Finite Group Databasebeta

← #11884319

Subgroups — #11884319

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C211yesmaximal, characteristic, complemented
2C2×#63795C211yesmaximal, characteristic, complemented
3#10594003C211yesmaximal, characteristic, complemented
4#10593895C211yesmaximal, characteristic, complemented
5#10592414C211yesmaximal, characteristic, complemented
6C3×#4711C211yesmaximal, characteristic, complemented
7C3×#4706C211yesmaximal, characteristic, complemented
8#10590969C211yesmaximal, characteristic, complemented
9#10590969C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590946C211yesmaximal, characteristic, complemented
12#10590853C211yesmaximal, characteristic, complemented
13#10590830C211yesmaximal, characteristic, complemented
14#10590366C211yesmaximal, characteristic, complemented
15#10590365C211yesmaximal, characteristic, complemented
16#79879—31nomaximal
17#79496—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×#3746C2211yescharacteristic, complemented
23C2×#3746C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic
25C2×#3744C2211yescharacteristic
26#64084C2211yescharacteristic
27#64078C2211yescharacteristic, complemented
28C2×C3×D24C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic, complemented
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic, complemented
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63909C2211yescharacteristic
37#63908—21no—
38#63906—21no—
39#63891—21no—
40#63891—21no—
41#63890—21no—
42D3×C4⋊Dic3—21no—
43#63857C2211yescharacteristic
44#63857C2211yescharacteristic
45#63857C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50#63807—24no—
51#63795—24no—
52C32×#97C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic
54C3×#821C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#817C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63564C2211yescharacteristic
63C2×#912—31no—
64C2×#911—31no—
65C2×#908—31no—
66C2×#904—31no—
67#5555—31no—
68#5554—31no—
69#5551—31no—
70#5550—31no—
71C3×#442—31no—
72C3×#435—31no—
73#5137—31no—
74#5114—31no—
75#5019—31no—
76#5016—31no—
77#4867—31no—
78#4864—31no—
79#4844—31no—
80#4841—31no—
81#4783—31no—
82#4783—31no—
83#4781—31no—
84#4776—31no—
85#4734—31no—
86#4733—31no—
87#4733—31no—
88#4731—31no—
89#4715—31no—
90#4715—31no—
91#4715—61no—
92#4711D311yescharacteristic, complemented
93#4706D311yescharacteristic, complemented
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×D12D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116#3795—22no—
117#3795—22no—
118#3795—22no—
119#3795—41no—
120#3795—41no—
121#3795—41no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124C32×C42C2311yescharacteristic
125#3752—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)—21no—
128C4⋊(C3⋊Dic3)—21no—
129#3746—22no—
130#3746—41no—
131#3744—22no—
132#3744—41no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24D414yescomplemented
143C3×ΓL(1,𝔽25)—22no—
144C3×D3×C8—22no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3716—22no—
153#3716—22no—
154#3716—22no—
155#3714—22no—
156#3267—91noSylow
157C2×#237—31no—
158C2×#237—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×D8—31no—
166C2×C3×M16—31no—
167C22×C3×C8—31no—
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171#938—61no—
172#937—61no—
173C2×#214—31no—
174C2×#214—31no—
175C2×#214—31no—
176C2×#213—31no—
177#930—31no—
178#930—61no—
179#930—61no—
180C2×(C2×D3)⋊C4—61no—
181C2×C4⋊Dic3—61no—
182#924—31no—
183#924—31no—
184#924—31no—
185#912—64no—
186#911—64no—
187#908—64no—
188C2×Dic12—31no—
189C2×Dic12—31no—
190C2×Dic12—31no—
191C2×Dic12—31no—
192C2×Dic12—61no—
193C2×Dic12—61no—
194#904—64no—
195C2×D24—31no—
196C2×D24C2×D311yescharacteristic
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—61no—
205C2×#204—61no—
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic
207C2×D3×C8C2×D311yescharacteristic, complemented
208#897—31no—
209#897—31no—
210#897—31no—
211#895—31no—
212#894—61no—
213D3×C4⋊C4—61no—
214#886—61no—
215#886—61no—
216#886—61no—
217#884—61no—
218#883—61no—
219#883—61no—
220#882—61no—
221D3×C22⋊C4—61no—
222#875—31no—
223#875—31no—
224#875—61no—
225C4×D12C2×D311yescharacteristic
226C4×D12C2×D311yescharacteristic
227C4×D12C2×D311yescharacteristic, complemented
228#869—31no—
229#869—31no—
230#869—61no—
231C3×#106—31no—
232C3×C4⋊C8—31no—
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236C3×C22⋊C8—31no—
237C3×#97—21no—
238C3×#97C2×D311yescharacteristic, complemented
239C3×#97C2×D311yescharacteristic, complemented
240#821—31no—
241#821C2×D311yescharacteristic
242#821C2×D311yescharacteristic, complemented
243(C2×D3)⋊C8C2×D311yescharacteristic
244(C2×D3)⋊C8C2×D311yescharacteristic, complemented
245#817C2×D311yescharacteristic, complemented
246#816—31no—
247#816—31no—
248#816—31no—
249#810—31no—
250#810—31no—
251#810—31no—
252#809—31no—
253C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270#634—21no—
271#634—21no—
272#634—21no—
273#634—21no—
274#634—21no—
275#634—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—41no—
283C3×D12C2×D412yes—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3—81no—
291#626—42no—
292#626—81no—
293#625—42no—
294#625—42no—
295#625—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8—21no—
300C32×C8C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—31no—
317#435—31no—
318C23×D3—61no—
319C23×D3—61no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338#237—62no—
339#237—62no—
340#237—62no—
341#237—121no—
342#237—121no—
343#237—121no—
344D3×D4—62no—
345D3×D4—121no—
346#235—62no—
347#235—62no—
348#235—62no—
349#235—121no—
350#235—121no—
351#235—121no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—61no—
355C2×D12—62no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—121no—
359C2×D12D1211yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3C22×D311yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—31no—
370C2×Dic6—31no—
371C2×Dic6—31no—
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C3×D8—34no—
379C3×M16—62no—
380C2×C3×C8—21no—
381C2×C3×C8—21no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8—62no—
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—21no—
397C3×C42C22×D311yescharacteristic
398C3×C42C22×D311yescharacteristic
399#217—61no—
400#217—61no—
401#217—61no—
402#214—62no—
403#214—62no—
404#214—62no—
405#213—62no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—121no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4D1211yescharacteristic
420(C2×D3)⋊C4D1211yescharacteristic
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—121no—
429C4⋊Dic3—121no—
430C4⋊Dic3D1211yescharacteristic
431C4⋊Dic3C22×D311yescharacteristic
432C4⋊Dic3C22×D311yescharacteristic
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438Dic12—62no—
439Dic12—62no—
440Dic12—122no—
441Dic12—121no—
442Dic12—121no—
443Dic12—122no—
444D24—62no—
445D24D1214yescomplemented
446#204—62no—
447#204—62no—
448#204—62no—
449#204—62no—
450#204—62no—
451#204—122no—
452#204—121no—
453#204—121no—
454#204—122no—
455ΓL(1,𝔽25)—22no—
456D3×C8—22no—
457C22×C32C22×D411yescharacteristic
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473D32—84no—
474C32×C4—21no—
475C32×C4—21no—
476C32×C4C22×D411yescharacteristic
477C32×C4H(5,𝔽2)11yescharacteristic
478C3⋊Dic3—41no—
479C3⋊Dic3—41no—
480C3⋊Dic3—41no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—91no—
486C2×#41—91no—
487C2×#41—91no—
488C22×D4—91no—
489AGL(1,ℤ/8)—184no—
490#135—184no—
491C2×Q16—91no—
492C2×Q16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—91no—
500C2×M16—31no—
501C22×C8—31no—
502C4⋊Q8—91no—
503#124—91no—
504#123—181no—
505#123—181no—
506#123—181no—
507C22⋊Q8—91no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—91no—
511#121—181no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—31no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—181no—
519#106—31no—
520C4⋊C8—31no—
521#103—91no—
522#103—91no—
523#103—91no—
524#102—31no—
525#102—31no—
526#102—91no—
527C22⋊C8—31no—
528C22⋊C8—31no—
529#97D3211yescharacteristic, complemented
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—61no—
533C23×C3—61no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—121no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3C2×D1211yescharacteristic
546C22×D3C2×D1211yescharacteristic
547C3×D4—32no—
548C3×D4—32no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—121no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—122no—
564C2×C3×C4—241no—
565C2×C3×C4C2×D1211yescharacteristic
566C2×C3×C4C2×D1211yescharacteristic
567C2×C3×C4D3×D411yescharacteristic
568C2×C3×C4D3×D411yescharacteristic
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571#67—122no—
572#67—122no—
573#67—122no—
574#67—122no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—241no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3C2×D1211yescharacteristic
594C2×Dic3C2×D1211yescharacteristic
595D12—21no—
596D12—21no—
597D12—41no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—121no—
603D12—121no—
604D12—122no—
605D12—241no—
606D12C2×D1212yes—
607D12C2×D1212yes—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—42no—
613C4×D3—81no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—122no—
617Dic6—61no—
618Dic6—61no—
619Dic6—61no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6—121no—
631Dic6—121no—
632Dic6—121no—
633Dic6—121no—
634Dic6—121no—
635C3×C8—22no—
636C3×C8—21no—
637C3×C8—21no—
638C3×C8—22no—
639C3×C8—61no—
640C3×C8—61no—
641C3×C8C2×D1212yes—
642C3×C8D3×D412yes—
643C3⋊C8—21no—
644C3⋊C8—21no—
645C2×C32D4211yescharacteristic
646C2×C32#57511yescharacteristic
647C2×C32#57711yescharacteristic
648C3⋊D3—81no—
649C3×D3—41no—
650C3×D3—42no—
651C3×D3—41no—
652C3×D3—42no—
653C24—181no—
654#41—182no—
655#41—182no—
656#41—182no—
657#41—361no—
658#41—361no—
659#41—361no—
660C2×Q8—91no—
661C2×Q8—91no—
662C2×Q8—91no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—31no—
666C2×D4—91no—
667C2×D4—181no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—361no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—181no—
679C22×C4—181no—
680C22×C4—181no—
681Q16—182no—
682Q16—361no—
683SD16—182no—
684SD16—182no—
685SD16—182no—
686SD16—182no—
687SD16—361no—
688D8—34no—
689D8—182no—
690M16—62no—
691C2×C8—31no—
692C2×C8—31no—
693C2×C8—62no—
694C2×C8C2×D3211yescharacteristic
695C2×C8C2×D3211yescharacteristic
696C4⋊C4—31no—
697C4⋊C4—31no—
698C4⋊C4—31no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C4⋊C4—181no—
702C4⋊C4—181no—
703C4⋊C4—181no—
704C22⋊C4—31no—
705C22⋊C4—31no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C42C2×D3211yescharacteristic
715C22×C3—21no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3C22×D1211yescharacteristic
729C22×C3C2×D3×D411yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—241no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—244no—
752C2×D3—244no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4C22×D1211yescharacteristic
766C3×C4C2×D3×D411yescharacteristic
767C3×C4#100911yescharacteristic
768C3×C4#100911yescharacteristic
769Dic3—21no—
770Dic3—21no—
771Dic3—41no—
772Dic3—41no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—241no—
780Dic3—241no—
781Dic3—241no—
782C32#326711yescharacteristic, complemented, Sylow
783C23—31no—
784C23—31no—
785C23—61no—
786C23—61no—
787C23—181no—
788C23—362no—
789C23—362no—
790C23—721no—
791Q8—181no—
792Q8—181no—
793Q8—181no—
794Q8—181no—
795Q8—181no—
796Q8—181no—
797D4—32no—
798D4—32no—
799D4—61no—
800D4—61no—
801D4—121no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—362no—
808D4—721no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—122no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—241no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4D3×D1211yescharacteristic
826C2×C4D3×D1211yescharacteristic
827C2×C4C22×D3211yescharacteristic
828C8—21no—
829C8—61no—
830C8—61no—
831C8D3×D1212yes—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—121no—
836C2×C3—121no—
837C2×C3—122no—
838C2×C3—122no—
839C2×C3D4×D1211yescharacteristic
840C2×C3D4×D1211yescharacteristic
841C2×C3#574811yescharacteristic
842C2×C3#575111yescharacteristic
843C2×C3#577311yescharacteristic
844C2×C3#577511yescharacteristic
845D3—42no—
846D3—42no—
847D3—41no—
848D3—41no—
849D3—241no—
850D3—241no—
851D3—481no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—62no—
859C22—62no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22C2×D3×D1211yescharacteristic
869C4—21no—
870C4—21no—
871C4—61no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4—361no—
876C4—361no—
877C4—361no—
878C4C2×D3×D1211yescharacteristic
879C4#6430811yescharacteristic
880C3—21no—
881C3#7949611yescharacteristic, complemented
882C3#7987911yescharacteristic, complemented
883C2—121no—
884C2—121no—
885C2—122no—
886C2—122no—
887C2—721no—
888C2D12211yescharacteristic
889C2#1059471211yescharacteristic
890C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#63807C2semidirect
2. C2×#63795C2semidirect
3. #10594003C2semidirect
4. #10593895C2semidirect
5. #10592414C2semidirect
6. C3×#4711C2semidirect
7. C3×#4706C2semidirect
8. #10590969C2semidirect
9. #10590969C2semidirect
10. #10590968C2semidirect
11. #10590946C2semidirect
12. #10590853C2semidirect
13. #10590830C2semidirect
14. #10590366C2semidirect
15. #10590365C2semidirect
21. C2×#3795C22semidirect
22. C2×#3746C22semidirect
23. C2×#3746C22semidirect
27. #64078C22semidirect
30. C2×C3×D3×C8C22semidirect
33. C3×C4×D12C22semidirect
45. #63857C22semidirect
48. C2×#3716C22semidirect
52. C32×#97C22semidirect
54. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#817C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
61. #63567C22semidirect
92. #4711D3semidirect
93. #4706D3semidirect
142. C3×D24D4semidirect
207. C2×D3×C8C2×D3semidirect
227. C4×D12C2×D3semidirect
238. C3×#97C2×D3semidirect
239. C3×#97C2×D3semidirect
242. #821C2×D3semidirect
244. (C2×D3)⋊C8C2×D3semidirect
245. #817C2×D3semidirect
253. C4⋊(C3⋊C8)C2×D3semidirect
445. D24D12semidirect
529. #97D32semidirect
782. C32#3267semidirect
881. C3#79496semidirect
882. C3#79879semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
C2×#637952
#105940032
#105938952
#105924142
C3×#47112
C3×#47062
#105909692
#105909682
#105909462
#105908532
#105908302
#105903662
#105903652
#798793
#794963