Finite Group Databasebeta

← #11876912

Subgroups — #11876912

Order 1152.

857 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#10595950C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4#10591178C211yesmaximal, characteristic, complemented
5#10591176C211yesmaximal, characteristic, complemented
6#10591165C211yesmaximal, characteristic
7#10591121C211yesmaximal, characteristic, complemented
8#10590383C211yesmaximal, characteristic, complemented
9#10590370C211yesmaximal, characteristic, complemented
10#10590362C211yesmaximal, characteristic, complemented
11#10590360C211yesmaximal, characteristic, complemented
12#10590346C211yesmaximal, characteristic, complemented
13#10590304C211yesmaximal, characteristic, complemented
14#10590293C211yesmaximal, characteristic, complemented
15#10590274C211yesmaximal, characteristic, complemented
16#83139—31nomaximal
17#78534—31nomaximal
18C2×C32×C42C2211yescharacteristic
19#64139C2211yescharacteristic
20#64138—21no—
21C4×#638—21no—
22#64133C2211yescharacteristic
23#64085—21no—
24#64084C2211yescharacteristic
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26#64081—21no—
27#64079C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#929—21no—
31C3×C4×#67—21no—
32C3×#924C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35C3×#876—21no—
36C3×#875C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×#872—21no—
39C3×#870C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C3×#803C2211yescharacteristic
46C3×#803C2211yescharacteristic
47C3×C4×C3⋊C8C2211yescharacteristic
48C3×C4×C3⋊C8C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61C3×#529—31no—
62#5479—31no—
63#5479—31no—
64#5479—61no—
65#5479D311yescharacteristic, complemented
66C3×C4×M16—31no—
67#5137—31no—
68#5135—31no—
69#5134—31no—
70#5134—31no—
71#5068—31no—
72#5065—31no—
73#5059—31no—
74#5056—31no—
75#5052—31no—
76#5049—31no—
77#5042—31no—
78#5039—31no—
79#5030—31no—
80#5026—31no—
81#5018—31no—
82#5014—31no—
83C4×#208D311yescharacteristic, complemented
84#4716—31no—
85#4711—31no—
86#4710—31no—
87#4710—31no—
88#4697—31no—
89#4697—31no—
90#4696—31no—
91#4683—31no—
92C22×C32×C4D411yescharacteristic
93C22×C32×C4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C32×C42D411yescharacteristic
104C32×C42D411yescharacteristic
105C32×C42C2311yescharacteristic
106C32×C42C2311yescharacteristic
107#3757—21no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×#208—22no—
132C3×#208—22no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3719—22no—
138#3717—22no—
139#3716—22no—
140#3714—22no—
141#3183—91noSylow
142C2×C3×M16—31no—
143C2×C3×M16—31no—
144C3×#126—61no—
145C3×#125—31no—
146C3×#124—31no—
147C3×#123—61no—
148C3×C22⋊Q8—31no—
149C3×#121—31no—
150C3×C4×Q8—31no—
151C3×C4×D4—31no—
152C3×C4×D4—61no—
153C3×#117—61no—
154C2×C3×C42—21no—
155C2×C3×C42C2×D311yescharacteristic
156C2×C3×C42C2×D311yescharacteristic
157C2×#216—31no—
158C2×#215—31no—
159C2×#214—31no—
160C2×#213—31no—
161#930—31no—
162#930—31no—
163#930—61no—
164#930C2×D311yescharacteristic
165#929—21no—
166#929—62no—
167#929—61no—
168#929—61no—
169C4×#67—21no—
170C4×#67—62no—
171C4×#67—61no—
172C4×#67—61no—
173#924—31no—
174#924—31no—
175#924—61no—
176#924C2×D311yescharacteristic
177C2×#208C2×D311yescharacteristic
178C2×#208C2×D311yescharacteristic
179C2×Dic12—31no—
180C2×D24—31no—
181C2×#204—31no—
182C2×#204—31no—
183#876—21no—
184#876—62no—
185#876—61no—
186#876—61no—
187#875—31no—
188#875—31no—
189#875—61no—
190#875C2×D311yescharacteristic
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—61no—
194C4×D12C2×D311yescharacteristic
195#872—21no—
196#872—62no—
197#872—61no—
198#872—61no—
199#870—31no—
200#870—31no—
201#870—61no—
202#870C2×D311yescharacteristic
203C4×Dic6—31no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C4×Dic6C2×D311yescharacteristic
207C3×#97—31no—
208C3×#97—31no—
209C3×C4×C8—31no—
210C3×C4×C8—31no—
211#835—31no—
212#835—31no—
213#832—31no—
214#832—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#818—31no—
220#818—31no—
221#817—31no—
222#817—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#810—31no—
228#810—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235#803C2×D311yescharacteristic
236#803C2×D311yescharacteristic
237C4×C3⋊C8C2×D311yescharacteristic
238C4×C3⋊C8C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—41no—
245C2×C32×C4—41no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252#638—42no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4×C3⋊D3—42no—
259#634—21no—
260#634—21no—
261C3×#67—42no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8#4112yes—
273C3×C3⋊C8#4112yes—
274#529—31no—
275#529—91no—
276#499—91no—
277#495—91no—
278#488—91no—
279#488—91no—
280#470—91no—
281#469—91no—
282#468—91no—
283#468—91no—
284#442—91no—
285#441—91no—
286#440—91no—
287#440—91no—
288C4×M16—31no—
289C2×C3×Q8—31no—
290C2×C3×D4—31no—
291C2×C3×D4—61no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—61no—
296C22×C3×C4D1211yescharacteristic
297C22×C3×C4D1211yescharacteristic
298C22×C3×C4#6711yescharacteristic
299C22×C3×C4#6711yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C2×#67—21no—
303C2×#67—62no—
304C2×#67—61no—
305C2×#67—61no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—61no—
309C2×D12C22×D311yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—62no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×Dic6—31no—
315C2×Dic6—31no—
316C2×Dic6—61no—
317C2×Dic6C22×D311yescharacteristic
318C3×M16—62no—
319C3×M16—62no—
320C2×C3×C8—31no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C22⋊C4—61no—
331C3×C22⋊C4—61no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C22⋊C4—61no—
335C3×C42—21no—
336C3×C42—21no—
337C3×C42—21no—
338C3×C42—21no—
339C3×C42—61no—
340C3×C42D1211yescharacteristic
341C3×C42D1211yescharacteristic
342C3×C42#6711yescharacteristic
343C3×C42#6711yescharacteristic
344C3×C42C22×D311yescharacteristic
345C3×C42C22×D311yescharacteristic
346C3×C42C22×D311yescharacteristic
347C3×C42C22×D311yescharacteristic
348#217—21no—
349#217—62no—
350#217—61no—
351#217—61no—
352#216—62no—
353#215—62no—
354#214—62no—
355#213—62no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
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—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—62no—
385Dic3⋊C4—62no—
386Dic3⋊C4—62no—
387Dic3⋊C4—62no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—21no—
397C4×Dic3—62no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400#208—22no—
401#208—22no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—62no—
407D24—62no—
408#204—62no—
409#204—62no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4C2×#4111yescharacteristic
426C32×C4C2×#4111yescharacteristic
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C2×Q16—91no—
434C2×SD16—91no—
435C2×SD16—91no—
436C2×D8—91no—
437C2×M16—31no—
438C2×M16—31no—
439#126—61no—
440#126—181no—
441#125—31no—
442#125—91no—
443#124—31no—
444#124—91no—
445#123—61no—
446#123—181no—
447C22⋊Q8—31no—
448C22⋊Q8—91no—
449#121—31no—
450#121—91no—
451C4×Q8—31no—
452C4×Q8—91no—
453C4×D4—31no—
454C4×D4—61no—
455C4×D4—91no—
456C4×D4—181no—
457#117—61no—
458#117—181no—
459C2×C42D3211yescharacteristic
460#107—91no—
461#107—91no—
462#106—91no—
463#106—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471#102—91no—
472#97—31no—
473#97—31no—
474C4×C8—31no—
475C4×C8—31no—
476C23×C3—21no—
477C23×C3—61no—
478C23×C3C2×D1211yescharacteristic
479C23×C3C2×#6711yescharacteristic
480C22×D3—21no—
481C22×D3—62no—
482C22×D3—61no—
483C22×D3—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×D4—61no—
487C3×D4—61no—
488C3×D4—122no—
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—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—122no—
511C2×C3×C4C2×D1211yescharacteristic
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4C2×D1211yescharacteristic
514C2×C3×C4C2×D1211yescharacteristic
515C2×C3×C4C2×D1211yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—42no—
524#67—124no—
525#67—122no—
526#67—122no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539D12—21no—
540D12—21no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—61no—
545D12—121no—
546D12—121no—
547C4×D3—42no—
548C4×D3—124no—
549C4×D3—122no—
550C4×D3—122no—
551Dic6—21no—
552Dic6—21no—
553Dic6—61no—
554Dic6—61no—
555Dic6—61no—
556Dic6—61no—
557Dic6—121no—
558Dic6—121no—
559C3×C8—32no—
560C3×C8—32no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8#23512yes—
566C3⋊C8#23512yes—
567C2×C32—41no—
568C2×C32#53211yescharacteristic
569C2×C32#57511yescharacteristic
570C2×C32#57511yescharacteristic
571C3⋊D3—81no—
572C3×D3—81no—
573C2×Q8—31no—
574C2×Q8—91no—
575C2×D4—31no—
576C2×D4—61no—
577C2×D4—91no—
578C2×D4—181no—
579C22×C4—61no—
580C22×C4—181no—
581C22×C4#62611yescharacteristic
582C22×C4#62611yescharacteristic
583C22×C4C2×D3211yescharacteristic
584Q16—182no—
585SD16—182no—
586SD16—182no—
587D8—182no—
588M16—62no—
589M16—62no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—61no—
617C42—181no—
618C42#62611yescharacteristic
619C42#62611yescharacteristic
620C42C2×D3211yescharacteristic
621C42C2×D3211yescharacteristic
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C22×D1211yescharacteristic
636C22×C3C22×#6711yescharacteristic
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—122no—
641C2×D3—122no—
642C2×D3—122no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C3×C4—22no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4C2×#23511yescharacteristic
670C3×C4C2×#23511yescharacteristic
671C3×C4D3×#4111yescharacteristic
672C3×C4D3×#4111yescharacteristic
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—122no—
677Dic3—122no—
678Dic3—122no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685C32#318311yescharacteristic, complemented, Sylow
686C23—61no—
687C23—181no—
688C23C2×#62611yescharacteristic
689Q8—61no—
690Q8—61no—
691Q8—181no—
692Q8—181no—
693D4—61no—
694D4—61no—
695D4—122no—
696D4—181no—
697D4—181no—
698D4—362no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—122no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—362no—
711C2×C4C2×#62611yescharacteristic
712C2×C4C2×#62611yescharacteristic
713C2×C4C2×#62611yescharacteristic
714C2×C4C2×#62611yescharacteristic
715C2×C4C2×#62611yescharacteristic
716C2×C4C22×D3211yescharacteristic
717C8—32no—
718C8—32no—
719C8—61no—
720C8—61no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—42no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—241no—
728C2×C3#547711yescharacteristic
729C2×C3#574811yescharacteristic
730C2×C3#574811yescharacteristic
731C2×C3#582211yescharacteristic
732C2×C3#582211yescharacteristic
733C2×C3#583211yescharacteristic
734D3—81no—
735D3—242no—
736D3—241no—
737D3—241no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—361no—
745C22—361no—
746C22—361no—
747C22C22×#62611yescharacteristic
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—361no—
757C4—361no—
758C4—361no—
759C4D3×#23511yescharacteristic
760C4D3×#23511yescharacteristic
761C3—21no—
762C3#7853411yescharacteristic, complemented
763C3#8313911yescharacteristic, complemented
764C2—41no—
765C2—241no—
766C2—721no—
767C2#1059479511yescharacteristic
768C2#1059479511yescharacteristic
769C2#1059502911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radical#10591165C2
hypercenterC2×C42D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595950C2semidirect
2. C3×#5479C2semidirect
3. C3×C4×#208C2semidirect
4. #10591178C2semidirect
5. #10591176C2semidirect
7. #10591121C2semidirect
8. #10590383C2semidirect
9. #10590370C2semidirect
10. #10590362C2semidirect
11. #10590360C2semidirect
12. #10590346C2semidirect
13. #10590304C2semidirect
14. #10590293C2semidirect
15. #10590274C2semidirect
65. #5479D3semidirect
83. C4×#208D3semidirect
685. C32#3183semidirect
762. C3#78534semidirect
763. C3#83139semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×#54792
C3×C4×#2082
#105911782
#105911762
#105911652
#105911212
#105903832
#105903702
#105903622
#105903602
#105903462
#105903042
#105902932
#105902742
#831393
#785343