Finite Group Databasebeta

← #11895753

Subgroups — #11895753

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5539C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic, complemented
3#10592714C211yesmaximal, characteristic, complemented
4C3×#5014C211yesmaximal, characteristic, complemented
5#10591481C211yesmaximal, characteristic, complemented
6#10591481C211yesmaximal, characteristic, complemented
7#10591404C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590550C211yesmaximal, characteristic, complemented
10#10590548C211yesmaximal, characteristic, complemented
11#10590470C211yesmaximal, characteristic, complemented
12#10590466C211yesmaximal, characteristic, complemented
13#10590282C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590251C211yesmaximal, characteristic, complemented
16#83638—31nomaximal
17#79851—31nomaximal
18C2×#3799—21no—
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64083C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#924—21no—
27C2×C3×Dic3⋊C4—21no—
28C3×#890C2211yescharacteristic
29C3×#888C2211yescharacteristic
30C3×#878—21no—
31C3×#878—21no—
32C3×C4×D12C2211yescharacteristic
33C3×#870C2211yescharacteristic
34C3×C4×Dic6C2211yescharacteristic
35#63911C2211yescharacteristic
36#63911C2211yescharacteristic
37#63910—21no—
38#63910—21no—
39#63909—21no—
40#63894C2211yescharacteristic
41#63894C2211yescharacteristic
42#63636C2211yescharacteristic
43#63636C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#808C2211yescharacteristic
48C3×#803C2211yescharacteristic
49#63576C2211yescharacteristic
50#63574C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#554—31no—
62#5577—31no—
63#5553—31no—
64#5539D311yescharacteristic, complemented
65C3×#442—31no—
66#5150—31no—
67#5150—31no—
68#5088—31no—
69#5084—31no—
70#5067—31no—
71#5067—31no—
72#5066—31no—
73#5066—31no—
74#5024—31no—
75#5015—31no—
76#5015—31no—
77#5015—31no—
78#5015—31no—
79#5015—61no—
80#5014—31no—
81#5014D311yescharacteristic, complemented
82C4×#213—31no—
83#5009—31no—
84#4871—31no—
85#4870—31no—
86#4785—31no—
87#4764—31no—
88#4760—31no—
89#4756—31no—
90#4713—31no—
91#4701—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C2×C3×D12C2311yescharacteristic
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⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114#3753—22no—
115#3753—22no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
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#3722—21no—
138#3722—21no—
139#3366—91noSylow
140C2×#239—61no—
141C2×#235—61no—
142C2×C3×D8—31no—
143C3×C4⋊Q8—31no—
144C3×#125—31no—
145C3×#125—31no—
146C3×C22⋊Q8—61no—
147C3×C22⋊Q8—61no—
148C3×C22⋊Q8—61no—
149C3×C4×Q8—31no—
150C3×C4×D4—21no—
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C3×C4×D4C2×D311yescharacteristic
155C3×C4×D4C2×D311yescharacteristic
156C2×C3×C4⋊C4—61no—
157#940—31no—
158#940—31no—
159D4×Dic3C2×D311yescharacteristic
160D4×Dic3C2×D311yescharacteristic
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—61no—
166C2×#213—61no—
167C2×#213C2×D311yescharacteristic
168#930—61no—
169#924—21no—
170C2×Dic3⋊C4—21no—
171#895—61no—
172#895—61no—
173#895—61no—
174#893—31no—
175#893—31no—
176#890C2×D311yescharacteristic
177#888C2×D311yescharacteristic
178#884—61no—
179#884—61no—
180#878—21no—
181#878—21no—
182#874—31no—
183#874—31no—
184#874—31no—
185#874—31no—
186#874—61no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12C2×D311yescharacteristic
190#870C2×D311yescharacteristic
191C4×Dic6C2×D311yescharacteristic
192C3×#106—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#97—31no—
196#832—31no—
197#832—31no—
198#832C2×D311yescharacteristic
199#821—31no—
200#821—31no—
201#821—31no—
202#821—31no—
203#815—31no—
204Dic3⋊C8—31no—
205Dic3⋊C8—31no—
206C8×Dic3—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—31no—
216#809—31no—
217#809—61no—
218#809—61no—
219#809C2×D311yescharacteristic
220#808—31no—
221#808—31no—
222#808C2×D311yescharacteristic
223#807—31no—
224#807—31no—
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—
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
244C4⋊(C3⋊D3)—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—42no—
249C4⋊(C3⋊D3)—81no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—42no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×C4×D3—42no—
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—91no—
280#478—91no—
281#476—91no—
282#459—91no—
283#459—91no—
284#459—91no—
285#446—91no—
286#442—31no—
287#442—91no—
288C4×D8—91no—
289C2×C3×Q8—31no—
290C2×C3×Q8—61no—
291C2×C3×D4—21no—
292C2×C3×D4—31no—
293C2×C3×D4C22×D311yescharacteristic
294C2×C3×D4C22×D311yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—41no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307#239—124no—
308#235—124no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—121no—
324C2×D12—121no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×Dic6—21no—
332C2×Dic6#6711yescharacteristic
333C3×D8—62no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—41no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—21no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42C22×D311yescharacteristic
360C3×C42C22×D311yescharacteristic
361#217—21no—
362#217—21no—
363#213—22no—
364#213—62no—
365#213—62no—
366#213—62no—
367#213—62no—
368#213—122no—
369#213—122no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—21no—
376C4⋊Dic3#6711yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4#6711yescharacteristic
385Dic3⋊C4#6711yescharacteristic
386C4×Dic3C22×D311yescharacteristic
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396C22×C32—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32C22×D411yescharacteristic
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—
408C2×C3×D3—41no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C42−1+411yescharacteristic
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3AGL(1,ℤ/8)12yes—
421C2×#41—181no—
422C2×D8—31no—
423C2×D8—91no—
424C2×D8—91no—
425C4⋊Q8—31no—
426#127—91no—
427#127—91no—
428#127—91no—
429#125—31no—
430#125—31no—
431C22⋊Q8—61no—
432C22⋊Q8—61no—
433C22⋊Q8—61no—
434#121—181no—
435#121—181no—
436#121—181no—
437C4×Q8—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4D3211yescharacteristic
444C2×C4⋊C4—61no—
445#107—91no—
446#106—31no—
447#106—91no—
448C4⋊C8—91no—
449C4⋊C8—91no—
450C4⋊C8—91no—
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#102—91no—
460#102—91no—
461#97—31no—
462#97—91no—
463C4×C8—91no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—41no—
467C23×C3—61no—
468C22×D3—21no—
469C22×D3—61no—
470C22×D3—61no—
471C22×D3—61no—
472C22×D3—61no—
473C22×D3—121no—
474C22×D3—121no—
475C3×Q8—62no—
476C3×Q8—241no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—22no—
480C3×D4—41no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4#23512yescomplemented
484C3×D4#23912yescomplemented
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—41no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—81no—
499C2×C3×C4—81no—
500C2×C3×C4—82no—
501C2×C3×C4—122no—
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—21no—
517C2×Dic3—42no—
518C2×Dic3—81no—
519C2×Dic3C2×#6711yescharacteristic
520C2×Dic3C2×#6711yescharacteristic
521C2×Dic3C2×#6711yescharacteristic
522C2×Dic3C2×#6711yescharacteristic
523D12—21no—
524D12—21no—
525D12—61no—
526D12—61no—
527D12—61no—
528D12—61no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—121no—
534D12—121no—
535D12—121no—
536D12—121no—
537D12—122no—
538D12—122no—
539D12—122no—
540D12—122no—
541D12—242no—
542D12—241no—
543D12—241no—
544D12—242no—
545D12—241no—
546D12—241no—
547C4×D3—42no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552Dic6—22no—
553Dic6—81no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C3⋊C8—121no—
564C2×C32—42no—
565C2×C32#54811yescharacteristic
566C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
567C2×C32#57611yescharacteristic
568C3⋊D3—81no—
569C3⋊D3—81no—
570C3×D3—81no—
571#41—364no—
572C2×Q8—31no—
573C2×Q8—61no—
574C2×D4—31no—
575C2×D4—91no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4—181no—
580C2×D4—181no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4C2×D3211yescharacteristic
584C22×C4—21no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—181no—
589C22×C4—181no—
590D8—62no—
591D8—182no—
592D8—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—91no—
596C2×C8—91no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4C2×D3211yescharacteristic
609C22⋊C4—21no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—31no—
617C42C2×D3211yescharacteristic
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3C2×D3×D411yescharacteristic
632C22×C3C22×#6711yescharacteristic
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—241no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3—241no—
654C3×C4—22no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—32no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4C2×#23511yescharacteristic
673C3×C4C2×#23911yescharacteristic
674C3×C4#100711yescharacteristic
675C3×C4#101011yescharacteristic
676Dic3—21no—
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3#94912yes—
683C32#336611yescharacteristic, complemented, Sylow
684C23—21no—
685C23—61no—
686C23—181no—
687C23—181no—
688Q8—62no—
689Q8—241no—
690D4—21no—
691D4—61no—
692D4—61no—
693D4—181no—
694D4—181no—
695D4—181no—
696D4—181no—
697D4—362no—
698D4—362no—
699D4—362no—
700D4—721no—
701D4—721no—
702D4—721no—
703D4#379912yescomplemented
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—81no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—241no—
716C2×C4—362no—
717C2×C4—362no—
718C2×C4D3×#6711yescharacteristic
719C2×C4D3×#6711yescharacteristic
720C2×C4C22×D3211yescharacteristic
721C8—61no—
722C8—61no—
723C8—181no—
724C8—181no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—42no—
729C2×C3—42no—
730C2×C3—82no—
731C2×C3—241no—
732C2×C3#555211yescharacteristic
733C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
734C2×C3#577411yescharacteristic
735C2×C3#581711yescharacteristic
736C2×C3C2×#94911yescharacteristic
737C2×C3#583511yescharacteristic
738D3—81no—
739D3—241no—
740D3—241no—
741D3—241no—
742D3—241no—
743D3—481no—
744D3—481no—
745C22—22no—
746C22—41no—
747C22—41no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—361no—
752C22—361no—
753C22—361no—
754C22—361no—
755C22—361no—
756C22—361no—
757C22C2×D3×#6711yescharacteristic
758C4—21no—
759C4—21no—
760C4—32no—
761C4—41no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4#6429711yescharacteristic
769C4C2×#379911yescharacteristic
770C3—21no—
771C3#7985111yescharacteristic, complemented
772C3#8363811yescharacteristic, complemented
773C2—42no—
774C2—241no—
775C2—721no—
776C2—721no—
777C2#1059490211yescharacteristic
778C2#1059509711yescharacteristic
779C2D3×#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. #10593902C2semidirect
3. #10592714C2semidirect
4. C3×#5014C2semidirect
5. #10591481C2semidirect
6. #10591481C2semidirect
7. #10591404C2semidirect
8. #10591400C2semidirect
9. #10590550C2semidirect
10. #10590548C2semidirect
11. #10590470C2semidirect
12. #10590466C2semidirect
13. #10590282C2semidirect
14. #10590270C2semidirect
15. #10590251C2semidirect
64. #5539D3semidirect
81. #5014D3semidirect
238. C32×D4#41semidirect
483. C3×D4#235semidirect
484. C3×D4#239semidirect
683. C32#3366semidirect
703. D4#3799semidirect
771. C3#79851semidirect
772. C3#83638semidirect

Maximal subgroups

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

subgroupindex
C3×#55392
#105939022
#105927142
C3×#50142
#105914812
#105914042
#105914002
#105905502
#105905482
#105904702
#105904662
#105902822
#105902702
#105902512
#836383
#798513