Finite Group Databasebeta

← #11884096

Subgroups — #11884096

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#638C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3C2×#63940C211yesmaximal, characteristic, complemented
4#10595070C211yesmaximal, characteristic
5C3×#5227C211yesmaximal, characteristic, complemented
6#10591652C211yesmaximal, characteristic, complemented
7#10591612C211yesmaximal, characteristic, complemented
8#10591611C211yesmaximal, characteristic, complemented
9#10591603C211yesmaximal, characteristic, complemented
10#10591601C211yesmaximal, characteristic, complemented
11#10591572C211yesmaximal, characteristic, complemented
12#10591569C211yesmaximal, characteristic, complemented
13#10591176C211yesmaximal, characteristic, complemented
14#10591173C211yesmaximal, characteristic, complemented
15#10591149C211yesmaximal, characteristic, complemented
16#83987—31nomaximal
17#80061—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×#3802C2211yescharacteristic
22#64155—21no—
23#64155C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25#64153—21no—
26#64153C2211yescharacteristic, complemented
27C4×#638—21no—
28C4×#638C2211yescharacteristic
29#64133—21no—
30#64133C2211yescharacteristic, complemented
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#216C2211yescharacteristic, complemented
33C3×#942—24no—
34C2×C3×#215C2211yescharacteristic
35C2×C3×#215C2211yescharacteristic
36C2×C3×#215C2211yescharacteristic
37C2×C3×#215C2211yescharacteristic
38C3×#930C2211yescharacteristic
39C2×C3×#208C2211yescharacteristic, complemented
40#63983—21no—
41#63970—21no—
42#63940—24no—
43D3×(C2×D3)⋊C4—21no—
44#63905—21no—
45#63898C2211yescharacteristic
46#63871C2211yescharacteristic
47#63863C2211yescharacteristic
48C2×#3719C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic
50C2×#3716C2211yescharacteristic
51C2×#3710C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#63557C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64#5829—31no—
65Q8×#67—31no—
66Q8×#67—31no—
67Q8×#67—61no—
68C2×#942D311yescharacteristic, complemented
69C2×D3×SD16—31no—
70C2×D3×SD16—31no—
71#5612—31no—
72C3×#448—31no—
73#5239—31no—
74#5227D311yescharacteristic, complemented
75#5190—31no—
76#5188—31no—
77#5186—31no—
78#5185—31no—
79#5169—31no—
80#5169—31no—
81#5167—31no—
82#5166—31no—
83#5164—31no—
84#5162—31no—
85#5134—31no—
86#5127—31no—
87#5042—31no—
88#4818—31no—
89#4817—31no—
90#4813—31no—
91#4809—31no—
92#4733—31no—
93#4728—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×#638D411yescharacteristic
103Q8×C3⋊D3—22no—
104Q8×C3⋊D3—41no—
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634—21no—
108C2×#634C2311yescharacteristic
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C3×#235—22no—
112C3×#235—41no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×Dic6C2311yescharacteristic
117C2×#625—21no—
118C2×D3×Dic3—21no—
119#3802—22no—
120#3802—41no—
121#3757—21no—
122#3757D411yescharacteristic
123#3752—21no—
124#3752D411yescharacteristic
125C4⋊(C3⋊Dic3)—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128#3750—21no—
129#3750—21no—
130#3750—21no—
131#3750D411yescharacteristic
132C4×C3⋊Dic3—21no—
133C4×C3⋊Dic3C2311yescharacteristic
134C3×#216—22no—
135C3×#216—22no—
136C3×#215—22no—
137C3×#215—22no—
138C3×#215—41no—
139C3×#215D414yescomplemented
140C3×(C2×D3)⋊C4—21no—
141C3×C4⋊Dic3C2311yescharacteristic
142C3×#208—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148#3722—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#3710—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—21no—
159C22×C3×Q8C2×D311yescharacteristic, complemented
160C22×C3×Q8C2×D311yescharacteristic, complemented
161C2×D3×Q8—31no—
162C2×D3×Q8—31no—
163C2×D3×Q8—61no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×#235C2×D311yescharacteristic
167C3×#137—64no—
168C2×C3×Q16—31no—
169C2×C3×Q16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×M16—31no—
175C3×#121—31no—
176#947—31no—
177#946—31no—
178#946—31no—
179#946—31no—
180#946—61no—
181#946—61no—
182#946—61no—
183#946—62no—
184Q8×Dic3—31no—
185Q8×Dic3—31no—
186Q8×Dic3—61no—
187#944—31no—
188#944—31no—
189#944—61no—
190#944—61no—
191#944—61no—
192#944—62no—
193C2×#216—31no—
194C2×#216C2×D311yescharacteristic, complemented
195C2×#216C2×D311yescharacteristic, complemented
196#942—24no—
197C2×#215C2×D311yescharacteristic
198C2×#215C2×D311yescharacteristic
199C2×#215C2×D311yescharacteristic
200C2×#215C2×D311yescharacteristic
201#939—61no—
202#938—61no—
203#937—61no—
204#937—61no—
205#936—31no—
206D4×Dic3—31no—
207C2×#214—31no—
208C2×#214—31no—
209#930C2×D311yescharacteristic
210#929—61no—
211C4×#67—31no—
212C4×#67—31no—
213C4×#67—61no—
214C4×#67—61no—
215C4×#67—61no—
216C4×#67—62no—
217C2×(C2×D3)⋊C4—61no—
218#924—31no—
219#924—31no—
220#924—61no—
221#924—61no—
222#924—61no—
223#924—62no—
224C2×#208C2×D311yescharacteristic, complemented
225D3×SD16—64no—
226D3×SD16—64no—
227C2×Dic12—31no—
228C2×#204—31no—
229C2×#204—31no—
230C2×D3×C8—31no—
231C2×D3×C8—31no—
232#897—31no—
233#893—31no—
234#883—61no—
235D3×C22⋊C4—61no—
236C3×#103—31no—
237C3×#103—31no—
238C3×C22⋊C8—31no—
239#835—31no—
240#835C2×D311yescharacteristic, complemented
241#835C2×D311yescharacteristic, complemented
242#832—31no—
243#832—31no—
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246#821—31no—
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249#818—31no—
250#816—31no—
251#816—31no—
252#815—31no—
253#815—31no—
254Dic3⋊C8—31no—
255Dic3⋊C8—31no—
256#810—31no—
257#807—31no—
258C23×C32C2×D411yescharacteristic
259C22×C3⋊D3C2×D411yescharacteristic
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—81no—
265C32×Q8—21no—
266C32×Q8—21no—
267C32×Q8—21no—
268C32×Q8—42no—
269C32×Q8C2×D412yes—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277#638—22no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3C2×D411yescharacteristic
281C2×C3⋊Dic3C2×D411yescharacteristic
282C2×C3⋊Dic3C2×D411yescharacteristic
283C4×C3⋊D3—21no—
284C4×C3⋊D3—21no—
285C4×C3⋊D3—42no—
286#634—21no—
287#634—21no—
288#634—42no—
289C3×#67—42no—
290C3×#67—81no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12C2×D412yes—
297C3×C4×D3—42no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300#625—42no—
301D3×Dic3—81no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#137—31no—
307C22×SD16—91no—
308D4×Q8—91no—
309#546—91no—
310#497—91no—
311#468—91no—
312#467—91no—
313#464—91no—
314#461—91no—
315#452—91no—
316#451—91no—
317#450—91no—
318#448—31no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—22no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8—22no—
329C2×C3×Q8—22no—
330C2×C3×Q8—21no—
331C2×C3×Q8—21no—
332C2×C3×Q8—31no—
333C2×C3×Q8—42no—
334C2×C3×Q8—41no—
335C2×C3×Q8—41no—
336C2×C3×Q8—42no—
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—
344C2×C3×D4—61no—
345C22×C3×C4—22no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—61no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—21no—
353C2×#67—21no—
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C22×Dic3—61no—
360D3×Q8—62no—
361D3×Q8—62no—
362D3×Q8—122no—
363D3×Q8—121no—
364D3×Q8—121no—
365D3×Q8—122no—
366D3×D4—62no—
367D3×D4—62no—
368D3×D4—121no—
369D3×D4—121no—
370#235—22no—
371#235—41no—
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×C4×D3—21no—
375C2×C4×D3—31no—
376C2×C4×D3—31no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—62no—
381C2×C4×D3—61no—
382C2×Dic6—31no—
383C2×Dic6—31no—
384C2×Dic6—61no—
385C2×Dic6—61no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6C22×D311yescharacteristic
389C3×Q16—62no—
390C3×Q16—62no—
391C3×SD16—34no—
392C3×SD16—62no—
393C3×SD16—62no—
394C3×SD16—121no—
395C3×M16—62no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C3×C4⋊C4—31no—
401C3×C22⋊C4—61no—
402#217—31no—
403#217—31no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—62no—
409#217—61no—
410#217—61no—
411#216—22no—
412#216—22no—
413#216—121no—
414#215—22no—
415#215—22no—
416#215—41no—
417#215#6714yescomplemented
418#214—62no—
419#214—62no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
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—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—62no—
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3—62no—
439C4⋊Dic3C22×D311yescharacteristic
440Dic3⋊C4—31no—
441Dic3⋊C4—31no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447Dic3⋊C4—61no—
448Dic3⋊C4—61no—
449Dic3⋊C4—61no—
450Dic3⋊C4—62no—
451Dic3⋊C4—62no—
452Dic3⋊C4—62no—
453Dic3⋊C4—62no—
454Dic3⋊C4—61no—
455Dic3⋊C4—61no—
456C4×Dic3—31no—
457C4×Dic3—31no—
458C4×Dic3—61no—
459C4×Dic3—61no—
460C4×Dic3—61no—
461C4×Dic3—62no—
462#208—22no—
463C2×C3⋊C8C22×D311yescharacteristic
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466C2×C3⋊C8C22×D311yescharacteristic
467Dic12—121no—
468#204—62no—
469#204—62no—
470D3×C8—62no—
471D3×C8—62no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32C22×D411yescharacteristic
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3#13712yescomplemented
479C2×C3×D3—22no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485D32—84no—
486C32×C4—22no—
487C32×C4—21no—
488C32×C4—41no—
489C32×C4C22×D411yescharacteristic
490C32×C4H(5,𝔽2)11yescharacteristic
491C3⋊Dic3—21no—
492C3⋊Dic3—21no—
493C3⋊Dic3—21no—
494C3⋊Dic3—41no—
495C3⋊Dic3—41no—
496C3×Dic3—41no—
497C3×Dic3—41no—
498C2×#41—31no—
499C22×Q8—91no—
500C22×Q8D3211yescharacteristic, complemented
501C22×D4—91no—
502#137—64no—
503C2×Q16—31no—
504C2×Q16—31no—
505C2×Q16—91no—
506C2×SD16—31no—
507C2×SD16—31no—
508C2×SD16—31no—
509C2×SD16—31no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—184no—
513C2×M16—31no—
514C22×C8—91no—
515C4⋊Q8—91no—
516C4⋊Q8—181no—
517#124—91no—
518#123—181no—
519C22⋊Q8—91no—
520C22⋊Q8—91no—
521C22⋊Q8—91no—
522C22⋊Q8—181no—
523C22⋊Q8—181no—
524#121—31no—
525#121—181no—
526#120—181no—
527C4×Q8—91no—
528C4×D4—91no—
529C4×D4—91no—
530C4×D4—181no—
531C2×C22⋊C4—181no—
532#107—91no—
533C4⋊C8—91no—
534#103—31no—
535#103—31no—
536#103—91no—
537#103—91no—
538#102—91no—
539#102—91no—
540C22⋊C8—31no—
541C22⋊C8—91no—
542#97—91no—
543C23×C3—21no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3D3×D411yescharacteristic
547C23×C3D3×D411yescharacteristic
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—31no—
551C22×D3—31no—
552C22×D3—61no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—241no—
558C22×D3—241no—
559C3×Q8—22no—
560C3×Q8—21no—
561C3×Q8—21no—
562C3×Q8—21no—
563C3×Q8—21no—
564C3×Q8—21no—
565C3×Q8—21no—
566C3×Q8—22no—
567C3×Q8—41no—
568C3×Q8—41no—
569C3×Q8—42no—
570C3×Q8—42no—
571C3×Q8—44no—
572C3×Q8—61no—
573C3×Q8—61no—
574C3×Q8D3×D412yes—
575C3×Q8C2×#6712yes—
576C3×D4—32no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—122no—
581C3×D4—241no—
582C2×C3×C4—22no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—22no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—42no—
597C2×C3×C4—42no—
598C2×C3×C4—44no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—122no—
602C2×C3×C4D3×D411yescharacteristic
603C2×C3×C4D3×D411yescharacteristic
604C2×C3×C4C23×D311yescharacteristic
605C2×C3×C4C23×D311yescharacteristic
606#67—42no—
607#67—62no—
608#67—62no—
609#67—64no—
610#67—81no—
611#67—122no—
612#67—122no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—241no—
631D12—21no—
632D12—21no—
633D12—21no—
634D12C2×#6712yes—
635C4×D3—42no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—61no—
639C4×D3—61no—
640C4×D3—121no—
641C4×D3—121no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—124no—
645C4×D3—241no—
646Dic6—21no—
647Dic6—21no—
648Dic6—61no—
649Dic6—61no—
650Dic6—61no—
651Dic6—61no—
652Dic6—121no—
653Dic6—121no—
654Dic6—122no—
655Dic6—122no—
656Dic6—124no—
657C3×C8—32no—
658C3×C8—61no—
659C3×C8—61no—
660C3×C8—61no—
661C3⋊C8—21no—
662C3⋊C8—21no—
663C3⋊C8—21no—
664C3⋊C8C2×#6712yes—
665C2×C32—41no—
666C2×C32D4211yescharacteristic
667C2×C32C2×#13711yescharacteristic
668C2×C32#57711yescharacteristic
669C3⋊D3—22no—
670C3×D3—42no—
671C3×D3—81no—
672C24—181no—
673#41—62no—
674#41—121no—
675C2×Q8—21no—
676C2×Q8—22no—
677C2×Q8—31no—
678C2×Q8—41no—
679C2×Q8—91no—
680C2×Q8—181no—
681C2×Q8—182no—
682C2×Q8—361no—
683C2×Q8C2×D3211yescharacteristic
684C2×Q8C2×D3211yescharacteristic
685C2×D4—31no—
686C2×D4—31no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—91no—
690C2×D4—181no—
691C2×D4—182no—
692C2×D4—361no—
693C22×C4—21no—
694C22×C4—61no—
695C22×C4—91no—
696C22×C4—181no—
697C22×C4—181no—
698C22×C4C2×D3211yescharacteristic
699Q16—62no—
700Q16—62no—
701Q16—361no—
702SD16—34no—
703SD16—62no—
704SD16—62no—
705SD16—121no—
706SD16—182no—
707SD16—182no—
708M16—62no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—182no—
714C4⋊C4—31no—
715C4⋊C4—91no—
716C4⋊C4—91no—
717C4⋊C4—181no—
718C4⋊C4—181no—
719C4⋊C4—181no—
720C4⋊C4—181no—
721C4⋊C4—181no—
722C4⋊C4—181no—
723C22⋊C4—61no—
724C22⋊C4—91no—
725C22⋊C4—91no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C42—91no—
733C42—181no—
734C22×C3—22no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—62no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3C2×D3×D411yescharacteristic
751C22×C3C2×D3×D411yescharacteristic
752C2×D3—22no—
753C2×D3—32no—
754C2×D3—32no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—62no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—244no—
768C2×D3—244no—
769C3×C4—24no—
770C3×C4—22no—
771C3×C4—21no—
772C3×C4—22no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—41no—
777C3×C4—42no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—121no—
781C3×C4—121no—
782C3×C4C2×D3×D411yescharacteristic
783C3×C4#100411yescharacteristic
784C3×C4#100411yescharacteristic
785C3×C4C22×#6711yescharacteristic
786Dic3—41no—
787Dic3—41no—
788Dic3—62no—
789Dic3—61no—
790Dic3—61no—
791Dic3—61no—
792Dic3—61no—
793Dic3—61no—
794Dic3—61no—
795Dic3—121no—
796Dic3—121no—
797Dic3—122no—
798Dic3—122no—
799Dic3—121no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803C32#326611yescharacteristic, complemented, Sylow
804C23—61no—
805C23—61no—
806C23—91no—
807C23—362no—
808C23—362no—
809C23—721no—
810C23#381111yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—42no—
815Q8—61no—
816Q8—61no—
817Q8—181no—
818Q8—181no—
819Q8—362no—
820Q8D3×#6712yes—
821D4—32no—
822D4—61no—
823D4—61no—
824D4—61no—
825D4—122no—
826D4—182no—
827D4—241no—
828D4—362no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—42no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—91no—
837C2×C4—91no—
838C2×C4—91no—
839C2×C4—122no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4—181no—
844C2×C4—362no—
845C2×C4—721no—
846C2×C4#381111yescharacteristic
847C2×C4C22×D3211yescharacteristic
848C8—32no—
849C8—61no—
850C8—61no—
851C8—61no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—42no—
856C2×C3—41no—
857C2×C3—41no—
858C2×C3—122no—
859C2×C3—241no—
860C2×C3#559011yescharacteristic
861C2×C3#576211yescharacteristic
862C2×C3D3×#13711yescharacteristic
863C2×C3D3×#13711yescharacteristic
864C2×C3#577811yescharacteristic
865C2×C3D4×#6711yescharacteristic
866D3—42no—
867D3—62no—
868D3—62no—
869D3—81no—
870D3—122no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—62no—
875C22—92no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—181no—
882C22—181no—
883C22—724no—
884C22C2×#381111yescharacteristic
885C4—21no—
886C4—22no—
887C4—41no—
888C4—121no—
889C4—121no—
890C4—181no—
891C4—181no—
892C4—181no—
893C4—361no—
894C4—361no—
895C4C2×D3×#6711yescharacteristic
896C4#6433011yescharacteristic
897C3—21no—
898C3#8006111yescharacteristic, complemented
899C3#8398711yescharacteristic, complemented
900C2—41no—
901C2—122no—
902C2—182no—
903C2—241no—
904C2#1059532211yescharacteristic
905C2#1059532411yescharacteristic
906C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10595070C2
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. Q8×#638C2semidirect
2. C2×C3×#942C2semidirect
3. C2×#63940C2semidirect
5. C3×#5227C2semidirect
6. #10591652C2semidirect
7. #10591612C2semidirect
8. #10591611C2semidirect
9. #10591603C2semidirect
10. #10591601C2semidirect
11. #10591572C2semidirect
12. #10591569C2semidirect
13. #10591176C2semidirect
14. #10591173C2semidirect
15. #10591149C2semidirect
18. C22×C32×Q8C22semidirect
24. Q8×C3⋊Dic3C22semidirect
26. #64153C22semidirect
30. #64133C22semidirect
31. C2×C3×#216C22semidirect
32. C2×C3×#216C22semidirect
39. C2×C3×#208C22semidirect
48. C2×#3719C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#830C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
62. #63555C22semidirect
68. C2×#942D3semidirect
74. #5227D3semidirect
139. C3×#215D4semidirect
159. C22×C3×Q8C2×D3semidirect
160. C22×C3×Q8C2×D3semidirect
194. C2×#216C2×D3semidirect
195. C2×#216C2×D3semidirect
224. C2×#208C2×D3semidirect
240. #835C2×D3semidirect
241. #835C2×D3semidirect
244. #830C2×D3semidirect
417. #215#67semidirect
478. C2×C3⋊D3#137semidirect
500. C22×Q8D32semidirect
803. C32#3266semidirect
898. C3#80061semidirect
899. C3#83987semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
C2×C3×#9422
C2×#639402
#105950702
C3×#52272
#105916522
#105916122
#105916112
#105916032
#105916012
#105915722
#105915692
#105911762
#105911732
#105911492
#839873
#800613