Finite Group Databasebeta

← #11872819

Subgroups — #11872819

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic
2#10594355C211yesmaximal, characteristic, complemented
3#10592475C211yesmaximal, characteristic
4C3×#4766C211yesmaximal, characteristic, complemented
5C3×#4757C211yesmaximal, characteristic, complemented
6#10591489C211yesmaximal, characteristic, complemented
7#10591467C211yesmaximal, characteristic
8#10591401C211yesmaximal, characteristic, complemented
9#10590773C211yesmaximal, characteristic, complemented
10#10590760C211yesmaximal, characteristic, complemented
11#10590715C211yesmaximal, characteristic, complemented
12#10590647C211yesmaximal, characteristic, complemented
13#10590468C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590450C211yesmaximal, characteristic, complemented
16#81147—31nomaximal
17#79787—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3754C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21#64106C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C3×#890C2211yescharacteristic, complemented
26C3×#887C2211yescharacteristic, complemented
27#63974—21no—
28C2×#3722—21no—
29#63952—21no—
30#63952—21no—
31#63894C2211yescharacteristic
32#63894C2211yescharacteristic
33#63874C2211yescharacteristic
34#63871C2211yescharacteristic
35#63869—21no—
36#63868—21no—
37#63866C2211yescharacteristic, complemented
38#63849C2211yescharacteristic
39#63848—21no—
40#63845—21no—
41#63844C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63647C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#818C2211yescharacteristic, complemented
48C3×#816C2211yescharacteristic, complemented
49C3×#815C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5698—31no—
62#5583—31no—
63#5545—31no—
64#5545—31no—
65C3×#478—31no—
66C3×#440—31no—
67#5169—31no—
68#5162—31no—
69#5066—31no—
70C4×#215—31no—
71#5019—31no—
72C4×#214—31no—
73#4891—31no—
74#4889—31no—
75#4888—31no—
76#4888—31no—
77#4868—31no—
78#4852—31no—
79#4841—31no—
80#4840—31no—
81#4818—31no—
82#4814—31no—
83#4776—31no—
84#4776—31no—
85#4776—31no—
86#4776—61no—
87#4766D311yescharacteristic, complemented
88#4758—31no—
89#4757D311yescharacteristic, complemented
90#4710—31no—
91#4709—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#624—21no—
104C2×#624—21no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3754—22no—
108#3752—21no—
109C4⋊(C3⋊Dic3)—21no—
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111#3744—22no—
112C3×#217—21no—
113C3×#217—21no—
114C3×#214—22no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126#3724—21no—
127#3724D411yescharacteristic
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722D411yescharacteristic
137#3722D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3717—22no—
141#3123—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×C3×SD16—31no—
146C3×#125—31no—
147C3×C4×Q8—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150#946—31no—
151#944—31no—
152C2×#215—31no—
153D4×Dic3C2×D311yescharacteristic
154D4×Dic3C2×D311yescharacteristic
155C2×#214—31no—
156C2×#214—31no—
157C2×#214—61no—
158C2×#214C2×D311yescharacteristic
159C4×#67—61no—
160C4×#67—61no—
161C2×(C2×D3)⋊C4—61no—
162C2×(C2×D3)⋊C4—61no—
163C2×#204—31no—
164C2×#204—31no—
165C2×#204—31no—
166C2×#204—61no—
167#898—61no—
168#898—61no—
169#898—61no—
170#897—31no—
171#897—31no—
172#897—31no—
173#897—61no—
174#893—31no—
175#893—31no—
176#892—31no—
177#892—31no—
178#890—61no—
179#890—61no—
180#890C2×D311yescharacteristic, complemented
181#889—61no—
182#887—31no—
183#887C2×D311yescharacteristic, complemented
184#67⋊C4—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#876—61no—
189C4×D12—31no—
190C4×D12—31no—
191#872—31no—
192#872—31no—
193#870—61no—
194#869—31no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102C2×D311yescharacteristic
204C3×#102C2×D311yescharacteristic
205C3×#97—31no—
206#835—31no—
207#832C2×D311yescharacteristic
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—61no—
214#818C2×D311yescharacteristic, complemented
215#816—31no—
216#816—31no—
217#816C2×D311yescharacteristic, complemented
218#815C2×D311yescharacteristic, complemented
219Dic3⋊C8—31no—
220Dic3⋊C8C2×D311yescharacteristic, complemented
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#808—31no—
230#808—31no—
231#808C2×D311yescharacteristic, complemented
232#807C2×D311yescharacteristic, complemented
233C4⋊(C3⋊C8)—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—24no—
238C22×C3⋊D3—81no—
239C22×C3⋊D3—81no—
240C22×C3⋊D3C2×D411yescharacteristic
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245#638—24no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)#4112yes—
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252#634—21no—
253#634—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×Dic6—21no—
265C3×Dic6—21no—
266#624—81no—
267#624—81no—
268C32×C8—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
273#518—91no—
274#485—91no—
275#485—91no—
276#478—31no—
277#478—91no—
278#461—91no—
279#461—91no—
280#450—91no—
281#450—91no—
282#440—31no—
283#440—91no—
284C4×SD16—91no—
285C4×SD16—91no—
286#433—91no—
287C23×D3—61no—
288C23×D3—61no—
289C23×D3—121no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4C22×D311yescharacteristic
293C2×C3×D4C22×D311yescharacteristic
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C2×#67—61no—
297C2×#67—61no—
298C2×#67—121no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301D3×D4—62no—
302D3×D4—62no—
303D3×D4—62no—
304D3×D4—62no—
305D3×D4—122no—
306D3×D4—122no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—61no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C2×Dic6C22×D311yescharacteristic
321C3×SD16—62no—
322C2×C3×C8—21no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C2×C3×C8C22×D311yescharacteristic
326C2×C3×C8C22×D311yescharacteristic
327C3×C4⋊C4—21no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C42—31no—
339C3×C42—31no—
340C3×C42—61no—
341#217—21no—
342#217—21no—
343#215—62no—
344#214—22no—
345#214—62no—
346#214—62no—
347#214—122no—
348(C2×D3)⋊C4—31no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
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—121no—
363C4⋊Dic3—21no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—121no—
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384C4×Dic3—21no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3C22×D311yescharacteristic
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396#204—62no—
397#204—62no—
398#204—62no—
399#204—122no—
400C22×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—21no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—84no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3⋊Dic3—21no—
415C3⋊Dic3—41no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C22×D4—91no—
425C2×SD16—31no—
426C2×SD16—91no—
427C2×SD16—91no—
428C2×SD16—91no—
429C4⋊Q8—91no—
430#126—181no—
431#126—181no—
432#125—31no—
433#125—181no—
434#125—181no—
435C22⋊Q8—91no—
436C22⋊Q8—91no—
437C4×Q8—31no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—181no—
444C4×D4—181no—
445#117—91no—
446#117—91no—
447C2×C22⋊C4—181no—
448C2×C22⋊C4—181no—
449#107—31no—
450#107—31no—
451#106—31no—
452#106—91no—
453C4⋊C8—31no—
454C4⋊C8—91no—
455#103—31no—
456#103—91no—
457#103—91no—
458#103—91no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102D3211yescharacteristic
463C22⋊C8—91no—
464C22⋊C8—91no—
465#97—31no—
466C4×C8—91no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—41no—
470C22×D3—31no—
471C22×D3—31no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—64no—
476C22×D3—64no—
477C22×D3—121no—
478C22×D3—124no—
479C22×D3—241no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—242no—
484C22×D3—242no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—22no—
490C3×D4—41no—
491C3×D4#23512yes—
492C3×D4#23912yes—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—241no—
506C2×C3×C4—241no—
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—64no—
510#67—64no—
511#67—124no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—81no—
522C2×Dic3—81no—
523C2×Dic3—121no—
524C2×Dic3D3×D411yescharacteristic
525C2×Dic3D3×D411yescharacteristic
526C2×Dic3D3×D411yescharacteristic
527C2×Dic3D3×D411yescharacteristic
528D12—32no—
529D12—32no—
530D12—62no—
531D12—61no—
532D12—61no—
533D12—121no—
534C4×D3—61no—
535C4×D3—61no—
536C4×D3—61no—
537C4×D3—61no—
538C4×D3—121no—
539C4×D3—121no—
540C4×D3—241no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544Dic6—21no—
545Dic6—21no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—121no—
551Dic6—121no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—41no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C2×C32—42no—
563C2×C32#52511yescharacteristic
564C2×C32#57711yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—41no—
567C3⋊D3—42no—
568C24—181no—
569C2×Q8—31no—
570C2×Q8—91no—
571C2×D4—91no—
572C2×D4—181no—
573C2×D4—182no—
574C2×D4—182no—
575C2×D4C2×D3211yescharacteristic
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—91no—
579C22×C4—181no—
580C22×C4—181no—
581SD16—62no—
582SD16—182no—
583SD16—182no—
584SD16—182no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8C2×D3211yescharacteristic
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—91no—
596C4⋊C4—91no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—91no—
606C22⋊C4—91no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C42—31no—
613C42—31no—
614C42—61no—
615C42—181no—
616C42—181no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—21no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—62no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—62no—
636C2×D3—61no—
637C2×D3—62no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—122no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—241no—
646C2×D3—241no—
647C2×D3—244no—
648C2×D3—244no—
649C2×D3—248no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—81no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4C2×#23511yescharacteristic
664C3×C4C2×#23911yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—61no—
676Dic3—61no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681C32#312311yescharacteristic, complemented, Sylow
682C23—21no—
683C23—91no—
684C23—184no—
685C23—181no—
686C23—721no—
687C23—721no—
688Q8—61no—
689Q8—61no—
690Q8—181no—
691Q8—181no—
692D4—21no—
693D4—92no—
694D4—184no—
695D4—181no—
696D4#379912yes—
697C2×C4—21no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—91no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—241no—
711C2×C4—241no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4C22×D3211yescharacteristic
715C8—21no—
716C8—61no—
717C8—61no—
718C8—181no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—42no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3#554711yescharacteristic
726C2×C3#562711yescharacteristic
727C2×C3#577011yescharacteristic
728C2×C3#577511yescharacteristic
729C2×C3#577511yescharacteristic
730C2×C3#577811yescharacteristic
731D3—122no—
732D3—121no—
733D3—122no—
734D3—121no—
735D3—122no—
736D3—242no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—181no—
741C22—182no—
742C22—181no—
743C22—181no—
744C22—361no—
745C22—361no—
746C22—724no—
747C22D32×D411yescharacteristic
748C4—41no—
749C4—61no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—181no—
758C4—361no—
759C4C2×#379911yescharacteristic
760C4#6431211yescharacteristic
761C3—21no—
762C3#7978711yescharacteristic, complemented
763C3#8114711yescharacteristic, complemented
764C2—42no—
765C2—361no—
766C2—362no—
767C2#1059406611yescharacteristic
768C2#1059473611yescharacteristic
769C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#102D32
hypocenterC32#3123
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
2. #10594355C2semidirect
4. C3×#4766C2semidirect
5. C3×#4757C2semidirect
6. #10591489C2semidirect
8. #10591401C2semidirect
9. #10590773C2semidirect
10. #10590760C2semidirect
11. #10590715C2semidirect
12. #10590647C2semidirect
13. #10590468C2semidirect
14. #10590458C2semidirect
15. #10590450C2semidirect
25. C3×#890C22semidirect
26. C3×#887C22semidirect
37. #63866C22semidirect
41. #63844C22semidirect
47. C3×#818C22semidirect
48. C3×#816C22semidirect
49. C3×#815C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
87. #4766D3semidirect
89. #4757D3semidirect
180. #890C2×D3semidirect
183. #887C2×D3semidirect
214. #818C2×D3semidirect
217. #816C2×D3semidirect
218. #815C2×D3semidirect
220. Dic3⋊C8C2×D3semidirect
231. #808C2×D3semidirect
232. #807C2×D3semidirect
681. C32#3123semidirect
762. C3#79787semidirect
763. C3#81147semidirect

Maximal subgroups

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

subgroupindex
#105952232
#105943552
#105924752
C3×#47662
C3×#47572
#105914892
#105914672
#105914012
#105907732
#105907602
#105907152
#105906472
#105904682
#105904582
#105904502
#811473
#797873