Finite Group Databasebeta

← #11884280

Subgroups — #11884280

Order 1152.

1066 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic, complemented
2C2×C3×#911C211yesmaximal, characteristic, complemented
3#10595252C211yesmaximal, characteristic, complemented
4#10595244C211yesmaximal, characteristic, complemented
5#10592851C211yesmaximal, characteristic, complemented
6#10591497C211yesmaximal, characteristic, complemented
7#10591476C211yesmaximal, characteristic, complemented
8#10591461C211yesmaximal, characteristic, complemented
9#10591461C211yesmaximal, characteristic, complemented
10#10591458C211yesmaximal, characteristic, complemented
11#10591450C211yesmaximal, characteristic, complemented
12#10590870C211yesmaximal, characteristic, complemented
13#10590854C211yesmaximal, characteristic, complemented
14#10590829C211yesmaximal, characteristic, complemented
15#10590722C211yesmaximal, characteristic, complemented
16#83954—31nomaximal
17#83921—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic
23D4×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C3×#214C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C3×#912—24no—
30C3×#911—24no—
31C2×C3×Dic12C2211yescharacteristic, complemented
32C2×C3×#204C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic, complemented
35#63980—21no—
36#63980—21no—
37#63976—21no—
38C2×#3724—21no—
39#63961—21no—
40#63961—21no—
41#63961—21no—
42C2×(C2×D3)⋊Dic3—21no—
43#63908C2211yescharacteristic
44C4×#625C2211yescharacteristic
45#63873C2211yescharacteristic, complemented
46#63863C2211yescharacteristic
47#63856C2211yescharacteristic
48#63856C2211yescharacteristic
49#63856C2211yescharacteristic, complemented
50C2×#3718C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic
52#63659C2211yescharacteristic
53#63659C2211yescharacteristic, complemented
54#63644C2211yescharacteristic, complemented
55#63642C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65#5829—31no—
66#5824—31no—
67#5824—31no—
68#5806—31no—
69C2×#912D311yescharacteristic, complemented
70C2×#911D311yescharacteristic, complemented
71#5239—31no—
72#5239—31no—
73#5238—31no—
74#5218—31no—
75#5190—31no—
76#5189—31no—
77#5173—31no—
78#5173—31no—
79#5171—31no—
80#5169—31no—
81#5167—31no—
82#5165—31no—
83#5162—31no—
84#5162—31no—
85#5158—31no—
86#5153—31no—
87#5152—31no—
88#5152—31no—
89#5152—61no—
90#5137—31no—
91#5127—31no—
92#5114—31no—
93#5111—31no—
94C23×C3×D3—21no—
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C22×C3⋊Dic3—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—22no—
108C3×#237—22no—
109C3×#237—41no—
110C3×#237—41no—
111C3×#237—41no—
112C3×D3×D4—22no—
113C3×D3×D4—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×#625—21no—
121C2×#625D411yescharacteristic
122C32×D8D414yescomplemented
123C2×C32×C8C2311yescharacteristic
124#3757—21no—
125#3757—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#214—22no—
131C3×#214—22no—
132C3×#214—22no—
133C3×#213—22no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×Dic12—22no—
137C3×#204—22no—
138C3×ΓL(1,𝔽25)—22no—
139C3×D3×C8—22no—
140#3724—21no—
141#3724—21no—
142#3724—21no—
143#3724—21no—
144#3724—21no—
145#3724D411yescharacteristic
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153(C2×D3)⋊Dic3D411yescharacteristic
154#3718—41no—
155#3715—41no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×D4—31no—
161C2×#237C2×D311yescharacteristic
162C2×#237C2×D311yescharacteristic
163C2×#237C2×D311yescharacteristic, complemented
164C2×D3×D4C2×D311yescharacteristic
165C3×AGL(1,ℤ/8)—64no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—21no—
173C2×C3×D8—31no—
174C2×C3×D8C2×D311yescharacteristic
175C2×C3×D8C2×D311yescharacteristic
176C2×C3×M16—31no—
177C22×C3×C8—31no—
178#953—61no—
179C2×#217—61no—
180#947—31no—
181#946—31no—
182#946—31no—
183#946—31no—
184#944—31no—
185#944—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#215—31no—
189#939—61no—
190#939—61no—
191#939—61no—
192#939—61no—
193#938—31no—
194#937—61no—
195#936—31no—
196#935—61no—
197#935—61no—
198#935—61no—
199D4×Dic3—31no—
200D4×Dic3—31no—
201D4×Dic3—31no—
202D4×Dic3—31no—
203D4×Dic3—61no—
204D4×Dic3—61no—
205C2×#214—31no—
206C2×#214C2×D311yescharacteristic
207C2×#214C2×D311yescharacteristic
208C2×#214C2×D311yescharacteristic, complemented
209C2×#213C2×D311yescharacteristic
210#930—31no—
211#929—61no—
212#929—61no—
213#929—61no—
214C4×#67—31no—
215C4×#67—31no—
216C2×(C2×D3)⋊C4—61no—
217#924—31no—
218#924—31no—
219#924—31no—
220C2×Dic3⋊C4—61no—
221C2×Dic3⋊C4—61no—
222#912—24no—
223#911—24no—
224C2×Dic12C2×D311yescharacteristic, complemented
225C2×#204C2×D311yescharacteristic
226C2×ΓL(1,𝔽25)C2×D311yescharacteristic
227C2×D3×C8C2×D311yescharacteristic, complemented
228#835—31no—
229#835—31no—
230#835—31no—
231#832—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#821—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243#817—31no—
244#817—31no—
245#817—61no—
246#816—31no—
247#816—31no—
248#816—31no—
249#815—31no—
250#815—31no—
251#815—61no—
252Dic3⋊C8—31no—
253Dic3⋊C8—31no—
254C23×C32—21no—
255C23×C32—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C32×D4—21no—
263C32×D4—21no—
264C32×D4C2×D412yes—
265C32×D4C2×D412yes—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—42no—
270C2×C3⋊Dic3—81no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—42no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#625—41no—
298#625—81no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—31no—
304C2×#135—31no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—62no—
323C3×#41—121no—
324C3×#41—121no—
325C3×#41—121no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—62no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—121no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C22×D311yescharacteristic
341C2×C3×D4C22×D311yescharacteristic
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—21no—
351C2×#67—31no—
352C2×#67—31no—
353C2×#67—61no—
354C2×#67—61no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—121no—
363C22×Dic3—121no—
364#237—22no—
365#237—22no—
366#237—22no—
367#237—41no—
368#237—41no—
369#237—41no—
370D3×D4—22no—
371D3×D4—41no—
372C2×D12C22×D311yescharacteristic
373C2×C4×D3C22×D311yescharacteristic
374C2×C4×D3C22×D311yescharacteristic
375C2×Dic6C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—62no—
379C3×SD16—62no—
380C3×SD16—62no—
381C3×SD16—62no—
382C3×SD16—62no—
383C3×D8—24no—
384C3×D8—62no—
385C3×D8#6714yescomplemented
386C3×D8#6714yescomplemented
387C3×M16—62no—
388C2×C3×C8—21no—
389C2×C3×C8—31no—
390C2×C3×C8—31no—
391C2×C3×C8—62no—
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394#217—31no—
395#217—31no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—121no—
407#217—121no—
408#216—121no—
409#216—121no—
410#215—121no—
411#214—22no—
412#214—22no—
413#214—22no—
414#214—121no—
415#213—22no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430Dic3⋊C4—31no—
431Dic3⋊C4—31no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442C4×Dic3—31no—
443C4×Dic3—31no—
444C4×Dic3—61no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450Dic12—22no—
451#204—22no—
452ΓL(1,𝔽25)—22no—
453D3×C8—22no—
454C22×C32—22no—
455C22×C32—22no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—84no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3⋊Dic3—41no—
476C3⋊Dic3—41no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C2×#41—31no—
484C2×#41—31no—
485C22×D4—31no—
486AGL(1,ℤ/8)—64no—
487#135—64no—
488C2×Q16—31no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—91no—
495C2×D8—31no—
496C2×D8D3211yescharacteristic
497C2×M16—31no—
498C22×C8—31no—
499C4⋊Q8—91no—
500#124—91no—
501#123—181no—
502#123—181no—
503#123—181no—
504C22⋊Q8—91no—
505C22⋊Q8—91no—
506C22⋊Q8—91no—
507#121—91no—
508#121—181no—
509#121—181no—
510#120—181no—
511C4×D4—91no—
512C4×D4—91no—
513C4×D4—91no—
514C2×C4⋊C4—181no—
515C2×C22⋊C4—181no—
516#106—91no—
517C4⋊C8—91no—
518#103—91no—
519#103—91no—
520#103—91no—
521#102—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—31no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3—122no—
537C23×C3—122no—
538C23×C3—241no—
539C22×D3—21no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—81no—
543C22×D3D3×D411yescharacteristic
544C22×D3D3×D411yescharacteristic
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—41no—
558C3×D4—41no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—122no—
562C3×D4—122no—
563C3×D4—122no—
564C3×D4—122no—
565C3×D4C2×#6712yes—
566C3×D4C2×#6712yes—
567C3×D4C2×#6712yes—
568C3×D4C2×#6712yes—
569C2×C3×C4—21no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—122no—
580C2×C3×C4—122no—
581C2×C3×C4—122no—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—42no—
585#67—42no—
586#67—42no—
587#67—42no—
588#67—121no—
589#67—121no—
590#67—241no—
591#67—241no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—31no—
599C2×Dic3—42no—
600C2×Dic3—42no—
601C2×Dic3—42no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—122no—
611C2×Dic3—122no—
612C2×Dic3—242no—
613C2×Dic3—241no—
614C2×Dic3—241no—
615C2×Dic3—242no—
616C2×Dic3D3×D411yescharacteristic
617C2×Dic3D3×D411yescharacteristic
618D12—21no—
619D12—21no—
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—21no—
623C4×D3—21no—
624Dic6—21no—
625Dic6—21no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630C3×C8—22no—
631C3×C8—61no—
632C3×C8—61no—
633C3×C8C2×#6712yes—
634C3×C8C2×#6712yes—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C2×C32—42no—
641C2×C32—42no—
642C2×C32D4211yescharacteristic
643C2×C32#57511yescharacteristic
644C2×C32#57711yescharacteristic
645C3×D3—41no—
646C3×D3—41no—
647C3×D3—81no—
648C24—61no—
649#41—62no—
650#41—62no—
651#41—62no—
652#41—121no—
653#41—121no—
654#41—121no—
655C2×Q8—31no—
656C2×Q8—31no—
657C2×Q8—31no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—62no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—91no—
665C2×D4—121no—
666C2×D4—181no—
667C2×D4C2×D3211yescharacteristic
668C2×D4C2×D3211yescharacteristic
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676Q16—62no—
677Q16—361no—
678SD16—62no—
679SD16—62no—
680SD16—62no—
681SD16—62no—
682SD16—361no—
683D8—62no—
684D8#62514yescomplemented
685M16—62no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—62no—
689C2×C8—91no—
690C2×C8C2×D3211yescharacteristic
691C4⋊C4—91no—
692C4⋊C4—91no—
693C4⋊C4—91no—
694C4⋊C4—181no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C22⋊C4—91no—
700C22⋊C4—91no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—91no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—244no—
739C22×C3C2×D3×D411yescharacteristic
740C22×C3C2×D3×D411yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—84no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—61no—
754C3×C4—61no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4—121no—
758C3×C4#100411yescharacteristic
759C3×C4#100411yescharacteristic
760C3×C4C22×#6711yescharacteristic
761C3×C4C22×#6711yescharacteristic
762Dic3—21no—
763Dic3—21no—
764Dic3—41no—
765Dic3—41no—
766Dic3—41no—
767Dic3—61no—
768Dic3—61no—
769Dic3—61no—
770Dic3—61no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—241no—
778Dic3—241no—
779C32#326711yescharacteristic, complemented, Sylow
780C23—21no—
781C23—21no—
782C23—31no—
783C23—31no—
784C23—61no—
785C23—122no—
786C23—122no—
787C23—241no—
788Q8—61no—
789Q8—61no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794D4—21no—
795D4—21no—
796D4—61no—
797D4—61no—
798D4—122no—
799D4—122no—
800D4—122no—
801D4—122no—
802D4—361no—
803D4—721no—
804D4C2×#62512yes—
805D4C2×#62512yes—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—362no—
823C2×C4—721no—
824C2×C4C22×D3211yescharacteristic
825C8—61no—
826C8—61no—
827C8—181no—
828C8C2×#62512yes—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—42no—
835C2×C3—42no—
836C2×C3—82no—
837C2×C3—82no—
838C2×C3—121no—
839C2×C3—121no—
840C2×C3—241no—
841C2×C3#576811yescharacteristic
842C2×C3#577011yescharacteristic
843C2×C3#577311yescharacteristic
844C2×C3#577511yescharacteristic
845C2×C3D4×#6711yescharacteristic
846C2×C3D4×#6711yescharacteristic
847D3—41no—
848D3—41no—
849D3—81no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—121no—
863C22—121no—
864C22—121no—
865C22—244no—
866C22D32×D411yescharacteristic
867C4—61no—
868C4—61no—
869C4—121no—
870C4—121no—
871C4—121no—
872C4—181no—
873C4—181no—
874C4—361no—
875C4—361no—
876C4#6431311yescharacteristic
877C4C22×#62511yescharacteristic
878C3—21no—
879C3#8392111yescharacteristic, complemented
880C3#8395411yescharacteristic, complemented
881C2—42no—
882C2—42no—
883C2—121no—
884C2—121no—
885C2—241no—
886C2#1059472911yescharacteristic
887C2#1059473611yescharacteristic
888C2D4×#62511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#912C2semidirect
2. C2×C3×#911C2semidirect
3. #10595252C2semidirect
4. #10595244C2semidirect
5. #10592851C2semidirect
6. #10591497C2semidirect
7. #10591476C2semidirect
8. #10591461C2semidirect
9. #10591461C2semidirect
10. #10591458C2semidirect
11. #10591450C2semidirect
12. #10590870C2semidirect
13. #10590854C2semidirect
14. #10590829C2semidirect
15. #10590722C2semidirect
20. C2×C3×#237C22semidirect
24. D4×C3⋊Dic3C22semidirect
27. C2×C3×#214C22semidirect
31. C2×C3×Dic12C22semidirect
34. C2×C3×D3×C8C22semidirect
45. #63873C22semidirect
49. #63856C22semidirect
50. C2×#3718C22semidirect
53. #63659C22semidirect
54. #63644C22semidirect
55. #63642C22semidirect
56. #63572C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
59. #63566C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. C2×#912D3semidirect
70. C2×#911D3semidirect
122. C32×D8D4semidirect
163. C2×#237C2×D3semidirect
208. C2×#214C2×D3semidirect
224. C2×Dic12C2×D3semidirect
227. C2×D3×C8C2×D3semidirect
385. C3×D8#67semidirect
386. C3×D8#67semidirect
684. D8#625semidirect
779. C32#3267semidirect
879. C3#83921semidirect
880. C3#83954semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
C2×C3×#9112
#105952522
#105952442
#105928512
#105914972
#105914762
#105914612
#105914582
#105914502
#105908702
#105908542
#105908292
#105907222
#839543
#839213