Finite Group Databasebeta

← #11895796

Subgroups — #11895796

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 773 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5690C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic, complemented
3#10592766C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5#10590589C211yesmaximal, characteristic, complemented
6#10590550C211yesmaximal, characteristic, complemented
7#10590548C211yesmaximal, characteristic, complemented
8#10590547C211yesmaximal, characteristic, complemented
9#10590547C211yesmaximal, characteristic, complemented
10#10590468C211yesmaximal, characteristic, complemented
11#10590466C211yesmaximal, characteristic, complemented
12#10590456C211yesmaximal, characteristic, complemented
13#10590349C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590252C211yesmaximal, characteristic, complemented
16#83638—31nomaximal
17#81152—31nomaximal
18C2×#3799—21no—
19C32×#125C2211yescharacteristic
20#64083C2211yescharacteristic
21C3×#897—21no—
22C3×#896—21no—
23C3×#896—21no—
24C3×#893C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4—21no—
27C3×#890C2211yescharacteristic
28C3×#888C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63911C2211yescharacteristic
33#63911C2211yescharacteristic
34#63910—21no—
35#63910—21no—
36#63909—21no—
37#63894C2211yescharacteristic
38#63894C2211yescharacteristic
39C2×#3714C2211yescharacteristic
40C2×#3714C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42#63636C2211yescharacteristic
43#63636C2211yescharacteristic
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63630C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×C4⋊(C3⋊C8)C2211yescharacteristic
52#63574C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#554—31no—
62#5690D311yescharacteristic, complemented
63#5577—31no—
64#5553—31no—
65C3×#478—31no—
66#5088—31no—
67#5084—31no—
68#5067—31no—
69#5067—31no—
70#5067—31no—
71#5067—61no—
72#5066—31no—
73#5066D311yescharacteristic, complemented
74#5024—31no—
75#5015—31no—
76#5015—31no—
77#5015—31no—
78#5014—31no—
79#5014—31no—
80#5014—31no—
81C4×#213—31no—
82#4891—31no—
83#4872—31no—
84#4870—31no—
85#4869—31no—
86#4843—31no—
87#4828—31no—
88#4786—31no—
89#4786—31no—
90#4764—31no—
91#4760—31no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6D411yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3799—44no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C42C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3722—21no—
135#3722—21no—
136#3714—22no—
137#3714—22no—
138#3713—22no—
139#3366—91noSylow
140C2×#239—61no—
141C2×#235—61no—
142C3×C4⋊Q8—31no—
143C3×#125—21no—
144C3×#125—31no—
145C3×#125C2×D311yescharacteristic
146C3×#125C2×D311yescharacteristic
147C3×C22⋊Q8—61no—
148C3×C22⋊Q8—61no—
149C3×C22⋊Q8—61no—
150C3×C4×Q8—31no—
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C2×C3×C4⋊C4—61no—
156#940—31no—
157#940—31no—
158C2×#213—31no—
159C2×#213—31no—
160C2×#213—31no—
161C2×#213—31no—
162#930—61no—
163C2×D24—31no—
164C2×D24—31no—
165#897—21no—
166#896—21no—
167#896—21no—
168#895—61no—
169#895—61no—
170#895—61no—
171#893—31no—
172#893—31no—
173#893C2×D311yescharacteristic
174#893C2×D311yescharacteristic
175D3×C4⋊C4—21no—
176#890C2×D311yescharacteristic
177#888C2×D311yescharacteristic
178#884—61no—
179#884—61no—
180#874—31no—
181#874—31no—
182#874—31no—
183#874—31no—
184#874—61no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12C2×D311yescharacteristic
188C4×D12C2×D311yescharacteristic
189C4×Dic6C2×D311yescharacteristic
190C3×#107—31no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×#102—31no—
194C3×#102—31no—
195#832—31no—
196#832—31no—
197#821—31no—
198#821—31no—
199#815—31no—
200Dic3⋊C8—31no—
201Dic3⋊C8—31no—
202C8×Dic3—31no—
203#809—31no—
204#809—31no—
205#809—31no—
206#809—31no—
207#809—31no—
208#809—31no—
209#809—31no—
210#809—31no—
211#809—31no—
212#809—31no—
213#809—31no—
214#809—31no—
215#809—61no—
216#809—61no—
217#809—61no—
218#809—61no—
219#809C2×D311yescharacteristic
220#809C2×D311yescharacteristic
221#808—31no—
222#808—31no—
223#808C2×D311yescharacteristic
224#807C2×D311yescharacteristic
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)C2×D311yescharacteristic
228#803—31no—
229#803—31no—
230#803—31no—
231#803—61no—
232C4×C3⋊C8—31no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)—42no—
247C4⋊(C3⋊D3)—81no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12#4112yescomplemented
258C3×C4×D3—42no—
259C3×C4×D3—42no—
260C3×C4×D3—81no—
261C3×C4×D3—81no—
262C3×Dic6—22no—
263C3×Dic6—81no—
264#626—42no—
265#626—42no—
266#626—81no—
267#626—81no—
268#624—42no—
269#624—42no—
270C3⋊(C3⋊C8)—21no—
271C3⋊(C3⋊C8)—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274#554—31no—
275#550—91no—
276#490—91no—
277#490—91no—
278#486—91no—
279#478—31no—
280#478—91no—
281#476—91no—
282#459—91no—
283#459—91no—
284#459—91no—
285#446—91no—
286#442—91no—
287#442—91no—
288C4×D8—91no—
289C2×C3×Q8—31no—
290C2×C3×Q8—61no—
291C2×C3×D4—31no—
292C2×C3×D4—31no—
293C22×C3×C4—61no—
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C22×C3×C4—61no—
297C2×#67—61no—
298C2×#67—61no—
299C2×#67—61no—
300C2×#67—61no—
301#239—124no—
302#235—124no—
303C2×D12—31no—
304C2×D12—31no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—61no—
308C2×D12—61no—
309C2×D12—61no—
310C2×D12—61no—
311C2×D12—61no—
312C2×D12—61no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—121no—
318C2×D12—121no—
319C2×D12C22×D311yescharacteristic
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6—21no—
330C2×Dic6#6711yescharacteristic
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—41no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42—31no—
359C3×C42—31no—
360C3×C42C22×D311yescharacteristic
361C3×C42C22×D311yescharacteristic
362#213—62no—
363#213—62no—
364#213—62no—
365#213—62no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374C4⋊Dic3—21no—
375C4⋊Dic3#6711yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4#6711yescharacteristic
381Dic3⋊C4#6711yescharacteristic
382C4×Dic3C22×D311yescharacteristic
383C4×Dic3C22×D311yescharacteristic
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392D24—62no—
393D24—62no—
394C22×C32C22×D411yescharacteristic
395C2×C3⋊D3—41no—
396C2×C3⋊D3—41no—
397C2×C3⋊D3—41no—
398C2×C3⋊D3—41no—
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
401C2×C3×D3—22no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4C2×#4111yescharacteristic
412C32×C42−1+411yescharacteristic
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3AGL(1,ℤ/8)12yes—
419C2×#41—181no—
420C2×D8—91no—
421C2×D8—91no—
422C2×D8—91no—
423C4⋊Q8—31no—
424#127—91no—
425#127—91no—
426#127—91no—
427#125—31no—
428#125D3211yescharacteristic
429C22⋊Q8—61no—
430C22⋊Q8—61no—
431C22⋊Q8—61no—
432#121—181no—
433#121—181no—
434#121—181no—
435C4×Q8—31no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—91no—
441C4×D4—91no—
442C2×C4⋊C4—61no—
443#107—31no—
444#106—31no—
445#106—91no—
446C4⋊C8—31no—
447C4⋊C8—91no—
448C4⋊C8—91no—
449#102—31no—
450#102—31no—
451#102—91no—
452#102—91no—
453#102—91no—
454#102—91no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#97—91no—
460#97—91no—
461C4×C8—91no—
462C23×C3—61no—
463C23×C3—61no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—61no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—121no—
471C22×D3—121no—
472C3×Q8—62no—
473C3×Q8—241no—
474C3×D4—32no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—61no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—122no—
494C2×C3×C4—122no—
495C2×C3×C4—241no—
496C2×C3×C4—241no—
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4C2×#6711yescharacteristic
500C2×C3×C4C2×#6711yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502C2×C3×C4C23×D311yescharacteristic
503#67—122no—
504#67—122no—
505#67—241no—
506#67—241no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3C2×#6711yescharacteristic
510C2×Dic3C2×#6711yescharacteristic
511C2×Dic3C2×#6711yescharacteristic
512C2×Dic3C2×#6711yescharacteristic
513D12—21no—
514D12—21no—
515D12—21no—
516D12—61no—
517D12—61no—
518D12—61no—
519D12—61no—
520D12—61no—
521D12—61no—
522D12—61no—
523D12—61no—
524D12—121no—
525D12—121no—
526D12—121no—
527D12—121no—
528D12—122no—
529D12—122no—
530D12—122no—
531D12—122no—
532D12—242no—
533D12—241no—
534D12—241no—
535D12—242no—
536D12—241no—
537D12—241no—
538D12#23912yescomplemented
539C4×D3—42no—
540C4×D3—42no—
541C4×D3—81no—
542C4×D3—81no—
543C4×D3—122no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3—122no—
547Dic6—22no—
548Dic6—81no—
549C3×C8—61no—
550C3×C8—61no—
551C3⋊C8—21no—
552C3⋊C8—21no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—121no—
558C3⋊C8—121no—
559C2×C32#54811yescharacteristic
560C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
561C2×C32#57611yescharacteristic
562C3⋊D3—81no—
563C3⋊D3—81no—
564C3×D3—42no—
565C3×D3—81no—
566#41—364no—
567C2×Q8—31no—
568C2×Q8—61no—
569C2×D4—31no—
570C2×D4—31no—
571C2×D4—91no—
572C2×D4—91no—
573C2×D4—181no—
574C2×D4—181no—
575C2×D4—181no—
576C2×D4—181no—
577C2×D4—181no—
578C2×D4—181no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585D8—182no—
586D8—182no—
587D8—182no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8—91no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4C2×D3211yescharacteristic
603C4⋊C4C2×D3211yescharacteristic
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—31no—
611C42—31no—
612C42C2×D3211yescharacteristic
613C22×C3—21no—
614C22×C3—62no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C22×#6711yescharacteristic
622C2×D3—22no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—241no—
641C2×D3—241no—
642C2×D3—241no—
643C2×D3—241no—
644C2×D3—241no—
645C2×D3—241no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—32no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—81no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4C2×#23911yescharacteristic
667C3×C4#100711yescharacteristic
668C3×C4#100711yescharacteristic
669C3×C4D3×#4111yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—41no—
674Dic3—41no—
675Dic3#94912yes—
676C32#336611yescharacteristic, complemented, Sylow
677C23—61no—
678C23—61no—
679C23—181no—
680C23—181no—
681Q8—62no—
682Q8—241no—
683D4—32no—
684D4—61no—
685D4—61no—
686D4—61no—
687D4—181no—
688D4—181no—
689D4—181no—
690D4—181no—
691D4—362no—
692D4—362no—
693D4—362no—
694D4—721no—
695D4—721no—
696D4—721no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—241no—
708C2×C4—241no—
709C2×C4—362no—
710C2×C4—362no—
711C2×C4D3×#6711yescharacteristic
712C2×C4D3×#6711yescharacteristic
713C2×C4C22×D3211yescharacteristic
714C8—61no—
715C8—61no—
716C8—181no—
717C8—181no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—122no—
722C2×C3—241no—
723C2×C3#563311yescharacteristic
724C2×C3#576911yescharacteristic
725C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
726C2×C3#581711yescharacteristic
727C2×C3C2×#94911yescharacteristic
728C2×C3#583511yescharacteristic
729D3—42no—
730D3—81no—
731D3—241no—
732D3—241no—
733D3—241no—
734D3—241no—
735D3—481no—
736D3—481no—
737C22—62no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—361no—
744C22—361no—
745C22—361no—
746C22—361no—
747C22—361no—
748C22—361no—
749C22C2×D3×#6711yescharacteristic
750C4—21no—
751C4—21no—
752C4—32no—
753C4—41no—
754C4—41no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—121no—
759C4—121no—
760C4#6431611yescharacteristic
761C4D3×#23911yescharacteristic
762C3—21no—
763C3#8115211yescharacteristic, complemented
764C3#8363811yescharacteristic, complemented
765C2—122no—
766C2—241no—
767C2—721no—
768C2—721no—
769C2#1059540211yescharacteristic
770C2D3×#94911yescharacteristic
771C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
hypercenter#125D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5690C2semidirect
2. #10593902C2semidirect
3. #10592766C2semidirect
4. C3×#5066C2semidirect
5. #10590589C2semidirect
6. #10590550C2semidirect
7. #10590548C2semidirect
8. #10590547C2semidirect
9. #10590547C2semidirect
10. #10590468C2semidirect
11. #10590466C2semidirect
12. #10590456C2semidirect
13. #10590349C2semidirect
14. #10590344C2semidirect
15. #10590252C2semidirect
62. #5690D3semidirect
73. #5066D3semidirect
257. C3×D12#41semidirect
538. D12#239semidirect
676. C32#3366semidirect
763. C3#81152semidirect
764. C3#83638semidirect

Maximal subgroups

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

subgroupindex
C3×#56902
#105939022
#105927662
C3×#50662
#105905892
#105905502
#105905482
#105905472
#105904682
#105904662
#105904562
#105903492
#105903442
#105902522
#836383
#811523