Finite Group Databasebeta

← #11895755

Subgroups — #11895755

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×#5539C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic, complemented
3#10592713C211yesmaximal, characteristic, complemented
4C3×#5015C211yesmaximal, characteristic, complemented
5#10591481C211yesmaximal, characteristic, complemented
6#10591481C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10590550C211yesmaximal, characteristic, complemented
10#10590548C211yesmaximal, characteristic, complemented
11#10590469C211yesmaximal, characteristic, complemented
12#10590465C211yesmaximal, characteristic, complemented
13#10590308C211yesmaximal, characteristic, complemented
14#10590279C211yesmaximal, characteristic, complemented
15#10590252C211yesmaximal, characteristic, complemented
16#83638—31nomaximal
17#80321—31nomaximal
18C2×#3796—21no—
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#924—21no—
27C2×C3×Dic3⋊C4—21no—
28C3×#890C2211yescharacteristic
29C3×#888C2211yescharacteristic
30C3×#878—21no—
31C3×#878—21no—
32C3×#874C2211yescharacteristic
33C3×#870C2211yescharacteristic
34C3×C4×Dic6C2211yescharacteristic
35#63916—21no—
36#63911C2211yescharacteristic
37#63911C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63886—21no—
41#63886—21no—
42#63659C2211yescharacteristic
43#63636C2211yescharacteristic
44#63635C2211yescharacteristic
45#63630C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×C4⋊(C3⋊C8)C2211yescharacteristic
49#63575C2211yescharacteristic
50#63573C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#554—31no—
62#5718—31no—
63#5577—31no—
64#5539D311yescharacteristic, complemented
65C3×#459—31no—
66#5152—31no—
67#5150—31no—
68#5150—31no—
69Dic3×D8—31no—
70#5088—31no—
71#5084—31no—
72#5071—31no—
73#5067—31no—
74#5067—31no—
75#5066—31no—
76#5066—31no—
77#5024—31no—
78#5015—31no—
79#5015—31no—
80#5015D311yescharacteristic, complemented
81#5014—31no—
82#5014—31no—
83#5014—31no—
84#5014—61no—
85C4×#213—31no—
86#4847—31no—
87#4828—31no—
88#4766—31no—
89#4764—31no—
90#4761—31no—
91#4760—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
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⋊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×#217—21no—
120C3×#217—21no—
121C3×#213—22no—
122C3×#213—22no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3366—91noSylow
140C2×#239—61no—
141C2×#237—61no—
142C2×C3×D8—31no—
143C2×C3×D8—31no—
144C3×C4⋊Q8—31no—
145C3×#127—31no—
146C3×#125—31no—
147C3×#125—31no—
148C3×C22⋊Q8—61no—
149C3×C22⋊Q8—61no—
150C3×C22⋊Q8—61no—
151C3×C4×Q8—31no—
152C3×C4×D4—21no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×C4×D4C2×D311yescharacteristic
156C3×C4×D4C2×D311yescharacteristic
157C2×C3×C4⋊C4—61no—
158#940—31no—
159#940—31no—
160#939—61no—
161#939—61no—
162#938—61no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3C2×D311yescharacteristic
166D4×Dic3C2×D311yescharacteristic
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—61no—
170C2×#213C2×D311yescharacteristic
171C2×#213C2×D311yescharacteristic
172#924—21no—
173C2×Dic3⋊C4—21no—
174#895—61no—
175#895—61no—
176#895—61no—
177#890C2×D311yescharacteristic
178#888C2×D311yescharacteristic
179#878—21no—
180#878—21no—
181#874—31no—
182#874—31no—
183#874C2×D311yescharacteristic
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189#870C2×D311yescharacteristic
190C4×Dic6C2×D311yescharacteristic
191C3×C4⋊C8—31no—
192C3×#102—31no—
193C3×#102—31no—
194#832—31no—
195#832—31no—
196#832—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—61no—
201#821—31no—
202#821—31no—
203#818—31no—
204#817—31no—
205#815—31no—
206Dic3⋊C8—31no—
207Dic3⋊C8—31no—
208C8×Dic3—31no—
209#809—31no—
210#809—31no—
211#809—31no—
212#809—31no—
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—61no—
218#809C2×D311yescharacteristic
219#809C2×D311yescharacteristic
220#808—31no—
221#808—31no—
222#808—31no—
223#808—61no—
224#807—31no—
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#4112yescomplemented
239C2×C32×C4—21no—
240C2×C32×C4—81no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)—21no—
247C4×C3⋊D3—42no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—42no—
251C2×C3×Dic3—81no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—42no—
261C3×D12—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—91no—
277#490—91no—
278#486—91no—
279#478—91no—
280#478—91no—
281#476—91no—
282#459—31no—
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—21no—
292C2×C3×D4—31no—
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C22×D311yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—41no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311#239—124no—
312#237—124no—
313C2×D12—21no—
314C2×D12—21no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—121no—
329C2×Dic6—21no—
330C2×Dic6#6711yescharacteristic
331C3×D8—62no—
332C3×D8—62no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—41no—
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—21no—
359#217—21no—
360#217—61no—
361#217—61no—
362#213—22no—
363#213—22no—
364#213—64no—
365#213—62no—
366#213—62no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3#6711yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4#6711yescharacteristic
384Dic3⋊C4#6711yescharacteristic
385C4×Dic3C22×D311yescharacteristic
386C4×Dic3C22×D311yescharacteristic
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—61no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395C22×C32—22no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32C22×D411yescharacteristic
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—
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—181no—
421C2×D8—31no—
422C2×D8—31no—
423C2×D8—91no—
424C4⋊Q8—31no—
425#127—31no—
426#127—91no—
427#127—91no—
428#125—31no—
429#125—31no—
430C22⋊Q8—61no—
431C22⋊Q8—61no—
432C22⋊Q8—61no—
433#121—181no—
434#121—181no—
435#121—181no—
436C4×Q8—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—91no—
440C4×D4—91no—
441C4×D4—91no—
442C4×D4D3211yescharacteristic
443C2×C4⋊C4—61no—
444#107—91no—
445#106—91no—
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×Q8—241no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—22no—
478C3×D4—41no—
479C3×D4—61no—
480C3×D4—61no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—122no—
484C3×D4—241no—
485C3×D4#23712yescomplemented
486C3×D4#23912yescomplemented
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—81no—
500C2×C3×C4—81no—
501C2×C3×C4—82no—
502C2×C3×C4—122no—
503C2×C3×C4—241no—
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4C2×#6711yescharacteristic
507C2×C3×C4C2×#6711yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—122no—
511#67—122no—
512#67—241no—
513#67—241no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—42no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—81no—
520C2×Dic3—121no—
521C2×Dic3—122no—
522C2×Dic3—122no—
523C2×Dic3C2×#6711yescharacteristic
524C2×Dic3C2×#6711yescharacteristic
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527D12—21no—
528D12—21no—
529D12—21no—
530D12—21no—
531D12—42no—
532D12—62no—
533D12—61no—
534D12—61no—
535D12—61no—
536D12—61no—
537D12—81no—
538D12—121no—
539D12—122no—
540D12—122no—
541D12—241no—
542D12—241no—
543C4×D3—122no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3—122no—
547C4×D3—242no—
548Dic6—22no—
549Dic6—81no—
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—42no—
561C2×C32#54811yescharacteristic
562C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
563C2×C32#57611yescharacteristic
564C3⋊D3—81no—
565C3×D3—81no—
566C3×D3—81no—
567#41—364no—
568C2×Q8—31no—
569C2×Q8—61no—
570C2×D4—31no—
571C2×D4—31no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—91no—
575C2×D4—181no—
576C2×D4—181no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—21no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586D8—62no—
587D8—62no—
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—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
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—22no—
615C22×C3—22no—
616C22×C3—21no—
617C22×C3—42no—
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—122no—
639C2×D3—121no—
640C2×D3—121no—
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×C4C2×#23711yescharacteristic
665C3×C4C2×#23911yescharacteristic
666C3×C4#100711yescharacteristic
667C3×C4#101011yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676Dic3#94912yes—
677C32#336611yescharacteristic, complemented, Sylow
678C23—21no—
679C23—61no—
680C23—61no—
681C23—181no—
682Q8—62no—
683Q8—241no—
684D4—21no—
685D4—61no—
686D4—61no—
687D4—61no—
688D4—61no—
689D4—122no—
690D4—181no—
691D4—181no—
692D4—241no—
693D4—362no—
694D4—362no—
695D4—721no—
696D4—721no—
697D4#379612yescomplemented
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—81no—
706C2×C4—122no—
707C2×C4—181no—
708C2×C4—241no—
709C2×C4—362no—
710C2×C4—362no—
711C2×C4—362no—
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—42no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3—241no—
726C2×C3—241no—
727C2×C3#559811yescharacteristic
728C2×C3#575711yescharacteristic
729C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
730C2×C3#581711yescharacteristic
731C2×C3C2×#94911yescharacteristic
732C2×C3#583511yescharacteristic
733D3—81no—
734D3—81no—
735D3—242no—
736D3—241no—
737D3—241no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—361no—
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—
761C4C2×#379611yescharacteristic
762C4#6429711yescharacteristic
763C3—21no—
764C3#8032111yescharacteristic, complemented
765C3#8363811yescharacteristic, complemented
766C2—42no—
767C2—241no—
768C2—241no—
769C2—721no—
770C2#1059490011yescharacteristic
771C2#1059509611yescharacteristic
772C2D3×#94911yescharacteristic
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×#5539C2semidirect
2. #10593900C2semidirect
3. #10592713C2semidirect
4. C3×#5015C2semidirect
5. #10591481C2semidirect
6. #10591481C2semidirect
7. #10591430C2semidirect
8. Dic3×#213C2semidirect
9. #10590550C2semidirect
10. #10590548C2semidirect
11. #10590469C2semidirect
12. #10590465C2semidirect
13. #10590308C2semidirect
14. #10590279C2semidirect
15. #10590252C2semidirect
64. #5539D3semidirect
80. #5015D3semidirect
238. C32×D4#41semidirect
485. C3×D4#237semidirect
486. C3×D4#239semidirect
677. C32#3366semidirect
697. D4#3796semidirect
764. C3#80321semidirect
765. C3#83638semidirect

Maximal subgroups

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

subgroupindex
C3×#55392
#105939002
#105927132
C3×#50152
#105914812
#105914302
Dic3×#2132
#105905502
#105905482
#105904692
#105904652
#105903082
#105902792
#105902522
#836383
#803213