Finite Group Databasebeta

← #11895745

Subgroups — #11895745

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic, complemented
2#10593938C211yesmaximal, characteristic, complemented
3#10592713C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic, complemented
6#10591477C211yesmaximal, characteristic, complemented
7#10591429C211yesmaximal, characteristic, complemented
8#10591429C211yesmaximal, characteristic, complemented
9#10590589C211yesmaximal, characteristic, complemented
10#10590558C211yesmaximal, characteristic, complemented
11#10590542C211yesmaximal, characteristic, complemented
12#10590456C211yesmaximal, characteristic, complemented
13#10590355C211yesmaximal, characteristic, complemented
14#10590279C211yesmaximal, characteristic, complemented
15#10590252C211yesmaximal, characteristic, complemented
16#83581—31nomaximal
17#81152—31nomaximal
18C2×C3×#235—21no—
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C3×#940C2211yescharacteristic
24C3×#930—21no—
25C3×#893C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#884—21no—
28C3×#884—21no—
29C3×#874C2211yescharacteristic
30C3×#870C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63918C2211yescharacteristic
33#63895—21no—
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic
36#63888—21no—
37#63883—21no—
38#63869C2211yescharacteristic
39#63865—21no—
40C2×#3714C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42#63659C2211yescharacteristic
43#63636C2211yescharacteristic
44#63635C2211yescharacteristic
45#63630C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#808C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#550—31no—
62#5690—31no—
63#5579—31no—
64#5553D311yescharacteristic, complemented
65C3×#478—31no—
66#5072—31no—
67#5072—31no—
68#5072—31no—
69#5071—31no—
70#5071—31no—
71#5070—31no—
72#5067—31no—
73#5024—31no—
74#5014—31no—
75#5014—31no—
76#5014—31no—
77#5014—61no—
78C4×#213—31no—
79#5009—31no—
80#5009D311yescharacteristic, complemented
81#5008—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×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C3×#235—44no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×Dic6D411yescharacteristic
108C2×#627—21no—
109C2×#624—21no—
110C2×#624—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114#3753—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3714—22no—
138#3714—22no—
139#3366—91noSylow
140C2×C3×#41—61no—
141C2×#235—21no—
142C3×#127—31no—
143C3×#127—31no—
144C3×#127—31no—
145C3×#125—31no—
146C3×#121—61no—
147C3×#121—61no—
148C3×#121—61no—
149C3×C4×Q8—31no—
150C3×C4×D4—21no—
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153C3×C4×D4C2×D311yescharacteristic
154C3×C4×D4C2×D311yescharacteristic
155#946—61no—
156#940C2×D311yescharacteristic
157#940C2×D311yescharacteristic
158C2×#213—31no—
159C2×#213—31no—
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—61no—
163#930—21no—
164C2×D24—31no—
165C2×D24—31no—
166#897—61no—
167#896—61no—
168#896—61no—
169#896—61no—
170#896—61no—
171#893—31no—
172#893—31no—
173#893C2×D311yescharacteristic
174#893C2×D311yescharacteristic
175D3×C4⋊C4—61no—
176D3×C4⋊C4—61no—
177#890—31no—
178#888—31no—
179#884—21no—
180#884—21no—
181#874C2×D311yescharacteristic
182C4×D12—31no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—61no—
187#870—31no—
188#870C2×D311yescharacteristic
189#869—31no—
190C4×Dic6C2×D311yescharacteristic
191C3×#107—31no—
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×#102—31no—
195C3×#102—31no—
196#832—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#832C2×D311yescharacteristic
207#821—31no—
208#821—31no—
209#815—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212C8×Dic3—31no—
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—61no—
220#808—31no—
221#808—31no—
222#808—61no—
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—
233C23×C32—21no—
234C22×C3⋊D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C32×D4—21no—
238C32×D4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—42no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)#4112yescomplemented
247C4×C3⋊D3—81no—
248C3×#67—42no—
249C3×#67—42no—
250C3×#67—81no—
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—21no—
262C3×D12—42no—
263C3×D12—81no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×Dic6—22no—
267#627—81no—
268#624—42no—
269#624—81no—
270C3⋊(C3⋊C8)—21no—
271C3⋊(C3⋊C8)—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274#554—91no—
275#550—31no—
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—
289C3×#41—124no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—31no—
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—41no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—21no—
311#235—44no—
312C2×D12—21no—
313C2×D12—21no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12C22×D311yescharacteristic
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—121no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6#6711yescharacteristic
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—21no—
349C3×C42—31no—
350C3×C42—31no—
351C3×C42C22×D311yescharacteristic
352C3×C42C22×D311yescharacteristic
353#213—62no—
354#213—62no—
355#213—62no—
356#213—62no—
357#213—64no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3#6711yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
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—
394D24—62no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32C22×D411yescharacteristic
399C2×C3⋊D3—22no—
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—
407C2×C3×D3—41no—
408C32×C4—21no—
409C32×C4—21no—
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×Dic3—41no—
419C3×Dic3AGL(1,ℤ/8)12yes—
420C2×#41—61no—
421C2×D8—91no—
422C2×D8—91no—
423C2×D8—91no—
424C4⋊Q8—91no—
425#127—31no—
426#127—31no—
427#127—31no—
428#125—31no—
429#125—91no—
430C22⋊Q8—181no—
431C22⋊Q8—181no—
432C22⋊Q8—181no—
433#121—61no—
434#121—61no—
435#121—61no—
436C4×Q8—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—91no—
440C4×D4—91no—
441C4×D4—91no—
442C4×D4D3211yescharacteristic
443C2×C4⋊C4—181no—
444#107—31no—
445#106—31no—
446#106—91no—
447C4⋊C8—31no—
448C4⋊C8—91no—
449C4⋊C8—91no—
450#102—31no—
451#102—31no—
452#102—91no—
453#102—91no—
454#102—91no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#102—91no—
460#97—91no—
461#97—91no—
462C4×C8—91no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—41no—
466C23×C3—61no—
467C23×C3—61no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—61no—
471C22×D3—61no—
472C22×D3—121no—
473C3×Q8—62no—
474C3×D4—22no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—41no—
480C3×D4—61no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—61no—
484C3×D4—122no—
485C3×D4—122no—
486C3×D4—122no—
487C3×D4—241no—
488C3×D4—241no—
489C3×D4—241no—
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—42no—
501C2×C3×C4—42no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—82no—
505C2×C3×C4—122no—
506C2×C3×C4—122no—
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4C2×#6711yescharacteristic
510C2×C3×C4C2×#6711yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—42no—
514#67—42no—
515#67—81no—
516#67—81no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—121no—
522C2×Dic3C2×#6711yescharacteristic
523C2×Dic3C2×#6711yescharacteristic
524C2×Dic3C2×#6711yescharacteristic
525C2×Dic3C2×#6711yescharacteristic
526D12—21no—
527D12—21no—
528D12—21no—
529D12—21no—
530D12—32no—
531D12—32no—
532D12—42no—
533D12—62no—
534D12—61no—
535D12—61no—
536D12—81no—
537D12—121no—
538C4×D3—42no—
539C4×D3—42no—
540C4×D3—122no—
541C4×D3—122no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—242no—
547Dic6—22no—
548Dic6—241no—
549Dic6—241no—
550C3×C8—61no—
551C3×C8—61no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—62no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—121no—
560C2×C32—81no—
561C2×C32#54811yescharacteristic
562C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
563C2×C32#57611yescharacteristic
564C3⋊D3—42no—
565C3×D3—81no—
566C3×D3—81no—
567#41—124no—
568C2×Q8—31no—
569C2×Q8—181no—
570C2×D4—31no—
571C2×D4—31no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—91no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—21no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586D8—182no—
587D8—182no—
588D8—182no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—91no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4C2×D3211yescharacteristic
605C22⋊C4—21no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C42—31no—
612C42—31no—
613C42C2×D3211yescharacteristic
614C22×C3—21no—
615C22×C3—42no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C22×#6711yescharacteristic
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—122no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—241no—
646C2×D3—241no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4#100711yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4#101011yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676Dic3#93212yes—
677C32#336611yescharacteristic, complemented, Sylow
678C23—21no—
679C23—61no—
680C23—61no—
681C23—181no—
682Q8—62no—
683Q8—721no—
684D4—21no—
685D4—21no—
686D4—61no—
687D4—61no—
688D4—61no—
689D4—61no—
690D4—92no—
691D4—122no—
692D4—122no—
693D4—122no—
694D4—181no—
695D4—241no—
696D4—241no—
697D4—241no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—42no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—181no—
709C2×C4—362no—
710C2×C4—721no—
711C2×C4—721no—
712C2×C4D3×#6711yescharacteristic
713C2×C4D3×#6711yescharacteristic
714C2×C4C22×D3211yescharacteristic
715C8—61no—
716C8—61no—
717C8—181no—
718C8—181no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—82no—
723C2×C3—81no—
724C2×C3—81no—
725C2×C3—241no—
726C2×C3—241no—
727C2×C3#563311yescharacteristic
728C2×C3#576911yescharacteristic
729C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
730C2×C3C2×#93211yescharacteristic
731C2×C3#583111yescharacteristic
732C2×C3#583511yescharacteristic
733D3—81no—
734D3—81no—
735D3—122no—
736D3—122no—
737D3—242no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—182no—
748C22—361no—
749C22—361no—
750C22C2×D3×#6711yescharacteristic
751C4—21no—
752C4—21no—
753C4—32no—
754C4—41no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—121no—
759C4—121no—
760C4—361no—
761C4#6429711yescharacteristic
762C4#6430611yescharacteristic
763C3—21no—
764C3#8115211yescharacteristic, complemented
765C3#8358111yescharacteristic, complemented
766C2—81no—
767C2—241no—
768C2—241no—
769C2—362no—
770C2#1059483011yescharacteristic
771C2D3×#93211yescharacteristic
772C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5553C2semidirect
2. #10593938C2semidirect
3. #10592713C2semidirect
4. C3×#5009C2semidirect
5. #10591487C2semidirect
6. #10591477C2semidirect
7. #10591429C2semidirect
8. #10591429C2semidirect
9. #10590589C2semidirect
10. #10590558C2semidirect
11. #10590542C2semidirect
12. #10590456C2semidirect
13. #10590355C2semidirect
14. #10590279C2semidirect
15. #10590252C2semidirect
64. #5553D3semidirect
80. #5009D3semidirect
246. C4⋊(C3⋊D3)#41semidirect
677. C32#3366semidirect
764. C3#81152semidirect
765. C3#83581semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105939382
#105927132
C3×#50092
#105914872
#105914772
#105914292
#105905892
#105905582
#105905422
#105904562
#105903552
#105902792
#105902522
#835813
#811523