Finite Group Databasebeta

← #11884098

Subgroups — #11884098

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10595067C211yesmaximal, characteristic
5#10592926C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591608C211yesmaximal, characteristic, complemented
9#10591607C211yesmaximal, characteristic, complemented
10#10591594C211yesmaximal, characteristic, complemented
11#10591566C211yesmaximal, characteristic, complemented
12#10591564C211yesmaximal, characteristic, complemented
13#10591178C211yesmaximal, characteristic, complemented
14#10591170C211yesmaximal, characteristic, complemented
15#10591147C211yesmaximal, characteristic, complemented
16#83987—31nomaximal
17#83559—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24#64139C2211yescharacteristic
25C3×#946—21no—
26C3×#946C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic, complemented
28C3×#944—21no—
29C3×#944C2211yescharacteristic, complemented
30C2×C3×#216C2211yescharacteristic, complemented
31C2×C3×#216C2211yescharacteristic, complemented
32C3×#942—24no—
33C2×C3×#215C2211yescharacteristic
34C2×C3×#215C2211yescharacteristic
35C3×C4×#67—21no—
36C3×C4×#67C2211yescharacteristic
37C3×#924—21no—
38C3×#924C2211yescharacteristic, complemented
39C2×C3×#208C2211yescharacteristic, complemented
40#63983—21no—
41#63971—21no—
42D3×#215—24no—
43D3×(C2×D3)⋊C4—21no—
44Dic3×D12C2211yescharacteristic
45#63864C2211yescharacteristic
46#63856C2211yescharacteristic
47#63850—21no—
48C2×#3718C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C3×D4×Q8—31no—
65#5829—31no—
66Q8×#67D311yescharacteristic, complemented
67C2×#942D311yescharacteristic, complemented
68C22×#215—31no—
69C2×D3×SD16—31no—
70#5550—31no—
71#5239—31no—
72#5228—31no—
73#5227—31no—
74#5227—31no—
75#5227—61no—
76#5190—31no—
77#5188—31no—
78#5186—31no—
79#5185—31no—
80#5169—31no—
81#5164—31no—
82#5162—31no—
83#5134—31no—
84#5127—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—
94C22×D32—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×#638—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C3×D3×Q8—22no—
107C3×D3×Q8—41no—
108C3×#235—22no—
109C3×#235—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6—21no—
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3755—22no—
122#3755—41no—
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217—21no—
128C3×#217D411yescharacteristic
129C3×#216—22no—
130C3×#216—22no—
131C3×#215—22no—
132C3×#215D414yescomplemented
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3—21no—
143C3×C4×Dic3C2311yescharacteristic
144C3×#208—22no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3724—21no—
148#3722—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3718—41no—
153#3717—22no—
154#3715—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—21no—
159C22×C3×Q8—31no—
160C22×C3×Q8C2×D311yescharacteristic, complemented
161C22×C3×Q8C2×D311yescharacteristic, complemented
162C2×D3×Q8C2×D311yescharacteristic
163C2×D3×D4—31no—
164C2×#235C2×D311yescharacteristic
165C22×D12—31no—
166C3×#137—64no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×M16—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#947—31no—
182#946—21no—
183#946—31no—
184#946C2×D311yescharacteristic
185Q8×Dic3C2×D311yescharacteristic, complemented
186#944—21no—
187#944C2×D311yescharacteristic, complemented
188C2×#216—31no—
189C2×#216—31no—
190C2×#216C2×D311yescharacteristic, complemented
191C2×#216C2×D311yescharacteristic, complemented
192#942—24no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196C2×#215—31no—
197C2×#215—31no—
198C2×#215—31no—
199C2×#215—61no—
200C2×#215—61no—
201C2×#215—64no—
202C2×#215C2×D311yescharacteristic
203C2×#215C2×D311yescharacteristic
204#939—61no—
205#937—61no—
206#937—61no—
207D4×Dic3—31no—
208C2×#214—31no—
209#930—31no—
210#930—31no—
211#930—61no—
212#929—61no—
213C4×#67—21no—
214C4×#67C2×D311yescharacteristic
215C2×(C2×D3)⋊C4—61no—
216#924—21no—
217#924—31no—
218#924C2×D311yescharacteristic, complemented
219C2×#208C2×D311yescharacteristic, complemented
220C22×C3⋊C8—31no—
221D3×SD16—64no—
222C2×#204—31no—
223C2×D3×C8—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—31no—
235#835—61no—
236#835—61no—
237#832—31no—
238#830—31no—
239#830—31no—
240#830—31no—
241#830—61no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244#818—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×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
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
273#638—81no—
274C2×C3⋊Dic3—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C3×#67—22no—
278C3×#67—42no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296#626—42no—
297D3×Dic3—81no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—31no—
303C22×SD16—91no—
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—
317C23×D3—61no—
318C23×D3—61no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—21no—
323C2×C3×Q8—22no—
324C2×C3×Q8—22no—
325C2×C3×Q8—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×Q8—41no—
330C2×C3×Q8—42no—
331C2×C3×Q8—41no—
332C2×C3×Q8—41no—
333C2×C3×Q8—42no—
334C2×C3×Q8—61no—
335C2×C3×Q8—62no—
336C2×C3×Q8—121no—
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×Q8C22×D311yescharacteristic
339C2×C3×Q8C22×D311yescharacteristic
340C2×C3×Q8C22×D311yescharacteristic
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—61no—
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×C4—61no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—21no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—121no—
358C2×#67#6711yescharacteristic
359C22×Dic3—61no—
360D3×Q8—22no—
361D3×Q8—41no—
362D3×D4—62no—
363D3×D4—121no—
364#235—22no—
365#235—41no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—61no—
369C2×D12—62no—
370C2×D12—61no—
371C2×D12—121no—
372C2×D12C22×D311yescharacteristic
373C2×C4×D3—21no—
374C2×C4×D3—21no—
375C2×C4×D3—61no—
376C2×C4×D3C22×D311yescharacteristic
377C2×Dic6—21no—
378C2×Dic6C22×D311yescharacteristic
379C2×Dic6C22×D311yescharacteristic
380C3×Q16—62no—
381C3×Q16—62no—
382C3×SD16—34no—
383C3×SD16—62no—
384C3×M16—62no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C42—31no—
399C3×C42—61no—
400#217—21no—
401#217—61no—
402#217—61no—
403#217#6711yescharacteristic
404#216—22no—
405#216—22no—
406#216—121no—
407#216—121no—
408#215—22no—
409#215—62no—
410#215—62no—
411#215—62no—
412#215—62no—
413#215—122no—
414#215—121no—
415#215—121no—
416#215—122no—
417#215#6714yescomplemented
418#214—62no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4#6711yescharacteristic
430C4⋊Dic3—21no—
431C4⋊Dic3—31no—
432C4⋊Dic3—31no—
433C4⋊Dic3—61no—
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—21no—
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438Dic3⋊C4—21no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4#6711yescharacteristic
442C4×Dic3—21no—
443C4×Dic3C22×D311yescharacteristic
444#208—22no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—62no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454#204—62no—
455D3×C8—62no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32C22×D411yescharacteristic
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—22no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3#13712yescomplemented
469D32—84no—
470C32×C4—22no—
471C32×C4—21no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—41no—
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×Q8D3211yescharacteristic, complemented
485C22×D4—91no—
486#137—64no—
487C2×Q16—31no—
488C2×Q16—31no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—31no—
498C22×C8—91no—
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×C3D3×D411yescharacteristic
531C23×C3C2×#6711yescharacteristic
532C22×D3—21no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—241no—
541C22×D3—241no—
542C22×D3C2×#6711yescharacteristic
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—22no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—22no—
551C3×Q8—41no—
552C3×Q8—41no—
553C3×Q8—42no—
554C3×Q8—42no—
555C3×Q8—44no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×Q8—61no—
560C3×Q8—122no—
561C3×Q8D3×D412yes—
562C3×Q8C2×#6712yes—
563C3×D4—32no—
564C3×D4—62no—
565C3×D4—61no—
566C3×D4—122no—
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—21no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—42no—
585C2×C3×C4—42no—
586C2×C3×C4—44no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—122no—
593C2×C3×C4—122no—
594C2×C3×C4D3×D411yescharacteristic
595C2×C3×C4C2×#6711yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597C2×C3×C4C23×D311yescharacteristic
598#67—22no—
599#67—42no—
600#67—122no—
601#67—241no—
602#67—241no—
603#67—242no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—121no—
610C2×Dic3—241no—
611C2×Dic3C2×#6711yescharacteristic
612C2×Dic3C2×#6711yescharacteristic
613C2×Dic3C2×#6711yescharacteristic
614D12—21no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—121no—
620D12—121no—
621D12—122no—
622D12C2×#6712yes—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—42no—
626C4×D3—42no—
627C4×D3—241no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631Dic6—21no—
632Dic6—42no—
633C3×C8—32no—
634C3×C8—61no—
635C3⋊C8—21no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8—121no—
642C3⋊C8C2×#6712yes—
643C2×C32—41no—
644C2×C32D4211yescharacteristic
645C2×C32C2×#13711yescharacteristic
646C2×C32#57711yescharacteristic
647C3⋊D3—81no—
648C3×D3—22no—
649C3×D3—42no—
650C24—181no—
651#41—62no—
652#41—121no—
653C2×Q8—21no—
654C2×Q8—22no—
655C2×Q8—31no—
656C2×Q8—31no—
657C2×Q8—41no—
658C2×Q8—61no—
659C2×Q8—62no—
660C2×Q8—121no—
661C2×Q8C2×D3211yescharacteristic
662C2×Q8C2×D3211yescharacteristic
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—61no—
666C2×D4—91no—
667C2×D4—181no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—21no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—181no—
676C22×C4C2×D3211yescharacteristic
677Q16—62no—
678Q16—62no—
679Q16—361no—
680SD16—34no—
681SD16—62no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685SD16—361no—
686M16—62no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—91no—
690C2×C8—91no—
691C2×C8—182no—
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—91no—
700C4⋊C4—181no—
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C42—31no—
711C42—61no—
712C22×C3—22no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—32no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—62no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C22×#6711yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—22no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—241no—
742C2×D3—241no—
743C2×D3—241no—
744C2×D3—244no—
745C2×D3—244no—
746C2×D3#94212yescomplemented
747C3×C4—22no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—41no—
754C3×C4—42no—
755C3×C4—42no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4#100411yescharacteristic
766C3×C4#100411yescharacteristic
767C3×C4C22×#6711yescharacteristic
768Dic3—21no—
769Dic3—21no—
770Dic3—21no—
771Dic3—41no—
772Dic3—41no—
773Dic3—41no—
774Dic3—121no—
775Dic3—121no—
776Dic3—241no—
777C32#326611yescharacteristic, complemented, Sylow
778C23—31no—
779C23—61no—
780C23—181no—
781C23—362no—
782C23—362no—
783C23—721no—
784C23D3×#6711yescharacteristic
785Q8—21no—
786Q8—21no—
787Q8—21no—
788Q8—42no—
789Q8—61no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—122no—
794Q8D3×#6712yes—
795D4—32no—
796D4—62no—
797D4—61no—
798D4—122no—
799D4—181no—
800D4—181no—
801D4—362no—
802D4—721no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—42no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—181no—
819C2×C4—721no—
820C2×C4D3×#6711yescharacteristic
821C2×C4C22×D3211yescharacteristic
822C8—32no—
823C8—61no—
824C8—181no—
825C8—181no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—42no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—62no—
833C2×C3—122no—
834C2×C3D3×#13711yescharacteristic
835C2×C3#577811yescharacteristic
836C2×C3D4×#6711yescharacteristic
837C2×C3D4×#6711yescharacteristic
838C2×C3C2×#94211yescharacteristic
839C2×C3#583711yescharacteristic
840D3—22no—
841D3—42no—
842D3—241no—
843D3—241no—
844D3—481no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—32no—
849C22—61no—
850C22—61no—
851C22—62no—
852C22—121no—
853C22—121no—
854C22—361no—
855C22—361no—
856C22—361no—
857C22—724no—
858C22C2×D3×#6711yescharacteristic
859C4—21no—
860C4—22no—
861C4—41no—
862C4—61no—
863C4—61no—
864C4—61no—
865C4—121no—
866C4—121no—
867C4—121no—
868C4—361no—
869C4C2×D3×#6711yescharacteristic
870C4#6433011yescharacteristic
871C3—21no—
872C3#8355911yescharacteristic, complemented
873C3#8398711yescharacteristic, complemented
874C2—41no—
875C2—62no—
876C2—122no—
877C2—721no—
878C2D3×#94211yescharacteristic
879C2#1059531911yescharacteristic
880C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10595067C2
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. C2×C3×#942C2semidirect
3. C2×D3×#215C2semidirect
5. #10592926C2semidirect
6. #10591651C2semidirect
7. #10591635C2semidirect
8. #10591608C2semidirect
9. #10591607C2semidirect
10. #10591594C2semidirect
11. #10591566C2semidirect
12. #10591564C2semidirect
13. #10591178C2semidirect
14. #10591170C2semidirect
15. #10591147C2semidirect
18. C22×C32×Q8C22semidirect
27. C3×Q8×Dic3C22semidirect
29. C3×#944C22semidirect
30. C2×C3×#216C22semidirect
31. C2×C3×#216C22semidirect
38. C3×#924C22semidirect
39. C2×C3×#208C22semidirect
48. C2×#3718C22semidirect
52. #63662C22semidirect
53. #63662C22semidirect
54. #63657C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
62. #63554C22semidirect
66. Q8×#67D3semidirect
67. C2×#942D3semidirect
132. C3×#215D4semidirect
160. C22×C3×Q8C2×D3semidirect
161. C22×C3×Q8C2×D3semidirect
185. Q8×Dic3C2×D3semidirect
187. #944C2×D3semidirect
190. C2×#216C2×D3semidirect
191. C2×#216C2×D3semidirect
218. #924C2×D3semidirect
219. C2×#208C2×D3semidirect
417. #215#67semidirect
468. C2×C3×D3#137semidirect
484. C22×Q8D32semidirect
746. C2×D3#942semidirect
777. C32#3266semidirect
872. C3#83559semidirect
873. C3#83987semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
C2×C3×#9422
C2×D3×#2152
#105950672
#105929262
#105916512
#105916352
#105916082
#105916072
#105915942
#105915662
#105915642
#105911782
#105911702
#105911472
#839873
#835593