Finite Group Databasebeta

← #11895798

Subgroups — #11895798

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 767 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5690C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic, complemented
3#10592765C211yesmaximal, characteristic, complemented
4C3×#5067C211yesmaximal, characteristic, complemented
5#10590550C211yesmaximal, characteristic, complemented
6#10590548C211yesmaximal, characteristic, complemented
7#10590547C211yesmaximal, characteristic, complemented
8#10590547C211yesmaximal, characteristic, complemented
9#10590467C211yesmaximal, characteristic, complemented
10#10590465C211yesmaximal, characteristic, complemented
11#10590455C211yesmaximal, characteristic, complemented
12#10590452C211yesmaximal, characteristic, complemented
13#10590347C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590251C211yesmaximal, characteristic, complemented
16#83638—31nomaximal
17#81708—31nomaximal
18C2×#3796—21no—
19C32×#125C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C3×#897—21no—
22C3×#896—21no—
23C3×#896—21no—
24C3×#893C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4—21no—
27C3×#890C2211yescharacteristic
28C3×#888C2211yescharacteristic
29C3×#874C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63916—21no—
33#63911C2211yescharacteristic
34#63911C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63886—21no—
38#63886—21no—
39C2×#3714C2211yescharacteristic
40C2×#3713C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42#63636C2211yescharacteristic
43#63636C2211yescharacteristic
44#63635C2211yescharacteristic
45#63634C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#803C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#554—31no—
62#5718—31no—
63#5690D311yescharacteristic, complemented
64#5577—31no—
65C3×#490—31no—
66#5088—31no—
67#5084—31no—
68#5072—31no—
69#5067—31no—
70#5067D311yescharacteristic, complemented
71#5066—31no—
72#5066—31no—
73#5066—31no—
74#5066—61no—
75#5024—31no—
76#5015—31no—
77#5015—31no—
78#5015—31no—
79#5014—31no—
80#5014—31no—
81C4×#213—31no—
82#4786—31no—
83#4786—31no—
84#4785—31no—
85#4764—31no—
86#4763—31no—
87#4761—31no—
88#4760—31no—
89#4756—31no—
90#4711—31no—
91#4701—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C3×D12—21no—
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
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×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—44no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3D411yescharacteristic
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(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136#3714—22no—
137#3713—22no—
138#3713—22no—
139#3366—91noSylow
140C2×#239—61no—
141C2×#237—61no—
142C3×C4⋊Q8—31no—
143C3×#127—31no—
144C3×#125—21no—
145C3×#125—31no—
146C3×#125C2×D311yescharacteristic
147C3×#125C2×D311yescharacteristic
148C3×C22⋊Q8—61no—
149C3×C22⋊Q8—61no—
150C3×C22⋊Q8—61no—
151C3×C4×Q8—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C2×C3×C4⋊C4—61no—
156#940—31no—
157#940—31no—
158#939—61no—
159#939—61no—
160#938—61no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—31no—
168C2×D24—31no—
169#897—21no—
170#896—21no—
171#896—21no—
172#895—61no—
173#895—61no—
174#895—61no—
175#893C2×D311yescharacteristic
176#893C2×D311yescharacteristic
177D3×C4⋊C4—21no—
178#890C2×D311yescharacteristic
179#888C2×D311yescharacteristic
180#874—31no—
181#874—31no—
182#874C2×D311yescharacteristic
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—61no—
188C4×D12C2×D311yescharacteristic
189C4×Dic6C2×D311yescharacteristic
190C3×#102—31no—
191C3×#102—31no—
192C3×#102—31no—
193C3×#102—31no—
194C3×#97—31no—
195#832—31no—
196#832—31no—
197#832—31no—
198#821—31no—
199#821—31no—
200#817—31no—
201#815—31no—
202Dic3⋊C8—31no—
203Dic3⋊C8—31no—
204C8×Dic3—31no—
205#809—31no—
206#809—31no—
207#809—31no—
208#809—31no—
209#809—31no—
210#809—31no—
211#809—31no—
212#809—61no—
213#809—61no—
214#809C2×D311yescharacteristic
215#809C2×D311yescharacteristic
216#809C2×D311yescharacteristic
217#809C2×D311yescharacteristic
218#808—31no—
219#808—31no—
220#808—31no—
221#808—61no—
222#807—31no—
223#807—31no—
224#807—61no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—61no—
230#803—31no—
231#803C2×D311yescharacteristic
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
242C2×C3⋊Dic3—21no—
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—21no—
245C4×C3⋊D3—42no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12—21no—
253C3×D12—21no—
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—42no—
257C3×D12—81no—
258C3×D12#4112yescomplemented
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—
268D3×Dic3—42no—
269D3×Dic3—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—31no—
277#490—91no—
278#486—91no—
279#478—91no—
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—
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C22×C3×C4—61no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C2×#67—61no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305#239—124no—
306#237—124no—
307C2×D12—21no—
308C2×D12—21no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—61no—
312C2×D12—61no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12C22×D311yescharacteristic
317C2×D12C22×D311yescharacteristic
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—121no—
327C2×Dic6—21no—
328C2×Dic6#6711yescharacteristic
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42—31no—
355C3×C42—31no—
356C3×C42C22×D311yescharacteristic
357C3×C42C22×D311yescharacteristic
358#217—61no—
359#217—61no—
360#213—62no—
361#213—62no—
362#213—62no—
363#213—62no—
364#213—62no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
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—21no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3#6711yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4#6711yescharacteristic
382Dic3⋊C4#6711yescharacteristic
383C4×Dic3C22×D311yescharacteristic
384C4×Dic3C22×D311yescharacteristic
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8—61no—
391C2×C3⋊C8C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393D24—62no—
394C22×C32C22×D411yescharacteristic
395C2×C3⋊D3—41no—
396C2×C3⋊D3—41no—
397C2×C3⋊D3—41no—
398C2×C3×D3—22no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
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—41no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
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—31no—
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—91no—
440C4×D4—91no—
441C4×D4—91no—
442C2×C4⋊C4—61no—
443#107—91no—
444#106—91no—
445#106—91no—
446C4⋊C8—91no—
447C4⋊C8—91no—
448C4⋊C8—91no—
449#102—31no—
450#102—31no—
451#102—31no—
452#102—31no—
453#102—91no—
454#102—91no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#97—31no—
460#97—91no—
461C4×C8—91no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—121no—
471C3×Q8—62no—
472C3×Q8—241no—
473C3×D4—32no—
474C3×D4—61no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—61no—
478C3×D4—61no—
479C3×D4—122no—
480C3×D4—241no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—122no—
496C2×C3×C4—241no—
497C2×C3×C4—241no—
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4C2×#6711yescharacteristic
501C2×C3×C4C2×#6711yescharacteristic
502C2×C3×C4C23×D311yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504#67—122no—
505#67—122no—
506#67—241no—
507#67—241no—
508C2×Dic3—21no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—121no—
512C2×Dic3—122no—
513C2×Dic3—122no—
514C2×Dic3C2×#6711yescharacteristic
515C2×Dic3C2×#6711yescharacteristic
516C2×Dic3C2×#6711yescharacteristic
517C2×Dic3C2×#6711yescharacteristic
518D12—21no—
519D12—21no—
520D12—21no—
521D12—21no—
522D12—21no—
523D12—42no—
524D12—62no—
525D12—61no—
526D12—61no—
527D12—61no—
528D12—61no—
529D12—81no—
530D12—121no—
531D12—122no—
532D12—122no—
533D12—241no—
534D12—241no—
535D12#23912yescomplemented
536C4×D3—42no—
537C4×D3—81no—
538C4×D3—81no—
539C4×D3—122no—
540C4×D3—122no—
541C4×D3—122no—
542C4×D3—122no—
543C4×D3—242no—
544Dic6—22no—
545Dic6—81no—
546C3×C8—61no—
547C3×C8—61no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—121no—
555C3⋊C8—121no—
556C2×C32#54811yescharacteristic
557C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
558C2×C32#57611yescharacteristic
559C3⋊D3—81no—
560C3×D3—42no—
561C3×D3—81no—
562C3×D3—81no—
563#41—364no—
564C2×Q8—31no—
565C2×Q8—61no—
566C2×D4—31no—
567C2×D4—31no—
568C2×D4—31no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—91no—
572C2×D4—181no—
573C2×D4—181no—
574C2×D4—181no—
575C2×D4—181no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582D8—182no—
583D8—182no—
584D8—182no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8—91no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4C2×D3211yescharacteristic
600C4⋊C4C2×D3211yescharacteristic
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—181no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C42—31no—
608C42—31no—
609C42C2×D3211yescharacteristic
610C22×C3—21no—
611C22×C3—62no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3—121no—
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—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—122no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—241no—
639C2×D3—241no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—32no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4C2×#23911yescharacteristic
660C3×C4#100711yescharacteristic
661C3×C4D3×#4111yescharacteristic
662C3×C4#101011yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—121no—
668Dic3—121no—
669Dic3—241no—
670Dic3#94912yes—
671C32#336611yescharacteristic, complemented, Sylow
672C23—61no—
673C23—61no—
674C23—61no—
675C23—181no—
676Q8—62no—
677Q8—241no—
678D4—32no—
679D4—61no—
680D4—61no—
681D4—61no—
682D4—61no—
683D4—61no—
684D4—122no—
685D4—181no—
686D4—181no—
687D4—241no—
688D4—362no—
689D4—362no—
690D4—721no—
691D4—721no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—61no—
699C2×C4—122no—
700C2×C4—181no—
701C2×C4—241no—
702C2×C4—241no—
703C2×C4—362no—
704C2×C4—362no—
705C2×C4—362no—
706C2×C4D3×#6711yescharacteristic
707C2×C4D3×#6711yescharacteristic
708C2×C4C22×D3211yescharacteristic
709C8—61no—
710C8—61no—
711C8—181no—
712C8—181no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—122no—
717C2×C3—241no—
718C2×C3—241no—
719C2×C3#567711yescharacteristic
720C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
721C2×C3#577411yescharacteristic
722C2×C3#581711yescharacteristic
723C2×C3C2×#94911yescharacteristic
724C2×C3#583511yescharacteristic
725D3—42no—
726D3—81no—
727D3—81no—
728D3—242no—
729D3—241no—
730D3—241no—
731C22—62no—
732C22—121no—
733C22—121no—
734C22—121no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—361no—
741C22—361no—
742C22—361no—
743C22C2×D3×#6711yescharacteristic
744C4—21no—
745C4—21no—
746C4—32no—
747C4—41no—
748C4—41no—
749C4—61no—
750C4—61no—
751C4—61no—
752C4—121no—
753C4—361no—
754C4#6431511yescharacteristic
755C4D3×#23911yescharacteristic
756C3—21no—
757C3#8170811yescharacteristic, complemented
758C3#8363811yescharacteristic, complemented
759C2—122no—
760C2—241no—
761C2—241no—
762C2—721no—
763C2#1059540111yescharacteristic
764C2D3×#94911yescharacteristic
765C2#1059545411yescharacteristic
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. #10593900C2semidirect
3. #10592765C2semidirect
4. C3×#5067C2semidirect
5. #10590550C2semidirect
6. #10590548C2semidirect
7. #10590547C2semidirect
8. #10590547C2semidirect
9. #10590467C2semidirect
10. #10590465C2semidirect
11. #10590455C2semidirect
12. #10590452C2semidirect
13. #10590347C2semidirect
14. #10590346C2semidirect
15. #10590251C2semidirect
63. #5690D3semidirect
70. #5067D3semidirect
258. C3×D12#41semidirect
535. D12#239semidirect
671. C32#3366semidirect
757. C3#81708semidirect
758. C3#83638semidirect

Maximal subgroups

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

subgroupindex
C3×#56902
#105939002
#105927652
C3×#50672
#105905502
#105905482
#105905472
#105904672
#105904652
#105904552
#105904522
#105903472
#105903462
#105902512
#836383
#817083