Finite Group Databasebeta

← #11884137

Subgroups — #11884137

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2#10595400C211yesmaximal, characteristic, complemented
3#10595244C211yesmaximal, characteristic
4C2×#63929C211yesmaximal, characteristic, complemented
5#10592861C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7#10591611C211yesmaximal, characteristic, complemented
8#10591594C211yesmaximal, characteristic, complemented
9#10591587C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591446C211yesmaximal, characteristic, complemented
12#10590848C211yesmaximal, characteristic, complemented
13#10590822C211yesmaximal, characteristic, complemented
14#10590796C211yesmaximal, characteristic, complemented
15#10590723C211yesmaximal, characteristic, complemented
16#83866—31nomaximal
17#80241—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C2×C32×SD16C2211yescharacteristic
23#64153C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2211yescharacteristic
25C2×#3754C2211yescharacteristic
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×D3×SD16—24no—
31C2×C3×#204C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33#63980—21no—
34#63976—21no—
35#63961—21no—
36C2×(C2×D3)⋊Dic3—21no—
37#63929—24no—
38#63908C2211yescharacteristic
39C4×#625C2211yescharacteristic
40#63887—21no—
41#63879—21no—
42#63863C2211yescharacteristic
43#63857C2211yescharacteristic
44#63856C2211yescharacteristic
45#63851—21no—
46#63843C2211yescharacteristic, complemented
47#63839—21no—
48C2×#3719C2211yescharacteristic, complemented
49C2×#3718C2211yescharacteristic, complemented
50C2×#3716C2211yescharacteristic
51C2×#3711C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64#5829—31no—
65C2×#951—31no—
66Q8×#67—31no—
67#5806—31no—
68C2×#915—31no—
69C2×D3×SD16D311yescharacteristic, complemented
70#5632—31no—
71C3×#452—31no—
72#5228—31no—
73#5218—31no—
74#5190—31no—
75#5186—31no—
76#5174—31no—
77#5173D311yescharacteristic, complemented
78#5170—31no—
79#5167—31no—
80#5166—31no—
81#5164—31no—
82#5162—31no—
83#5162—31no—
84#5162—61no—
85#5116—31no—
86#5111—31no—
87#5049—31no—
88#4813—31no—
89#4798—31no—
90#4776—31no—
91#4757—31no—
92#4738—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C3×#237—22no—
105C3×#237—41no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#627—21no—
116C2×#625—21no—
117C2×#625D411yescharacteristic
118C2×D3×Dic3—21no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C32×SD16—22no—
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124#3754—22no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127#3750—21no—
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#216—41no—
131C3×#215—22no—
132C3×#214D414yescomplemented
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—22no—
139C3×D3×C8—22no—
140#3724—21no—
141#3724D411yescharacteristic
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151Dic32—21no—
152#3719—22no—
153#3718—22no—
154#3716—41no—
155#3711—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8C2×D311yescharacteristic
162C2×#237C2×D311yescharacteristic
163C2×D3×D4C2×D311yescharacteristic
164C22×Dic6—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—21no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—64no—
171C2×C3×SD16C2×D311yescharacteristic
172C2×C3×SD16C2×D311yescharacteristic
173C22×C3×C8—31no—
174C3×C22⋊Q8—31no—
175#953—61no—
176C2×#217—61no—
177#951—64no—
178#947—31no—
179#946—31no—
180#946—61no—
181#946C2×D311yescharacteristic, complemented
182Q8×Dic3—31no—
183#944—31no—
184#944—31no—
185#944—61no—
186#944—61no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216C2×D311yescharacteristic, complemented
191C2×#215C2×D311yescharacteristic
192#939—61no—
193#939—61no—
194#938—31no—
195#937—61no—
196#936—31no—
197#935—61no—
198D4×Dic3—31no—
199D4×Dic3—31no—
200D4×Dic3—61no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—61no—
205C2×#214C2×D311yescharacteristic
206#930—31no—
207#929—61no—
208C4×#67—31no—
209C4×#67—31no—
210C4×#67—61no—
211C2×(C2×D3)⋊C4—61no—
212#924—31no—
213#924—31no—
214#924—61no—
215C2×#208—31no—
216#915—64no—
217D3×SD16—24no—
218C2×Dic12—31no—
219C2×#204—31no—
220C2×#204C2×D311yescharacteristic
221C2×ΓL(1,𝔽25)—31no—
222C2×D3×C8C2×D311yescharacteristic
223#897—31no—
224#896—61no—
225#888—61no—
226#887—31no—
227#67⋊C4—61no—
228#878—61no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#832—31no—
237#832C2×D311yescharacteristic
238#830—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8C2×D311yescharacteristic, complemented
241#818—31no—
242#816—31no—
243#816—31no—
244#816—31no—
245#816—61no—
246#816C2×D311yescharacteristic, complemented
247#815—31no—
248#815—31no—
249Dic3⋊C8—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—61no—
252#809—31no—
253#807—31no—
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C32×D4—21no—
264C32×D4C2×D412yes—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—81no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C2×C3⋊Dic3C2×D411yescharacteristic
272#634—21no—
273#634—21no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—42no—
293C3×Dic6C2×D412yes—
294#627—42no—
295#625—22no—
296#625—81no—
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—31no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—31no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—121no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4—121no—
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—31no—
344C2×#67—31no—
345C2×#67—61no—
346C2×#67—61no—
347C22×Dic3—21no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—121no—
352D3×Q8—22no—
353D3×Q8—41no—
354D3×Q8—62no—
355D3×Q8—121no—
356#237—22no—
357#237—41no—
358D3×D4—22no—
359D3×D4—41no—
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—61no—
363C2×C4×D3C22×D311yescharacteristic
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—21no—
366C2×Dic6—31no—
367C2×Dic6—31no—
368C2×Dic6—61no—
369C2×Dic6—62no—
370C2×Dic6—61no—
371C2×Dic6—61no—
372C2×Dic6—121no—
373C2×Dic6C22×D311yescharacteristic
374C2×Dic6C22×D311yescharacteristic
375C3×Q16—121no—
376C3×SD16—22no—
377C3×SD16—22no—
378C3×SD16—34no—
379C3×SD16—42no—
380C3×SD16—62no—
381C3×SD16—62no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8—62no—
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C22⋊C4—61no—
391#217—31no—
392#217—31no—
393#217—61no—
394#217—61no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—121no—
401#216—41no—
402#216—62no—
403#216—62no—
404#216—62no—
405#215—22no—
406#214—62no—
407#214—62no—
408#214—122no—
409#214—121no—
410#214#6714yescomplemented
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3C22×D311yescharacteristic
425Dic3⋊C4—21no—
426Dic3⋊C4—31no—
427Dic3⋊C4—31no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—121no—
437Dic3⋊C4—121no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—61no—
441C4×Dic3—61no—
442C4×Dic3—61no—
443#208—62no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449Dic12—62no—
450#204—22no—
451#204—121no—
452ΓL(1,𝔽25)—62no—
453D3×C8—22no—
454C22×C32—22no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—84no—
467C2×C3×D3#13712yescomplemented
468C32×C4—41no—
469C32×C4C22×D411yescharacteristic
470C32×C4H(5,𝔽2)11yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—22no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—31no—
481C22×Q8—31no—
482C22×Q8—91no—
483C22×D4—31no—
484#137—184no—
485C2×Q16—31no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—64no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16D3211yescharacteristic
495C2×M16—91no—
496C22×C8—31no—
497C4⋊Q8—91no—
498C4⋊Q8—181no—
499#124—91no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—91no—
503C22⋊Q8—91no—
504C22⋊Q8—181no—
505C22⋊Q8—181no—
506#121—91no—
507#121—181no—
508#120—181no—
509C4×Q8—91no—
510C4×D4—91no—
511C4×D4—91no—
512C4×D4—181no—
513C2×C22⋊C4—181no—
514#107—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#103—91no—
519#103—91no—
520#102—31no—
521#102—91no—
522C22⋊C8—31no—
523C22⋊C8—91no—
524#97—91no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—31no—
528C23×C3—31no—
529C23×C3—41no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—122no—
533C23×C3—241no—
534C22×D3—21no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3—81no—
538C22×D3D3×D411yescharacteristic
539C22×D3D3×D411yescharacteristic
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—32no—
545C3×Q8—41no—
546C3×Q8—41no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—122no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—22no—
554C3×D4—41no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—122no—
558C3×D4—122no—
559C3×D4D3×D412yes—
560C3×D4C2×#6712yes—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—41no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—122no—
575C2×C3×C4—122no—
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—42no—
579#67—42no—
580#67—62no—
581#67—62no—
582#67—241no—
583#67—241no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—42no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—122no—
601C2×Dic3—241no—
602C2×Dic3—241no—
603C2×Dic3—242no—
604C2×Dic3D3×D411yescharacteristic
605C2×Dic3D3×D411yescharacteristic
606D12—21no—
607D12—21no—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—42no—
613C4×D3—122no—
614Dic6—21no—
615Dic6—21no—
616Dic6—21no—
617Dic6—42no—
618Dic6—61no—
619Dic6—61no—
620Dic6—61no—
621Dic6—61no—
622Dic6—121no—
623Dic6—121no—
624Dic6—122no—
625Dic6—122no—
626Dic6C2×#6712yes—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—32no—
630C3×C8—41no—
631C3×C8—61no—
632C3⋊C8—21no—
633C3⋊C8—61no—
634C3⋊C8—61no—
635C3⋊C8—121no—
636C3⋊C8C2×#6712yes—
637C2×C32—42no—
638C2×C32D4211yescharacteristic
639C2×C32C2×#13711yescharacteristic
640C2×C32#57711yescharacteristic
641C3×D3—22no—
642C3×D3—41no—
643C3×D3—81no—
644C24—61no—
645#41—62no—
646#41—121no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—61no—
650C2×Q8—62no—
651C2×Q8—91no—
652C2×Q8—121no—
653C2×Q8—181no—
654C2×Q8—182no—
655C2×Q8—361no—
656C2×Q8C2×D3211yescharacteristic
657C2×D4—31no—
658C2×D4—61no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—91no—
662C2×D4—121no—
663C2×D4—181no—
664C2×D4C2×D3211yescharacteristic
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—181no—
670C22×C4—181no—
671Q16—121no—
672Q16—182no—
673Q16—182no—
674SD16—22no—
675SD16—34no—
676SD16—62no—
677SD16—62no—
678SD16—182no—
679SD16—361no—
680M16—182no—
681C2×C8—31no—
682C2×C8—31no—
683C2×C8—62no—
684C2×C8—91no—
685C2×C8C2×D3211yescharacteristic
686C4⋊C4—31no—
687C4⋊C4—61no—
688C4⋊C4—91no—
689C4⋊C4—91no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4—181no—
695C22⋊C4—61no—
696C22⋊C4—91no—
697C22⋊C4—91no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—91no—
705C42—181no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—21no—
709C22×C3—32no—
710C22×C3—42no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—244no—
726C22×C3C2×D3×D411yescharacteristic
727C22×C3C2×D3×D411yescharacteristic
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—84no—
737C2×D3#91512yescomplemented
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—61no—
743C3×C4—62no—
744C3×C4—61no—
745C3×C4—81no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4C2×D3×D411yescharacteristic
749C3×C4#100411yescharacteristic
750C3×C4#100411yescharacteristic
751C3×C4C22×#6711yescharacteristic
752Dic3—22no—
753Dic3—21no—
754Dic3—21no—
755Dic3—41no—
756Dic3—41no—
757Dic3—62no—
758Dic3—61no—
759Dic3—61no—
760Dic3—61no—
761Dic3—61no—
762Dic3—121no—
763Dic3—121no—
764Dic3—121no—
765Dic3—121no—
766Dic3—121no—
767Dic3—241no—
768Dic3—241no—
769C32#326611yescharacteristic, complemented, Sylow
770C23—21no—
771C23—31no—
772C23—31no—
773C23—61no—
774C23—122no—
775C23—122no—
776C23—241no—
777Q8—21no—
778Q8—21no—
779Q8—32no—
780Q8—61no—
781Q8—61no—
782Q8—61no—
783Q8—122no—
784Q8—181no—
785Q8—181no—
786Q8—362no—
787D4—21no—
788D4—61no—
789D4—61no—
790D4—122no—
791D4—122no—
792D4—182no—
793D4—721no—
794D4D3×#6712yes—
795C2×C4—21no—
796C2×C4—31no—
797C2×C4—31no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—122no—
808C2×C4—122no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—362no—
812C2×C4—721no—
813C2×C4C22×D3211yescharacteristic
814C8—21no—
815C8—32no—
816C8—61no—
817C8—181no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—42no—
822C2×C3—42no—
823C2×C3—62no—
824C2×C3—82no—
825C2×C3—121no—
826C2×C3—241no—
827C2×C3#559011yescharacteristic
828C2×C3C2×#91511yescharacteristic
829C2×C3#576211yescharacteristic
830C2×C3#577011yescharacteristic
831C2×C3D3×#13711yescharacteristic
832C2×C3D4×#6711yescharacteristic
833D3—22no—
834D3—41no—
835D3—81no—
836C22—22no—
837C22—32no—
838C22—41no—
839C22—41no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—244no—
849C22D32×D411yescharacteristic
850C4—41no—
851C4—61no—
852C4—61no—
853C4—62no—
854C4—121no—
855C4—121no—
856C4—181no—
857C4—181no—
858C4—361no—
859C4—361no—
860C4#6431311yescharacteristic
861C4C2×D3×#6711yescharacteristic
862C3—21no—
863C3#8024111yescharacteristic, complemented
864C3#8386611yescharacteristic, complemented
865C2—42no—
866C2—62no—
867C2—121no—
868C2—241no—
869C2D3×#91511yescharacteristic
870C2#1059475311yescharacteristic
871C2#1059528711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595244C2
hypercenterC2×SD16D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×SD16C2semidirect
2. #10595400C2semidirect
4. C2×#63929C2semidirect
5. #10592861C2semidirect
6. C3×#5173C2semidirect
7. #10591611C2semidirect
8. #10591594C2semidirect
9. #10591587C2semidirect
10. #10591459C2semidirect
11. #10591446C2semidirect
12. #10590848C2semidirect
13. #10590822C2semidirect
14. #10590796C2semidirect
15. #10590723C2semidirect
21. C2×D3×Dic6C22semidirect
23. #64153C22semidirect
26. C3×#946C22semidirect
27. C2×C3×#216C22semidirect
46. #63843C22semidirect
48. C2×#3719C22semidirect
49. C2×#3718C22semidirect
51. C2×#3711C22semidirect
52. #63662C22semidirect
53. #63643C22semidirect
54. #63641C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#816C22semidirect
58. #63575C22semidirect
59. #63566C22semidirect
62. #63555C22semidirect
69. C2×D3×SD16D3semidirect
77. #5173D3semidirect
132. C3×#214D4semidirect
181. #946C2×D3semidirect
190. C2×#216C2×D3semidirect
240. (C2×D3)⋊C8C2×D3semidirect
246. #816C2×D3semidirect
410. #214#67semidirect
467. C2×C3×D3#137semidirect
737. C2×D3#915semidirect
769. C32#3266semidirect
863. C3#80241semidirect
864. C3#83866semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
#105954002
#105952442
C2×#639292
#105928612
C3×#51732
#105916112
#105915942
#105915872
#105914592
#105914462
#105908482
#105908222
#105907962
#105907232
#838663
#802413