Finite Group Databasebeta

← #11884480

Subgroups — #11884480

Order 1152.

1096 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic, complemented
2#10595428C211yesmaximal, characteristic, complemented
3#10595410C211yesmaximal, characteristic, complemented
4C2×#63941C211yesmaximal, characteristic, complemented
5#10592886C211yesmaximal, characteristic, complemented
6C3×#5185C211yesmaximal, characteristic, complemented
7#10591619C211yesmaximal, characteristic, complemented
8#10591590C211yesmaximal, characteristic, complemented
9#10591588C211yesmaximal, characteristic, complemented
10#10591586C211yesmaximal, characteristic, complemented
11#10591566C211yesmaximal, characteristic, complemented
12#10590945C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590753C211yesmaximal, characteristic, complemented
15#10590727C211yesmaximal, characteristic, complemented
16#83922—31nomaximal
17#80628—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21C2×#3802C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23#64155C2211yescharacteristic
24C2×#3755C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#919—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic, complemented
33#63941—24no—
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63916—21no—
37#63916C2211yescharacteristic
38#63911—21no—
39#63911C2211yescharacteristic, complemented
40#63909—21no—
41#63909C2211yescharacteristic, complemented
42#63908C2211yescharacteristic
43#63905—21no—
44C4×#626—21no—
45C4×#626C2211yescharacteristic
46Dic3×D12C2211yescharacteristic
47#63885—21no—
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3712C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63647C2211yescharacteristic
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5834—31no—
65#5829—31no—
66C2×#919D311yescharacteristic, complemented
67C2×#914—31no—
68C2×#914—31no—
69#5676—31no—
70#5577—31no—
71C3×#464—31no—
72#5238—31no—
73#5238—31no—
74#5187—31no—
75#5187—31no—
76#5187—61no—
77#5185D311yescharacteristic, complemented
78#5176—31no—
79#5174—31no—
80#5172—31no—
81#5164—31no—
82#5156—31no—
83#5150—31no—
84#5115—31no—
85#5111—31no—
86#5058—31no—
87#5026—31no—
88#4843—31no—
89#4836—31no—
90#4812—31no—
91#4810—31no—
92#4775—31no—
93#4773—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97#3832—22no—
98#3832—41no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C3×#239—22no—
104C3×#239—22no—
105C3×#239—41no—
106C3×#239—41no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626D411yescharacteristic
120C2×#625—21no—
121C2×#625—21no—
122C2×D3×Dic3—21no—
123#3802—22no—
124#3802—41no—
125C32×Q16—22no—
126C2×C32×C8C2311yescharacteristic
127#3755—41no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#215—22no—
133C3×#215—22no—
134C3×#215D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24—22no—
144C3×D3×C8—22no—
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#3714—22no—
153#3714—22no—
154#3713—41no—
155#3712—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—61no—
162C2×#239C2×D311yescharacteristic
163C2×#239C2×D311yescharacteristic, complemented
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C3×#135—64no—
167C2×C3×Q16—21no—
168C2×C3×Q16C2×D311yescharacteristic, complemented
169C2×C3×Q16C2×D311yescharacteristic, complemented
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C3×#124—31no—
176C3×C4×Q8—31no—
177#947C2×D311yescharacteristic
178#946—31no—
179#946—31no—
180#946—61no—
181Q8×Dic3C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—61no—
185C2×#215C2×D311yescharacteristic
186C2×#215C2×D311yescharacteristic
187C2×#215C2×D311yescharacteristic, complemented
188#940—31no—
189#940—61no—
190#939—61no—
191#938—31no—
192#938—31no—
193#938—61no—
194#937—61no—
195D4×Dic3—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200#930—31no—
201#930—31no—
202#930—61no—
203#929—61no—
204C4×#67—31no—
205C4×#67—61no—
206C2×(C2×D3)⋊C4—61no—
207#919—24no—
208#914—64no—
209#914—64no—
210C2×D24—31no—
211C2×D24—31no—
212C2×D24C2×D311yescharacteristic
213C2×ΓL(1,𝔽25)—31no—
214C2×ΓL(1,𝔽25)—31no—
215C2×D3×C8C2×D311yescharacteristic, complemented
216#895—31no—
217#895—31no—
218#895—61no—
219#895—61no—
220#884—61no—
221#883—61no—
222#882—61no—
223D3×C22⋊C4—61no—
224#874—31no—
225#874—61no—
226C4×D12—31no—
227C4×D12—31no—
228C4×D12—61no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#835C2×D311yescharacteristic, complemented
236#832—31no—
237#832—31no—
238#830—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243#821C2×D311yescharacteristic
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—61no—
248#818—31no—
249#815—31no—
250Dic3⋊C8C2×D311yescharacteristic, complemented
251#809—31no—
252#807—31no—
253#803—31no—
254C22×C3⋊D3—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×Q8—21no—
266C32×Q8C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—42no—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277C4×C3⋊D3—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—42no—
288C3×D12—42no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294#626—41no—
295#626—42no—
296#626—81no—
297#626—81no—
298#626—81no—
299#625—42no—
300#625—81no—
301D3×Dic3—81no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—31no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—31no—
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—21no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—31no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C22×Dic3—61no—
351#239—22no—
352#239—22no—
353#239—41no—
354#239—41no—
355#239—62no—
356#239—62no—
357#239—122no—
358#239—121no—
359#239—121no—
360#239—122no—
361D3×D4—62no—
362D3×D4—62no—
363D3×D4—121no—
364D3×D4—121no—
365C2×D12—21no—
366C2×D12—21no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3—31no—
384C2×C4×D3—31no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—121no—
390C2×C4×D3C22×D311yescharacteristic
391C3×Q16—22no—
392C3×Q16—22no—
393C3×Q16—42no—
394C3×SD16—34no—
395C3×SD16—62no—
396C3×SD16—62no—
397C3×D8—62no—
398C2×C3×C8—21no—
399C2×C3×C8—31no—
400C2×C3×C8—31no—
401C2×C3×C8—62no—
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C3×C4⋊C4—31no—
405C3×C4⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C42—31no—
409C3×C42—61no—
410#217—31no—
411#217—61no—
412#217—61no—
413#217—61no—
414#215—22no—
415#215—22no—
416#215—121no—
417#215—121no—
418#215—122no—
419#215#6714yescomplemented
420#213—62no—
421#213—62no—
422#213—121no—
423#213—121no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—121no—
437C4⋊Dic3—21no—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—31no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4—121no—
447C4×Dic3—21no—
448C4×Dic3C22×D311yescharacteristic
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454D24—22no—
455D24—62no—
456D24—62no—
457ΓL(1,𝔽25)—62no—
458ΓL(1,𝔽25)—62no—
459D3×C8—22no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3×D3—22no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—22no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—21no—
485C3⋊Dic3—41no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—31no—
492C2×#41—91no—
493C22×D4—91no—
494AGL(1,ℤ/8)—184no—
495#135—64no—
496C2×Q16D3211yescharacteristic, complemented
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—31no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—91no—
506C22×C8—31no—
507#127—91no—
508#127—181no—
509#124—31no—
510#123—181no—
511C22⋊Q8—91no—
512#121—91no—
513#121—91no—
514#121—91no—
515#121—181no—
516#121—181no—
517#121—181no—
518#120—181no—
519C4×Q8—31no—
520C4×D4—91no—
521C4×D4—91no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—91no—
525C4⋊C8—31no—
526#103—31no—
527#103—91no—
528#102—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532C22⋊C8—91no—
533C22⋊C8—91no—
534#97—91no—
535C23×C3—31no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—31no—
543C22×D3—31no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—241no—
553C22×D3—241no—
554C22×D3D3×D411yescharacteristic
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—21no—
561C3×Q8—22no—
562C3×Q8—41no—
563C3×Q8—41no—
564C3×Q8—41no—
565C3×Q8D3×D412yes—
566C3×Q8C2×#6712yes—
567C3×D4—32no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—122no—
574C3×D4—122no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
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—41no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—122no—
589C2×C3×C4—122no—
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592#67—121no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—241no—
597#67—241no—
598#67—241no—
599#67—241no—
600#67—241no—
601C2×Dic3—21no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—121no—
608C2×Dic3—241no—
609C2×Dic3D3×D411yescharacteristic
610C2×Dic3D3×D411yescharacteristic
611C2×Dic3D3×D411yescharacteristic
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—21no—
617D12—42no—
618D12—42no—
619D12—62no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—121no—
625D12—122no—
626D12—122no—
627D12—124no—
628D12—121no—
629D12—122no—
630D12—241no—
631D12—241no—
632D12—241no—
633D12C2×#6712yes—
634C4×D3—21no—
635C4×D3—21no—
636C4×D3—42no—
637C4×D3—42no—
638C4×D3—61no—
639C4×D3—61no—
640C4×D3—61no—
641C4×D3—61no—
642C4×D3—121no—
643C4×D3—121no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—124no—
647C4×D3—241no—
648C3×C8—21no—
649C3×C8—21no—
650C3×C8—32no—
651C3×C8—41no—
652C3×C8—61no—
653C3⋊C8—21no—
654C3⋊C8—61no—
655C3⋊C8—61no—
656C3⋊C8—121no—
657C3⋊C8C2×#6712yes—
658C2×C32D4211yescharacteristic
659C2×C32#57511yescharacteristic
660C2×C32#57611yescharacteristic
661C3⋊D3—41no—
662C3⋊D3—81no—
663C3×D3—42no—
664C3×D3—41no—
665C3×D3—81no—
666C3×D3—81no—
667C24—181no—
668#41—62no—
669#41—62no—
670#41—121no—
671#41—121no—
672#41—182no—
673#41—361no—
674C2×Q8C2×D3211yescharacteristic
675C2×Q8C2×D3211yescharacteristic
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—182no—
690C2×D4—181no—
691C2×D4—361no—
692C22×C4—31no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—91no—
696C22×C4—181no—
697C22×C4—181no—
698Q16—22no—
699SD16—34no—
700SD16—62no—
701SD16—62no—
702SD16—361no—
703D8—62no—
704D8—182no—
705D8—182no—
706D8—361no—
707M16—182no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8—91no—
712C2×C8C2×D3211yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—61no—
715C4⋊C4—91no—
716C4⋊C4—91no—
717C4⋊C4—181no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—91no—
721C22⋊C4—91no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C42—31no—
728C42—61no—
729C22×C3—21no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—62no—
733C22×C3—61no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C2×D3×D411yescharacteristic
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—22no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—61no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—122no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—244no—
775C2×D3—244no—
776C3×C4—22no—
777C3×C4—22no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—42no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—61no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—81no—
787C3×C4—121no—
788C3×C4C2×D3×D411yescharacteristic
789C3×C4#100411yescharacteristic
790C3×C4#100911yescharacteristic
791C3×C4C22×#6711yescharacteristic
792Dic3—21no—
793Dic3—21no—
794Dic3—21no—
795Dic3—41no—
796Dic3—61no—
797Dic3—61no—
798Dic3—121no—
799Dic3—121no—
800Dic3—121no—
801Dic3—241no—
802C32#326811yescharacteristic, complemented, Sylow
803C23—31no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—91no—
808C23—181no—
809C23—362no—
810C23—362no—
811C23—721no—
812Q8—21no—
813Q8—21no—
814Q8—21no—
815Q8D3×#6712yes—
816D4—32no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—61no—
821D4—61no—
822D4—122no—
823D4—122no—
824D4—181no—
825D4—181no—
826D4—362no—
827D4—361no—
828D4—362no—
829D4—362no—
830D4—721no—
831D4—721no—
832D4—721no—
833D4—721no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—31no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—91no—
843C2×C4—122no—
844C2×C4—122no—
845C2×C4—181no—
846C2×C4—181no—
847C2×C4—181no—
848C2×C4—362no—
849C2×C4—721no—
850C2×C4C22×D3211yescharacteristic
851C8—21no—
852C8—32no—
853C8—61no—
854C8—181no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—122no—
859C2×C3—121no—
860C2×C3—241no—
861C2×C3—241no—
862C2×C3#560911yescharacteristic
863C2×C3#576811yescharacteristic
864C2×C3#576911yescharacteristic
865C2×C3#576911yescharacteristic
866C2×C3#577711yescharacteristic
867C2×C3D4×#6711yescharacteristic
868D3—41no—
869D3—42no—
870D3—81no—
871D3—81no—
872D3—121no—
873D3—121no—
874D3—241no—
875D3—242no—
876D3—241no—
877D3—241no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—62no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—181no—
891C22—181no—
892C22—181no—
893C22—361no—
894C22—361no—
895C22—361no—
896C22—724no—
897C22D32×D411yescharacteristic
898C4—22no—
899C4—41no—
900C4—61no—
901C4—61no—
902C4—61no—
903C4—121no—
904C4—181no—
905C4—361no—
906C4#6431411yescharacteristic
907C4C2×D3×#6711yescharacteristic
908C3—21no—
909C3#8062811yescharacteristic, complemented
910C3#8392211yescharacteristic, complemented
911C2—121no—
912C2—122no—
913C2—241no—
914C2—241no—
915C2—361no—
916C2—721no—
917C2#1059476311yescharacteristic
918C2#1059477111yescharacteristic
919C2#1059529111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#919C2semidirect
2. #10595428C2semidirect
3. #10595410C2semidirect
4. C2×#63941C2semidirect
5. #10592886C2semidirect
6. C3×#5185C2semidirect
7. #10591619C2semidirect
8. #10591590C2semidirect
9. #10591588C2semidirect
10. #10591586C2semidirect
11. #10591566C2semidirect
12. #10590945C2semidirect
13. #10590826C2semidirect
14. #10590753C2semidirect
15. #10590727C2semidirect
20. C2×C3×#239C22semidirect
22. C2×C32×Q16C22semidirect
24. C2×#3755C22semidirect
26. C3×Q8×Dic3C22semidirect
29. C2×C3×#215C22semidirect
32. C2×C3×D3×C8C22semidirect
39. #63911C22semidirect
41. #63909C22semidirect
52. #63662C22semidirect
53. #63648C22semidirect
55. C3×#835C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63575C22semidirect
59. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
66. C2×#919D3semidirect
77. #5185D3semidirect
134. C3×#215D4semidirect
163. C2×#239C2×D3semidirect
168. C2×C3×Q16C2×D3semidirect
169. C2×C3×Q16C2×D3semidirect
181. Q8×Dic3C2×D3semidirect
187. C2×#215C2×D3semidirect
215. C2×D3×C8C2×D3semidirect
235. #835C2×D3semidirect
250. Dic3⋊C8C2×D3semidirect
419. #215#67semidirect
496. C2×Q16D32semidirect
802. C32#3268semidirect
909. C3#80628semidirect
910. C3#83922semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
#105954282
#105954102
C2×#639412
#105928862
C3×#51852
#105916192
#105915902
#105915882
#105915862
#105915662
#105909452
#105908262
#105907532
#105907272
#839223
#806283