Finite Group Databasebeta

← #11872356

Subgroups — #11872356

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
1C3×#5504C211yesmaximal, characteristic, complemented
2#10594985C211yesmaximal, characteristic, complemented
3#10592667C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic, complemented
5#10591163C211yesmaximal, characteristic, complemented
6#10591161C211yesmaximal, characteristic, complemented
7#10591056C211yesmaximal, characteristic, complemented
8#10590549C211yesmaximal, characteristic, complemented
9#10590547C211yesmaximal, characteristic, complemented
10#10590544C211yesmaximal, characteristic, complemented
11#10590542C211yesmaximal, characteristic, complemented
12#10590457C211yesmaximal, characteristic, complemented
13#10590456C211yesmaximal, characteristic, complemented
14#10590455C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#82568—31nomaximal
17#81272—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20#64139C2211yescharacteristic
21C3×#930C2211yescharacteristic
22C3×C4×#67—21no—
23C3×C4×#67—21no—
24C3×#926C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#892—21no—
28C3×D3×C4⋊C4—21no—
29C3×#887C2211yescharacteristic
30C3×#887C2211yescharacteristic
31#63971—21no—
32#63958—21no—
33#63911C2211yescharacteristic
34#63894C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63890—21no—
37#63869C2211yescharacteristic
38#63854—21no—
39C2×#3717C2211yescharacteristic
40C2×#3715C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63657C2211yescharacteristic
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63635C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#520—31no—
62#5619—31no—
63#5535—31no—
64#5504D311yescharacteristic, complemented
65C3×#480—31no—
66#5238—31no—
67#5238—31no—
68#5037—31no—
69#5027—31no—
70#5026—31no—
71C4×#215—31no—
72#5022—31no—
73#5015—31no—
74#5014—31no—
75C4×#213—31no—
76#5009—31no—
77#5000—31no—
78#4968—31no—
79#4968—31no—
80#4968—61no—
81#4967D311yescharacteristic, complemented
82#4891—31no—
83#4889—31no—
84#4877—31no—
85#4872—31no—
86#4786—31no—
87#4785—31no—
88#4762—31no—
89#4758—31no—
90#4734—31no—
91#4720—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—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×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217D411yescharacteristic
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137#3717—22no—
138#3715—22no—
139#3714—22no—
140#3713—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C3×#121—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—61no—
150C3×C4×D4—61no—
151C3×#117—31no—
152C3×#117—61no—
153C2×C3×C4⋊C4—21no—
154C2×C3×C4⋊C4—61no—
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C4⋊C4C2×D311yescharacteristic
157C2×#215—31no—
158C2×#215—31no—
159#940—31no—
160#939—61no—
161#938—61no—
162D4×Dic3—31no—
163C2×#214—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167#930—31no—
168#930—31no—
169#930—61no—
170#930C2×D311yescharacteristic
171C4×#67—21no—
172C4×#67—21no—
173#926C2×D311yescharacteristic
174C2×D24—31no—
175C2×#204—31no—
176#894—61no—
177#894—61no—
178#893—31no—
179#893C2×D311yescharacteristic
180#893C2×D311yescharacteristic
181#892—21no—
182D3×C4⋊C4—21no—
183#890—31no—
184#887C2×D311yescharacteristic
185#887C2×D311yescharacteristic
186#886—61no—
187#884—61no—
188#884—61no—
189#883—61no—
190#874—31no—
191C4×D12—31no—
192C4×D12—31no—
193#870—31no—
194C3×#107—31no—
195C3×#107—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C22⋊C8—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#830—31no—
204#830—31no—
205#830—61no—
206#830C2×D311yescharacteristic
207#821—31no—
208#816—31no—
209#815—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212C8×Dic3—31no—
213#810—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—61no—
220#809—61no—
221#809C2×D311yescharacteristic
222#809C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—61no—
228#808—61no—
229#807C2×D311yescharacteristic
230#807C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—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×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—81no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246#638—81no—
247C2×C3⋊Dic3—21no—
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×C4×D3—81no—
264C3×C4×D3—81no—
265C3×Dic6—21no—
266C3×Dic6#4112yes—
267#626—81no—
268#626—81no—
269#624—81no—
270D3×Dic3—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—31no—
277#481—91no—
278#480—31no—
279#479—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
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—21no—
299C22×C3×C4—21no—
300C22×C3×C4—41no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—121no—
313C22×Dic3—61no—
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—21no—
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6C22×D311yescharacteristic
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—41no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—31no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42—61no—
355#217—61no—
356#217#6711yescharacteristic
357#217#6711yescharacteristic
358#215—62no—
359#215—62no—
360#214—62no—
361#213—62no—
362#213—62no—
363#213—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—121no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3#6711yescharacteristic
378C4⋊Dic3#6711yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3C22×D311yescharacteristic
388C4×Dic3C22×D311yescharacteristic
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397D24—62no—
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×C4—41no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
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—91no—
426C2×SD16—91no—
427C2×D8—91no—
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—31no—
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—61no—
442C4×D4—61no—
443C4×D4—91no—
444C4×D4—91no—
445#117—31no—
446#117—61no—
447C2×C4⋊C4—61no—
448C2×C4⋊C4D3211yescharacteristic
449#107—31no—
450#107—31no—
451#106—91no—
452#106—91no—
453C4⋊C8—91no—
454C4⋊C8—91no—
455#103—91no—
456#103—91no—
457#102—31no—
458#102—31no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463C22⋊C8—31no—
464C22⋊C8—91no—
465#97—91no—
466C4×C8—91no—
467C23×C3—21no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3D3×D411yescharacteristic
471C23×C3C2×#6711yescharacteristic
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—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—64no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—81no—
507C2×C3×C4—81no—
508C2×C3×C4—82no—
509C2×C3×C4—241no—
510C2×C3×C4—241no—
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—24no—
516#67—81no—
517#67—241no—
518#67—241no—
519#67—241no—
520#67—241no—
521#67—242no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—121no—
527C2×Dic3—241no—
528C2×Dic3C2×#6711yescharacteristic
529C2×Dic3C2×#6711yescharacteristic
530C2×Dic3C2×#6711yescharacteristic
531C2×Dic3C2×#6711yescharacteristic
532D12—21no—
533D12—21no—
534D12—21no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12—121no—
541D12—241no—
542D12—241no—
543D12#23512yes—
544C4×D3—24no—
545C4×D3—81no—
546C4×D3—81no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550Dic6—21no—
551Dic6#23512yes—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C3⋊C8—121no—
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—21no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4C2×D3211yescharacteristic
587SD16—182no—
588SD16—182no—
589D8—182no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C4⋊C4—21no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4C2×D3211yescharacteristic
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—31no—
616C42—61no—
617C42—61no—
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×C3C2×D3×D411yescharacteristic
635C22×C3C22×#6711yescharacteristic
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—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—62no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—81no—
666C3×C4—81no—
667C3×C4—121no—
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23511yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672Dic3—22no—
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681C32#311911yescharacteristic, complemented, Sylow
682C23—61no—
683C23—61no—
684C23—181no—
685C23D3×#6711yescharacteristic
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—21no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—64no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—81no—
711C2×C4—181no—
712C2×C4—241no—
713C2×C4—241no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4D3×#6711yescharacteristic
717C2×C4C22×D3211yescharacteristic
718C8—61no—
719C8—61no—
720C8—181no—
721C8—181no—
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#565611yescharacteristic
731C2×C3#575711yescharacteristic
732C2×C3#577811yescharacteristic
733C2×C3#579111yescharacteristic
734C2×C3#583511yescharacteristic
735C2×C3#583711yescharacteristic
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×#6711yescharacteristic
754C4—21no—
755C4—41no—
756C4—41no—
757C4—61no—
758C4—61no—
759C4—62no—
760C4—61no—
761C4—61no—
762C4—121no—
763C4—361no—
764C4D3×#23511yescharacteristic
765C4D3×#23511yescharacteristic
766C3—21no—
767C3#8127211yescharacteristic, complemented
768C3#8256811yescharacteristic, complemented
769C2—41no—
770C2—122no—
771C2—241no—
772C2—721no—
773C2#1059489611yescharacteristic
774C2#1059509611yescharacteristic
775C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5504C2semidirect
2. #10594985C2semidirect
3. #10592667C2semidirect
4. C3×#4967C2semidirect
5. #10591163C2semidirect
6. #10591161C2semidirect
7. #10591056C2semidirect
8. #10590549C2semidirect
9. #10590547C2semidirect
10. #10590544C2semidirect
11. #10590542C2semidirect
12. #10590457C2semidirect
13. #10590456C2semidirect
14. #10590455C2semidirect
15. #10590453C2semidirect
64. #5504D3semidirect
81. #4967D3semidirect
681. C32#3119semidirect
767. C3#81272semidirect
768. C3#82568semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
#105949852
#105926672
C3×#49672
#105911632
#105911612
#105910562
#105905492
#105905472
#105905442
#105905422
#105904572
#105904562
#105904552
#105904532
#825683
#812723