Finite Group Databasebeta

← #11884107

Subgroups — #11884107

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
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63951C211yesmaximal, characteristic, complemented
4#10594889C211yesmaximal, characteristic
5C3×#5228C211yesmaximal, characteristic, complemented
6#10591656C211yesmaximal, characteristic, complemented
7#10591612C211yesmaximal, characteristic, complemented
8#10591611C211yesmaximal, characteristic, complemented
9#10591592C211yesmaximal, characteristic, complemented
10#10591590C211yesmaximal, characteristic, complemented
11#10591572C211yesmaximal, characteristic, complemented
12#10591569C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14#10591172C211yesmaximal, characteristic, complemented
15#10591157C211yesmaximal, characteristic, complemented
16#83866—31nomaximal
17#80204—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22#64155—21no—
23#64155C2211yescharacteristic, complemented
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25#64153—21no—
26#64153C2211yescharacteristic, complemented
27C4×#638—21no—
28C4×#638C2211yescharacteristic
29#64133—21no—
30#64133C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#215—24no—
34C2×C3×#215C2211yescharacteristic
35C2×C3×#215C2211yescharacteristic
36C2×C3×#215C2211yescharacteristic
37C2×C3×#215C2211yescharacteristic
38C3×#924C2211yescharacteristic
39C22×C3×C3⋊C8C2211yescharacteristic
40#63977—21no—
41D3×#217—21no—
42#63951—24no—
43#63916C2211yescharacteristic
44#63898C2211yescharacteristic
45#63886—21no—
46#63884—21no—
47#63863C2211yescharacteristic
48C2×#3719C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic
50C2×#3716C2211yescharacteristic
51C2×#3712C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64Q8×#67—31no—
65Q8×#67—31no—
66Q8×#67—61no—
67C22×#215D311yescharacteristic, complemented
68#5806—31no—
69C2×#918—31no—
70C2×#915—31no—
71#5630—31no—
72C3×#451—31no—
73#5228D311yescharacteristic, complemented
74#5218—31no—
75#5190—31no—
76#5187—31no—
77#5185—31no—
78#5174—31no—
79#5173—31no—
80#5170—31no—
81#5167—31no—
82#5166—31no—
83#5164—31no—
84#5162—31no—
85#5116—31no—
86#5111—31no—
87#5051—31no—
88#4818—31no—
89#4817—31no—
90#4812—31no—
91#4806—31no—
92#4731—31no—
93#4730—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×#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×D12—22no—
110C2×C3×D12—21no—
111C2×C3×D12—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119#3796—22no—
120#3796—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×#217—21no—
135C3×#216—22no—
136C3×#216—41no—
137C3×#215—22no—
138C3×#215—22no—
139C3×#215—22no—
140C3×#215D414yescomplemented
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C2×C3×C3⋊C8—22no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
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#3716—22no—
154#3716—41no—
155#3712—22no—
156#3266—91noSylow
157C22×C3×Q8—21no—
158C22×C3×Q8C2×D311yescharacteristic
159C22×C3×Q8C2×D311yescharacteristic
160C22×C3×D4—31no—
161C2×#239—31no—
162C2×D3×Q8—31no—
163C2×D3×Q8—31no—
164C2×D3×Q8—61no—
165C2×#237—31no—
166C22×D12C2×D311yescharacteristic
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—64no—
174C22×C3×C8—31no—
175C3×C22⋊Q8—31no—
176#953—61no—
177C2×#217—61no—
178#947—31no—
179#946—31no—
180#946—31no—
181#946—61no—
182#946—61no—
183#946—61no—
184#946—62no—
185Q8×Dic3—31no—
186Q8×Dic3—31no—
187Q8×Dic3—61no—
188#944—31no—
189#944—31no—
190#944—61no—
191#944—61no—
192#944—61no—
193#944—62no—
194C2×#216—31no—
195C2×#216C2×D311yescharacteristic, complemented
196C2×#216C2×D311yescharacteristic, complemented
197C2×#215—24no—
198C2×#215C2×D311yescharacteristic
199C2×#215C2×D311yescharacteristic
200C2×#215C2×D311yescharacteristic
201C2×#215C2×D311yescharacteristic
202#939—61no—
203#938—31no—
204#936—31no—
205#935—61no—
206D4×Dic3—31no—
207C2×#214—31no—
208C2×#214—31no—
209C4×#67—31no—
210C4×#67—31no—
211C4×#67—61no—
212C4×#67—61no—
213C4×#67—61no—
214C4×#67—62no—
215#924—31no—
216#924—31no—
217#924—61no—
218#924—61no—
219#924—61no—
220#924—62no—
221#924C2×D311yescharacteristic
222C22×C3⋊C8C2×D311yescharacteristic
223#918—64no—
224#915—64no—
225C2×Dic12—31no—
226C2×#204—31no—
227C2×#204—31no—
228C2×ΓL(1,𝔽25)—31no—
229C2×ΓL(1,𝔽25)—31no—
230#895—31no—
231#895—61no—
232#894—61no—
233#893—31no—
234#882—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
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—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—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—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—42no—
295C3×D12C2×D412yes—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#626—42no—
299#626—81no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#137—91no—
307C22×SD16—31no—
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—31no—
317#450—91no—
318#448—91no—
319#440—91no—
320#435—91no—
321C24×C3—61no—
322C23×D3—21no—
323C2×C3×Q8—22no—
324C2×C3×Q8—21no—
325C2×C3×Q8—21no—
326C2×C3×Q8—22no—
327C2×C3×Q8—22no—
328C2×C3×Q8—21no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8—42no—
332C2×C3×Q8—41no—
333C2×C3×Q8—41no—
334C2×C3×Q8—42no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×Q8C22×D311yescharacteristic
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—62no—
342C2×C3×D4—61no—
343C2×C3×D4—121no—
344C22×C3×C4—22no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—31no—
351C2×#67—31no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357#239—62no—
358#239—121no—
359D3×Q8—62no—
360D3×Q8—62no—
361D3×Q8—122no—
362D3×Q8—121no—
363D3×Q8—121no—
364D3×Q8—122no—
365#237—62no—
366#237—121no—
367C2×D12—22no—
368C2×D12—21no—
369C2×D12—41no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×C4×D3—31no—
375C2×C4×D3—31no—
376C2×C4×D3—61no—
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—121no—
391C3×SD16—34no—
392C3×SD16—62no—
393C3×SD16—62no—
394C3×SD16—62no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—62no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—61no—
402C3×C22⋊C4—61no—
403#217—21no—
404#217—31no—
405#217—31no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217—62no—
412#217—61no—
413#217—61no—
414#216—22no—
415#216—41no—
416#216—62no—
417#215—22no—
418#215—22no—
419#215—22no—
420#215#6714yescomplemented
421#214—62no—
422#214—121no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—31no—
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—61no—
432(C2×D3)⋊C4—62no—
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—61no—
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3—62no—
439C4⋊Dic3C22×D311yescharacteristic
440Dic3⋊C4—21no—
441Dic3⋊C4—31no—
442Dic3⋊C4—31no—
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—
462C2×C3⋊C8—22no—
463C2×C3⋊C8C22×D311yescharacteristic
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466C2×C3⋊C8C22×D311yescharacteristic
467Dic12—62no—
468#204—62no—
469#204—121no—
470ΓL(1,𝔽25)—62no—
471ΓL(1,𝔽25)—62no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32#13712yescomplemented
475C22×C32C22×D411yescharacteristic
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—21no—
479C2×C3×D3—22no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—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—91no—
499C22×Q8—91no—
500C22×Q8D3211yescharacteristic
501C22×D4—31no—
502#137—184no—
503C2×Q16—31no—
504C2×Q16—31no—
505C2×Q16—91no—
506C2×SD16—31no—
507C2×SD16—31no—
508C2×SD16—31no—
509C2×SD16—31no—
510C2×SD16—64no—
511C2×SD16—91no—
512C2×SD16—91no—
513C2×M16—91no—
514C22×C8—31no—
515C4⋊Q8—91no—
516C4⋊Q8—181no—
517#124—91no—
518#123—181no—
519C22⋊Q8—31no—
520C22⋊Q8—91no—
521C22⋊Q8—91no—
522C22⋊Q8—181no—
523C22⋊Q8—181no—
524#121—91no—
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×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C23×C3D3×D411yescharacteristic
550C23×C3D3×D411yescharacteristic
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—31no—
554C22×D3—31no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—61no—
558C22×D3—81no—
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—
581C2×C3×C4—22no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—42no—
596C2×C3×C4—42no—
597C2×C3×C4—44no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4D3×D411yescharacteristic
601C2×C3×C4D3×D411yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604#67—64no—
605#67—62no—
606#67—62no—
607#67—122no—
608#67—241no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—122no—
627C2×Dic3—241no—
628D12—21no—
629D12—21no—
630D12—21no—
631D12—42no—
632D12—122no—
633D12—241no—
634D12C2×#6712yes—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—61no—
639C4×D3—121no—
640C4×D3—121no—
641C4×D3—122no—
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—22no—
666C2×C32D4211yescharacteristic
667C2×C32C2×#13711yescharacteristic
668C2×C32#57711yescharacteristic
669C3⋊D3—41no—
670C3×D3—42no—
671C3×D3—81no—
672C24—61no—
673#41—182no—
674#41—361no—
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—62no—
688C2×D4—61no—
689C2×D4—91no—
690C2×D4—121no—
691C2×D4—181no—
692C2×D4—181no—
693C22×C4—21no—
694C22×C4—91no—
695C22×C4—181no—
696C22×C4—181no—
697C22×C4—181no—
698C22×C4C2×D3211yescharacteristic
699Q16—62no—
700Q16—121no—
701Q16—182no—
702SD16—34no—
703SD16—62no—
704SD16—62no—
705SD16—62no—
706SD16—182no—
707SD16—361no—
708M16—182no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—62no—
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—91no—
717C4⋊C4—91no—
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—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—22no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—62no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—244no—
749C22×C3#91512yescomplemented
750C22×C3#91812yescomplemented
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C2×D3—22no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—62no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—84no—
767C2×D3—121no—
768C2×D3—121no—
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—122no—
808C23—122no—
809C23—241no—
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—362no—
828D4—721no—
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—181no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4—362no—
844C2×C4—362no—
845C2×C4—721no—
846C2×C4#381111yescharacteristic
847C2×C4C22×D3211yescharacteristic
848C8—32no—
849C8—61no—
850C8—61no—
851C8—61no—
852C2×C3—22no—
853C2×C3—22no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—42no—
858C2×C3—122no—
859C2×C3—241no—
860C2×C3#559011yescharacteristic
861C2×C3C2×#91511yescharacteristic
862C2×C3#576211yescharacteristic
863C2×C3C2×#91811yescharacteristic
864C2×C3#577811yescharacteristic
865C2×C3D4×#6711yescharacteristic
866D3—42no—
867D3—81no—
868D3—122no—
869D3—121no—
870D3—121no—
871C22—21no—
872C22—21no—
873C22—62no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—181no—
880C22—181no—
881C22—181no—
882C22—244no—
883C22#6395112yescomplemented
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#8020411yescharacteristic, complemented
899C3#8386611yescharacteristic, complemented
900C2—22no—
901C2—122no—
902C2—241no—
903C2—361no—
904C2#1059532411yescharacteristic
905C2C2×#6395111yescharacteristic
906C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10594889C2
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. C22×C3×#215C2semidirect
3. C2×#63951C2semidirect
5. C3×#5228C2semidirect
6. #10591656C2semidirect
7. #10591612C2semidirect
8. #10591611C2semidirect
9. #10591592C2semidirect
10. #10591590C2semidirect
11. #10591572C2semidirect
12. #10591569C2semidirect
13. #10591187C2semidirect
14. #10591172C2semidirect
15. #10591157C2semidirect
19. C2×Q8×C3⋊D3C22semidirect
23. #64155C22semidirect
24. Q8×C3⋊Dic3C22semidirect
26. #64153C22semidirect
31. C2×C3×#216C22semidirect
32. C2×C3×#216C22semidirect
48. C2×#3719C22semidirect
51. C2×#3712C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
61. #63557C22semidirect
62. #63555C22semidirect
67. C22×#215D3semidirect
73. #5228D3semidirect
140. C3×#215D4semidirect
195. C2×#216C2×D3semidirect
196. C2×#216C2×D3semidirect
240. #835C2×D3semidirect
241. #835C2×D3semidirect
420. #215#67semidirect
474. C22×C32#137semidirect
749. C22×C3#915semidirect
750. C22×C3#918semidirect
803. C32#3266semidirect
883. C22#63951semidirect
898. C3#80204semidirect
899. C3#83866semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
C22×C3×#2152
C2×#639512
#105948892
C3×#52282
#105916562
#105916122
#105916112
#105915922
#105915902
#105915722
#105915692
#105911872
#105911722
#105911572
#838663
#802043