Finite Group Databasebeta

← #11884105

Subgroups — #11884105

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63946C211yesmaximal, characteristic, complemented
4#10594886C211yesmaximal, characteristic
5#10592927C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic, complemented
7#10591605C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10591587C211yesmaximal, characteristic, complemented
10#10591583C211yesmaximal, characteristic, complemented
11#10591566C211yesmaximal, characteristic, complemented
12#10591564C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14#10591169C211yesmaximal, characteristic, complemented
15#10591155C211yesmaximal, characteristic, complemented
16#83866—31nomaximal
17#83559—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24#64133C2211yescharacteristic
25C3×#946—21no—
26C3×#946C2211yescharacteristic, complemented
27C3×Q8×Dic3C2211yescharacteristic, complemented
28C3×#944—21no—
29C3×#944C2211yescharacteristic, complemented
30C2×C3×#215—24no—
31C2×C3×#215C2211yescharacteristic
32C2×C3×#215C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic
34C2×C3×#215C2211yescharacteristic
35C3×C4×#67—21no—
36C3×C4×#67C2211yescharacteristic
37C3×#924—21no—
38C3×#924C2211yescharacteristic
39C22×C3×C3⋊C8C2211yescharacteristic
40#63976—21no—
41D3×#217—21no—
42#63946—24no—
43#63908C2211yescharacteristic
44Dic3×D12C2211yescharacteristic
45#63885—21no—
46#63884—21no—
47#63860C2211yescharacteristic
48C2×#3719C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63657C2211yescharacteristic
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64C3×D4×Q8—31no—
65Q8×#67D311yescharacteristic, complemented
66C2×#942—31no—
67C22×#215D311yescharacteristic, complemented
68#5806—31no—
69C2×#915—31no—
70#5550—31no—
71#5228—31no—
72#5228—31no—
73#5228—61no—
74#5227—31no—
75#5218—31no—
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#5086—31no—
86#5083—31no—
87#5051—31no—
88#5049—31no—
89#5047—31no—
90#5046—31no—
91#5028—31no—
92#5026—31no—
93#5011—31no—
94C23×C3×D3—21no—
95C2×C32×Q8—21no—
96C2×C32×Q8—22no—
97C2×C32×Q8—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67D411yescharacteristic
104C3×D3×Q8—22no—
105C3×D3×Q8—41no—
106C2×C3×D12—22no—
107C2×C3×D12—21no—
108C2×C3×D12—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6—21no—
114C2×C3×Dic6C2311yescharacteristic
115C2×#625—21no—
116C2×#625—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119#3795—22no—
120#3795—41no—
121#3757—21no—
122#3756—22no—
123#3756—41no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217D411yescharacteristic
130C3×#215—22no—
131C3×#215—22no—
132C3×#215—22no—
133C3×#215D414yescomplemented
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3—21no—
144C3×C4×Dic3C2311yescharacteristic
145C2×C3×C3⋊C8—22no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—22no—
153#3715—22no—
154#3715—41no—
155#3711—22no—
156#3266—91noSylow
157C22×C3×Q8—21no—
158C22×C3×Q8—31no—
159C22×C3×Q8C2×D311yescharacteristic
160C22×C3×Q8C2×D311yescharacteristic
161C22×C3×D4—31no—
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×#237—31no—
164C2×#235—31no—
165C22×D12C2×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×C4⋊Q8—31no—
173C3×C4⋊Q8—61no—
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8—61no—
177C3×C22⋊Q8—61no—
178C3×C4×Q8—31no—
179C3×C4×D4—31no—
180C3×C4×D4—61no—
181#953—61no—
182C2×#217—61no—
183#946—21no—
184#946C2×D311yescharacteristic, complemented
185Q8×Dic3C2×D311yescharacteristic, complemented
186#944—21no—
187#944C2×D311yescharacteristic, complemented
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#216—31no—
192C2×#216—31no—
193C2×#216—61no—
194C2×#216—61no—
195#942—64no—
196C2×#215—24no—
197C2×#215—31no—
198C2×#215—31no—
199C2×#215C2×D311yescharacteristic
200C2×#215C2×D311yescharacteristic
201C2×#215C2×D311yescharacteristic
202C2×#215C2×D311yescharacteristic
203#939—61no—
204#938—31no—
205#937—61no—
206#936—31no—
207#935—61no—
208D4×Dic3—31no—
209C2×#214—31no—
210C2×#214—31no—
211#930—31no—
212C4×#67—21no—
213C4×#67C2×D311yescharacteristic
214#924—21no—
215#924—31no—
216#924—31no—
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#894—61no—
225#884—61no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#835—61no—
236#832—31no—
237#832—31no—
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#809—31no—
250#809—31no—
251#807—31no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—42no—
265C32×Q8C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—42no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275#634—21no—
276#634—21no—
277C3×#67—22no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—42no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—42no—
294#625—42no—
295#625—81no—
296D3×Dic3—42no—
297D3×Dic3—81no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—31no—
304D4×Q8—31no—
305#546—91no—
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—61no—
318C23×D3—21no—
319C2×C3×Q8—21no—
320C2×C3×Q8—21no—
321C2×C3×Q8—22no—
322C2×C3×Q8—22no—
323C2×C3×Q8—21no—
324C2×C3×Q8—21no—
325C2×C3×Q8—31no—
326C2×C3×Q8—41no—
327C2×C3×Q8—42no—
328C2×C3×Q8—41no—
329C2×C3×Q8—41no—
330C2×C3×Q8—42no—
331C2×C3×Q8—61no—
332C2×C3×Q8—62no—
333C2×C3×Q8—121no—
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—62no—
342C2×C3×D4—61no—
343C2×C3×D4—121no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—41no—
349C22×C3×C4—61no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67#6711yescharacteristic
357C22×Dic3—61no—
358C22×Dic3—61no—
359D3×Q8—22no—
360D3×Q8—41no—
361#237—62no—
362#237—121no—
363#235—62no—
364#235—121no—
365C2×D12—22no—
366C2×D12—21no—
367C2×D12—41no—
368C2×D12C22×D311yescharacteristic
369C2×D12C22×D311yescharacteristic
370C2×C4×D3—21no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3C22×D311yescharacteristic
374C2×Dic6—21no—
375C2×Dic6—31no—
376C2×Dic6—31no—
377C2×Dic6—61no—
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×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C42—31no—
398C3×C42—61no—
399#217—21no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—121no—
407#217#6711yescharacteristic
408#216—62no—
409#216—62no—
410#216—62no—
411#216—122no—
412#216—121no—
413#216—121no—
414#216—122no—
415#215—22no—
416#215—22no—
417#215—22no—
418#215—62no—
419#215—121no—
420#215#6714yescomplemented
421#214—62no—
422#214—121no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4#6711yescharacteristic
429C4⋊Dic3—21no—
430C4⋊Dic3—31no—
431C4⋊Dic3—31no—
432C4⋊Dic3—61no—
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—21no—
435Dic3⋊C4—21no—
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—121no—
441Dic3⋊C4#6711yescharacteristic
442C4×Dic3—21no—
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#13712yescomplemented
459C22×C32C22×D411yescharacteristic
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—84no—
470C32×C4—22no—
471C32×C4—21no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—41no—
476C3⋊Dic3—41no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×Q8—31no—
484C22×Q8D3211yescharacteristic
485C22×D4—31no—
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—31no—
500C4⋊Q8—61no—
501#124—91no—
502#123—181no—
503C22⋊Q8—31no—
504C22⋊Q8—31no—
505C22⋊Q8—61no—
506C22⋊Q8—61no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—31no—
512C4×D4—31no—
513C4×D4—61no—
514C4×D4—91no—
515C2×C22⋊C4—181no—
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—31no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—122no—
533C23×C3—241no—
534C23×C3D3×D411yescharacteristic
535C23×C3C2×#6711yescharacteristic
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—81no—
541C22×D3C2×#6711yescharacteristic
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—22no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—22no—
550C3×Q8—41no—
551C3×Q8—41no—
552C3×Q8—42no—
553C3×Q8—42no—
554C3×Q8—44no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—122no—
558C3×Q8D3×D412yes—
559C3×Q8C2×#6712yes—
560C3×D4—32no—
561C3×D4—62no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—122no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—44no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—122no—
591C2×C3×C4D3×D411yescharacteristic
592C2×C3×C4C2×#6711yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595#67—22no—
596#67—122no—
597#67—122no—
598#67—241no—
599#67—241no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—121no—
607C2×Dic3—121no—
608C2×Dic3—122no—
609C2×Dic3—241no—
610C2×Dic3C2×#6711yescharacteristic
611C2×Dic3C2×#6711yescharacteristic
612C2×Dic3C2×#6711yescharacteristic
613D12—21no—
614D12—21no—
615D12—21no—
616D12—42no—
617D12C2×#6712yes—
618C4×D3—21no—
619C4×D3—21no—
620C4×D3—42no—
621C4×D3—122no—
622C4×D3—241no—
623Dic6—21no—
624Dic6—21no—
625Dic6—42no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—32no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—61no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C3⋊C8—121no—
641C3⋊C8C2×#6712yes—
642C2×C32—22no—
643C2×C32D4211yescharacteristic
644C2×C32C2×#13711yescharacteristic
645C2×C32#57711yescharacteristic
646C3×D3—41no—
647C3×D3—42no—
648C3×D3—81no—
649C24—61no—
650#41—182no—
651#41—361no—
652C2×Q8—21no—
653C2×Q8—22no—
654C2×Q8—31no—
655C2×Q8—41no—
656C2×Q8—61no—
657C2×Q8—62no—
658C2×Q8—91no—
659C2×Q8—121no—
660C2×Q8C2×D3211yescharacteristic
661C2×Q8C2×D3211yescharacteristic
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—121no—
668C2×D4—181no—
669C2×D4—181no—
670C22×C4—21no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4C2×D3211yescharacteristic
676Q16—182no—
677Q16—182no—
678Q16—361no—
679SD16—34no—
680SD16—62no—
681SD16—62no—
682SD16—62no—
683SD16—182no—
684SD16—361no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—62no—
689C2×C8—91no—
690C2×C8—91no—
691C4⋊C4—31no—
692C4⋊C4—31no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—91no—
699C4⋊C4—181no—
700C22⋊C4—31no—
701C22⋊C4—31no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—61no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—22no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—62no—
722C22×C3—61no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—244no—
729C22×C3#91512yescomplemented
730C22×C3#94212yescomplemented
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C22×#6711yescharacteristic
733C2×D3—21no—
734C2×D3—22no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—84no—
743C3×C4—22no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—22no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—41no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—121no—
758C3×C4—121no—
759C3×C4C2×D3×D411yescharacteristic
760C3×C4#100411yescharacteristic
761C3×C4#100411yescharacteristic
762C3×C4C22×#6711yescharacteristic
763Dic3—21no—
764Dic3—21no—
765Dic3—21no—
766Dic3—41no—
767Dic3—41no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771Dic3—121no—
772Dic3—241no—
773Dic3—241no—
774C32#326611yescharacteristic, complemented, Sylow
775C23—31no—
776C23—61no—
777C23—61no—
778C23—122no—
779C23—122no—
780C23—241no—
781C23D3×#6711yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—21no—
785Q8—42no—
786Q8—61no—
787Q8—61no—
788Q8—122no—
789Q8—181no—
790Q8—181no—
791Q8D3×#6712yes—
792D4—32no—
793D4—62no—
794D4—61no—
795D4—61no—
796D4—61no—
797D4—122no—
798D4—362no—
799D4—721no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—42no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—122no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—362no—
816C2×C4—721no—
817C2×C4D3×#6711yescharacteristic
818C2×C4C22×D3211yescharacteristic
819C8—32no—
820C8—61no—
821C8—181no—
822C8—181no—
823C2×C3—22no—
824C2×C3—22no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—42no—
829C2×C3—122no—
830C2×C3—121no—
831C2×C3—241no—
832C2×C3C2×#91511yescharacteristic
833C2×C3#576211yescharacteristic
834C2×C3D4×#6711yescharacteristic
835C2×C3D4×#6711yescharacteristic
836C2×C3C2×#94211yescharacteristic
837C2×C3#583711yescharacteristic
838D3—41no—
839D3—42no—
840D3—81no—
841C22—21no—
842C22—21no—
843C22—61no—
844C22—61no—
845C22—62no—
846C22—61no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22—244no—
853C22#6394612yescomplemented
854C22C2×D3×#6711yescharacteristic
855C4—21no—
856C4—22no—
857C4—41no—
858C4—61no—
859C4—61no—
860C4—61no—
861C4—121no—
862C4—121no—
863C4—361no—
864C4—361no—
865C4C2×D3×#6711yescharacteristic
866C4#6433011yescharacteristic
867C3—21no—
868C3#8355911yescharacteristic, complemented
869C3#8386611yescharacteristic, complemented
870C2—22no—
871C2—121no—
872C2—122no—
873C2—241no—
874C2#1059531811yescharacteristic
875C2C2×#6394611yescharacteristic
876C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC22×Q8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C3×Q8×#67C2semidirect
2. C22×C3×#215C2semidirect
3. C2×#63946C2semidirect
5. #10592927C2semidirect
6. #10591655C2semidirect
7. #10591605C2semidirect
8. #10591604C2semidirect
9. #10591587C2semidirect
10. #10591583C2semidirect
11. #10591566C2semidirect
12. #10591564C2semidirect
13. #10591187C2semidirect
14. #10591169C2semidirect
15. #10591155C2semidirect
19. C2×C3×D3×Q8C22semidirect
22. C2×#3756C22semidirect
23. C2×#3756C22semidirect
26. C3×#946C22semidirect
27. C3×Q8×Dic3C22semidirect
29. C3×#944C22semidirect
48. C2×#3719C22semidirect
51. C2×#3711C22semidirect
52. #63662C22semidirect
53. #63662C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
65. Q8×#67D3semidirect
67. C22×#215D3semidirect
133. C3×#215D4semidirect
162. C2×D3×Q8C2×D3semidirect
184. #946C2×D3semidirect
185. Q8×Dic3C2×D3semidirect
187. #944C2×D3semidirect
420. #215#67semidirect
458. C22×C32#137semidirect
729. C22×C3#915semidirect
730. C22×C3#942semidirect
774. C32#3266semidirect
853. C22#63946semidirect
868. C3#83559semidirect
869. C3#83866semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
C22×C3×#2152
C2×#639462
#105948862
#105929272
#105916552
#105916052
#105916042
#105915872
#105915832
#105915662
#105915642
#105911872
#105911692
#105911552
#838663
#835593