Finite Group Databasebeta

← #11884478

Subgroups — #11884478

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic, complemented
2#10595427C211yesmaximal, characteristic, complemented
3#10595412C211yesmaximal, characteristic, complemented
4C2×#63939C211yesmaximal, characteristic, complemented
5#10592884C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7#10591621C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10591587C211yesmaximal, characteristic, complemented
10#10591586C211yesmaximal, characteristic, complemented
11#10591572C211yesmaximal, characteristic, complemented
12#10590944C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590749C211yesmaximal, characteristic, complemented
15#10590723C211yesmaximal, characteristic, complemented
16#83922—31nomaximal
17#80266—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21C2×D3×D12C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23#64156C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#919—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic, complemented
33#63939—24no—
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63914—21no—
37#63914C2211yescharacteristic, complemented
38#63909C2211yescharacteristic
39#63908—21no—
40#63908—21no—
41#63908C2211yescharacteristic
42#63908C2211yescharacteristic, complemented
43C4×#625—21no—
44C4×#625C2211yescharacteristic
45#63898C2211yescharacteristic
46#63886—21no—
47#63850—21no—
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63641C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58#63575C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5834—31no—
65#5834—31no—
66#5829—31no—
67C2×#949—31no—
68C2×#919D311yescharacteristic, complemented
69C2×#914—31no—
70#5630—31no—
71C3×#452—31no—
72#5238—31no—
73#5238—31no—
74#5187D311yescharacteristic, complemented
75#5185—31no—
76#5185—31no—
77#5185—61no—
78#5176—31no—
79#5176—31no—
80#5174—31no—
81#5172—31no—
82#5164—31no—
83#5156—31no—
84#5150—31no—
85#5115—31no—
86#5111—31no—
87#5049—31no—
88#4817—31no—
89#4810—31no—
90#4786—31no—
91#4775—31no—
92#4732—31no—
93#4728—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C3×#239—22no—
99C3×#239—22no—
100C3×#239—22no—
101C3×#239—41no—
102C3×#239—41no—
103C3×#239—41no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#625—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×#625—21no—
121C2×#625D411yescharacteristic
122C2×D3×Dic3—21no—
123D3×D12—22no—
124D3×D12—41no—
125C32×Q16—22no—
126C2×C32×C8C2311yescharacteristic
127#3755—22no—
128#3752—21no—
129#3752—21no—
130C4⋊(C3⋊Dic3)—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132C4×C3⋊Dic3—21no—
133C4×C3⋊Dic3C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#215—22no—
136C3×#215—41no—
137C3×#215D414yescomplemented
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24—22no—
144C3×D3×C8—22no—
145#3724D411yescharacteristic
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151(C2×D3)⋊Dic3D411yescharacteristic
152#3714—22no—
153#3714—41no—
154#3713—22no—
155#3711—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×#239C2×D311yescharacteristic
161C2×#239C2×D311yescharacteristic
162C2×#239C2×D311yescharacteristic, complemented
163C2×D3×D4—31no—
164C22×D12—31no—
165C3×#135—64no—
166C2×C3×Q16—21no—
167C2×C3×Q16C2×D311yescharacteristic, complemented
168C2×C3×Q16C2×D311yescharacteristic, complemented
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—31no—
173C22×C3×C8—31no—
174C3×C22⋊Q8—31no—
175#949—64no—
176#947—31no—
177#947—31no—
178#947—61no—
179#946C2×D311yescharacteristic
180Q8×Dic3—31no—
181Q8×Dic3—31no—
182Q8×Dic3—61no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—61no—
186C2×#215C2×D311yescharacteristic
187C2×#215C2×D311yescharacteristic, complemented
188C2×#215C2×D311yescharacteristic, complemented
189#940—31no—
190#940—31no—
191#940—61no—
192#940—61no—
193#939—61no—
194#938—31no—
195#938—31no—
196#938—61no—
197#938—61no—
198#937—61no—
199D4×Dic3—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204#930—31no—
205#930—31no—
206#930—31no—
207#930—61no—
208#930—61no—
209#929—61no—
210C4×#67—31no—
211C4×#67—31no—
212C4×#67—61no—
213C4×#67—61no—
214C2×(C2×D3)⋊C4—61no—
215C2×#208—31no—
216#919—24no—
217#914—64no—
218C2×D24—31no—
219C2×D24—31no—
220C2×D24C2×D311yescharacteristic
221C2×ΓL(1,𝔽25)—31no—
222C2×D3×C8C2×D311yescharacteristic, complemented
223#895—31no—
224#895—61no—
225#894—61no—
226#893—31no—
227#882—61no—
228D3×C22⋊C4—61no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—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, complemented
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8C2×D311yescharacteristic
246#818—31no—
247#815—31no—
248#815—31no—
249Dic3⋊C8—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—61no—
252#809—31no—
253#807—31no—
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
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
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×D12—42no—
285C3×D12—42no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294#626—42no—
295#626—81no—
296#625—41no—
297#625—42no—
298#625—81no—
299#625—81no—
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—91no—
314#459—91no—
315#452—31no—
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—62no—
326C3×#41—121no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—21no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C2×#67—31no—
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—61no—
358C22×Dic3—61no—
359#239—22no—
360#239—22no—
361#239—22no—
362#239—41no—
363#239—41no—
364#239—41no—
365D3×D4—62no—
366D3×D4—121no—
367C2×D12—21no—
368C2×D12—21no—
369C2×D12—21no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—61no—
373C2×D12—62no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3—61no—
384C2×C4×D3C22×D311yescharacteristic
385C2×C4×D3C22×D311yescharacteristic
386C3×Q16—22no—
387C3×Q16—22no—
388C3×Q16—42no—
389C3×SD16—34no—
390C3×SD16—62no—
391C3×SD16—121no—
392C3×D8—62no—
393C2×C3×C8—21no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C2×C3×C8—62no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C3×C4⋊C4—31no—
400C3×C4⋊C4—61no—
401C3×C22⋊C4—61no—
402#217—31no—
403#217—31no—
404#217—61no—
405#217—61no—
406#217—61no—
407#215—22no—
408#215—41no—
409#215—62no—
410#215—62no—
411#215—122no—
412#215#6714yescomplemented
413#213—62no—
414#213—62no—
415#213—62no—
416#213—121no—
417(C2×D3)⋊C4—21no—
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—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—121no—
430(C2×D3)⋊C4—121no—
431C4⋊Dic3—31no—
432C4⋊Dic3—31no—
433C4⋊Dic3—61no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3—121no—
437C4⋊Dic3C22×D311yescharacteristic
438Dic3⋊C4—21no—
439Dic3⋊C4—31no—
440Dic3⋊C4—31no—
441C4×Dic3—31no—
442C4×Dic3—31no—
443C4×Dic3—61no—
444C4×Dic3—61no—
445C4×Dic3—61no—
446C4×Dic3—121no—
447#208—62no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—22no—
454D24—62no—
455D24—121no—
456ΓL(1,𝔽25)—62no—
457D3×C8—22no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
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—22no—
479C32×C4—41no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—21no—
483C3⋊Dic3—21no—
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—31no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—64no—
494C2×Q16D3211yescharacteristic, complemented
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—31no—
505#127—91no—
506#127—181no—
507#124—91no—
508#123—181no—
509C22⋊Q8—31no—
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—31no—
525#103—91no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—31no—
534C23×C3—31no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—121no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3D3×D411yescharacteristic
551C22×D3D3×D411yescharacteristic
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—22no—
559C3×Q8—41no—
560C3×Q8—41no—
561C3×Q8—41no—
562C3×Q8D3×D412yes—
563C3×Q8C2×#6712yes—
564C3×D4—32no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—122no—
588C2×C3×C4—122no—
589C2×C3×C4—122no—
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592#67—122no—
593#67—121no—
594#67—121no—
595#67—122no—
596#67—122no—
597#67—241no—
598#67—241no—
599#67—241no—
600#67—241no—
601#67—241no—
602#67—241no—
603#67—241no—
604C2×Dic3—21no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—121no—
614C2×Dic3—241no—
615C2×Dic3D3×D411yescharacteristic
616C2×Dic3D3×D411yescharacteristic
617D12—21no—
618D12—21no—
619D12—21no—
620D12—21no—
621D12—21no—
622D12—42no—
623D12—42no—
624D12—42no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—121no—
630D12—121no—
631D12—122no—
632D12—241no—
633D12C2×#6712yes—
634C4×D3—21no—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—42no—
639C4×D3—42no—
640C4×D3—42no—
641C4×D3—241no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—32no—
645C3×C8—41no—
646C3×C8—61no—
647C3⋊C8—21no—
648C3⋊C8—61no—
649C3⋊C8—61no—
650C3⋊C8—121no—
651C3⋊C8C2×#6712yes—
652C2×C32D4211yescharacteristic
653C2×C32#57511yescharacteristic
654C2×C32#57611yescharacteristic
655C3⋊D3—81no—
656C3×D3—41no—
657C3×D3—42no—
658C3×D3—41no—
659C3×D3—81no—
660C3×D3—81no—
661C24—181no—
662#41—62no—
663#41—62no—
664#41—62no—
665#41—121no—
666#41—121no—
667#41—121no—
668C2×Q8C2×D3211yescharacteristic
669C2×Q8C2×D3211yescharacteristic
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—91no—
677C2×D4—91no—
678C2×D4—181no—
679C2×D4—182no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—361no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—181no—
692Q16—22no—
693SD16—34no—
694SD16—62no—
695SD16—121no—
696SD16—182no—
697D8—62no—
698D8—182no—
699D8—182no—
700D8—361no—
701M16—182no—
702C2×C8—31no—
703C2×C8—31no—
704C2×C8—62no—
705C2×C8—91no—
706C2×C8C2×D3211yescharacteristic
707C4⋊C4—31no—
708C4⋊C4—61no—
709C4⋊C4—91no—
710C4⋊C4—91no—
711C4⋊C4—181no—
712C22⋊C4—61no—
713C22⋊C4—91no—
714C22⋊C4—91no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C42—91no—
722C42—181no—
723C22×C3—21no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—62no—
730C22×C3—61no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
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—22no—
747C2×D3—21no—
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—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—241no—
763C2×D3—241no—
764C2×D3—241no—
765C2×D3—244no—
766C2×D3—244no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—42no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—61no—
775C3×C4—61no—
776C3×C4—81no—
777C3×C4—121no—
778C3×C4C2×D3×D411yescharacteristic
779C3×C4#100411yescharacteristic
780C3×C4#100411yescharacteristic
781C3×C4C22×#6711yescharacteristic
782Dic3—21no—
783Dic3—21no—
784Dic3—41no—
785Dic3—61no—
786Dic3—61no—
787Dic3—61no—
788Dic3—61no—
789Dic3—121no—
790Dic3—121no—
791Dic3—121no—
792Dic3—121no—
793Dic3—241no—
794C32#326811yescharacteristic, complemented, Sylow
795C23—31no—
796C23—31no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—181no—
801C23—362no—
802C23—362no—
803C23—721no—
804Q8—21no—
805Q8—21no—
806Q8—21no—
807Q8D3×#6712yes—
808D4—32no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—122no—
815D4—122no—
816D4—122no—
817D4—181no—
818D4—181no—
819D4—362no—
820D4—361no—
821D4—362no—
822D4—721no—
823D4—721no—
824D4—721no—
825D4—721no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—91no—
836C2×C4—91no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4—122no—
840C2×C4—181no—
841C2×C4—721no—
842C2×C4C22×D3211yescharacteristic
843C8—21no—
844C8—32no—
845C8—61no—
846C8—181no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—122no—
851C2×C3—121no—
852C2×C3—121no—
853C2×C3—241no—
854C2×C3—241no—
855C2×C3#559011yescharacteristic
856C2×C3#576811yescharacteristic
857C2×C3#576911yescharacteristic
858C2×C3#576911yescharacteristic
859C2×C3#577711yescharacteristic
860C2×C3D4×#6711yescharacteristic
861D3—41no—
862D3—41no—
863D3—42no—
864D3—81no—
865D3—81no—
866D3—241no—
867D3—241no—
868D3—481no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—62no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—361no—
885C22—361no—
886C22—361no—
887C22—724no—
888C22D32×D411yescharacteristic
889C4—22no—
890C4—41no—
891C4—61no—
892C4—61no—
893C4—121no—
894C4—181no—
895C4—181no—
896C4—361no—
897C4#6431311yescharacteristic
898C4C2×D3×#6711yescharacteristic
899C3—21no—
900C3#8026611yescharacteristic, complemented
901C3#8392211yescharacteristic, complemented
902C2—121no—
903C2—121no—
904C2—122no—
905C2—241no—
906C2—241no—
907C2—721no—
908C2#1059476311yescharacteristic
909C2#1059477111yescharacteristic
910C2#1059528711yescharacteristic
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. #10595427C2semidirect
3. #10595412C2semidirect
4. C2×#63939C2semidirect
5. #10592884C2semidirect
6. C3×#5187C2semidirect
7. #10591621C2semidirect
8. #10591588C2semidirect
9. #10591587C2semidirect
10. #10591586C2semidirect
11. #10591572C2semidirect
12. #10590944C2semidirect
13. #10590826C2semidirect
14. #10590749C2semidirect
15. #10590723C2semidirect
20. C2×C3×#239C22semidirect
22. C2×C32×Q16C22semidirect
24. Q8×C3⋊Dic3C22semidirect
28. C2×C3×#215C22semidirect
29. C2×C3×#215C22semidirect
32. C2×C3×D3×C8C22semidirect
37. #63914C22semidirect
42. #63908C22semidirect
52. #63662C22semidirect
54. #63641C22semidirect
55. C3×#835C22semidirect
56. C3×#821C22semidirect
58. #63575C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63555C22semidirect
68. C2×#919D3semidirect
74. #5187D3semidirect
137. C3×#215D4semidirect
162. C2×#239C2×D3semidirect
167. C2×C3×Q16C2×D3semidirect
168. C2×C3×Q16C2×D3semidirect
187. C2×#215C2×D3semidirect
188. C2×#215C2×D3semidirect
222. C2×D3×C8C2×D3semidirect
235. #835C2×D3semidirect
243. #821C2×D3semidirect
412. #215#67semidirect
494. C2×Q16D32semidirect
794. C32#3268semidirect
900. C3#80266semidirect
901. 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
#105954272
#105954122
C2×#639392
#105928842
C3×#51872
#105916212
#105915882
#105915872
#105915862
#105915722
#105909442
#105908262
#105907492
#105907232
#839223
#802663