Finite Group Databasebeta

← #11884496

Subgroups — #11884496

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595158C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×#63810C211yesmaximal, characteristic, complemented
4#10594629C211yesmaximal, characteristic, complemented
5#10592474C211yesmaximal, characteristic, complemented
6C3×#4786C211yesmaximal, characteristic, complemented
7C3×#4783C211yesmaximal, characteristic, complemented
8#10591520C211yesmaximal, characteristic, complemented
9#10591472C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590801C211yesmaximal, characteristic, complemented
12#10590737C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590503C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#80348—31nomaximal
17#80266—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22#64147C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C3×#940C2211yescharacteristic, complemented
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×Dic12C2211yescharacteristic, complemented
30C2×C3×D24C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#893C2211yescharacteristic
33#63979—21no—
34#63978—21no—
35Dic3×#67—21no—
36#63970—21no—
37#63925—24no—
38#63923—21no—
39D3×(C2×D3)⋊C4—21no—
40#63909—21no—
41#63908C2211yescharacteristic
42C4×#626C2211yescharacteristic
43#63890—21no—
44#63864C2211yescharacteristic
45Dic3×Dic6C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51#63810—24no—
52C32×#102C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63634C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63#5834—31no—
64C2×#949—31no—
65C2×#919—31no—
66C2×#912—31no—
67C2×#911—31no—
68#5718—31no—
69#5630—31no—
70#5554—31no—
71C3×#459—31no—
72C3×#452—31no—
73#5185—31no—
74#5176—31no—
75#5172—31no—
76#5158—31no—
77#5156—31no—
78#5074—31no—
79#5049—31no—
80#5018—31no—
81#4845—31no—
82#4836—31no—
83#4817—31no—
84#4810—31no—
85#4786D311yescharacteristic, complemented
86#4783D311yescharacteristic, complemented
87#4781—31no—
88#4780—31no—
89#4775—31no—
90#4775—31no—
91#4775—61no—
92#4732—31no—
93#4728—31no—
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C3×#237—22no—
105C3×#237—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626D411yescharacteristic
116C2×#625—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3796—22no—
122#3796—22no—
123#3796—41no—
124#3796—41no—
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127#3757—21no—
128#3753—22no—
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C8×C3⋊D3—22no—
133C3×#214—41no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×Dic12—22no—
142C3×D24—22no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3D411yescharacteristic
145#3722—21no—
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150Dic32—21no—
151#3717—22no—
152#3715—22no—
153#3715D414yescomplemented
154#3714—41no—
155#3711—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#237—31no—
161C2×#237—31no—
162C2×#237C2×D311yescharacteristic
163C2×D3×D4—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C2×C3×D8—31no—
169C3×#127—31no—
170C3×C22⋊Q8—31no—
171C3×C4×D4—31no—
172#949—64no—
173#947—31no—
174Q8×Dic3—31no—
175C2×#215—31no—
176C2×#215—31no—
177C2×#215—31no—
178#940—61no—
179#940—61no—
180#940C2×D311yescharacteristic, complemented
181#939—61no—
182#939—61no—
183#938—31no—
184#938—31no—
185#938—31no—
186#938—61no—
187#938—61no—
188D4×Dic3—61no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214C2×D311yescharacteristic, complemented
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—61no—
196C2×#213C2×D311yescharacteristic
197#930—31no—
198#930—61no—
199#930—61no—
200C4×#67—31no—
201C4×#67—61no—
202C2×(C2×D3)⋊C4—61no—
203C2×#208—31no—
204#919—64no—
205#912—64no—
206#911—64no—
207C2×Dic12C2×D311yescharacteristic, complemented
208C2×D24—31no—
209C2×D24C2×D311yescharacteristic
210C2×#204—31no—
211C2×ΓL(1,𝔽25)—31no—
212C2×D3×C8—31no—
213C2×D3×C8—31no—
214C2×D3×C8—61no—
215#897C2×D311yescharacteristic
216#895—31no—
217#895—31no—
218#895—61no—
219#895—61no—
220#894—61no—
221#893C2×D311yescharacteristic
222#886—61no—
223#882—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226#875—31no—
227C4×D12—31no—
228C4×Dic6—31no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—21no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic, complemented
234C3×#102C2×D311yescharacteristic, complemented
235C3×C22⋊C8—31no—
236#835—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8C2×D311yescharacteristic
245#816—31no—
246#815—31no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic, complemented
250#807—31no—
251#807—31no—
252#807—61no—
253#803—31no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×D4—21no—
264C32×D4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267#638—81no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—81no—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C3×#67—42no—
276C3×#67—42no—
277C3×#67—81no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—42no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—81no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6C2×D412yes—
295#626—41no—
296#626—42no—
297#626—42no—
298#626—42no—
299#625—81no—
300D3×Dic3—42no—
301D3×Dic3—42no—
302C32×C8—21no—
303C3⋊(C3⋊C8)C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—31no—
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—121no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
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—
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—21no—
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—121no—
350C22×Dic3—21no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353#239—62no—
354#239—62no—
355#239—121no—
356#239—121no—
357#237—22no—
358#237—41no—
359#237—62no—
360#237—62no—
361#237—121no—
362#237—121no—
363D3×D4—62no—
364D3×D4—121no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—61no—
369C2×D12—62no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—121no—
376C2×D12—121no—
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
387C2×Dic6C22×D311yescharacteristic
388C3×Q16—62no—
389C3×SD16—121no—
390C3×D8—62no—
391C3×D8—62no—
392C2×C3×C8—21no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C22×D311yescharacteristic
397C3×C4⋊C4—21no—
398C3×C4⋊C4—61no—
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C4⋊C4C22×D311yescharacteristic
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C42—31no—
404#217—31no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—121no—
409#215—34no—
410#215—62no—
411#215—62no—
412#214—34no—
413#214—41no—
414#214—62no—
415#213—22no—
416#213—62no—
417#213—62no—
418#213—122no—
419#213—121no—
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—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—121no—
433C4⋊Dic3—21no—
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—31no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439Dic3⋊C4—31no—
440Dic3⋊C4—61no—
441C4×Dic3—61no—
442C4×Dic3—61no—
443C4×Dic3C22×D311yescharacteristic
444#208—62no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450Dic12—22no—
451D24—22no—
452D24—121no—
453#204—62no—
454ΓL(1,𝔽25)—62no—
455D3×C8—62no—
456D3×C8—62no—
457D3×C8—122no—
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—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3×D3—22no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
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—22no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—91no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—91no—
505#127—31no—
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—31no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8—31no—
524#103—31no—
525#103—91no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102D3211yescharacteristic, complemented
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—41no—
537C23×C3—61no—
538C23×C3—61no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—31no—
542C22×D3—31no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—121no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—241no—
552C22×D3—241no—
553C22×D3D3×D411yescharacteristic
554C3×Q8—32no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—32no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—122no—
569C3×D4—122no—
570C3×D4—241no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—41no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—122no—
583C2×C3×C4—241no—
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586#67—42no—
587#67—42no—
588#67—81no—
589#67—121no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—241no—
594#67—241no—
595#67—241no—
596#67—241no—
597#67—242no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—42no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—121no—
607C2×Dic3—122no—
608C2×Dic3—122no—
609C2×Dic3D3×D411yescharacteristic
610C2×Dic3D3×D411yescharacteristic
611C2×Dic3D3×D411yescharacteristic
612D12—21no—
613D12—21no—
614D12—21no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—121no—
620D12—121no—
621D12—121no—
622D12—122no—
623D12—122no—
624D12—122no—
625D12—241no—
626D12—241no—
627D12—242no—
628D12D3×D412yes—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—61no—
632C4×D3—61no—
633C4×D3—61no—
634C4×D3—61no—
635C4×D3—81no—
636C4×D3—121no—
637C4×D3—121no—
638C4×D3—122no—
639C4×D3—122no—
640Dic6—21no—
641Dic6—21no—
642Dic6—21no—
643Dic6D3×D412yes—
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—41no—
647C3×C8—61no—
648C3×C8—61no—
649C3⋊C8—21no—
650C3⋊C8—21no—
651C3⋊C8—32no—
652C3⋊C8—32no—
653C3⋊C8—62no—
654C2×C32—81no—
655C2×C32D4211yescharacteristic
656C2×C32#57511yescharacteristic
657C2×C32#57611yescharacteristic
658C3⋊D3—41no—
659C3⋊D3—81no—
660C3×D3—41no—
661C3×D3—42no—
662C3×D3—81no—
663C24—181no—
664#41—62no—
665#41—121no—
666#41—182no—
667#41—182no—
668#41—361no—
669#41—361no—
670C2×Q8—31no—
671C2×Q8—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—91no—
678C2×D4—91no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—182no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—361no—
687C2×D4C2×D3211yescharacteristic
688C22×C4—31no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—91no—
692C22×C4—181no—
693C22×C4—181no—
694Q16—62no—
695SD16—94no—
696SD16—121no—
697SD16—182no—
698SD16—182no—
699D8—62no—
700D8—62no—
701D8—182no—
702D8—361no—
703M16—182no—
704C2×C8—31no—
705C2×C8—31no—
706C2×C8—91no—
707C2×C8—182no—
708C2×C8C2×D3211yescharacteristic
709C4⋊C4—61no—
710C4⋊C4—91no—
711C4⋊C4—91no—
712C4⋊C4—181no—
713C4⋊C4C2×D3211yescharacteristic
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—91no—
717C22⋊C4—91no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C42—31no—
724C42—181no—
725C22×C3—21no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—62no—
735C22×C3—61no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3C2×D3×D411yescharacteristic
745C22×C3C2×D3×D411yescharacteristic
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—21no—
749C2×D3—22no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—62no—
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—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—244no—
774C2×D3—244no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—61no—
780C3×C4—61no—
781C3×C4—62no—
782C3×C4—61no—
783C3×C4—81no—
784C3×C4—121no—
785C3×C4C2×D3×D411yescharacteristic
786C3×C4C2×D3×D411yescharacteristic
787C3×C4#100411yescharacteristic
788C3×C4#100911yescharacteristic
789Dic3—21no—
790Dic3—21no—
791Dic3—22no—
792Dic3—21no—
793Dic3—41no—
794Dic3—61no—
795Dic3—61no—
796Dic3—121no—
797Dic3—121no—
798Dic3—121no—
799Dic3—241no—
800C32#326811yescharacteristic, complemented, Sylow
801C23—21no—
802C23—31no—
803C23—61no—
804C23—61no—
805C23—91no—
806C23—181no—
807C23—362no—
808C23—362no—
809C23—721no—
810Q8—32no—
811Q8—61no—
812Q8—61no—
813Q8—61no—
814D4—21no—
815D4—21no—
816D4—32no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—122no—
821D4—122no—
822D4—181no—
823D4—181no—
824D4—241no—
825D4—361no—
826D4—362no—
827D4—362no—
828D4—362no—
829D4—721no—
830D4—721no—
831D4—721no—
832C2×C4—21no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—91no—
841C2×C4—122no—
842C2×C4—181no—
843C2×C4—181no—
844C2×C4—181no—
845C2×C4—241no—
846C2×C4—362no—
847C2×C4—362no—
848C2×C4C22×D3211yescharacteristic
849C8—21no—
850C8—61no—
851C8—61no—
852C8—92no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—81no—
857C2×C3—81no—
858C2×C3—122no—
859C2×C3—121no—
860C2×C3—161no—
861C2×C3—241no—
862C2×C3#559011yescharacteristic
863C2×C3#560911yescharacteristic
864C2×C3#575711yescharacteristic
865C2×C3#576911yescharacteristic
866C2×C3#577311yescharacteristic
867C2×C3#577711yescharacteristic
868D3—41no—
869D3—42no—
870D3—81no—
871D3—122no—
872D3—121no—
873D3—121no—
874D3—241no—
875D3—241no—
876D3—481no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—62no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—181no—
890C22—181no—
891C22—181no—
892C22—361no—
893C22—361no—
894C22—361no—
895C22—724no—
896C22D32×D411yescharacteristic
897C4—41no—
898C4—61no—
899C4—61no—
900C4—61no—
901C4—62no—
902C4—121no—
903C4—181no—
904C4—361no—
905C4#6430711yescharacteristic
906C4D32×D411yescharacteristic
907C3—21no—
908C3#8026611yescharacteristic, complemented
909C3#8034811yescharacteristic, complemented
910C2—81no—
911C2—121no—
912C2—122no—
913C2—241no—
914C2—361no—
915C2—721no—
916C2#1059427511yescharacteristic
917C2#1059473411yescharacteristic
918C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595158C2semidirect
2. C2×#63925C2semidirect
3. C2×#63810C2semidirect
4. #10594629C2semidirect
5. #10592474C2semidirect
6. C3×#4786C2semidirect
7. C3×#4783C2semidirect
8. #10591520C2semidirect
9. #10591472C2semidirect
10. #10590944C2semidirect
11. #10590801C2semidirect
12. #10590737C2semidirect
13. #10590617C2semidirect
14. #10590503C2semidirect
15. #10590478C2semidirect
21. C2×#3796C22semidirect
22. #64147C22semidirect
24. C2×C8×C3⋊D3C22semidirect
26. C3×#940C22semidirect
27. C2×C3×#214C22semidirect
29. C2×C3×Dic12C22semidirect
45. Dic3×Dic6C22semidirect
48. C2×#3715C22semidirect
52. C32×#102C22semidirect
54. #63634C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63566C22semidirect
61. #63557C22semidirect
62. #63554C22semidirect
85. #4786D3semidirect
86. #4783D3semidirect
153. #3715D4semidirect
180. #940C2×D3semidirect
191. C2×#214C2×D3semidirect
207. C2×Dic12C2×D3semidirect
233. C3×#102C2×D3semidirect
234. C3×#102C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
248. #810C2×D3semidirect
249. #809C2×D3semidirect
529. #102D32semidirect
800. C32#3268semidirect
908. C3#80266semidirect
909. C3#80348semidirect

Maximal subgroups

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

subgroupindex
#105951582
C2×#639252
C2×#638102
#105946292
#105924742
C3×#47862
C3×#47832
#105915202
#105914722
#105909442
#105908012
#105907372
#105906172
#105905032
#105904782
#803483
#802663