Finite Group Databasebeta

← #11884325

Subgroups — #11884325

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2#10595428C211yesmaximal, characteristic, complemented
3#10595248C211yesmaximal, characteristic, complemented
4C2×#63927C211yesmaximal, characteristic, complemented
5#10592872C211yesmaximal, characteristic, complemented
6C3×#5165C211yesmaximal, characteristic, complemented
7#10591627C211yesmaximal, characteristic, complemented
8#10591600C211yesmaximal, characteristic, complemented
9#10591599C211yesmaximal, characteristic, complemented
10#10591450C211yesmaximal, characteristic, complemented
11#10591430C211yesmaximal, characteristic, complemented
12#10590943C211yesmaximal, characteristic, complemented
13#10590825C211yesmaximal, characteristic, complemented
14#10590752C211yesmaximal, characteristic, complemented
15#10590727C211yesmaximal, characteristic, complemented
16#83921—31nomaximal
17#80567—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×#3802C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64155C2211yescharacteristic
24C2×#3756C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic, complemented
27C3×D4×Dic3C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#916—24no—
31C2×C3×#204C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic, complemented
33#63978—21no—
34#63966—21no—
35C2×Dic3⋊Dic3—21no—
36#63962—21no—
37#63927—24no—
38#63922—21no—
39D3×(C2×D3)⋊C4—21no—
40#63908C2211yescharacteristic
41#63905—21no—
42C4×#626C2211yescharacteristic
43Dic3×D12C2211yescharacteristic
44#63885—21no—
45#63871C2211yescharacteristic
46#63866C2211yescharacteristic, complemented
47#63857C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3712C2211yescharacteristic
52#63659C2211yescharacteristic, complemented
53#63647C2211yescharacteristic
54#63643C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5829—31no—
65#5824—31no—
66C2×#916D311yescharacteristic, complemented
67C2×#911—31no—
68C2×#911—31no—
69#5676—31no—
70#5555—31no—
71C3×#463—31no—
72#5239—31no—
73#5238—31no—
74#5190—31no—
75#5189—31no—
76#5173—31no—
77#5173—31no—
78#5173—61no—
79#5169—31no—
80#5165D311yescharacteristic, complemented
81#5162—31no—
82#5158—31no—
83#5152—31no—
84#5114—31no—
85#5111—31no—
86#5060—31no—
87#5014—31no—
88#4841—31no—
89#4836—31no—
90#4816—31no—
91#4808—31no—
92#4778—31no—
93#4776—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99#3830—22no—
100#3830—41no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#239—22no—
107C3×#239—41no—
108C3×#237—22no—
109C3×#237—41no—
110C2×C3×D12—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626D411yescharacteristic
117C2×#625—21no—
118C2×#625—21no—
119C2×D3×Dic3—21no—
120#3802—22no—
121#3802—41no—
122C32×SD16—22no—
123C2×C32×C8C2311yescharacteristic
124#3756—41no—
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217—21no—
130C3×#216—22no—
131C3×#213—22no—
132C3×#213D414yescomplemented
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×D3×C8—22no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152#3716—22no—
153#3716—22no—
154#3715—41no—
155#3712—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239C2×D311yescharacteristic
160C2×#237—31no—
161C2×#237—31no—
162C2×#237—61no—
163C2×#237C2×D311yescharacteristic, complemented
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16C2×D311yescharacteristic, complemented
171C2×C3×SD16C2×D311yescharacteristic, complemented
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C3×#124—31no—
176C3×C4×D4—31no—
177#947C2×D311yescharacteristic
178#946—31no—
179#946—31no—
180#946—31no—
181#946—61no—
182#944—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—61no—
186C2×#216C2×D311yescharacteristic, complemented
187C2×#215—31no—
188#939—61no—
189#939—61no—
190#938—31no—
191#937—61no—
192#935—61no—
193D4×Dic3—31no—
194D4×Dic3C2×D311yescharacteristic, complemented
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#213C2×D311yescharacteristic
199C2×#213C2×D311yescharacteristic
200#930—31no—
201#930—61no—
202#929—61no—
203#929—61no—
204C4×#67—31no—
205C2×(C2×D3)⋊C4—61no—
206C2×C4⋊Dic3—61no—
207#924—31no—
208C2×Dic3⋊C4—61no—
209#916—24no—
210#911—64no—
211#911—64no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204C2×D311yescharacteristic
215C2×ΓL(1,𝔽25)—31no—
216C2×ΓL(1,𝔽25)—31no—
217C2×D3×C8C2×D311yescharacteristic, complemented
218#897—31no—
219#897—31no—
220#886—61no—
221#886—61no—
222#884—61no—
223#883—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226C4×D12—31no—
227C4×D12—31no—
228#869—31no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#821C2×D311yescharacteristic
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—61no—
244#817—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—61no—
249#815—31no—
250Dic3⋊C8C2×D311yescharacteristic, complemented
251#809—31no—
252#808—31no—
253#803—31no—
254C23×C32—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×D4—21no—
265C32×D4C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—42no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275#634—21no—
276#634—21no—
277C3×#67—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—42no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#626—41no—
296#625—42no—
297#625—81no—
298D3×Dic3—81no—
299C32×C8—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—31no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—31no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—21no—
325C2×C3×Q8—31no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—21no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C2×#67—21no—
340C2×#67—31no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—121no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—121no—
354#239—22no—
355#239—41no—
356#237—22no—
357#237—41no—
358#237—62no—
359#237—62no—
360#237—122no—
361#237—121no—
362#237—121no—
363#237—122no—
364D3×D4—62no—
365D3×D4—62no—
366D3×D4—121no—
367D3×D4—121no—
368C2×D12—21no—
369C2×D12—31no—
370C2×D12C22×D311yescharacteristic
371C2×D12C22×D311yescharacteristic
372C2×C4×D3—21no—
373C2×C4×D3—31no—
374C2×C4×D3—31no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—61no—
381C2×Dic6C22×D311yescharacteristic
382C3×Q16—62no—
383C3×SD16—22no—
384C3×SD16—22no—
385C3×SD16—42no—
386C3×SD16—62no—
387C3×D8—34no—
388C3×D8—62no—
389C2×C3×C8—21no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C2×C3×C8—62no—
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C3×C4⋊C4—31no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—31no—
400#217—21no—
401#217—31no—
402#217—61no—
403#217—61no—
404#217—61no—
405#216—22no—
406#216—121no—
407#216—121no—
408#216—122no—
409#215—121no—
410#214—62no—
411#214—62no—
412#214—121no—
413#213—22no—
414#213#6714yescomplemented
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—31no—
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—121no—
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
430C4⋊Dic3—31no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—31no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—121no—
445C4×Dic3C22×D311yescharacteristic
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451#204—22no—
452#204—62no—
453#204—62no—
454ΓL(1,𝔽25)—62no—
455ΓL(1,𝔽25)—62no—
456D3×C8—22no—
457C22×C32—22no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473D32—84no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—21no—
478C3⋊Dic3—41no—
479C3⋊Dic3—41no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—31no—
487C2×#41—91no—
488C22×D4—91no—
489AGL(1,ℤ/8)—184no—
490#135—64no—
491C2×Q16—31no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16D3211yescharacteristic, complemented
498C2×D8—31no—
499C2×D8—31no—
500C2×M16—91no—
501C22×C8—31no—
502C4⋊Q8—91no—
503#124—31no—
504#123—181no—
505#123—181no—
506#123—181no—
507C22⋊Q8—91no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—91no—
511#121—181no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—91no—
516C4×D4—91no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—181no—
519#106—91no—
520C4⋊C8—31no—
521#103—31no—
522#103—91no—
523#103—91no—
524#102—31no—
525#102—91no—
526#102—91no—
527C22⋊C8—91no—
528C22⋊C8—91no—
529#97—91no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—61no—
535C23×C3—61no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—31no—
539C22×D3—31no—
540C22×D3—61no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3D3×D411yescharacteristic
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—22no—
559C3×D4—32no—
560C3×D4—41no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—122no—
565C3×D4—122no—
566C3×D4D3×D412yes—
567C3×D4C2×#6712yes—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
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—121no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—124no—
591#67—241no—
592#67—241no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—42no—
598C2×Dic3—42no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—122no—
607C2×Dic3—122no—
608C2×Dic3—124no—
609C2×Dic3—241no—
610C2×Dic3D3×D411yescharacteristic
611C2×Dic3D3×D411yescharacteristic
612C2×Dic3D3×D411yescharacteristic
613D12—21no—
614D12—21no—
615D12—21no—
616D12—42no—
617D12—121no—
618D12C2×#6712yes—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—42no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—61no—
626C4×D3—121no—
627C4×D3—121no—
628C4×D3—241no—
629Dic6—21no—
630Dic6—21no—
631Dic6—62no—
632Dic6—61no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—121no—
637C3×C8—21no—
638C3×C8—21no—
639C3×C8—32no—
640C3×C8—41no—
641C3×C8—61no—
642C3⋊C8—21no—
643C3⋊C8—61no—
644C3⋊C8—61no—
645C3⋊C8—121no—
646C3⋊C8C2×#6712yes—
647C2×C32—42no—
648C2×C32D4211yescharacteristic
649C2×C32#57511yescharacteristic
650C2×C32#57711yescharacteristic
651C3⋊D3—41no—
652C3×D3—42no—
653C3×D3—41no—
654C3×D3—81no—
655C24—181no—
656#41—62no—
657#41—62no—
658#41—121no—
659#41—121no—
660#41—182no—
661#41—361no—
662C2×Q8—31no—
663C2×Q8—91no—
664C2×Q8C2×D3211yescharacteristic
665C2×D4—31no—
666C2×D4—31no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—91no—
670C2×D4—181no—
671C2×D4—182no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—361no—
675C2×D4C2×D3211yescharacteristic
676C22×C4—31no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—91no—
681C22×C4—181no—
682C22×C4—181no—
683Q16—62no—
684Q16—361no—
685SD16—22no—
686SD16—62no—
687SD16—182no—
688SD16—182no—
689SD16—361no—
690D8—34no—
691D8—62no—
692M16—182no—
693C2×C8—31no—
694C2×C8—31no—
695C2×C8—62no—
696C2×C8—91no—
697C2×C8C2×D3211yescharacteristic
698C4⋊C4—31no—
699C4⋊C4—91no—
700C4⋊C4—91no—
701C4⋊C4—181no—
702C4⋊C4—181no—
703C4⋊C4—181no—
704C4⋊C4—181no—
705C4⋊C4—181no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—91no—
710C22⋊C4—91no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—31no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—21no—
720C22×C3—42no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—62no—
728C22×C3—61no—
729C22×C3—81no—
730C22×C3—81no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3C2×D3×D411yescharacteristic
737C22×C3C2×D3×D411yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—22no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—244no—
757C2×D3—244no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—81no—
766C3×C4—121no—
767C3×C4—121no—
768C3×C4C2×D3×D411yescharacteristic
769C3×C4#100411yescharacteristic
770C3×C4#100911yescharacteristic
771C3×C4C22×#6711yescharacteristic
772Dic3—21no—
773Dic3—21no—
774Dic3—21no—
775Dic3—41no—
776Dic3—41no—
777Dic3—61no—
778Dic3—61no—
779Dic3—121no—
780Dic3—122no—
781Dic3—121no—
782Dic3—121no—
783Dic3—121no—
784Dic3—121no—
785Dic3—241no—
786C32#326711yescharacteristic, complemented, Sylow
787C23—21no—
788C23—31no—
789C23—61no—
790C23—61no—
791C23—91no—
792C23—362no—
793C23—362no—
794C23—721no—
795Q8—21no—
796Q8—21no—
797Q8—61no—
798Q8—61no—
799Q8—181no—
800Q8—181no—
801D4—21no—
802D4—32no—
803D4—61no—
804D4—61no—
805D4—61no—
806D4—122no—
807D4—122no—
808D4—361no—
809D4—362no—
810D4—362no—
811D4—721no—
812D4D3×#6712yes—
813C2×C4—21no—
814C2×C4—31no—
815C2×C4—31no—
816C2×C4—31no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—91no—
822C2×C4—122no—
823C2×C4—122no—
824C2×C4—122no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—181no—
829C2×C4—362no—
830C2×C4—721no—
831C2×C4C22×D3211yescharacteristic
832C8—21no—
833C8—32no—
834C8—61no—
835C8—181no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—42no—
840C2×C3—42no—
841C2×C3—82no—
842C2×C3—122no—
843C2×C3—121no—
844C2×C3—241no—
845C2×C3#560911yescharacteristic
846C2×C3#576811yescharacteristic
847C2×C3#577011yescharacteristic
848C2×C3#577011yescharacteristic
849C2×C3#577311yescharacteristic
850C2×C3D4×#6711yescharacteristic
851D3—41no—
852D3—42no—
853D3—81no—
854D3—121no—
855D3—121no—
856D3—241no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—61no—
861C22—61no—
862C22—61no—
863C22—62no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22—181no—
870C22—181no—
871C22—181no—
872C22—724no—
873C22D32×D411yescharacteristic
874C4—41no—
875C4—61no—
876C4—61no—
877C4—61no—
878C4—121no—
879C4—121no—
880C4—181no—
881C4—361no—
882C4—361no—
883C4#6431411yescharacteristic
884C4C2×D3×#6711yescharacteristic
885C3—21no—
886C3#8056711yescharacteristic, complemented
887C3#8392111yescharacteristic, complemented
888C2—42no—
889C2—121no—
890C2—122no—
891C2—241no—
892C2—361no—
893C2#1059474511yescharacteristic
894C2#1059475711yescharacteristic
895C2#1059529111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3267
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×#916C2semidirect
2. #10595428C2semidirect
3. #10595248C2semidirect
4. C2×#63927C2semidirect
5. #10592872C2semidirect
6. C3×#5165C2semidirect
7. #10591627C2semidirect
8. #10591600C2semidirect
9. #10591599C2semidirect
10. #10591450C2semidirect
11. #10591430C2semidirect
12. #10590943C2semidirect
13. #10590825C2semidirect
14. #10590752C2semidirect
15. #10590727C2semidirect
20. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
24. C2×#3756C22semidirect
26. C2×C3×#216C22semidirect
27. C3×D4×Dic3C22semidirect
32. C2×C3×D3×C8C22semidirect
46. #63866C22semidirect
47. #63857C22semidirect
52. #63659C22semidirect
54. #63643C22semidirect
55. C3×#835C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63573C22semidirect
59. #63566C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
66. C2×#916D3semidirect
80. #5165D3semidirect
132. C3×#213D4semidirect
163. C2×#237C2×D3semidirect
170. C2×C3×SD16C2×D3semidirect
171. C2×C3×SD16C2×D3semidirect
186. C2×#216C2×D3semidirect
194. D4×Dic3C2×D3semidirect
217. C2×D3×C8C2×D3semidirect
233. #835C2×D3semidirect
250. Dic3⋊C8C2×D3semidirect
414. #213#67semidirect
497. C2×SD16D32semidirect
786. C32#3267semidirect
886. C3#80567semidirect
887. C3#83921semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
#105954282
#105952482
C2×#639272
#105928722
C3×#51652
#105916272
#105916002
#105915992
#105914502
#105914302
#105909432
#105908252
#105907522
#105907272
#839213
#805673