Finite Group Databasebeta

← #11884316

Subgroups — #11884316

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2#10594887C211yesmaximal, characteristic, complemented
3#10594886C211yesmaximal, characteristic, complemented
4C2×#63807C211yesmaximal, characteristic, complemented
5#10592836C211yesmaximal, characteristic, complemented
6C3×#5127C211yesmaximal, characteristic, complemented
7#10591173C211yesmaximal, characteristic, complemented
8#10591172C211yesmaximal, characteristic, complemented
9#10590962C211yesmaximal, characteristic, complemented
10#10590960C211yesmaximal, characteristic, complemented
11#10590897C211yesmaximal, characteristic, complemented
12#10590829C211yesmaximal, characteristic, complemented
13#10590771C211yesmaximal, characteristic, complemented
14#10590755C211yesmaximal, characteristic, complemented
15#10590752C211yesmaximal, characteristic, complemented
16#83954—31nomaximal
17#79496—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×C32×M16C2211yescharacteristic
23#64133C2211yescharacteristic
24#64133C2211yescharacteristic
25C2×#3746C2211yescharacteristic, complemented
26C3×C4×#67C2211yescharacteristic
27C3×#908—24no—
28C2×C3×D24C2211yescharacteristic
29C2×C3×D24C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic, complemented
33#63976—21no—
34#63970—21no—
35#63969—21no—
36D3×#217—21no—
37#63908C2211yescharacteristic
38#63905—21no—
39Dic3×D12C2211yescharacteristic
40Dic3×D12C2211yescharacteristic, complemented
41#63885—21no—
42#63884—21no—
43D3×Dic3⋊C4—21no—
44#63866C2211yescharacteristic, complemented
45#63860C2211yescharacteristic
46#63856C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3716C2211yescharacteristic, complemented
51#63807—24no—
52#63644C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5824—31no—
65#5806—31no—
66C2×#912—31no—
67C2×#908D311yescharacteristic, complemented
68C2×#904—31no—
69#5551—31no—
70#5550—31no—
71C3×#435—31no—
72#5239—31no—
73#5218—31no—
74#5173—31no—
75#5171—31no—
76#5167—31no—
77#5162—31no—
78#5158—31no—
79#5153—31no—
80#5152—31no—
81#5137—31no—
82#5137—31no—
83#5137—61no—
84#5127D311yescharacteristic, complemented
85#5114—31no—
86#4844—31no—
87#4841—31no—
88#4734—31no—
89#4733—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4711—31no—
94C23×C3×D3—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C3×#235—22no—
101C3×#235—41no—
102C2×C3×D12—22no—
103C2×C3×D12—21no—
104C2×C3×D12—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3795—22no—
119#3795—22no—
120#3795—41no—
121#3795—41no—
122C32×M16—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125#3757—21no—
126#3757—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130#3750—21no—
131#3746—22no—
132C3×#217D411yescharacteristic
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D24—22no—
139C3×D24D414yescomplemented
140C3×#204—22no—
141C3×#204—22no—
142C3×D3×C8—22no—
143#3724—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—41no—
153#3716—22no—
154#3716—22no—
155#3716—41no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235C2×D311yescharacteristic
164C22×D12C2×D311yescharacteristic
165C3×AGL(1,ℤ/8)—64no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C2×C3×D8—31no—
170C2×C3×M16—21no—
171C2×C3×M16C2×D311yescharacteristic
172C2×C3×M16C2×D311yescharacteristic
173C22×C3×C8—31no—
174C3×C4×D4—31no—
175#953—61no—
176C2×#217—61no—
177#946—31no—
178#944—31no—
179C2×#216—31no—
180#939—61no—
181#939—61no—
182#938—31no—
183#938—61no—
184#937—61no—
185#936—31no—
186#935—61no—
187#935—61no—
188D4×Dic3—31no—
189D4×Dic3—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—31no—
193#930—31no—
194#929—61no—
195C4×#67C2×D311yescharacteristic
196#924—31no—
197#924—31no—
198#924—31no—
199#924—31no—
200#924—31no—
201#924—61no—
202#924—61no—
203C2×Dic3⋊C4—61no—
204#912—64no—
205#908—24no—
206C2×Dic12—31no—
207C2×Dic12—31no—
208C2×Dic12—31no—
209C2×Dic12—61no—
210#904—64no—
211C2×D24C2×D311yescharacteristic
212C2×D24C2×D311yescharacteristic
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—31no—
216C2×#204C2×D311yescharacteristic
217C2×#204C2×D311yescharacteristic
218C2×D3×C8C2×D311yescharacteristic, complemented
219#894—61no—
220D3×C4⋊C4—61no—
221#884—61no—
222#883—61no—
223#883—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226C4×D12—31no—
227C4×D12—31no—
228#869—31no—
229C3×C4⋊C8—31no—
230C3×C22⋊C8—31no—
231C3×C22⋊C8—31no—
232C3×#97—31no—
233#835—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#830C2×D311yescharacteristic
238#821—31no—
239#821—31no—
240#821—31no—
241(C2×D3)⋊C8C2×D311yescharacteristic, complemented
242#817—31no—
243#817—31no—
244#817—61no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—31no—
249#816—31no—
250#816—61no—
251#816—61no—
252#815C2×D311yescharacteristic, complemented
253Dic3⋊C8C2×D311yescharacteristic, complemented
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270#634—21no—
271#634—21no—
272#634—21no—
273#634—21no—
274C3×#67—41no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292#625—42no—
293#625—42no—
294#625—81no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—81no—
299C32×C8—21no—
300C32×C8C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—31no—
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—91no—
317#435—31no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—121no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67D1211yescharacteristic
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348#237—62no—
349#237—62no—
350#237—121no—
351#237—121no—
352#235—22no—
353#235—41no—
354#235—62no—
355#235—62no—
356#235—121no—
357#235—121no—
358C2×D12—22no—
359C2×D12—21no—
360C2×D12—41no—
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—21no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3C22×D311yescharacteristic
370C2×Dic6—31no—
371C2×Dic6—31no—
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6C22×D311yescharacteristic
377C3×SD16—62no—
378C3×SD16—62no—
379C3×D8—34no—
380C3×D8—62no—
381C3×M16—22no—
382C3×M16—22no—
383C3×M16—42no—
384C2×C3×C8—21no—
385C2×C3×C8—21no—
386C2×C3×C8—31no—
387C2×C3×C8—31no—
388C2×C3×C8—62no—
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C3×C4⋊C4—31no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C42—31no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—121no—
408#217—121no—
409#217D1211yescharacteristic
410#216—121no—
411#214—62no—
412#214—62no—
413#214—121no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4D1211yescharacteristic
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—121no—
438Dic3⋊C4—121no—
439Dic3⋊C4D1211yescharacteristic
440C4×Dic3C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443Dic12—62no—
444Dic12—62no—
445Dic12—122no—
446Dic12—121no—
447D24—22no—
448D24#6714yescomplemented
449#204—22no—
450#204—22no—
451#204—62no—
452#204—62no—
453#204—121no—
454D3×C8—22no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32C22×D411yescharacteristic
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—84no—
472C32×C4—21no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—41no—
476C3⋊Dic3—41no—
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—31no—
487AGL(1,ℤ/8)—64no—
488#135—184no—
489C2×Q16—91no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—31no—
498C2×M16D3211yescharacteristic
499C22×C8—31no—
500C4⋊Q8—91no—
501#124—91no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—91no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—91no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8—31no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—31no—
527#97—31no—
528C23×C3—21no—
529C23×C3—31no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—122no—
535C23×C3—241no—
536C23×C3C2×D1211yescharacteristic
537C23×C3D3×D411yescharacteristic
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—81no—
544C22×D3C2×D1211yescharacteristic
545C3×Q8—61no—
546C3×Q8—61no—
547C3×D4—32no—
548C3×D4—32no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—122no—
554C3×D4—121no—
555C3×D4—122no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—122no—
571C2×C3×C4C2×D1211yescharacteristic
572C2×C3×C4D3×D411yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575#67—41no—
576#67—42no—
577#67—122no—
578#67—122no—
579#67—122no—
580#67—122no—
581#67—241no—
582#67—241no—
583C2×Dic3—21no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—122no—
597C2×Dic3—122no—
598C2×Dic3—122no—
599C2×Dic3—241no—
600C2×Dic3C2×D1211yescharacteristic
601C2×Dic3C2×D1211yescharacteristic
602C2×Dic3C2×D1211yescharacteristic
603D12—21no—
604D12—21no—
605D12—21no—
606D12—21no—
607D12—42no—
608D12C2×#6712yes—
609D12C2×#6712yes—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—42no—
613C4×D3—122no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—241no—
617Dic6—21no—
618Dic6—21no—
619Dic6—61no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—121no—
628Dic6—121no—
629Dic6—121no—
630Dic6—121no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—22no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3×C8D3×D412yes—
638C3×C8C2×#6712yes—
639C3⋊C8—21no—
640C3⋊C8—21no—
641C2×C32—41no—
642C2×C32D4211yescharacteristic
643C2×C32#57511yescharacteristic
644C2×C32#57711yescharacteristic
645C3×D3—41no—
646C3×D3—42no—
647C3×D3—42no—
648C3×D3—81no—
649C24—61no—
650#41—62no—
651#41—121no—
652#41—182no—
653#41—182no—
654#41—361no—
655#41—361no—
656C2×Q8—31no—
657C2×Q8—91no—
658C2×Q8—91no—
659C2×D4—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—62no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—121no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4C2×D3211yescharacteristic
677Q16—182no—
678Q16—361no—
679SD16—62no—
680SD16—62no—
681SD16—182no—
682SD16—182no—
683SD16—361no—
684D8—34no—
685D8—62no—
686M16—22no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—62no—
690C2×C8C2×D3211yescharacteristic
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—91no—
694C4⋊C4—91no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C22⋊C4—31no—
701C22⋊C4—31no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C42—31no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—244no—
734C22×C3C22×D1211yescharacteristic
735C22×C3C2×D3×D411yescharacteristic
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—21no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—84no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—41no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—121no—
758C3×C4C2×D3×D411yescharacteristic
759C3×C4#100411yescharacteristic
760C3×C4#100911yescharacteristic
761C3×C4C22×#6711yescharacteristic
762Dic3—21no—
763Dic3—21no—
764Dic3—21no—
765Dic3—41no—
766Dic3—121no—
767Dic3—121no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—241no—
775Dic3—241no—
776Dic3—241no—
777Dic3—241no—
778C32#326711yescharacteristic, complemented, Sylow
779C23—31no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—122no—
784C23—122no—
785C23—241no—
786C23D3×D1211yescharacteristic
787Q8—61no—
788Q8—61no—
789Q8—181no—
790Q8—181no—
791Q8—181no—
792Q8—181no—
793D4—32no—
794D4—32no—
795D4—61no—
796D4—61no—
797D4—61no—
798D4—61no—
799D4—122no—
800D4—121no—
801D4—122no—
802D4—362no—
803D4—362no—
804D4—721no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—122no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—362no—
819C2×C4—362no—
820C2×C4—362no—
821C2×C4—721no—
822C2×C4D3×D1211yescharacteristic
823C2×C4C22×D3211yescharacteristic
824C8—21no—
825C8—61no—
826C8—61no—
827C8D3×#6712yes—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—41no—
832C2×C3—41no—
833C2×C3—81no—
834C2×C3—122no—
835C2×C3—122no—
836C2×C3—121no—
837C2×C3—241no—
838C2×C3D4×D1211yescharacteristic
839C2×C3#574811yescharacteristic
840C2×C3#575111yescharacteristic
841C2×C3#577311yescharacteristic
842C2×C3#577511yescharacteristic
843C2×C3D4×#6711yescharacteristic
844D3—41no—
845D3—42no—
846D3—42no—
847D3—81no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—61no—
852C22—61no—
853C22—61no—
854C22—62no—
855C22—62no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—244no—
864C22C2×D3×D1211yescharacteristic
865C4—21no—
866C4—61no—
867C4—61no—
868C4—61no—
869C4—121no—
870C4—361no—
871C4—361no—
872C4—361no—
873C4—361no—
874C4#6430711yescharacteristic
875C4C2×D3×#6711yescharacteristic
876C3—21no—
877C3#7949611yescharacteristic, complemented
878C3#8395411yescharacteristic, complemented
879C2—41no—
880C2—121no—
881C2—122no—
882C2—122no—
883C2—241no—
884C2#1059471211yescharacteristic
885C2#1059471311yescharacteristic
886C2D12×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#908C2semidirect
2. #10594887C2semidirect
3. #10594886C2semidirect
4. C2×#63807C2semidirect
5. #10592836C2semidirect
6. C3×#5127C2semidirect
7. #10591173C2semidirect
8. #10591172C2semidirect
9. #10590962C2semidirect
10. #10590960C2semidirect
11. #10590897C2semidirect
12. #10590829C2semidirect
13. #10590771C2semidirect
14. #10590755C2semidirect
15. #10590752C2semidirect
21. C2×#3795C22semidirect
25. C2×#3746C22semidirect
32. C2×C3×D3×C8C22semidirect
40. Dic3×D12C22semidirect
44. #63866C22semidirect
46. #63856C22semidirect
47. C2×#3719C22semidirect
50. C2×#3716C22semidirect
52. #63644C22semidirect
53. #63643C22semidirect
54. #63643C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63566C22semidirect
62. #63563C22semidirect
67. C2×#908D3semidirect
84. #5127D3semidirect
139. C3×D24D4semidirect
218. C2×D3×C8C2×D3semidirect
241. (C2×D3)⋊C8C2×D3semidirect
252. #815C2×D3semidirect
253. Dic3⋊C8C2×D3semidirect
448. D24#67semidirect
778. C32#3267semidirect
877. C3#79496semidirect
878. C3#83954semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
#105948872
#105948862
C2×#638072
#105928362
C3×#51272
#105911732
#105911722
#105909622
#105909602
#105908972
#105908292
#105907712
#105907552
#105907522
#839543
#794963