#936C2211yescharacteristic
32C3×D4×Dic3C2212yes—
33C3×C4×#67C2212yes—
34C3×#926C2212yes—
35C3×#924C2212yes—
36C3×#897C2211yescharacteristic
37C3×#890C2211yescharacteristic
38C3×#888C2212yes—
39C3×#883C2212yes—
40C3×#879C2212yes—
41C3×#878C2214yes—
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46Dic3×#67C2214yes—
47#63969C2214yes—
48#63964C2214yes—
49#63956C2214yes—
50#63956C2214yes—
51#63956C2214yes—
52#63955C2214yes—
53#63955C2214yes—
54C4×#627C2212yes—
55D3×C4⋊Dic3C2211yescharacteristic
56#63887C2214yes—
57#63878C2214yes—
58D3×Dic3⋊C4C2212yes—
59C4×D3×Dic3C2212yes—
60#63872C2212yes—
61#63870C2214yes—
62#63869C2212yes—
63#63869C2212yes—
64#63866C2212yes—
65#63866C2212yes—
66#63857C2212yes—
67#63856C2212yes—
68#63847C2214yes—
69#63846C2214yes—
70#63846C2214yes—
71#63845C2214yes—
72#63844C2211yescharacteristic
73#63844C2212yes—
74#63844C2212yes—
75#63843C2214yes—
76#63843C2214yes—
77#63843C2212yes—
78Dic3×Dic6C2211yescharacteristic
79Dic3×Dic6C2212yes—
80Dic3×Dic6C2212yes—
81Dic3×Dic6C2212yes—
82#63841C2212yes—
83#63839C2214yes—
84#63837C2212yes—
85C3×D4×Q8—31no—
86C3×#529—31no—
87Q8×#67—32no—
88#5812—32no—
89#5728—32no—
90#5728—31no—
91#5721—32no—
92#5721—31no—
93#5701—34no—
94#5685—32no—
95#5671—32no—
96#5650—34no—
97#5639—32no—
98#5639—34no—
99#5625—32no—
100#5625—34no—
101#5622—32no—
102#5600—32no—
103C4×D3×Q8—31no—
104#5570—31no—
105#5570—31no—
106#5567—31no—
107#5557—32no—
108#5557D311yescharacteristic
109#5542—31no—
110#5542—31no—
111#5542—32no—
112#5542—61no—
113#5541—32no—
114D4×Dic6—32no—
115D4×Dic6D311yescharacteristic, complemented
116#5518—32no—
117#5516—32no—
118#5470—31no—
119C2×C4×Dic6—31no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C2×#634C2311yescharacteristic
123C2×#634C2312yes—
124C2×C3×#67C2312yes—
125C22×C3×Dic3C2314yes—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×Dic6—28no—
130C2×C3×Dic6C2314yes—
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×#627C2312yes—
135C2×D3×Dic3C2312yes—
136C2×D3×Dic3C2312yes—
137D3×Dic6—24no—
138C32×C4⋊C4C2311yescharacteristic
139C32×C22⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141#3757C2314yes—
142#3757C2314yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144C4⋊(C3⋊Dic3)C2312yes—
145C4⋊(C3⋊Dic3)C2312yes—
146#3750C2312yes—
147#3750C2314yes—
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2314yes—
150C3×#217C2314yes—
151C3×#217C2312yes—
152C3×#217C2312yes—
153C3×#217C2312yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4C2312yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2312yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2312yes—
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2312yes—
170#3724C2314yes—
171#3724C2314yes—
172#3724C2312yes—
173Dic3⋊Dic3C2312yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182Dic32C2312yes—
183Dic32C2312yes—
184Dic32C2314yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C22×C3×Q8—32no—
189C2×D3×Q8—31no—
190C22×Dic6—31no—
191C22×Dic6C2×D312yes—
192C3×C4⋊Q8—32no—
193C3×C4⋊Q8—31no—
194C3×#126—32no—
195C3×#125—31no—
196C3×#124—31no—
197C3×#123—32no—
198C3×C22⋊Q8—32no—
199C3×C22⋊Q8—31no—
200C3×C22⋊Q8—34no—
201C3×#121—31no—
202C3×C4×Q8—31no—
203C3×C4×Q8—31no—
204C3×C4×D4—21no—
205C3×C4×D4—32no—
206C3×C4×D4—32no—
207C3×C4×D4C2×D311yescharacteristic
208C3×C4×D4C2×D311yescharacteristic
209C3×#117—32no—
210C2×C3×C42—31no—
211#946—32no—
212#946—34no—
213Q8×Dic3—34no—
214Q8×Dic3—32no—
215Q8×Dic3—34no—
216Q8×Dic3—32no—
217Q8×Dic3—32no—
218Q8×Dic3—31no—
219Q8×Dic3—32no—
220#944—34no—
221#944—32no—
222#944—32no—
223#938C2×D311yescharacteristic
224#936—32no—
225#936—32no—
226#936—62no—
227#936C2×D311yescharacteristic
228#935—34no—
229D4×Dic3—34no—
230D4×Dic3C2×D312yes—
231C4×#67—34no—
232C4×#67C2×D312yes—
233#926—32no—
234#926—32no—
235#926—34no—
236#926—34no—
237#926—32no—
238#926—62no—
239#926C2×D312yes—
240C2×C4⋊Dic3—31no—
241#924—32no—
242#924—32no—
243#924—32no—
244#924—34no—
245#924—32no—
246#924—62no—
247#924C2×D312yes—
248C2×Dic3⋊C4—32no—
249C2×C4×Dic3—32no—
250#897—32no—
251#897C2×D311yescharacteristic
252#892—32no—
253#892—34no—
254D3×C4⋊C4—32no—
255D3×C4⋊C4—31no—
256#890—34no—
257#890—32no—
258#890—32no—
259#890—34no—
260#890—34no—
261#890—32no—
262#890—32no—
263#890C2×D311yescharacteristic
264#889—34no—
265#889—34no—
266#889—34no—
267#889—34no—
268#889—34no—
269#889—34no—
270#889—34no—
271#888—34no—
272#888C2×D312yes—
273#887—34no—
274#887—34no—
275#887—32no—
276#887—32no—
277#887—32no—
278#887—32no—
279#887—32no—
280#887—32no—
281#887—31no—
282#887—62no—
283#883—34no—
284#883C2×D312yes—
285#879—34no—
286#879—34no—
287#879—34no—
288#879—34no—
289#879—34no—
290#879—34no—
291#879—34no—
292#879—34no—
293#879—64no—
294#879C2×D312yes—
295#878—34no—
296#878—34no—
297#878C2×D314yes—
298#877—34no—
299#877—34no—
300#877—34no—
301C42×D3—32no—
302C42×D3C2×D311yescharacteristic
303#870—32no—
304#870—32no—
305#869—32no—
306#869—32no—
307#869—31no—
308#869—31no—
309#869—61no—
310#869C2×D311yescharacteristic
311C4×Dic6—31no—
312C4×Dic6—32no—
313C4×Dic6—32no—
314C4×Dic6—32no—
315C4×Dic6—31no—
316C4×Dic6—31no—
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—61no—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D311yescharacteristic
326C23×C32C2412yes—
327C22×C3×D3C2411yescharacteristic
328C32×D4—22no—
329C2×C32×C4—24no—
330C2×C32×C4C2411yescharacteristic
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2414yes—
336C2×C3⋊Dic3C2412yes—
337#634—22no—
338#634—24no—
339C3×#67—24no—
340C2×C3×Dic3—28no—
341C2×C3×Dic3C2411yescharacteristic
342C2×C3×Dic3C2411yescharacteristic
343C2×C3×Dic3C2414yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2412yes—
349C3×C4×D3—22no—
350C3×C4×D3—22no—
351C3×C4×D3—22no—
352C3×Dic6—24no—
353C3×Dic6—22no—
354C3×Dic6—28no—
355C3×Dic6#4114yes—
356#627—24no—
357D3×Dic3—24no—
358D3×Dic3—24no—
359#557—91no—
360#557—91no—
361#557—92no—
362#556—92no—
363#556—91no—
364#552—92no—
365#552—94no—
366D4×Q8—31no—
367D4×Q8—92no—
368#541—92no—
369#541—94no—
370#533—91no—
371#533—92no—
372#529—31no—
373#529—92no—
374#519—92no—
375C2×C4×Q8—91no—
376C2×C3×Q8—31no—
377C2×C3×Q8—31no—
378C2×C3×Q8—34no—
379C2×C3×Q8—32no—
380C2×C3×Q8—68no—
381C2×C3×D4—21no—
382C2×C3×D4—32no—
383C2×C3×D4C22×D311yescharacteristic
384C2×C3×D4C22×D311yescharacteristic
385C22×C3×C4—22no—
386C22×C3×C4—34no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4C22×D312yes—
391C22×C3×C4C22×D312yes—
392C2×#67C22×D312yes—
393C22×Dic3—32no—
394C22×Dic3—32no—
395C22×Dic3C22×D314yes—
396D3×Q8—64no—
397C2×C4×D3—32no—
398C2×C4×D3—32no—
399C2×C4×D3C22×D311yescharacteristic
400C2×C4×D3C22×D311yescharacteristic
401C2×C4×D3C22×D311yescharacteristic
402C2×Dic6—28no—
403C2×Dic6—31no—
404C2×Dic6—32no—
405C2×Dic6—32no—
406C2×Dic6—31no—
407C2×Dic6—32no—
408C2×Dic6—32no—
409C2×Dic6—61no—
410C2×Dic6—62no—
411C2×Dic6—64no—
412C2×Dic6C22×D312yes—
413C2×Dic6C22×D311yescharacteristic
414C2×Dic6C22×D314yes—
415C2×Dic6C22×D311yescharacteristic
416C3×C4⋊C4—21no—
417C3×C4⋊C4—32no—
418C3×C4⋊C4—32no—
419C3×C4⋊C4—31no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—32no—
422C3×C4⋊C4—31no—
423C3×C4⋊C4—32no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4C22×D311yescharacteristic
428C3×C4⋊C4C22×D311yescharacteristic
429C3×C22⋊C4—22no—
430C3×C22⋊C4—32no—
431C3×C22⋊C4—32no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—32no—
435C3×C22⋊C4C22×D312yes—
436C3×C22⋊C4C22×D312yes—
437C3×C42—21no—
438C3×C42—31no—
439C3×C42—31no—
440C3×C42—32no—
441C3×C42—32no—
442C3×C42—31no—
443C3×C42C22×D311yescharacteristic
444C3×C42C22×D311yescharacteristic
445#217—34no—
446#217—34no—
447#217—34no—
448#217—34no—
449#217—34no—
450#217—64no—
451#217—64no—
452#217C22×D314yes—
453#217C22×D312yes—
454#217C22×D312yes—
455#217C22×D312yes—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4C22×D312yes—
458C4⋊Dic3—31no—
459C4⋊Dic3—32no—
460C4⋊Dic3—31no—
461C4⋊Dic3—32no—
462C4⋊Dic3—32no—
463C4⋊Dic3—32no—
464C4⋊Dic3—32no—
465C4⋊Dic3—32no—
466C4⋊Dic3—34no—
467C4⋊Dic3—34no—
468C4⋊Dic3—34no—
469C4⋊Dic3—34no—
470C4⋊Dic3—34no—
471C4⋊Dic3—34no—
472C4⋊Dic3—61no—
473C4⋊Dic3—62no—
474C4⋊Dic3—62no—
475C4⋊Dic3C22×D311yescharacteristic
476C4⋊Dic3C22×D311yescharacteristic
477C4⋊Dic3C22×D312yes—
478C4⋊Dic3C22×D312yes—
479C4⋊Dic3C22×D312yes—
480C4⋊Dic3C22×D312yes—
481Dic3⋊C4—32no—
482Dic3⋊C4—32no—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—32no—
486Dic3⋊C4—32no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—32no—
492Dic3⋊C4—32no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—62no—
500Dic3⋊C4—64no—
501Dic3⋊C4C22×D312yes—
502Dic3⋊C4C22×D312yes—
503Dic3⋊C4C22×D314yes—
504Dic3⋊C4C22×D312yes—
505C4×Dic3—32no—
506C4×Dic3—32no—
507C4×Dic3—34no—
508C4×Dic3—34no—
509C4×Dic3—32no—
510C4×Dic3—34no—
511C4×Dic3—32no—
512C4×Dic3—34no—
513C4×Dic3—34no—
514C4×Dic3—34no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—34no—
518C4×Dic3—34no—
519C4×Dic3—62no—
520C4×Dic3—64no—
521C4×Dic3C22×D311yescharacteristic
522C4×Dic3C22×D312yes—
523C4×Dic3C22×D312yes—
524C4×Dic3C22×D311yescharacteristic
525C4×Dic3C22×D311yescharacteristic
526C22×C32—22no—
527C22×C32—22no—
528C22×C32—22no—
529C22×C32C2511yescharacteristic
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D32−1+412yes—
533C32×C4—22no—
534C32×C4—21no—
535C32×C4C2×#4112yes—
536C32×C42−1+412yes—
537C3⋊Dic3—22no—
538C3⋊Dic3—22no—
539C3⋊Dic3—24no—
540C3×Dic3—21no—
541C3×Dic3—24no—
542C3×Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—22no—
547C3×Dic3C2×#4114yes—
548C22×Q8—32no—
549C22×Q8—91no—
550C4⋊Q8—32no—
551C4⋊Q8—31no—
552C4⋊Q8—92no—
553C4⋊Q8—92no—
554C4⋊Q8—94no—
555C4⋊Q8—91no—
556#126—32no—
557#126—94no—
558#126—94no—
559#126—94no—
560#126—94no—
561#125—31no—
562#125—92no—
563#125—92no—
564#125—92no—
565#125—94no—
566#125—94no—
567#125—94no—
568#125—94no—
569#125—94no—
570#124—31no—
571#124—92no—
572#123—32no—
573#123—94no—
574C22⋊Q8—32no—
575C22⋊Q8—31no—
576C22⋊Q8—34no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—92no—
580C22⋊Q8—92no—
581C22⋊Q8—92no—
582#121—31no—
583C4×Q8—31no—
584C4×Q8—31no—
585C4×Q8—92no—
586C4×Q8—91no—
587C4×Q8—92no—
588C4×Q8—92no—
589C4×Q8—92no—
590C4×Q8—91no—
591C4×Q8—92no—
592C4×Q8—92no—
593C4×Q8—92no—
594C4×Q8—94no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—91no—
599C4×D4—32no—
600C4×D4—32no—
601C4×D4—94no—
602C4×D4D3211yescharacteristic
603#117—32no—
604#117—94no—
605#117—94no—
606#117—94no—
607#117—92no—
608#117—92no—
609C2×C4⋊C4—92no—
610C2×C4⋊C4—91no—
611C2×C42—31no—
612C2×C42—92no—
613C23×C3—22no—
614C23×C3—31no—
615C23×C3C23×D312yes—
616C23×C3C23×D312yes—
617C22×D3C23×D311yescharacteristic
618C3×Q8—34no—
619C3×Q8—68no—
620C3×Q8—62no—
621C3×Q8—64no—
622C3×D4—22no—
623C3×D4—22no—
624C3×D4—42no—
625C3×D4—64no—
626C2×C3×C4—24no—
627C2×C3×C4—24no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—22no—
631C2×C3×C4—21no—
632C2×C3×C4—32no—
633C2×C3×C4—31no—
634C2×C3×C4—31no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—34no—
638C2×C3×C4—32no—
639C2×C3×C4—31no—
640C2×C3×C4—44no—
641C2×C3×C4—62no—
642C2×C3×C4—68no—
643C2×C3×C4—62no—
644C2×C3×C4—62no—
645C2×C3×C4C23×D312yes—
646C2×C3×C4C23×D312yes—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653#67—24no—
654C2×Dic3—28no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—34no—
658C2×Dic3—34no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—64no—
664C2×Dic3—64no—
665C2×Dic3—64no—
666C2×Dic3C23×D311yescharacteristic
667C2×Dic3C23×D311yescharacteristic
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D314yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D311yescharacteristic
673C2×Dic3C23×D312yes—
674C4×D3—22no—
675C4×D3—22no—
676C4×D3—22no—
677C4×D3—64no—
678C4×D3—64no—
679Dic6—24no—
680Dic6—22no—
681Dic6—28no—
682Dic6—64no—
683Dic6—62no—
684Dic6—64no—
685Dic6—62no—
686Dic6—64no—
687Dic6—64no—
688Dic6—124no—
689Dic6—122no—
690Dic6#23714yes—
691C2×C32—42no—
692C2×C32C22×#4111yescharacteristic
693C2×C32C2×2−1+411yescharacteristic
694C2×C32C2×2−1+411yescharacteristic
695C3×D3—22no—
696C2×Q8—31no—
697C2×Q8—31no—
698C2×Q8—34no—
699C2×Q8—32no—
700C2×Q8—68no—
701C2×Q8—92no—
702C2×Q8—92no—
703C2×Q8—91no—
704C2×Q8—184no—
705C2×D4—32no—
706C2×D4C2×D3211yescharacteristic
707C22×C4—34no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—92no—
712C22×C4—92no—
713C22×C4C2×D3212yes—
714C4⋊C4—32no—
715C4⋊C4—31no—
716C4⋊C4—32no—
717C4⋊C4—32no—
718C4⋊C4—34no—
719C4⋊C4—32no—
720C4⋊C4—32no—
721C4⋊C4—32no—
722C4⋊C4—31no—
723C4⋊C4—32no—
724C4⋊C4—92no—
725C4⋊C4—92no—
726C4⋊C4—92no—
727C4⋊C4—94no—
728C4⋊C4—94no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—91no—
736C4⋊C4—92no—
737C4⋊C4—92no—
738C4⋊C4—92no—
739C4⋊C4—94no—
740C4⋊C4C2×D3211yescharacteristic
741C22⋊C4—32no—
742C22⋊C4—32no—
743C22⋊C4—34no—
744C22⋊C4—32no—
745C22⋊C4—32no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4C2×D3212yes—
750C42—31no—
751C42—31no—
752C42—31no—
753C42—32no—
754C42—32no—
755C42—92no—
756C42—92no—
757C42—94no—
758C42—94no—
759C42—94no—
760C42—92no—
761C42—94no—
762C42C2×D3211yescharacteristic
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—21no—
770C22×C3—32no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—61no—
775C22×C3—61no—
776C22×C3C24×D311yescharacteristic
777C22×C3C24×D311yescharacteristic
778C2×D3—21no—
779C2×D3—21no—
780C2×D3#101012yes—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—22no—
786C3×C4—22no—
787C3×C4—34no—
788C3×C4—42no—
789C3×C4—41no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—62no—
793C3×C4—64no—
794C3×C4—62no—
795C3×C4—61no—
796C3×C4—62no—
797C3×C4C2×#23712yes—
798C3×C4#100712yes—
799C3×C4D3×#4112yes—
800C3×C4#101012yes—
801Dic3—24no—
802Dic3—21no—
803Dic3—22no—
804Dic3—21no—
805Dic3—21no—
806Dic3—22no—
807Dic3—22no—
808Dic3—62no—
809Dic3—64no—
810Dic3—62no—
811Dic3—64no—
812Dic3—62no—
813Dic3—62no—
814Dic3—124no—
815Dic3—122no—
816Dic3—122no—
817Dic3C2×#23714yes—
818C32#352311yescharacteristic, complemented, Sylow
819C23—31no—
820C23C22×D3212yes—
821Q8—34no—
822Q8—68no—
823Q8—62no—
824Q8—64no—
825Q8—184no—
826Q8—184no—
827Q8—182no—
828D4—22no—
829D4—64no—
830C2×C4—24no—
831C2×C4—32no—
832C2×C4—31no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—34no—
839C2×C4—62no—
840C2×C4—68no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—92no—
844C2×C4—94no—
845C2×C4—92no—
846C2×C4—184no—
847C2×C4—184no—
848C2×C4C22×D3211yescharacteristic
849C2×C4C22×D3212yes—
850C2×C4C22×D3211yescharacteristic
851C2×C4C22×D3211yescharacteristic
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—42no—
856C2×C3—42no—
857C2×C3—62no—
858C2×C3—82no—
859C2×C3C22×#23711yescharacteristic
860C2×C3C2×#100711yescharacteristic
861C2×C3C2×D3×#4111yescharacteristic
862C2×C3C2×#101011yescharacteristic
863C2×C3C2×#101011yescharacteristic
864C2×C3D3×2−1+411yescharacteristic
865D3—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—32no—
870C22—61no—
871C22—61no—
872C22C23×D3211yescharacteristic
873C4—22no—
874C4—21no—
875C4—34no—
876C4—61no—
877C4—62no—
878C4—64no—
879C4—61no—
880C4—61no—
881C4—62no—
882C4—62no—
883C4—184no—
884C4—182no—
885C4—182no—
886C4#6429712yes—
887C4D3×#23712yes—
888C3—21no—
889C3#8612911yescharacteristic, complemented
890C3#8675311yescharacteristic, complemented
891C2—42no—
892C2—62no—
893C2C2×#6429711yescharacteristic
894C2C2×D3×#23711yescharacteristic
895C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC3×#938C22
hypercenterC4×D4D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596013C2semidirect
3. C3×D4×Dic6C2semidirect
4. #10595273C2semidirect
6. #10594942C2semidirect
7. Dic6×#67C2semidirect
8. #10594824C2semidirect
9. #10594818C2semidirect
10. #10594387C2semidirect
11. #10594318C2semidirect
12. #10594118C2semidirect
13. #10594027C2semidirect
14. C4×D3×Dic6C2semidirect
15. #10593861C2semidirect
16. #10593860C2semidirect
17. #10593859C2semidirect
115. D4×Dic6D3semidirect
818. C32#3523semidirect
889. C3#86129semidirect
890. C3#86753semidirect

Maximal subgroups

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

subgroupindex
#105960132
C3×#55572
C3×D4×Dic62
#105952732
#105951722
#105949422
Dic6×#672
#105948242
#105948182
#105943872
#105943182
#105941182
#105940272
C4×D3×Dic62
#105938612
#105938602
#105938592
#867533
#861293