Finite Group Databasebeta

← #11884310

Subgroups — #11884310

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×C3×#914C211yesmaximal, characteristic, complemented
2#10595357C211yesmaximal, characteristic, complemented
3#10595228C211yesmaximal, characteristic, complemented
4C2×#63807C211yesmaximal, characteristic, complemented
5#10592866C211yesmaximal, characteristic, complemented
6C3×#5171C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591599C211yesmaximal, characteristic, complemented
9#10591569C211yesmaximal, characteristic, complemented
10#10591519C211yesmaximal, characteristic, complemented
11#10591459C211yesmaximal, characteristic, complemented
12#10591434C211yesmaximal, characteristic, complemented
13#10590853C211yesmaximal, characteristic, complemented
14#10590781C211yesmaximal, characteristic, complemented
15#10590722C211yesmaximal, characteristic, complemented
16#83954—31nomaximal
17#80675—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×C32×SD16C2211yescharacteristic
23#64153C2211yescharacteristic, complemented
24C2×#3756C2211yescharacteristic, complemented
25#64145C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27C2×#3746C2211yescharacteristic, complemented
28C3×#946C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic
30C3×#938C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#914—24no—
33C2×C3×D24C2211yescharacteristic
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic, complemented
36#63976—21no—
37#63970—21no—
38#63969—21no—
39D3×#217—21no—
40#63905—21no—
41C4×#625C2211yescharacteristic
42#63898C2211yescharacteristic
43#63898C2211yescharacteristic, complemented
44#63885—21no—
45#63884—21no—
46D3×Dic3⋊C4—21no—
47#63857C2211yescharacteristic
48#63857C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3716C2211yescharacteristic, complemented
51#63807—24no—
52#63642C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×#817C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5824—31no—
65#5806—31no—
66C2×#914D311yescharacteristic, complemented
67C2×#912—31no—
68C2×#904—31no—
69#5631—31no—
70#5612—31no—
71C3×#465—31no—
72#5239—31no—
73#5218—31no—
74#5173—31no—
75#5171D311yescharacteristic, complemented
76#5167—31no—
77#5167—31no—
78#5167—61no—
79#5162—31no—
80#5158—31no—
81#5153—31no—
82#5152—31no—
83#5137—31no—
84#5127—31no—
85#5111—31no—
86#5047—31no—
87#5037—31no—
88#4869—31no—
89#4867—31no—
90#4818—31no—
91#4808—31no—
92#4787—31no—
93#4776—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×#239—22no—
102C3×#239—41no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×#625—21no—
112C2×#625—21no—
113C2×#625D411yescharacteristic
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×SD16—22no—
123C2×C32×C8C2311yescharacteristic
124#3757—21no—
125#3757—21no—
126#3756—41no—
127#3754—41no—
128#3750—21no—
129#3750—21no—
130C4×C3⋊Dic3C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3746—22no—
133C3×#217—21no—
134C3×#215—22no—
135C3×#213—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24D414yescomplemented
143C3×ΓL(1,𝔽25)—22no—
144C3×D3×C8—22no—
145#3724D411yescharacteristic
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153(C2×D3)⋊Dic3D411yescharacteristic
154#3716—22no—
155#3716—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239C2×D311yescharacteristic
160C2×#237—31no—
161C2×#237—31no—
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C3×AGL(1,ℤ/8)—64no—
166C2×C3×SD16—21no—
167C2×C3×SD16—31no—
168C2×C3×SD16C2×D311yescharacteristic
169C2×C3×SD16C2×D311yescharacteristic
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C2×C3×M16—31no—
173C22×C3×C8—31no—
174C3×C22⋊Q8—31no—
175C3×#121—31no—
176#953—61no—
177C2×#217—61no—
178#946C2×D311yescharacteristic, complemented
179#944—31no—
180#944—31no—
181#944—61no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—61no—
185C2×#215C2×D311yescharacteristic
186#939—61no—
187#939—61no—
188#938—61no—
189#938C2×D311yescharacteristic
190#937—61no—
191#936—31no—
192#936—31no—
193#936—61no—
194#935—61no—
195#935—61no—
196D4×Dic3—31no—
197D4×Dic3—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—61no—
203C2×#213C2×D311yescharacteristic
204#929—61no—
205C4×#67—31no—
206C4×#67—31no—
207#924—31no—
208#924—31no—
209C2×Dic3⋊C4—61no—
210#914—24no—
211#912—64no—
212C2×Dic12—31no—
213C2×Dic12—31no—
214C2×Dic12—61no—
215#904—64no—
216C2×D24C2×D311yescharacteristic
217C2×#204—31no—
218C2×#204—31no—
219C2×ΓL(1,𝔽25)C2×D311yescharacteristic
220C2×D3×C8C2×D311yescharacteristic, complemented
221#897—31no—
222#897—31no—
223#894—61no—
224#893—31no—
225#893—31no—
226D3×C4⋊C4—61no—
227#884—61no—
228#883—61no—
229#883—61no—
230D3×C22⋊C4—61no—
231C3×#106—31no—
232C3×#103—31no—
233C3×#102—31no—
234#835C2×D311yescharacteristic, complemented
235#832—31no—
236#832—31no—
237#832C2×D311yescharacteristic
238#830—31no—
239#830—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242#817C2×D311yescharacteristic, complemented
243#816—31no—
244#816—31no—
245#815—31no—
246#815—31no—
247#815—61no—
248Dic3⋊C8—31no—
249Dic3⋊C8—31no—
250#810—31no—
251#810—31no—
252#809—31no—
253#809—31no—
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×D4—21no—
265C32×D4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C2×C3⋊Dic3C2×D411yescharacteristic
272#634—21no—
273#634—21no—
274#634—21no—
275#634—21no—
276C3×#67—42no—
277C3×#67—81no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
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—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292#625—41no—
293#625—42no—
294#625—42no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—81no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
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—31no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—21no—
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—62no—
331C2×C3×D4—61no—
332C2×C3×D4—121no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—31no—
341C2×#67—31no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350#239—22no—
351#239—41no—
352#237—62no—
353#237—62no—
354#237—121no—
355#237—121no—
356D3×D4—22no—
357D3×D4—41no—
358#235—62no—
359#235—62no—
360#235—121no—
361#235—121no—
362C2×D12—21no—
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3C22×D311yescharacteristic
371C2×C4×D3C22×D311yescharacteristic
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—31no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C3×SD16—22no—
379C3×SD16—22no—
380C3×SD16—42no—
381C3×SD16—62no—
382C3×D8—34no—
383C3×D8—62no—
384C3×M16—62no—
385C2×C3×C8—21no—
386C2×C3×C8—31no—
387C2×C3×C8—31no—
388C2×C3×C8—62no—
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396#217—21no—
397#217—31no—
398#217—31no—
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#216—121no—
410#216—121no—
411#216—122no—
412#215—22no—
413#214—62no—
414#214—62no—
415#214—121no—
416#214—121no—
417#214—122no—
418#213—22no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3C22×D311yescharacteristic
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—31no—
432Dic3⋊C4—31no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—121no—
440Dic3⋊C4—121no—
441C4×Dic3—31no—
442C4×Dic3—31no—
443C4×Dic3—61no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449Dic12—62no—
450Dic12—62no—
451Dic12—122no—
452D24#6714yescomplemented
453#204—62no—
454#204—62no—
455ΓL(1,𝔽25)—22no—
456D3×C8—22no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
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—
473C2×C3×D3—84no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—21no—
478C3⋊Dic3—21no—
479C3⋊Dic3—41no—
480C3⋊Dic3—41no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—91no—
487C2×#41—91no—
488C22×D4—31no—
489AGL(1,ℤ/8)—64no—
490#135—184no—
491C2×Q16—91no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16D3211yescharacteristic
498C2×D8—31no—
499C2×D8—31no—
500C2×M16—31no—
501C22×C8—31no—
502C4⋊Q8—91no—
503#124—91no—
504#123—181no—
505#123—181no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—31no—
511#121—181no—
512#121—181no—
513#120—181no—
514C4×D4—91no—
515C4×D4—91no—
516C4×D4—91no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—181no—
519#106—31no—
520C4⋊C8—91no—
521#103—31no—
522#103—91no—
523#103—91no—
524#102—31no—
525#102—91no—
526#102—91no—
527C22⋊C8—91no—
528C22⋊C8—91no—
529#97—91no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—122no—
538C23×C3—122no—
539C23×C3—241no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—81no—
545C22×D3D3×D411yescharacteristic
546C22×D3D3×D411yescharacteristic
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—41no—
552C3×Q8—41no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—32no—
558C3×D4—32no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—122no—
564C3×D4—122no—
565C3×D4—241no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—122no—
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—42no—
582#67—81no—
583#67—121no—
584#67—121no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—122no—
604C2×Dic3—122no—
605C2×Dic3—122no—
606C2×Dic3—241no—
607C2×Dic3D3×D411yescharacteristic
608C2×Dic3D3×D411yescharacteristic
609D12—21no—
610D12—21no—
611D12—42no—
612D12C2×#6712yes—
613D12C2×#6712yes—
614C4×D3—21no—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—42no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—241no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—61no—
631Dic6—121no—
632Dic6—121no—
633Dic6—121no—
634Dic6—121no—
635C3×C8—22no—
636C3×C8—61no—
637C3×C8—61no—
638C3×C8D3×D412yes—
639C3×C8C2×#6712yes—
640C3⋊C8—21no—
641C3⋊C8—21no—
642C3⋊C8—62no—
643C3⋊C8—61no—
644C3⋊C8—61no—
645C2×C32—81no—
646C2×C32D4211yescharacteristic
647C2×C32#57511yescharacteristic
648C2×C32#57711yescharacteristic
649C3×D3—41no—
650C3×D3—41no—
651C3×D3—42no—
652C3×D3—42no—
653C24—61no—
654#41—62no—
655#41—121no—
656#41—182no—
657#41—182no—
658#41—361no—
659#41—361no—
660C2×Q8—91no—
661C2×Q8—91no—
662C2×Q8C2×D3211yescharacteristic
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—62no—
668C2×D4—61no—
669C2×D4—91no—
670C2×D4—121no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4C2×D3211yescharacteristic
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—61no—
677C22×C4—181no—
678C22×C4—181no—
679C22×C4—181no—
680C22×C4—181no—
681Q16—182no—
682Q16—361no—
683SD16—22no—
684SD16—62no—
685SD16—182no—
686SD16—182no—
687SD16—361no—
688D8—34no—
689D8—62no—
690M16—62no—
691C2×C8—31no—
692C2×C8—31no—
693C2×C8—62no—
694C2×C8—91no—
695C2×C8C2×D3211yescharacteristic
696C4⋊C4—31no—
697C4⋊C4—31no—
698C4⋊C4—61no—
699C4⋊C4—91no—
700C4⋊C4—181no—
701C4⋊C4—181no—
702C4⋊C4—181no—
703C4⋊C4—181no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—91no—
707C22⋊C4—91no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C42—91no—
715C22×C3—21no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—61no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—244no—
738C22×C3C2×D3×D411yescharacteristic
739C22×C3C2×D3×D411yescharacteristic
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—21no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—84no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—81no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4C2×D3×D411yescharacteristic
763C3×C4#100411yescharacteristic
764C3×C4#100911yescharacteristic
765C3×C4C22×#6711yescharacteristic
766Dic3—21no—
767Dic3—21no—
768Dic3—41no—
769Dic3—41no—
770Dic3—61no—
771Dic3—61no—
772Dic3—61no—
773Dic3—61no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—121no—
780Dic3—241no—
781Dic3—241no—
782C32#326711yescharacteristic, complemented, Sylow
783C23—21no—
784C23—31no—
785C23—31no—
786C23—61no—
787C23—61no—
788C23—122no—
789C23—122no—
790C23—241no—
791Q8—21no—
792Q8—21no—
793Q8—181no—
794Q8—181no—
795Q8—181no—
796Q8—181no—
797D4—21no—
798D4—21no—
799D4—32no—
800D4—32no—
801D4—61no—
802D4—61no—
803D4—122no—
804D4—122no—
805D4—241no—
806D4—361no—
807D4—362no—
808D4—362no—
809C2×C4—21no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—91no—
819C2×C4—91no—
820C2×C4—122no—
821C2×C4—181no—
822C2×C4—181no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4—362no—
826C2×C4—721no—
827C2×C4C22×D3211yescharacteristic
828C8—61no—
829C8—61no—
830C8—181no—
831C8D3×#6712yes—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—81no—
836C2×C3—81no—
837C2×C3—121no—
838C2×C3—122no—
839C2×C3—122no—
840C2×C3—121no—
841C2×C3—161no—
842C2×C3#560911yescharacteristic
843C2×C3#576211yescharacteristic
844C2×C3#576811yescharacteristic
845C2×C3#577311yescharacteristic
846C2×C3#577511yescharacteristic
847C2×C3D4×#6711yescharacteristic
848D3—41no—
849D3—41no—
850D3—42no—
851D3—42no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—62no—
862C22—62no—
863C22—121no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—244no—
868C22D32×D411yescharacteristic
869C4—41no—
870C4—61no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4—181no—
875C4—181no—
876C4—361no—
877C4—361no—
878C4#6431411yescharacteristic
879C4C2×D3×#6711yescharacteristic
880C3—21no—
881C3#8067511yescharacteristic, complemented
882C3#8395411yescharacteristic, complemented
883C2—81no—
884C2—121no—
885C2—121no—
886C2—122no—
887C2—122no—
888C2#1059474511yescharacteristic
889C2#1059474911yescharacteristic
890C2#1059528811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. #10595357C2semidirect
3. #10595228C2semidirect
4. C2×#63807C2semidirect
5. #10592866C2semidirect
6. C3×#5171C2semidirect
7. #10591655C2semidirect
8. #10591599C2semidirect
9. #10591569C2semidirect
10. #10591519C2semidirect
11. #10591459C2semidirect
12. #10591434C2semidirect
13. #10590853C2semidirect
14. #10590781C2semidirect
15. #10590722C2semidirect
21. C2×#3795C22semidirect
23. #64153C22semidirect
24. C2×#3756C22semidirect
27. C2×#3746C22semidirect
28. C3×#946C22semidirect
35. C2×C3×D3×C8C22semidirect
43. #63898C22semidirect
50. C2×#3716C22semidirect
52. #63642C22semidirect
53. C3×#835C22semidirect
55. C3×#817C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
60. #63562C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#914D3semidirect
75. #5171D3semidirect
142. C3×D24D4semidirect
178. #946C2×D3semidirect
220. C2×D3×C8C2×D3semidirect
234. #835C2×D3semidirect
242. #817C2×D3semidirect
452. D24#67semidirect
782. C32#3267semidirect
881. C3#80675semidirect
882. C3#83954semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105953572
#105952282
C2×#638072
#105928662
C3×#51712
#105916552
#105915992
#105915692
#105915192
#105914592
#105914342
#105908532
#105907812
#105907222
#839543
#806753