Finite Group Databasebeta

← #11884128

Subgroups — #11884128

Order 1152.

1082 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×#63929C211yesmaximal, characteristic, complemented
4Dic6×#67C211yesmaximal, characteristic, complemented
5#10592917C211yesmaximal, characteristic, complemented
6#10591517C211yesmaximal, characteristic, complemented
7#10591502C211yesmaximal, characteristic, complemented
8#10591491C211yesmaximal, characteristic, complemented
9#10591489C211yesmaximal, characteristic, complemented
10#10591461C211yesmaximal, characteristic, complemented
11#10591442C211yesmaximal, characteristic, complemented
12#10591440C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14#10591185C211yesmaximal, characteristic, complemented
15#10591155C211yesmaximal, characteristic, complemented
16#83866—31nomaximal
17#83506—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C2×#3754C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24#64133C2211yescharacteristic
25C3×#953—21no—
26C2×C3×#217—21no—
27C3×#939—21no—
28C3×#938C2211yescharacteristic
29C3×#936C2211yescharacteristic
30C3×#935—21no—
31C3×D4×Dic3C2211yescharacteristic
32C2×C3×#214—24no—
33C2×C3×#214C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C3×C4×#67C2211yescharacteristic
38C3×#924C2211yescharacteristic
39C22×C3×C3⋊C8C2211yescharacteristic
40Dic3×#67—21no—
41#63964—21no—
42#63929—24no—
43#63887—21no—
44#63866C2211yescharacteristic, complemented
45#63856C2211yescharacteristic, complemented
46Dic3×Dic6C2211yescharacteristic, complemented
47#63839—21no—
48C2×#3719C2211yescharacteristic, complemented
49C2×#3718C2211yescharacteristic, complemented
50C2×#3718C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63659C2211yescharacteristic
53#63659C2211yescharacteristic
54#63657C2211yescharacteristic
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64C3×#546—31no—
65C2×#951—31no—
66Q8×#67—31no—
67#5806D311yescharacteristic
68C22×#214D311yescharacteristic, complemented
69C2×#915—31no—
70D4×Dic6—31no—
71#5239—31no—
72#5228—31no—
73#5218—31no—
74#5218—31no—
75#5218—61no—
76#5174—31no—
77#5173—31no—
78#5170—31no—
79#5167—31no—
80#5166—31no—
81#5164—31no—
82#5162—31no—
83#5116—31no—
84#5111—31no—
85#5060—31no—
86#5054—31no—
87#5051—31no—
88#5050—31no—
89#5042—31no—
90#5040—31no—
91#5019—31no—
92#5018—31no—
93#5011—31no—
94C24×C32—21no—
95C2×C32×D4—22no—
96C2×C32×D4—21no—
97C2×C32×D4—41no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C3×#237—22no—
109C3×#237—41no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6—22no—
112C2×C3×Dic6—21no—
113C2×C3×Dic6—41no—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×D3×Dic3—21no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121#3757—21no—
122#3754—22no—
123#3754—41no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217D411yescharacteristic
134C3×#214—22no—
135C3×#214—22no—
136C3×#214—22no—
137C3×#214D414yescomplemented
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8—22no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146#3724—21no—
147Dic3⋊Dic3—21no—
148Dic3⋊Dic3—21no—
149Dic3⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3719—22no—
153#3718—22no—
154#3718—41no—
155#3711—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×D4—21no—
160C22×C3×D4C2×D311yescharacteristic
161C22×C3×D4C2×D311yescharacteristic
162C2×D3×Q8—31no—
163C2×#237C2×D311yescharacteristic
164C22×Dic6—31no—
165C22×Dic6C2×D311yescharacteristic
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—64no—
171C22×C3×C8—31no—
172C3×#124—31no—
173C3×#123—61no—
174C3×C22⋊Q8—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#120—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C22⋊C4—61no—
181#953—21no—
182C2×#217—21no—
183#951—64no—
184#946—31no—
185#946—61no—
186Q8×Dic3—31no—
187#944—31no—
188#944—61no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#216—31no—
192C2×#216—31no—
193C2×#216—31no—
194#939—21no—
195#938C2×D311yescharacteristic
196#936C2×D311yescharacteristic
197#935—21no—
198D4×Dic3—61no—
199D4×Dic3C2×D311yescharacteristic
200C2×#214—24no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—31no—
205C2×#214—61no—
206C2×#214—61no—
207C2×#214C2×D311yescharacteristic
208C2×#214C2×D311yescharacteristic
209C2×#214C2×D311yescharacteristic
210C2×#214C2×D311yescharacteristic
211C4×#67—61no—
212C4×#67C2×D311yescharacteristic
213#924—31no—
214#924—31no—
215#924—31no—
216#924—61no—
217#924—61no—
218#924C2×D311yescharacteristic
219C2×#208—31no—
220C22×C3⋊C8C2×D311yescharacteristic
221#915—64no—
222C2×Dic12—31no—
223C2×ΓL(1,𝔽25)—31no—
224#888—61no—
225#878—61no—
226#878—61no—
227#869—31no—
228C4×Dic6—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—61no—
237#832—61no—
238#830—31no—
239#830—31no—
240#830—31no—
241#830—61no—
242(C2×D3)⋊C8—31no—
243#818—31no—
244#816—31no—
245#816—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#810—31no—
250#810—31no—
251#807—31no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—42no—
257C23×C32—42no—
258C23×C32—81no—
259C23×C32C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C32×D4—21no—
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—42no—
265C32×D4C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272#634—21no—
273#634—21no—
274C3×#67—22no—
275C3×#67—42no—
276C3×#67—81no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—42no—
295C3×Dic6C2×D412yes—
296#627—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—31no—
304D4×Q8—91no—
305#546—31no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C24×C3—21no—
318C24×C3—21no—
319C24×C3—41no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—62no—
326C2×C3×Q8—61no—
327C2×C3×Q8—121no—
328C2×C3×D4—22no—
329C2×C3×D4—22no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—41no—
336C2×C3×D4—42no—
337C2×C3×D4—41no—
338C2×C3×D4—41no—
339C2×C3×D4—42no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4C22×D311yescharacteristic
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—21no—
354C2×#67—21no—
355C2×#67#6711yescharacteristic
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—61no—
360D3×Q8—62no—
361D3×Q8—121no—
362#237—22no—
363#237—41no—
364C2×C4×D3—61no—
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—22no—
367C2×Dic6—21no—
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—41no—
371C2×Dic6—61no—
372C2×Dic6—62no—
373C2×Dic6—61no—
374C2×Dic6—61no—
375C2×Dic6—121no—
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—34no—
380C3×SD16—62no—
381C3×SD16—62no—
382C3×SD16—62no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8—62no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—61no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—31no—
397#217—21no—
398#217—21no—
399#217—21no—
400#217—21no—
401#217—21no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—121no—
406#217#6711yescharacteristic
407#216—62no—
408#216—62no—
409#216—62no—
410#216—121no—
411#216—121no—
412#214—22no—
413#214—22no—
414#214—22no—
415#214—62no—
416#214—62no—
417#214—122no—
418#214—121no—
419#214—121no—
420#214—122no—
421#214#6714yescomplemented
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4#6711yescharacteristic
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3C22×D311yescharacteristic
431Dic3⋊C4—21no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—121no—
440Dic3⋊C4#6711yescharacteristic
441C4×Dic3—61no—
442C4×Dic3—61no—
443C4×Dic3C22×D311yescharacteristic
444#208—62no—
445C2×C3⋊C8—22no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454Dic12—62no—
455ΓL(1,𝔽25)—62no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—22no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—84no—
465C22×C32#13712yescomplemented
466C22×C32C22×D411yescharacteristic
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—22no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C22×Q8—31no—
484C22×Q8—91no—
485C22×D4D3211yescharacteristic
486#137—184no—
487C2×Q16—91no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—64no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×M16—91no—
498C22×C8—31no—
499C4⋊Q8—91no—
500C4⋊Q8—181no—
501#124—31no—
502#123—61no—
503C22⋊Q8—31no—
504C22⋊Q8—91no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—31no—
509#121—61no—
510#120—61no—
511C4×Q8—91no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—181no—
515C2×C22⋊C4—61no—
516#107—91no—
517C4⋊C8—91no—
518#103—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524C22⋊C8—91no—
525C22⋊C8—91no—
526#97—91no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—42no—
536C23×C3—42no—
537C23×C3—44no—
538C23×C3—42no—
539C23×C3—42no—
540C23×C3—82no—
541C23×C3—81no—
542C23×C3—81no—
543C23×C3—82no—
544C23×C3D3×D411yescharacteristic
545C23×C3C2×#6711yescharacteristic
546C22×D3C2×#6711yescharacteristic
547C3×Q8—32no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×Q8—122no—
554C3×D4—22no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—22no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—42no—
565C3×D4—42no—
566C3×D4—44no—
567C3×D4—62no—
568C3×D4—122no—
569C3×D4—241no—
570C3×D4D3×D412yes—
571C3×D4C2×#6712yes—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—122no—
590C2×C3×C4—122no—
591C2×C3×C4—241no—
592C2×C3×C4D3×D411yescharacteristic
593C2×C3×C4C2×#6711yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—22no—
597#67—42no—
598#67—81no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—42no—
604C2×Dic3—42no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—81no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3—122no—
613C2×Dic3C2×#6711yescharacteristic
614C2×Dic3C2×#6711yescharacteristic
615C2×Dic3C2×#6711yescharacteristic
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—122no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—21no—
623Dic6—21no—
624Dic6—42no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6—121no—
631Dic6—122no—
632Dic6—122no—
633Dic6C2×#6712yes—
634C3×C8—32no—
635C3×C8—61no—
636C3⋊C8—21no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C3⋊C8—121no—
643C3⋊C8C2×#6712yes—
644C2×C32—22no—
645C2×C32—42no—
646C2×C32—81no—
647C2×C32D4211yescharacteristic
648C2×C32C2×#13711yescharacteristic
649C2×C32#57711yescharacteristic
650C3×D3—41no—
651C24—21no—
652#41—62no—
653#41—121no—
654C2×Q8—31no—
655C2×Q8—31no—
656C2×Q8—31no—
657C2×Q8—62no—
658C2×Q8—61no—
659C2×Q8—91no—
660C2×Q8—121no—
661C2×Q8—181no—
662C2×Q8—182no—
663C2×Q8—361no—
664C2×D4—22no—
665C2×D4—21no—
666C2×D4—31no—
667C2×D4—41no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4C2×D3211yescharacteristic
671C2×D4C2×D3211yescharacteristic
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—181no—
677C22×C4C2×D3211yescharacteristic
678Q16—182no—
679Q16—182no—
680Q16—361no—
681SD16—34no—
682SD16—62no—
683SD16—62no—
684SD16—62no—
685SD16—182no—
686SD16—361no—
687M16—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—62no—
691C2×C8—91no—
692C2×C8—91no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—91no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C4⋊C4—181no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—31no—
712C42—181no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—21no—
720C22×C3—22no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—84no—
743C22×C3—84no—
744C22×C3—88no—
745C22×C3#91512yescomplemented
746C22×C3#95112yescomplemented
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C22×#6711yescharacteristic
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—41no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—62no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4#100411yescharacteristic
766C3×C4#100411yescharacteristic
767C3×C4C22×#6711yescharacteristic
768Dic3—22no—
769Dic3—21no—
770Dic3—21no—
771Dic3—21no—
772Dic3—41no—
773Dic3—41no—
774Dic3—41no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—241no—
780Dic3—241no—
781C32#326611yescharacteristic, complemented, Sylow
782C23—21no—
783C23—21no—
784C23—31no—
785C23—42no—
786C23—42no—
787C23—81no—
788C23D3×#6711yescharacteristic
789Q8—32no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—122no—
796Q8—181no—
797Q8—181no—
798Q8—362no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—42no—
803D4—62no—
804D4—122no—
805D4—241no—
806D4D3×#6712yes—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—31no—
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—122no—
819C2×C4—122no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—241no—
823C2×C4—362no—
824C2×C4D3×#6711yescharacteristic
825C2×C4C22×D3211yescharacteristic
826C8—32no—
827C8—61no—
828C8—181no—
829C8—181no—
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—42no—
836C2×C3—42no—
837C2×C3—42no—
838C2×C3—82no—
839C2×C3—82no—
840C2×C3—81no—
841C2×C3—81no—
842C2×C3—121no—
843C2×C3C2×#91511yescharacteristic
844C2×C3#576211yescharacteristic
845C2×C3D4×#6711yescharacteristic
846C2×C3D4×#6711yescharacteristic
847C2×C3C2×#95111yescharacteristic
848C2×C3#583611yescharacteristic
849D3—41no—
850C22—21no—
851C22—21no—
852C22—22no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—84no—
862C22#6392912yescomplemented
863C22C2×D3×#6711yescharacteristic
864C4—21no—
865C4—61no—
866C4—61no—
867C4—61no—
868C4—62no—
869C4—121no—
870C4—121no—
871C4—121no—
872C4—361no—
873C4—361no—
874C4C2×D3×#6711yescharacteristic
875C4#6433011yescharacteristic
876C3—21no—
877C3#8350611yescharacteristic, complemented
878C3#8386611yescharacteristic, complemented
879C2—22no—
880C2—42no—
881C2—81no—
882C2—121no—
883C2C2×#6392911yescharacteristic
884C2#1059510511yescharacteristic
885C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC22×D4D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. C2×#63929C2semidirect
4. Dic6×#67C2semidirect
5. #10592917C2semidirect
6. #10591517C2semidirect
7. #10591502C2semidirect
8. #10591491C2semidirect
9. #10591489C2semidirect
10. #10591461C2semidirect
11. #10591442C2semidirect
12. #10591440C2semidirect
13. #10591187C2semidirect
14. #10591185C2semidirect
15. #10591155C2semidirect
21. C2×D3×Dic6C22semidirect
44. #63866C22semidirect
45. #63856C22semidirect
46. Dic3×Dic6C22semidirect
48. C2×#3719C22semidirect
49. C2×#3718C22semidirect
50. C2×#3718C22semidirect
51. C2×#3711C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
68. C22×#214D3semidirect
137. C3×#214D4semidirect
421. #214#67semidirect
465. C22×C32#137semidirect
745. C22×C3#915semidirect
746. C22×C3#951semidirect
781. C32#3266semidirect
862. C22#63929semidirect
877. C3#83506semidirect
878. C3#83866semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
C22×C3×#2142
C2×#639292
Dic6×#672
#105929172
#105915172
#105915022
#105914912
#105914892
#105914612
#105914422
#105914402
#105911872
#105911852
#105911552
#838663
#835063