Finite Group Databasebeta

← #11906272

Subgroups — #11906272

Order 1152.

2039 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596049C211yesmaximal, characteristic
2C3×#5567C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595420C212yesmaximal, complemented
5#10595374C212yesmaximal
6#10594400C214yesmaximal
7#10594397C212yesmaximal
8#10594314C214yesmaximal, complemented
9#10594312C212yesmaximal, complemented
10C4×#3797C211yesmaximal, characteristic
11#10593866C211yesmaximal, characteristic
12#10593861C212yesmaximal, complemented
13#10593861C211yesmaximal, characteristic, complemented
14#10593856C211yesmaximal, characteristic, complemented
15#10593855C212yesmaximal
16#10593853C212yesmaximal, complemented
17#10593848C212yesmaximal
18#87046—31nomaximal
19#87031—31nomaximal
20C2×#3797C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22#64155C2211yescharacteristic
23#64153C2211yescharacteristic
24#64106C2211yescharacteristic
25#64105C2212yes—
26#64098C2212yes—
27#64097C2211yescharacteristic
28#64081C2212yes—
29C42×C3⋊D3C2211yescharacteristic
30C4×#634C2212yes—
31C4×#634C2211yescharacteristic
32C3×Q8×Dic3C2212yes—
33C3×#944C2212yes—
34C3×#889C2214yes—
35C3×#888C2212yes—
36C3×#888C2214yes—
37C3×#887C2212yes—
38C3×#870C2212yes—
39C3×#869C2212yes—
40C3×#869C2211yescharacteristic
41C3×#869C2211yescharacteristic
42C3×C4×Dic6C2212yes—
43C3×C4×Dic6C2212yes—
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63919C2212yes—
47#63918C2212yes—
48C4×#627C2212yes—
49#63900C2211yescharacteristic
50#63895C2214yes—
51#63888C2214yes—
52#63883C2212yes—
53C4×#624C2212yes—
54#63872C2212yes—
55#63872C2212yes—
56#63871C2212yes—
57#63871C2212yes—
58#63867C2214yes—
59#63866C2214yes—
60#63866C2212yes—
61#63849C2212yes—
62#63847C2214yes—
63#63846C2214yes—
64#63846C2214yes—
65#63846C2214yes—
66#63845C2214yes—
67#63844C2212yes—
68#63843C2212yes—
69#63843C2212yes—
70#63843C2212yes—
71#63843C2212yes—
72#63843C2211yescharacteristic
73#63843C2211yescharacteristic
74Dic3×Dic6C2212yes—
75Dic3×Dic6C2214yes—
76#63840C2214yes—
77#63839C2214yes—
78#63839C2214yes—
79#63838C2212yes—
80#63837C2214yes—
81#63837C2214yes—
82#63837C2214yes—
83#63836C2214yes—
84#63836C2214yes—
85C3×Q82—31no—
86C3×#557—31no—
87#5729—34no—
88#5729—32no—
89#5728—32no—
90#5728—32no—
91#5728—31no—
92#5728—31no—
93#5722—32no—
94#5722—31no—
95#5721—32no—
96#5721—34no—
97#5721—32no—
98#5721—31no—
99#5689—34no—
100#5689—32no—
101#5685—34no—
102#5685—32no—
103#5578—31no—
104#5578—31no—
105#5578—32no—
106#5578—32no—
107#5578—61no—
108#5572—32no—
109#5572—32no—
110C4×D3×Q8—31no—
111C4×D3×Q8—31no—
112#5570—31no—
113#5570—32no—
114#5569—32no—
115#5567—32no—
116#5567D311yescharacteristic, complemented
117Q8×Dic6—32no—
118Q8×Dic6—31no—
119Q8×Dic6D311yescharacteristic, complemented
120C2×C32×Q8C2311yescharacteristic
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×#634C2311yescharacteristic
125C2×#634C2312yes—
126C2×C3×Dic6C2312yes—
127C2×C3×Dic6C2312yes—
128C2×C3×Dic6C2314yes—
129C2×C3×Dic6C2311yescharacteristic
130C2×C3×Dic6C2311yescharacteristic
131C2×#627C2314yes—
132C2×#627C2312yes—
133C2×#624C2312yes—
134C2×#624C2312yes—
135#3797Q818yescomplemented
136C32×C4⋊C4C2311yescharacteristic
137C32×C4⋊C4C2312yes—
138C32×C42C2311yescharacteristic
139C32×C42C2312yes—
140#3752C2312yes—
141#3752C2312yes—
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4⋊(C3⋊Dic3)C2312yes—
144#3750C2312yes—
145#3750C2312yes—
146#3750C2312yes—
147#3750C2312yes—
148#3750C2312yes—
149C4×C3⋊Dic3C2311yescharacteristic
150C4×C3⋊Dic3C2312yes—
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2311yescharacteristic
153C3×C4⋊Dic3C2312yes—
154C3×C4⋊Dic3C2314yes—
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×C4⋊Dic3C2311yescharacteristic
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×C4×Dic3C2314yes—
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2314yes—
169C3×C4×Dic3C2312yes—
170#3724C2312yes—
171#3724C2314yes—
172Dic3⋊Dic3C2314yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180#3722C2314yes—
181Dic32C2314yes—
182Dic32C2314yes—
183Dic32C2312yes—
184Dic32C2314yes—
185Dic32C2312yes—
186#3502—91noSylow
187C2×D3×Q8—31no—
188C2×D3×Q8—31no—
189C3×C4⋊Q8—32no—
190C3×C4⋊Q8—34no—
191C3×C4⋊Q8—32no—
192C3×C4⋊Q8—32no—
193C3×C4⋊Q8—31no—
194C3×C4⋊Q8—31no—
195C3×#125—34no—
196C3×#125—32no—
197C3×C4×Q8—21no—
198C3×C4×Q8—32no—
199C3×C4×Q8—32no—
200C3×C4×Q8—32no—
201C3×C4×Q8—31no—
202C3×C4×Q8—31no—
203C3×C4×Q8—32no—
204C3×C4×Q8C2×D311yescharacteristic
205C3×C4×Q8C2×D311yescharacteristic
206#946—31no—
207#946—31no—
208#946—32no—
209#946—32no—
210#946—34no—
211#946—61no—
212Q8×Dic3—32no—
213Q8×Dic3—32no—
214Q8×Dic3—32no—
215Q8×Dic3—31no—
216Q8×Dic3—32no—
217Q8×Dic3—31no—
218Q8×Dic3—34no—
219Q8×Dic3—32no—
220Q8×Dic3C2×D312yes—
221#944—31no—
222#944—31no—
223#944—34no—
224#944—34no—
225#944—32no—
226#944—34no—
227#944—61no—
228#944C2×D312yes—
229#897—32no—
230#897—32no—
231#897—31no—
232#897—31no—
233#897—34no—
234#897—61no—
235#896—34no—
236#896—32no—
237#896—32no—
238#896—34no—
239#896—62no—
240#892—32no—
241#892—32no—
242#892—34no—
243#892—34no—
244D3×C4⋊C4—31no—
245D3×C4⋊C4—31no—
246D3×C4⋊C4—32no—
247D3×C4⋊C4—32no—
248#890—34no—
249#890—32no—
250#890—34no—
251#890—32no—
252#890—32no—
253#890—34no—
254#890—32no—
255#890—34no—
256#889—32no—
257#889—32no—
258#889—34no—
259#889—34no—
260#889—34no—
261#889—34no—
262#889—34no—
263#889—34no—
264#889—34no—
265#889—62no—
266#889C2×D314yes—
267#888—34no—
268#888—34no—
269#888—31no—
270#888—31no—
271#888—32no—
272#888—32no—
273#888—34no—
274#888—34no—
275#888—32no—
276#888—61no—
277#888C2×D314yes—
278#888C2×D312yes—
279#887—32no—
280#887—31no—
281#887—32no—
282#887—31no—
283#887—32no—
284#887—32no—
285#887—32no—
286#887—32no—
287#887—34no—
288#887—34no—
289#887—34no—
290#887—32no—
291#887C2×D312yes—
292#872—32no—
293#872—32no—
294#872—34no—
295#872—34no—
296#872—62no—
297C42×D3—31no—
298C42×D3—31no—
299C42×D3—32no—
300C42×D3—32no—
301C42×D3—61no—
302#870—34no—
303#870C2×D312yes—
304#869—34no—
305#869—32no—
306#869—32no—
307#869C2×D312yes—
308#869C2×D311yescharacteristic
309#869C2×D311yescharacteristic
310C4×Dic6—34no—
311C4×Dic6—32no—
312C4×Dic6—32no—
313C4×Dic6—31no—
314C4×Dic6—32no—
315C4×Dic6—31no—
316C4×Dic6—32no—
317C4×Dic6—34no—
318C4×Dic6—34no—
319C4×Dic6—34no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—62no—
323C4×Dic6—61no—
324C4×Dic6C2×D312yes—
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D312yes—
327C4×Dic6C2×D311yescharacteristic
328C22×C3⋊D3C2411yescharacteristic
329C32×Q8—22no—
330C2×C32×C4C2412yes—
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C3⋊Dic3C2411yescharacteristic
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2411yescharacteristic
339C2×C3⋊Dic3C2411yescharacteristic
340C4×C3⋊D3—22no—
341C4×C3⋊D3—41no—
342C4×C3⋊D3C2×Q814yes—
343#634—22no—
344#634—42no—
345C2×C3×Dic3C2414yes—
346C2×C3×Dic3C2414yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C3×Dic6—24no—
352C3×Dic6—44no—
353C3×Dic6—42no—
354C3×Dic6C2×Q814yes—
355C3×Dic6C2×Q814yes—
356#627—44no—
357#627C2×Q818yes—
358#624—42no—
359#624C2×Q818yes—
360Q82—31no—
361Q82—92no—
362Q82—91no—
363#557—31no—
364#557—92no—
365#557—92no—
366#557—91no—
367#557—92no—
368#557—94no—
369#544—94no—
370#544—92no—
371#533—92no—
372#533—92no—
373#533—91no—
374#533—91no—
375#519—92no—
376C2×C4×Q8—91no—
377C2×C3×Q8—21no—
378C2×C3×Q8—31no—
379C2×C3×Q8—31no—
380C2×C3×Q8—32no—
381C2×C3×Q8—32no—
382C2×C3×Q8—34no—
383C2×C3×Q8C22×D311yescharacteristic
384C2×C3×Q8C22×D311yescharacteristic
385D3×Q8—38no—
386D3×Q8—38no—
387C2×C4×D3—31no—
388C2×C4×D3—31no—
389C2×C4×D3—32no—
390C2×C4×D3—32no—
391C2×C4×D3—31no—
392C2×C4×D3—31no—
393C2×C4×D3—31no—
394C2×C4×D3—31no—
395C2×C4×D3—32no—
396C2×C4×D3—32no—
397C2×C4×D3—61no—
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×Dic6—32no—
401C2×Dic6—32no—
402C2×Dic6—31no—
403C2×Dic6—31no—
404C2×Dic6—32no—
405C2×Dic6—32no—
406C2×Dic6—34no—
407C2×Dic6—34no—
408C2×Dic6—62no—
409C2×Dic6—61no—
410C2×Dic6C22×D312yes—
411C2×Dic6C22×D314yes—
412C2×Dic6C22×D312yes—
413C2×Dic6C22×D311yescharacteristic
414C2×Dic6C22×D311yescharacteristic
415C3×C4⋊C4—21no—
416C3×C4⋊C4—22no—
417C3×C4⋊C4—32no—
418C3×C4⋊C4—32no—
419C3×C4⋊C4—31no—
420C3×C4⋊C4—34no—
421C3×C4⋊C4—32no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—32no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—32no—
428C3×C4⋊C4—34no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4C22×D311yescharacteristic
431C3×C4⋊C4C22×D311yescharacteristic
432C3×C4⋊C4C22×D312yes—
433C3×C4⋊C4C22×D312yes—
434C3×C42—21no—
435C3×C42—22no—
436C3×C42—32no—
437C3×C42—32no—
438C3×C42—34no—
439C3×C42—34no—
440C3×C42C22×D311yescharacteristic
441C3×C42C22×D311yescharacteristic
442C3×C42C22×D312yes—
443C3×C42C22×D312yes—
444(C2×D3)⋊C4—32no—
445(C2×D3)⋊C4—32no—
446(C2×D3)⋊C4—32no—
447(C2×D3)⋊C4—32no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452C4⋊Dic3—31no—
453C4⋊Dic3—32no—
454C4⋊Dic3—31no—
455C4⋊Dic3—32no—
456C4⋊Dic3—34no—
457C4⋊Dic3—32no—
458C4⋊Dic3—34no—
459C4⋊Dic3—32no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3—61no—
465C4⋊Dic3—62no—
466C4⋊Dic3C22×D312yes—
467C4⋊Dic3C22×D312yes—
468C4⋊Dic3C22×D311yescharacteristic
469C4⋊Dic3C22×D312yes—
470C4⋊Dic3C22×D311yescharacteristic
471C4⋊Dic3C22×D314yes—
472C4⋊Dic3C22×D312yes—
473Dic3⋊C4—32no—
474Dic3⋊C4—32no—
475Dic3⋊C4—32no—
476Dic3⋊C4—32no—
477Dic3⋊C4—32no—
478Dic3⋊C4—32no—
479Dic3⋊C4—32no—
480Dic3⋊C4—32no—
481Dic3⋊C4—32no—
482Dic3⋊C4—32no—
483Dic3⋊C4—34no—
484Dic3⋊C4—32no—
485Dic3⋊C4—32no—
486Dic3⋊C4—32no—
487Dic3⋊C4—32no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—62no—
496Dic3⋊C4—62no—
497Dic3⋊C4—62no—
498Dic3⋊C4—62no—
499Dic3⋊C4—62no—
500Dic3⋊C4C22×D314yes—
501Dic3⋊C4C22×D314yes—
502Dic3⋊C4C22×D314yes—
503Dic3⋊C4C22×D312yes—
504Dic3⋊C4C22×D312yes—
505Dic3⋊C4C22×D314yes—
506C4×Dic3—31no—
507C4×Dic3—31no—
508C4×Dic3—31no—
509C4×Dic3—31no—
510C4×Dic3—32no—
511C4×Dic3—32no—
512C4×Dic3—31no—
513C4×Dic3—31no—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—34no—
517C4×Dic3—34no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—61no—
525C4×Dic3—62no—
526C4×Dic3—61no—
527C4×Dic3—61no—
528C4×Dic3C22×D312yes—
529C4×Dic3C22×D312yes—
530C4×Dic3C22×D314yes—
531C4×Dic3C22×D314yes—
532C22×C32C2511yescharacteristic
533C2×C3⋊D3—21no—
534C2×C3⋊D3—21no—
535C2×C3⋊D3C22×Q812yes—
536C32×C4—22no—
537C32×C4—22no—
538C32×C4—21no—
539C32×C4C22×Q812yes—
540C32×C42−1+412yes—
541C3⋊Dic3—21no—
542C3⋊Dic3—22no—
543C3⋊Dic3—21no—
544C3⋊Dic3—22no—
545C3⋊Dic3C22×Q812yes—
546C3×Dic3—24no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C3×Dic3—24no—
550C3×Dic3C22×Q814yes—
551C3×Dic3C22×Q814yes—
552C22×Q8—91no—
553C4⋊Q8—32no—
554C4⋊Q8—32no—
555C4⋊Q8—34no—
556C4⋊Q8—31no—
557C4⋊Q8—31no—
558C4⋊Q8—32no—
559C4⋊Q8—92no—
560C4⋊Q8—92no—
561C4⋊Q8—94no—
562C4⋊Q8—94no—
563C4⋊Q8—92no—
564C4⋊Q8—94no—
565C4⋊Q8—94no—
566C4⋊Q8—91no—
567C4⋊Q8—91no—
568#125—34no—
569#125—32no—
570#125—94no—
571#125—94no—
572#125—94no—
573#125—92no—
574#125—94no—
575#125—94no—
576#125—94no—
577#125—92no—
578#125—92no—
579C22⋊Q8—94no—
580C22⋊Q8—92no—
581C22⋊Q8—94no—
582C22⋊Q8—92no—
583C22⋊Q8—91no—
584C22⋊Q8—91no—
585C22⋊Q8—92no—
586C4×Q8—32no—
587C4×Q8—32no—
588C4×Q8—31no—
589C4×Q8—31no—
590C4×Q8—32no—
591C4×Q8—32no—
592C4×Q8—92no—
593C4×Q8—94no—
594C4×Q8—94no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×Q8—94no—
598C4×Q8—92no—
599C4×Q8—92no—
600C4×Q8—91no—
601C4×Q8—91no—
602C4×Q8—92no—
603C4×Q8—92no—
604C4×Q8—92no—
605C4×Q8—92no—
606C4×Q8—92no—
607C4×Q8—91no—
608C4×Q8D3211yescharacteristic
609#117—94no—
610#117—94no—
611#117—92no—
612#117—92no—
613C2×C4⋊C4—92no—
614C2×C4⋊C4—91no—
615C2×C42—92no—
616C2×C42—91no—
617C22×D3—31no—
618C22×D3—31no—
619C22×D3—61no—
620C3×Q8—22no—
621C3×Q8—22no—
622C3×Q8—34no—
623C3×Q8—34no—
624C3×Q8—42no—
625C3×Q8—64no—
626C3×Q8—124no—
627C3×Q8—122no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—34no—
636C2×C3×C4—34no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4C23×D311yescharacteristic
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D312yes—
642C2×C3×C4C23×D312yes—
643C2×C3×C4C23×D312yes—
644C2×C3×C4C23×D312yes—
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649C2×Dic3—31no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—31no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3C23×D314yes—
665C2×Dic3C23×D314yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C4×D3—34no—
671C4×D3—34no—
672C4×D3—38no—
673C4×D3—38no—
674C4×D3—64no—
675C4×D3—62no—
676C4×D3—62no—
677C4×D3—122no—
678C4×D3—122no—
679C4×D3—122no—
680C4×D3—121no—
681C4×D3—121no—
682C4×D3—122no—
683Dic6—24no—
684Dic6—38no—
685Dic6—38no—
686Dic6—42no—
687Dic6—44no—
688Dic6—62no—
689Dic6—62no—
690Dic6—122no—
691Dic6—124no—
692Dic6—124no—
693Dic6—122no—
694Dic6—122no—
695Dic6—124no—
696Dic6D3×Q814yes—
697Dic6D3×Q814yes—
698C2×C32C23×Q811yescharacteristic
699C2×C32C2×2−1+411yescharacteristic
700C2×C32#58511yescharacteristic
701C3⋊D3—22no—
702C2×Q8—31no—
703C2×Q8—31no—
704C2×Q8—32no—
705C2×Q8—32no—
706C2×Q8—34no—
707C2×Q8—92no—
708C2×Q8—94no—
709C2×Q8—98no—
710C2×Q8—91no—
711C2×Q8—92no—
712C2×Q8C2×D3211yescharacteristic
713C22×C4—92no—
714C22×C4—92no—
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—91no—
718C4⋊C4—32no—
719C4⋊C4—31no—
720C4⋊C4—32no—
721C4⋊C4—31no—
722C4⋊C4—34no—
723C4⋊C4—32no—
724C4⋊C4—34no—
725C4⋊C4—32no—
726C4⋊C4—32no—
727C4⋊C4—34no—
728C4⋊C4—34no—
729C4⋊C4—34no—
730C4⋊C4—32no—
731C4⋊C4—92no—
732C4⋊C4—92no—
733C4⋊C4—92no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C4⋊C4—92no—
742C4⋊C4—92no—
743C4⋊C4—92no—
744C4⋊C4—92no—
745C4⋊C4—91no—
746C4⋊C4—92no—
747C4⋊C4—92no—
748C4⋊C4C2×D3211yescharacteristic
749C4⋊C4C2×D3212yes—
750C22⋊C4—94no—
751C22⋊C4—92no—
752C22⋊C4—92no—
753C42—32no—
754C42—32no—
755C42—34no—
756C42—34no—
757C42—92no—
758C42—92no—
759C42—94no—
760C42—94no—
761C42—94no—
762C42—91no—
763C42—91no—
764C42—91no—
765C42—92no—
766C42C2×D3211yescharacteristic
767C42C2×D3212yes—
768C22×C3—21no—
769C22×C3C24×D311yescharacteristic
770C22×C3C24×D311yescharacteristic
771C2×D3—32no—
772C2×D3—32no—
773C2×D3—62no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—121no—
779C2×D3—121no—
780C3×C4—22no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—21no—
784C3×C4—22no—
785C3×C4—21no—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—34no—
789C3×C4—34no—
790C3×C4—42no—
791C3×C4—41no—
792C3×C4—42no—
793C3×C4—64no—
794C3×C4—62no—
795C3×C4—64no—
796C3×C4—62no—
797C3×C4C2×D3×Q812yes—
798C3×C4C2×D3×Q812yes—
799C3×C4#100712yes—
800C3×C4#101012yes—
801Dic3—24no—
802Dic3—24no—
803Dic3—22no—
804Dic3—22no—
805Dic3—32no—
806Dic3—32no—
807Dic3—62no—
808Dic3—62no—
809Dic3—62no—
810Dic3—61no—
811Dic3—62no—
812Dic3—61no—
813Dic3—62no—
814Dic3—61no—
815Dic3—62no—
816Dic3—61no—
817Dic3—122no—
818Dic3—122no—
819Dic3—121no—
820Dic3C2×D3×Q814yes—
821Dic3C2×D3×Q814yes—
822C32#350211yescharacteristic, complemented, Sylow
823C23—91no—
824Q8—22no—
825Q8—34no—
826Q8—34no—
827Q8—64no—
828Q8—98no—
829Q8—122no—
830Q8—124no—
831Q8—182no—
832Q8—362no—
833Q8—364no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—34no—
837C2×C4—34no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—98no—
841C2×C4—91no—
842C2×C4—94no—
843C2×C4—91no—
844C2×C4—92no—
845C2×C4—92no—
846C2×C4—91no—
847C2×C4—182no—
848C2×C4—361no—
849C2×C4—362no—
850C2×C4C22×D3212yes—
851C2×C4C22×D3212yes—
852C2×C4C22×D3211yescharacteristic
853C2×C4C22×D3211yescharacteristic
854C2×C4C22×D3211yescharacteristic
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3C22×D3×Q811yescharacteristic
859C2×C3C22×D3×Q811yescharacteristic
860C2×C3C2×#100711yescharacteristic
861C2×C3C2×#101011yescharacteristic
862C2×C3#596611yescharacteristic
863C2×C3#596811yescharacteristic
864D3—62no—
865D3—62no—
866D3—122no—
867C22—92no—
868C22—181no—
869C22—181no—
870C22C23×D3211yescharacteristic
871C4—22no—
872C4—21no—
873C4—22no—
874C4—34no—
875C4—34no—
876C4—64no—
877C4—62no—
878C4—62no—
879C4—64no—
880C4—92no—
881C4—181no—
882C4—182no—
883C4—181no—
884C4—182no—
885C4#6429712yes—
886C4D32×Q812yes—
887C3—21no—
888C3#8703111yescharacteristic, complemented
889C3#8704611yescharacteristic, complemented
890C2—182no—
891C2C2×#6429711yescharacteristic
892C2C2×D32×Q811yescharacteristic
893C2#1059669811yescharacteristic
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
2. C3×#5567C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595420C2semidirect
8. #10594314C2semidirect
9. #10594312C2semidirect
12. #10593861C2semidirect
13. #10593861C2semidirect
14. #10593856C2semidirect
16. #10593853C2semidirect
116. #5567D3semidirect
119. Q8×Dic6D3semidirect
135. #3797Q8semidirect
822. C32#3502semidirect
888. C3#87031semidirect
889. C3#87046semidirect

Maximal subgroups

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

subgroupindex
#105960492
C3×#55672
C3×Q8×Dic62
#105954202
#105953742
#105944002
#105943972
#105943142
#105943122
C4×#37972
#105938662
#105938612
#105938562
#105938552
#105938532
#105938482
#870463
#870313