Finite Group Databasebeta

← #11884189

Subgroups — #11884189

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595070C211yesmaximal, characteristic
2#10594803C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic, complemented
4C2×#63796C211yesmaximal, characteristic, complemented
5#10592427C211yesmaximal, characteristic, complemented
6C3×#4738C211yesmaximal, characteristic, complemented
7C3×#4733C211yesmaximal, characteristic, complemented
8#10591180C211yesmaximal, characteristic, complemented
9#10590950C211yesmaximal, characteristic, complemented
10#10590943C211yesmaximal, characteristic, complemented
11#10590870C211yesmaximal, characteristic, complemented
12#10590855C211yesmaximal, characteristic, complemented
13#10590796C211yesmaximal, characteristic, complemented
14#10590748C211yesmaximal, characteristic, complemented
15#10590743C211yesmaximal, characteristic, complemented
16#80241—31nomaximal
17#80061—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×#3802C2211yescharacteristic
21C2×#3797C2211yescharacteristic
22C4×#638C2211yescharacteristic
23C2×#3748C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C3×#924C2211yescharacteristic, complemented
27C2×C3×Dic12C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31#63983—21no—
32#63970—21no—
33#63964—21no—
34#63952—21no—
35D3×(C2×D3)⋊C4—21no—
36#63905—21no—
37#63898C2211yescharacteristic
38#63888—21no—
39#63873C2211yescharacteristic, complemented
40#63871C2211yescharacteristic
41#63871C2211yescharacteristic
42#63863C2211yescharacteristic
43#63843C2211yescharacteristic, complemented
44#63839—21no—
45C2×#3718C2211yescharacteristic, complemented
46C2×#3718C2211yescharacteristic, complemented
47#63827—24no—
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51#63796—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63647C2211yescharacteristic
54#63642C2211yescharacteristic, complemented
55#63641C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#816C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60#63576C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic
63#5829—31no—
64C2×#951—31no—
65Q8×#67—31no—
66C2×#942—31no—
67C2×D3×SD16—31no—
68C2×D3×SD16—31no—
69#5632—31no—
70#5612—31no—
71C3×#452—31no—
72C3×#448—31no—
73#5190—31no—
74#5186—31no—
75#5169—31no—
76#5167—31no—
77#5166—31no—
78#5162—31no—
79#5049—31no—
80#5042—31no—
81#4818—31no—
82#4817—31no—
83#4813—31no—
84#4813—31no—
85#4809—31no—
86#4798—31no—
87#4776—31no—
88#4757—31no—
89#4738D311yescharacteristic, complemented
90#4733D311yescharacteristic, complemented
91#4728—31no—
92#4728—31no—
93#4728—61no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638D411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#235—22no—
102C3×#235—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6—22no—
107C2×C3×Dic6—21no—
108C2×C3×Dic6—41no—
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#627—21no—
114C2×#625—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802—41no—
119#3797—22no—
120#3797—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123#3757D411yescharacteristic
124#3752D411yescharacteristic
125#3750D411yescharacteristic
126C4×C3⋊Dic3C2311yescharacteristic
127#3748—22no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C8×C3⋊D3—22no—
131C3×#217—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic12—41no—
137C3×#204—22no—
138C3×#204—22no—
139C3×#204—41no—
140#3724—21no—
141#3724—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3718—22no—
152#3718—22no—
153#3715—22no—
154#3715—22no—
155#3715D414yescomplemented
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×#235C2×D311yescharacteristic
164C22×Dic6C2×D311yescharacteristic, complemented
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×C22⋊Q8—31no—
170C3×#121—31no—
171#951—64no—
172#947—31no—
173#946—31no—
174#946—31no—
175#946—61no—
176Q8×Dic3—31no—
177#944—31no—
178#944—31no—
179#944—61no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—31no—
184#942—64no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188#939—61no—
189#938—61no—
190#937—61no—
191#937—61no—
192#936—31no—
193D4×Dic3—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197#930C2×D311yescharacteristic
198#929—61no—
199C4×#67—31no—
200C4×#67—31no—
201C4×#67—61no—
202C4×#67—61no—
203C2×(C2×D3)⋊C4—61no—
204#924—61no—
205#924C2×D311yescharacteristic, complemented
206C2×#208—31no—
207C2×#208—31no—
208C2×#208—61no—
209D3×SD16—64no—
210D3×SD16—64no—
211C2×Dic12C2×D311yescharacteristic, complemented
212C2×#204C2×D311yescharacteristic
213C2×#204C2×D311yescharacteristic
214C2×#204C2×D311yescharacteristic
215C2×D3×C8—31no—
216C2×D3×C8—31no—
217C2×D3×C8—61no—
218#897—31no—
219#897—31no—
220#896—61no—
221#893—31no—
222#888—61no—
223#887—31no—
224#883—61no—
225#67⋊C4—61no—
226D3×C22⋊C4—61no—
227#878—61no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103—31no—
231C3×#102—31no—
232C3×C22⋊C8—21no—
233C3×C22⋊C8C2×D311yescharacteristic, complemented
234C3×C22⋊C8C2×D311yescharacteristic, complemented
235#835—31no—
236#832—31no—
237#821C2×D311yescharacteristic
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—61no—
241#816C2×D311yescharacteristic, complemented
242#816C2×D311yescharacteristic, complemented
243#816C2×D311yescharacteristic, complemented
244#815—31no—
245#815—31no—
246#815—61no—
247Dic3⋊C8—31no—
248Dic3⋊C8—31no—
249Dic3⋊C8—61no—
250#810—31no—
251#809—31no—
252#807—31no—
253#807—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265#638—22no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271C3×#67—42no—
272C3×#67—81no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12C2×D412yes—
284C3×C4×D3—42no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—42no—
293C3×Dic6C2×D412yes—
294#627—42no—
295#625—42no—
296#624—42no—
297D3×Dic3—81no—
298C32×C8—21no—
299C32×C8—21no—
300C3⋊(C3⋊C8)—21no—
301C3⋊(C3⋊C8)C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—31no—
312#451—91no—
313#450—91no—
314#448—31no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—62no—
326C2×C3×Q8—61no—
327C2×C3×Q8—121no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C22×C3×C4—21no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—31no—
340C2×#67—31no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C22×Dic3—21no—
345C22×Dic3—61no—
346D3×Q8—62no—
347D3×Q8—62no—
348D3×Q8—121no—
349D3×Q8—121no—
350D3×D4—62no—
351D3×D4—62no—
352D3×D4—121no—
353D3×D4—121no—
354#235—22no—
355#235—41no—
356C2×D12C22×D311yescharacteristic
357C2×D12C22×D311yescharacteristic
358C2×C4×D3—21no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×Dic6—22no—
366C2×Dic6—21no—
367C2×Dic6—41no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6C22×D311yescharacteristic
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×Q16—121no—
375C3×SD16—62no—
376C3×SD16—62no—
377C3×SD16—121no—
378C2×C3×C8—21no—
379C2×C3×C8—21no—
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C22×D311yescharacteristic
383C2×C3×C8C22×D311yescharacteristic
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389#217—21no—
390#217—31no—
391#217—31no—
392#217—61no—
393#217—61no—
394#217—61no—
395#217—61no—
396#216—62no—
397#216—62no—
398#216—62no—
399#216—62no—
400#215—34no—
401#215—62no—
402#215—62no—
403#214—34no—
404#214—62no—
405#214—62no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—31no—
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417C4⋊Dic3—61no—
418C4⋊Dic3—61no—
419C4⋊Dic3—61no—
420C4⋊Dic3C22×D311yescharacteristic
421C4⋊Dic3C22×D311yescharacteristic
422Dic3⋊C4—21no—
423Dic3⋊C4—31no—
424Dic3⋊C4—31no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433C4×Dic3—31no—
434C4×Dic3—31no—
435C4×Dic3—61no—
436C4×Dic3—61no—
437C4×Dic3—61no—
438#208—62no—
439#208—62no—
440#208—122no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—61no—
447Dic12—41no—
448#204—22no—
449#204—22no—
450#204—41no—
451D3×C8—62no—
452D3×C8—62no—
453D3×C8—122no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32C22×D411yescharacteristic
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3#13712yescomplemented
461C2×C3×D3—22no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467D32—84no—
468C32×C4—21no—
469C32×C4C22×D411yescharacteristic
470C32×C4H(5,𝔽2)11yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—21no—
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—31no—
481C22×Q8—31no—
482C22×Q8—91no—
483C22×D4—91no—
484#137—184no—
485C2×Q16—31no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—184no—
495C2×M16—91no—
496C22×C8—91no—
497C4⋊Q8—91no—
498C4⋊Q8—181no—
499#124—91no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—91no—
503C22⋊Q8—91no—
504C22⋊Q8—181no—
505C22⋊Q8—181no—
506#121—31no—
507#121—181no—
508#120—181no—
509C4×Q8—91no—
510C4×D4—91no—
511C4×D4—91no—
512C4×D4—181no—
513C2×C22⋊C4—181no—
514#107—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—31no—
518#103—31no—
519#103—91no—
520#102—31no—
521#102—91no—
522C22⋊C8—91no—
523C22⋊C8D3211yescharacteristic, complemented
524#97—91no—
525C23×C3—21no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3D3×D411yescharacteristic
529C23×C3D3×D411yescharacteristic
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—31no—
533C22×D3—31no—
534C22×D3—61no—
535C22×D3—122no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—241no—
540C22×D3—241no—
541C3×Q8—32no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—122no—
550C3×D4—32no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—122no—
555C3×D4—241no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—122no—
571C2×C3×C4—122no—
572C2×C3×C4D3×D411yescharacteristic
573C2×C3×C4D3×D411yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576#67—42no—
577#67—62no—
578#67—62no—
579#67—81no—
580#67—122no—
581#67—122no—
582#67—122no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—42no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—241no—
600D12—21no—
601D12—21no—
602D12—21no—
603D12D3×D412yes—
604C4×D3—42no—
605C4×D3—61no—
606C4×D3—61no—
607C4×D3—61no—
608C4×D3—61no—
609C4×D3—121no—
610C4×D3—121no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—241no—
614Dic6—21no—
615Dic6—21no—
616Dic6—21no—
617Dic6—21no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—42no—
622Dic6—122no—
623Dic6—122no—
624Dic6D3×D412yes—
625C3×C8—21no—
626C3×C8—21no—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—41no—
630C3×C8—41no—
631C3⋊C8—32no—
632C3⋊C8—32no—
633C3⋊C8—62no—
634C3⋊C8—61no—
635C3⋊C8—61no—
636C3⋊C8—121no—
637C2×C32—41no—
638C2×C32D4211yescharacteristic
639C2×C32C2×#13711yescharacteristic
640C2×C32#57711yescharacteristic
641C3⋊D3—22no—
642C3×D3—42no—
643C3×D3—81no—
644C24—181no—
645#41—62no—
646#41—121no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—31no—
650C2×Q8—31no—
651C2×Q8—62no—
652C2×Q8—61no—
653C2×Q8—121no—
654C2×Q8—181no—
655C2×Q8—182no—
656C2×Q8—361no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—91no—
662C2×D4—181no—
663C2×D4—182no—
664C2×D4—361no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—91no—
668C22×C4—181no—
669C22×C4—181no—
670C22×C4C2×D3211yescharacteristic
671Q16—121no—
672Q16—182no—
673Q16—182no—
674SD16—62no—
675SD16—62no—
676SD16—94no—
677SD16—121no—
678SD16—182no—
679SD16—182no—
680M16—182no—
681C2×C8—91no—
682C2×C8—91no—
683C2×C8—182no—
684C2×C8C2×D3211yescharacteristic
685C2×C8C2×D3211yescharacteristic
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—61no—
689C4⋊C4—91no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4—181no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—91no—
698C22⋊C4—91no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—91no—
705C42—181no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3C2×D3×D411yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C2×D3—22no—
725C2×D3—32no—
726C2×D3—32no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—62no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—244no—
740C2×D3—244no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—41no—
746C3×C4—62no—
747C3×C4—121no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4—121no—
751C3×C4—121no—
752C3×C4C2×D3×D411yescharacteristic
753C3×C4C2×D3×D411yescharacteristic
754C3×C4#100411yescharacteristic
755C3×C4#100411yescharacteristic
756Dic3—22no—
757Dic3—41no—
758Dic3—41no—
759Dic3—41no—
760Dic3—41no—
761Dic3—41no—
762Dic3—61no—
763Dic3—61no—
764Dic3—61no—
765Dic3—61no—
766Dic3—61no—
767Dic3—61no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771C32#326611yescharacteristic, complemented, Sylow
772C23—61no—
773C23—61no—
774C23—91no—
775C23—362no—
776C23—362no—
777C23—721no—
778C23#380211yescharacteristic
779Q8—32no—
780Q8—61no—
781Q8—61no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—61no—
786Q8—61no—
787Q8—122no—
788Q8—362no—
789D4—32no—
790D4—61no—
791D4—61no—
792D4—61no—
793D4—122no—
794D4—182no—
795D4—241no—
796D4—362no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—91no—
808C2×C4—122no—
809C2×C4—122no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4—362no—
813C2×C4—721no—
814C2×C4#380211yescharacteristic
815C2×C4C22×D3211yescharacteristic
816C8—21no—
817C8—21no—
818C8—92no—
819C8—181no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—41no—
824C2×C3—41no—
825C2×C3—81no—
826C2×C3—122no—
827C2×C3—241no—
828C2×C3#559011yescharacteristic
829C2×C3#559011yescharacteristic
830C2×C3#576211yescharacteristic
831C2×C3#577011yescharacteristic
832C2×C3D3×#13711yescharacteristic
833C2×C3D3×#13711yescharacteristic
834D3—42no—
835D3—62no—
836D3—62no—
837D3—81no—
838D3—122no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—62no—
843C22—92no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—181no—
850C22—181no—
851C22—724no—
852C22C2×#380211yescharacteristic
853C4—21no—
854C4—62no—
855C4—121no—
856C4—121no—
857C4—121no—
858C4—121no—
859C4—121no—
860C4—181no—
861C4—181no—
862C4—181no—
863C4D32×D411yescharacteristic
864C4#6431311yescharacteristic
865C3—21no—
866C3#8006111yescharacteristic, complemented
867C3#8024111yescharacteristic, complemented
868C2—41no—
869C2—122no—
870C2—182no—
871C2—241no—
872C2#1059427111yescharacteristic
873C2#1059468611yescharacteristic
874C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595070C2
hypercenterC22⋊C8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594803C2semidirect
3. C2×#63827C2semidirect
4. C2×#63796C2semidirect
5. #10592427C2semidirect
6. C3×#4738C2semidirect
7. C3×#4733C2semidirect
8. #10591180C2semidirect
9. #10590950C2semidirect
10. #10590943C2semidirect
11. #10590870C2semidirect
12. #10590855C2semidirect
13. #10590796C2semidirect
14. #10590748C2semidirect
15. #10590743C2semidirect
19. C22×C3×Dic6C22semidirect
23. C2×#3748C22semidirect
26. C3×#924C22semidirect
27. C2×C3×Dic12C22semidirect
39. #63873C22semidirect
43. #63843C22semidirect
45. C2×#3718C22semidirect
46. C2×#3718C22semidirect
52. C32×C22⋊C8C22semidirect
54. #63642C22semidirect
55. #63641C22semidirect
57. C3×#816C22semidirect
58. C3×#816C22semidirect
59. C3×#816C22semidirect
60. #63576C22semidirect
61. #63565C22semidirect
89. #4738D3semidirect
90. #4733D3semidirect
155. #3715D4semidirect
164. C22×Dic6C2×D3semidirect
205. #924C2×D3semidirect
211. C2×Dic12C2×D3semidirect
233. C3×C22⋊C8C2×D3semidirect
234. C3×C22⋊C8C2×D3semidirect
241. #816C2×D3semidirect
242. #816C2×D3semidirect
243. #816C2×D3semidirect
460. C2×C3⋊D3#137semidirect
523. C22⋊C8D32semidirect
771. C32#3266semidirect
866. C3#80061semidirect
867. C3#80241semidirect

Maximal subgroups

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

subgroupindex
#105950702
#105948032
C2×#638272
C2×#637962
#105924272
C3×#47382
C3×#47332
#105911802
#105909502
#105909432
#105908702
#105908552
#105907962
#105907482
#105907432
#802413
#800613