Finite Group Databasebeta

← #11872289

Subgroups — #11872289

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594992C211yesmaximal, characteristic, complemented
2#10594985C211yesmaximal, characteristic, complemented
3#10592434C211yesmaximal, characteristic, complemented
4C3×#4734C211yesmaximal, characteristic, complemented
5C3×#4720C211yesmaximal, characteristic, complemented
6#10591163C211yesmaximal, characteristic, complemented
7#10591094C211yesmaximal, characteristic, complemented
8#10590815C211yesmaximal, characteristic, complemented
9#10590799C211yesmaximal, characteristic, complemented
10#10590795C211yesmaximal, characteristic, complemented
11#10590772C211yesmaximal, characteristic, complemented
12#10590771C211yesmaximal, characteristic, complemented
13Dic3×#204C211yesmaximal, characteristic, complemented
14#10590753C211yesmaximal, characteristic, complemented
15#10590745C211yesmaximal, characteristic, complemented
16#80073—31nomaximal
17#79384—31nomaximal
18C2×C3×#235C2211yescharacteristic
19#64139C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C3×#930C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C2×C3×D24C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25#67⋊Dic3—21no—
26#67⋊Dic3—21no—
27#63971—21no—
28#63958—21no—
29#63911C2211yescharacteristic
30#63894C2211yescharacteristic
31Dic3×D12C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63890—21no—
35D3×C4⋊Dic3—21no—
36#63869C2211yescharacteristic
37#63854—21no—
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63841—21no—
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63644C2211yescharacteristic
47#63644C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63566C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5827—31no—
62#5619—31no—
63#5535—31no—
64#5523—31no—
65C3×#449—31no—
66C3×#433—31no—
67#5238—31no—
68#5163—31no—
69Dic3×SD16—31no—
70#5152—31no—
71#5150—31no—
72#5033—31no—
73#4848—31no—
74#4847—31no—
75#4843—31no—
76#4829—31no—
77#4817—31no—
78#4799—31no—
79#4763—31no—
80#4756—31no—
81#4736—31no—
82#4735—31no—
83#4735—31no—
84#4735—61no—
85#4734—31no—
86#4734D311yescharacteristic, complemented
87#4720D311yescharacteristic, complemented
88#4711—31no—
89#4710—31no—
90C4×D24—31no—
91C4×#204—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#235—22no—
99C3×#235—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C3×#217D411yescharacteristic
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3D411yescharacteristic
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C3×D24—22no—
128C3×#204—22no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3717—22no—
140#3714—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C3×#121—31no—
147C3×#117—31no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150C2×#215—31no—
151#940—31no—
152#939—61no—
153#938—61no—
154D4×Dic3—31no—
155D4×Dic3—31no—
156D4×Dic3—31no—
157D4×Dic3—61no—
158D4×Dic3—61no—
159C2×#213—31no—
160#930—31no—
161#930—31no—
162#930—61no—
163#930C2×D311yescharacteristic
164#926—61no—
165#926C2×D311yescharacteristic
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—61no—
169C2×C4⋊Dic3—61no—
170C2×D24—31no—
171C2×D24C2×D311yescharacteristic
172C2×#204—31no—
173C2×#204C2×D311yescharacteristic
174#894—61no—
175#894—61no—
176#893—31no—
177#892—61no—
178D3×C4⋊C4—61no—
179#890—31no—
180#886—61no—
181#884—61no—
182#884—61no—
183#883—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186#874—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191#870—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×C22⋊C8—21no—
199C3×C22⋊C8—31no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202C3×#97—31no—
203C3×C4×C8—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217#821—61no—
218#821C2×D311yescharacteristic
219#818—31no—
220#818—31no—
221#817—31no—
222#817—31no—
223#817—31no—
224#817—31no—
225#817—61no—
226#817—61no—
227#816—31no—
228#816C2×D311yescharacteristic
229#815C2×D311yescharacteristic
230Dic3⋊C8C2×D311yescharacteristic
231Dic3⋊C8C2×D311yescharacteristic
232C8×Dic3C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243#638—81no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—81no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C3×#67—24no—
251C3×#67—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—24no—
263C3×Dic6—21no—
264C3×Dic6#4112yes—
265#626—81no—
266#626—81no—
267#624—81no—
268D3×Dic3—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—91no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—31no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—31no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—31no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C22×C3×C4—21no—
298C22×C3×C4—61no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C2×#67—21no—
302C2×#67—21no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—121no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—121no—
314#235—22no—
315#235—22no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6C22×D311yescharacteristic
330C3×SD16—62no—
331C3×D8—62no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—61no—
346C3×C42—31no—
347C3×C42—31no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217D1211yescharacteristic
352#217D1211yescharacteristic
353#215—62no—
354#213—62no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—121no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—121no—
379C4⋊Dic3D1211yescharacteristic
380C4⋊Dic3D1211yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3C22×D311yescharacteristic
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395D24—22no—
396D24—62no—
397#204—22no—
398#204—62no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32C22×D411yescharacteristic
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3×D3—22no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—21no—
413C32×C4C2×#4111yescharacteristic
414C32×C4C2×#4111yescharacteristic
415C3⋊Dic3—41no—
416C3⋊Dic3—41no—
417C3⋊Dic3—41no—
418C3×Dic3—22no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C2×#41—31no—
425C2×SD16—31no—
426C2×SD16—91no—
427C2×D8—31no—
428C2×D8—91no—
429#127—91no—
430#125—91no—
431#123—181no—
432#123—181no—
433#121—31no—
434#121—91no—
435#121—181no—
436#121—181no—
437C4×Q8—91no—
438C4×Q8—91no—
439C4×D4—91no—
440C4×D4—91no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—181no—
444C4×D4—181no—
445#117—31no—
446#117—181no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—181no—
449#107—91no—
450#107—91no—
451#106—91no—
452#106—91no—
453C4⋊C8—31no—
454C4⋊C8—31no—
455#103—31no—
456#103—91no—
457#102—31no—
458#102—91no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463C22⋊C8—31no—
464C22⋊C8D3211yescharacteristic
465#97—31no—
466C4×C8—31no—
467C23×C3—21no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3C2×D1211yescharacteristic
471C23×C3D3×D411yescharacteristic
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—121no—
477C3×Q8—32no—
478C3×Q8—61no—
479C3×D4—32no—
480C3×D4—64no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—61no—
484C3×D4—241no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—64no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4C2×D1211yescharacteristic
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4C23×D311yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504#67—24no—
505#67—81no—
506#67—241no—
507#67—241no—
508#67—241no—
509#67—241no—
510#67—242no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—241no—
523C2×Dic3—241no—
524C2×Dic3—241no—
525C2×Dic3—241no—
526C2×Dic3—241no—
527C2×Dic3—242no—
528C2×Dic3C2×D1211yescharacteristic
529C2×Dic3C2×D1211yescharacteristic
530C2×Dic3C2×D1211yescharacteristic
531C2×Dic3C2×D1211yescharacteristic
532D12—21no—
533D12—21no—
534D12—21no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12—121no—
541D12—241no—
542D12—241no—
543D12#23712yes—
544C4×D3—24no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550Dic6—21no—
551Dic6#23712yes—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C2×C32—41no—
563C2×C32#52511yescharacteristic
564C2×C32#57611yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—81no—
567C3×D3—42no—
568C3×D3—81no—
569#41—62no—
570#41—62no—
571C2×Q8—31no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4—181no—
580C22×C4—61no—
581C22×C4—181no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4C2×D3211yescharacteristic
587SD16—62no—
588SD16—182no—
589D8—62no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8C2×D3211yescharacteristic
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—31no—
616C42—181no—
617C42—181no—
618C22×C3—22no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—62no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3C22×D1211yescharacteristic
635C22×C3C2×D3×D411yescharacteristic
636C2×D3—22no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—241no—
649C2×D3—241no—
650C2×D3—241no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—62no—
661C3×C4—121no—
662C3×C4C2×#23711yescharacteristic
663C3×C4C2×#23711yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666Dic3—21no—
667Dic3—21no—
668Dic3—21no—
669Dic3—21no—
670Dic3—22no—
671Dic3—41no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679Dic3—241no—
680Dic3—241no—
681C32#311911yescharacteristic, complemented, Sylow
682C23—61no—
683C23—61no—
684C23—181no—
685C23D3×D1211yescharacteristic
686Q8—32no—
687Q8—61no—
688D4—32no—
689D4—64no—
690D4—61no—
691D4—61no—
692D4—61no—
693D4—181no—
694D4—181no—
695D4—241no—
696D4—721no—
697D4—721no—
698D4—721no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—64no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—721no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4D3×D1211yescharacteristic
717C2×C4C22×D3211yescharacteristic
718C8—21no—
719C8—21no—
720C8—61no—
721C8—61no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—42no—
726C2×C3—41no—
727C2×C3—41no—
728C2×C3—122no—
729C2×C3—241no—
730C2×C3#552411yescharacteristic
731C2×C3#558611yescharacteristic
732C2×C3#575111yescharacteristic
733C2×C3#575211yescharacteristic
734C2×C3#577011yescharacteristic
735C2×C3#577411yescharacteristic
736D3—42no—
737D3—81no—
738D3—241no—
739D3—241no—
740D3—481no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—62no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—361no—
751C22—361no—
752C22—361no—
753C22C2×D3×D1211yescharacteristic
754C4—21no—
755C4—62no—
756C4—61no—
757C4—61no—
758C4—61no—
759C4—61no—
760C4—121no—
761C4—361no—
762C4—361no—
763C4—361no—
764C4D3×#23711yescharacteristic
765C4D3×#23711yescharacteristic
766C3—21no—
767C3#7938411yescharacteristic, complemented
768C3#8007311yescharacteristic, complemented
769C2—41no—
770C2—122no—
771C2—241no—
772C2—721no—
773C2#1059407811yescharacteristic
774C2#1059467911yescharacteristic
775C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3119
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
1. #10594992C2semidirect
2. #10594985C2semidirect
3. #10592434C2semidirect
4. C3×#4734C2semidirect
5. C3×#4720C2semidirect
6. #10591163C2semidirect
7. #10591094C2semidirect
8. #10590815C2semidirect
9. #10590799C2semidirect
10. #10590795C2semidirect
11. #10590772C2semidirect
12. #10590771C2semidirect
13. Dic3×#204C2semidirect
14. #10590753C2semidirect
15. #10590745C2semidirect
86. #4734D3semidirect
87. #4720D3semidirect
681. C32#3119semidirect
767. C3#79384semidirect
768. C3#80073semidirect

Maximal subgroups

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

subgroupindex
#105949922
#105949852
#105924342
C3×#47342
C3×#47202
#105911632
#105910942
#105908152
#105907992
#105907952
#105907722
#105907712
Dic3×#2042
#105907532
#105907452
#800733
#793843