Finite Group Databasebeta

← #11884489

Subgroups — #11884489

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 916 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#10595158C211yesmaximal, characteristic, complemented
4C2×#63798C211yesmaximal, characteristic, complemented
5#10592873C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7#10591656C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591578C211yesmaximal, characteristic, complemented
10#10591516C211yesmaximal, characteristic, complemented
11#10591450C211yesmaximal, characteristic, complemented
12#10591428C211yesmaximal, characteristic, complemented
13#10590831C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15#10590726C211yesmaximal, characteristic, complemented
16#83922—31nomaximal
17#81858—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
20C2×#3802C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64155C2211yescharacteristic
24#64147C2211yescharacteristic
25C2×#3743C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#916—24no—
33C2×C3×D24C2211yescharacteristic
34C2×C3×#204C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic, complemented
36#63979—21no—
37#63978—21no—
38Dic3×#67—21no—
39#63970—21no—
40#63922—21no—
41D3×(C2×D3)⋊C4—21no—
42#63908C2211yescharacteristic
43#63908C2211yescharacteristic, complemented
44#63905—21no—
45C4×#626C2211yescharacteristic
46Dic3×D12C2211yescharacteristic
47#63885—21no—
48Dic3×Dic6C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51#63798—24no—
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63645C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5834—31no—
65#5829—31no—
66C2×#916D311yescharacteristic, complemented
67C2×#914—31no—
68C2×#911—31no—
69#5718—31no—
70#5676—31no—
71C3×#496—31no—
72#5238—31no—
73#5238—31no—
74#5187—31no—
75#5185—31no—
76#5176D311yescharacteristic, complemented
77#5174—31no—
78#5174—31no—
79#5174—61no—
80#5173—31no—
81#5172—31no—
82#5164—31no—
83#5158—31no—
84#5157—31no—
85#5156—31no—
86#5156—31no—
87#5150—31no—
88#5115—31no—
89#5111—31no—
90#5072—31no—
91#5054—31no—
92#4710—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#239—22no—
104C3×#239—41no—
105C3×#237—22no—
106C3×#237—41no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626D411yescharacteristic
116C2×#625—21no—
117C2×#625—21no—
118C2×#625—21no—
119C2×D3×Dic3—21no—
120C2×D3×Dic3—21no—
121#3802—22no—
122#3802—41no—
123#3796—22no—
124#3796—41no—
125C32×SD16—22no—
126C2×C32×C8C2311yescharacteristic
127#3757—21no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3743—22no—
134C3×#216—22no—
135C3×#215—41no—
136C3×#213—22no—
137C3×#213—41no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24—22no—
144C3×#204D414yescomplemented
145C3×D3×C8—22no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3D411yescharacteristic
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153Dic32—21no—
154#3715—22no—
155#3713—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic
161C2×#237—31no—
162C2×#237C2×D311yescharacteristic, complemented
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C3×#135—64no—
166C2×C3×Q16—31no—
167C2×C3×SD16—21no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16C2×D311yescharacteristic, complemented
171C2×C3×SD16C2×D311yescharacteristic, complemented
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C22×C3×C8—31no—
176C3×#127—31no—
177C3×#124—31no—
178#947C2×D311yescharacteristic
179#946—31no—
180#946—31no—
181#946—61no—
182Q8×Dic3—31no—
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215C2×D311yescharacteristic, complemented
186#940—61no—
187#940—61no—
188#940C2×D311yescharacteristic, complemented
189#939—61no—
190#939—61no—
191#939—61no—
192#938—31no—
193#938—31no—
194#938—31no—
195#938—31no—
196#938—61no—
197#938—61no—
198#937—61no—
199D4×Dic3—31no—
200D4×Dic3—61no—
201C2×#214—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213C2×D311yescharacteristic
205C2×#213C2×D311yescharacteristic
206#930—31no—
207#930—31no—
208#930—61no—
209#929—61no—
210C4×#67—31no—
211C4×#67—61no—
212C2×(C2×D3)⋊C4—61no—
213#916—24no—
214#914—64no—
215#911—64no—
216C2×D24C2×D311yescharacteristic
217C2×#204C2×D311yescharacteristic
218C2×ΓL(1,𝔽25)—31no—
219C2×ΓL(1,𝔽25)—31no—
220C2×ΓL(1,𝔽25)—61no—
221C2×D3×C8C2×D311yescharacteristic, complemented
222#884—61no—
223#883—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226C4×D12—31no—
227C4×D12—31no—
228C4×Dic6—31no—
229C3×#97—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—31no—
239#832—61no—
240#830—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247#818—31no—
248#818—31no—
249#818—61no—
250#816—31no—
251#815C2×D311yescharacteristic, complemented
252Dic3⋊C8—31no—
253C4⋊(C3⋊C8)—31no—
254C23×C32—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269#638—81no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C3×#67—42no—
276C3×#67—42no—
277C3×#67—81no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
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×Dic6C2×D412yes—
295#626—41no—
296#626—42no—
297#625—42no—
298#625—81no—
299#625—81no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C32×C8C2×D412yes—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—31no—
308#550—91no—
309#546—91no—
310#496—31no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—121no—
326C3×#41—121no—
327C2×C3×Q8—21no—
328C2×C3×Q8—31no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C22×D311yescharacteristic
341C22×C3×C4—31no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—21no—
347C2×#67—31no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—121no—
358C22×Dic3—21no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361#239—22no—
362#239—41no—
363#239—62no—
364#239—121no—
365#237—22no—
366#237—41no—
367#237—62no—
368#237—121no—
369D3×D4—62no—
370D3×D4—62no—
371D3×D4—121no—
372D3×D4—121no—
373C2×D12—21no—
374C2×D12—31no—
375C2×D12—61no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—21no—
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3C22×D311yescharacteristic
386C2×Dic6C22×D311yescharacteristic
387C3×Q16—62no—
388C3×SD16—22no—
389C3×SD16—22no—
390C3×SD16—34no—
391C3×SD16—42no—
392C3×SD16—121no—
393C3×D8—62no—
394C3×D8—62no—
395C3×D8—121no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—62no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C42—31no—
405#217—31no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217—121no—
412#216—22no—
413#215—41no—
414#215—62no—
415#214—62no—
416#213—22no—
417#213—41no—
418#213—62no—
419#213—62no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—31no—
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—121no—
431C4⋊Dic3—31no—
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439Dic3⋊C4—31no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—121no—
444C4×Dic3—61no—
445C4×Dic3—61no—
446C4×Dic3C22×D311yescharacteristic
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452D24—22no—
453#204#6714yescomplemented
454ΓL(1,𝔽25)—62no—
455ΓL(1,𝔽25)—62no—
456ΓL(1,𝔽25)—122no—
457D3×C8—22no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32C22×D411yescharacteristic
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3×D3—22no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477D32—84no—
478C32×C4—41no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3⋊Dic3—21no—
482C3⋊Dic3—41no—
483C3⋊Dic3—41no—
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—64no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×SD16D3211yescharacteristic, complemented
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—31no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—31no—
505#127—31no—
506#127—181no—
507#124—31no—
508#123—181no—
509C22⋊Q8—91no—
510#121—91no—
511#121—91no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121—181no—
516#120—181no—
517C4×Q8—91no—
518C4×D4—91no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8—91no—
524#103—91no—
525#103—91no—
526#102—91no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532#97—31no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—41no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—31no—
544C22×D3—31no—
545C22×D3—61no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—241no—
551C22×D3—241no—
552C22×D3D3×D411yescharacteristic
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—32no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×Q8—61no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—32no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—122no—
574C3×D4—122no—
575C3×D4—122no—
576C3×D4—241no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—41no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—122no—
588C2×C3×C4—122no—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591#67—42no—
592#67—42no—
593#67—81no—
594#67—121no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—241no—
599#67—241no—
600#67—241no—
601#67—241no—
602#67—241no—
603#67—241no—
604#67—242no—
605C2×Dic3—21no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—42no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3—241no—
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620C2×Dic3D3×D411yescharacteristic
621D12—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—21no—
626D12—42no—
627D12—121no—
628D12—122no—
629D12C2×#6712yes—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—42no—
633C4×D3—61no—
634C4×D3—61no—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—121no—
638C4×D3—121no—
639C4×D3—122no—
640C4×D3—241no—
641Dic6—21no—
642Dic6C2×#6712yes—
643C3×C8—22no—
644C3×C8—61no—
645C3×C8—61no—
646C3×C8D3×D412yes—
647C3×C8C2×#6712yes—
648C3⋊C8—21no—
649C3⋊C8—21no—
650C3⋊C8—61no—
651C3⋊C8—61no—
652C3⋊C8—121no—
653C2×C32—81no—
654C2×C32D4211yescharacteristic
655C2×C32#57511yescharacteristic
656C2×C32#57611yescharacteristic
657C3⋊D3—41no—
658C3×D3—42no—
659C3×D3—41no—
660C3×D3—81no—
661C3×D3—81no—
662C24—181no—
663#41—62no—
664#41—62no—
665#41—121no—
666#41—121no—
667#41—182no—
668#41—361no—
669C2×Q8—31no—
670C2×Q8C2×D3211yescharacteristic
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—91no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—182no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—361no—
686C2×D4C2×D3211yescharacteristic
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—91no—
691C22×C4—181no—
692C22×C4—181no—
693Q16—62no—
694SD16—22no—
695SD16—34no—
696SD16—121no—
697SD16—182no—
698D8—62no—
699D8—62no—
700D8—121no—
701D8—182no—
702M16—182no—
703C2×C8—31no—
704C2×C8—31no—
705C2×C8—62no—
706C2×C8—91no—
707C2×C8C2×D3211yescharacteristic
708C4⋊C4—91no—
709C4⋊C4—91no—
710C4⋊C4—91no—
711C4⋊C4—181no—
712C4⋊C4—181no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—91no—
716C22⋊C4—91no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C42—31no—
723C42—181no—
724C22×C3—21no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—62no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C2×D3×D411yescharacteristic
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—22no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—244no—
770C2×D3—244no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—62no—
776C3×C4—61no—
777C3×C4—61no—
778C3×C4—61no—
779C3×C4—81no—
780C3×C4C2×D3×D411yescharacteristic
781C3×C4#100411yescharacteristic
782C3×C4#100411yescharacteristic
783C3×C4C22×#6711yescharacteristic
784Dic3—21no—
785Dic3—21no—
786Dic3—22no—
787Dic3—21no—
788Dic3—61no—
789Dic3—61no—
790Dic3—121no—
791Dic3—121no—
792Dic3—121no—
793Dic3—121no—
794Dic3—121no—
795Dic3—241no—
796Dic3—241no—
797C32#326811yescharacteristic, complemented, Sylow
798C23—21no—
799C23—31no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—91no—
804C23—362no—
805C23—362no—
806C23—721no—
807Q8—21no—
808Q8—21no—
809Q8—32no—
810Q8—61no—
811D4—21no—
812D4—21no—
813D4—32no—
814D4—61no—
815D4—61no—
816D4—61no—
817D4—61no—
818D4—61no—
819D4—122no—
820D4—122no—
821D4—122no—
822D4—241no—
823D4—361no—
824D4—362no—
825D4—362no—
826D4—721no—
827D4—721no—
828D4—721no—
829C2×C4—21no—
830C2×C4—31no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—91no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4—362no—
844C2×C4—721no—
845C2×C4C22×D3211yescharacteristic
846C8—61no—
847C8—61no—
848C8—181no—
849C8D3×#6712yes—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—81no—
854C2×C3—81no—
855C2×C3—122no—
856C2×C3—121no—
857C2×C3—161no—
858C2×C3—241no—
859C2×C3—241no—
860C2×C3#571711yescharacteristic
861C2×C3#576811yescharacteristic
862C2×C3#576911yescharacteristic
863C2×C3#577311yescharacteristic
864C2×C3#577411yescharacteristic
865C2×C3D4×#6711yescharacteristic
866D3—41no—
867D3—42no—
868D3—81no—
869D3—81no—
870D3—121no—
871D3—121no—
872D3—241no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—62no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—181no—
889C22—181no—
890C22—181no—
891C22—724no—
892C22D32×D411yescharacteristic
893C4—41no—
894C4—61no—
895C4—61no—
896C4—61no—
897C4—62no—
898C4—181no—
899C4—361no—
900C4—361no—
901C4#6431311yescharacteristic
902C4C2×D3×#6711yescharacteristic
903C3—21no—
904C3#8185811yescharacteristic, complemented
905C3#8392211yescharacteristic, complemented
906C2—81no—
907C2—121no—
908C2—122no—
909C2—241no—
910C2—241no—
911C2—361no—
912C2#1059474511yescharacteristic
913C2#1059475511yescharacteristic
914C2#1059529311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3268
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. #10595158C2semidirect
4. C2×#63798C2semidirect
5. #10592873C2semidirect
6. C3×#5176C2semidirect
7. #10591656C2semidirect
8. #10591586C2semidirect
9. #10591578C2semidirect
10. #10591516C2semidirect
11. #10591450C2semidirect
12. #10591428C2semidirect
13. #10590831C2semidirect
14. #10590766C2semidirect
15. #10590726C2semidirect
19. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#215C22semidirect
29. C3×#940C22semidirect
35. C2×C3×D3×C8C22semidirect
43. #63908C22semidirect
48. Dic3×Dic6C22semidirect
52. #63662C22semidirect
53. #63659C22semidirect
54. #63645C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
60. #63563C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#916D3semidirect
76. #5176D3semidirect
144. C3×#204D4semidirect
162. C2×#237C2×D3semidirect
170. C2×C3×SD16C2×D3semidirect
171. C2×C3×SD16C2×D3semidirect
183. C2×#216C2×D3semidirect
185. C2×#215C2×D3semidirect
188. #940C2×D3semidirect
221. C2×D3×C8C2×D3semidirect
251. #815C2×D3semidirect
453. #204#67semidirect
498. C2×SD16D32semidirect
797. C32#3268semidirect
904. C3#81858semidirect
905. C3#83922semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
#105954282
#105951582
C2×#637982
#105928732
C3×#51762
#105916562
#105915862
#105915782
#105915162
#105914502
#105914282
#105908312
#105907662
#105907262
#839223
#818583