Finite Group Databasebeta

← #11871277

Subgroups — #11871277

Order 1152.

1042 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D4×Dic3C211yesmaximal, characteristic, complemented
2#10594369C211yesmaximal, characteristic, complemented
3#10592484C211yesmaximal, characteristic, complemented
4C3×#4773C211yesmaximal, characteristic, complemented
5C3×#4761C211yesmaximal, characteristic, complemented
6#10591481C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic, complemented
8#10591436C211yesmaximal, characteristic, complemented
9#10590781C211yesmaximal, characteristic, complemented
10#10590753C211yesmaximal, characteristic, complemented
11#10590677C211yesmaximal, characteristic, complemented
12#10590661C211yesmaximal, characteristic, complemented
13#10590465C211yesmaximal, characteristic, complemented
14#10590462C211yesmaximal, characteristic, complemented
15#10590441C211yesmaximal, characteristic, complemented
16#81046—31nomaximal
17#79990—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×D3×Dic3—21no—
20C2×#3796—21no—
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23#64102C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×#888C2211yescharacteristic, complemented
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31D3×#217—21no—
32#63911C2211yescharacteristic, complemented
33#63909C2211yescharacteristic
34#63907—21no—
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic, complemented
37Dic3×D12C2211yescharacteristic
38D3×C4⋊Dic3C2211yescharacteristic
39#63886—21no—
40#63881—21no—
41C4×D3×Dic3C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63648C2211yescharacteristic, complemented
45#63642C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61C2×D4×Dic3—31no—
62#5725—31no—
63#5596—31no—
64C4×D3×D4—31no—
65C3×#476—31no—
66C3×#447—31no—
67#5217—31no—
68#5152—31no—
69#5152—31no—
70#5150—31no—
71#5150—31no—
72#5084—31no—
73#5034—31no—
74#5015—31no—
75#4869—31no—
76#4869—31no—
77#4863—31no—
78#4863—31no—
79#4843—31no—
80#4835—31no—
81#4785—31no—
82#4785—31no—
83#4785—31no—
84#4785—31no—
85#4785—61no—
86#4773—31no—
87#4773D311yescharacteristic, complemented
88#4761—31no—
89#4761D311yescharacteristic, complemented
90#4735—31no—
91#4719—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—44no—
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116#3796—44no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3757—21no—
120#3753—22no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D24—22no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32D411yescharacteristic
141Dic32D411yescharacteristic
142#3714—22no—
143#3109—91noSylow
144C22×C3×D4—31no—
145C23×Dic3—61no—
146C2×#239—61no—
147C2×#237—61no—
148C2×D3×D4C2×D311yescharacteristic
149C22×C4×D3—61no—
150C2×C3×D8—31no—
151C2×C3×D8—31no—
152C3×C4⋊Q8—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155C2×#217—61no—
156#947—61no—
157#940—31no—
158#939—61no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167D4×Dic3C2×D311yescharacteristic
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172C2×#213C2×D311yescharacteristic
173#930—31no—
174C4×#67—61no—
175C2×C4⋊Dic3—31no—
176C2×C4×Dic3—31no—
177C2×D24—31no—
178C2×D24C2×D311yescharacteristic
179#895—31no—
180#895—61no—
181#895C2×D311yescharacteristic
182#893—31no—
183#893—31no—
184#893—31no—
185#893—31no—
186#893—61no—
187#893—61no—
188D3×C4⋊C4—31no—
189#888C2×D311yescharacteristic, complemented
190#885—61no—
191#67⋊C4—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194#874—31no—
195C4×D12—31no—
196C42×D3—31no—
197C3×#106—31no—
198C3×#106—31no—
199C3×C4⋊C8—31no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102C2×D311yescharacteristic
204C3×#102C2×D311yescharacteristic
205C3×C22⋊C8—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832C2×D311yescharacteristic
210#830—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#817—31no—
219#817C2×D311yescharacteristic, complemented
220#815—31no—
221#815—31no—
222#815—31no—
223#815—31no—
224#815—61no—
225Dic3⋊C8—31no—
226Dic3⋊C8C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#809—31no—
230#809C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#808C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237C23×C32—21no—
238C22×C3⋊D3—21no—
239C22×C3×D3—24no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yescomplemented
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4×C3⋊D3—42no—
256C3×#67—24no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—42no—
267C3×D12#4112yescomplemented
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—42no—
271#626—42no—
272#626—42no—
273#626—42no—
274D3×Dic3—22no—
275D3×Dic3—22no—
276D3×Dic3—42no—
277D3×Dic3—42no—
278D3×Dic3—42no—
279D3×Dic3—42no—
280C32×C8—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—91no—
285C2×C4×D4—91no—
286#481—91no—
287#481—91no—
288#476—31no—
289#476—91no—
290#459—91no—
291#459—91no—
292#447—31no—
293#447—91no—
294#442—91no—
295#442—91no—
296#442—91no—
297#442—91no—
298#432—91no—
299C24×C3—61no—
300C23×D3—21no—
301C2×C3×Q8—61no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—62no—
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C22×Dic3—21no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—121no—
327C22×Dic3—124no—
328#239—124no—
329#237—124no—
330D3×D4—22no—
331D3×D4—22no—
332C2×D12—21no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12C22×D311yescharacteristic
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—121no—
350C2×C4×D3—124no—
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—21no—
353C3×D8—62no—
354C3×D8—62no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—31no—
369#217—21no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—121no—
376#213—22no—
377#213—62no—
378#213—64no—
379#213—62no—
380#213—62no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—121no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—61no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—22no—
412D24—62no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—48no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3AGL(1,ℤ/8)12yes—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4C2×#4111yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3AGL(1,ℤ/8)12yes—
441C2×#41—181no—
442C22×D4—31no—
443C23×C4—181no—
444C2×D8—31no—
445C2×D8—31no—
446C2×D8—91no—
447C2×D8—91no—
448C4⋊Q8—31no—
449#127—91no—
450#124—181no—
451#121—31no—
452#121—91no—
453#121—181no—
454C4×D4—31no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462C4×D4—181no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465C2×C42—91no—
466#106—31no—
467#106—31no—
468#106—91no—
469#106—91no—
470C4⋊C8—31no—
471C4⋊C8—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102D3211yescharacteristic
480C22⋊C8—31no—
481C22⋊C8—91no—
482#97—91no—
483#97—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—64no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—122no—
492C23×C3—122no—
493C22×D3—24no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—121no—
501C22×D3D3×D411yescharacteristic
502C3×Q8—122no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—22no—
506C3×D4—32no—
507C3×D4—41no—
508C3×D4—64no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—122no—
513C3×D4#23712yescomplemented
514C3×D4#23912yescomplemented
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—24no—
530#67—122no—
531#67—122no—
532#67—122no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—42no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—121no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3—122no—
550C2×Dic3—122no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C2×Dic3—242no—
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557D12—21no—
558D12—21no—
559D12—21no—
560D12—42no—
561D12—62no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—121no—
567D12—122no—
568D12—122no—
569D12—122no—
570D12#23712yescomplemented
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—62no—
574C4×D3—62no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—122no—
581C4×D3—242no—
582Dic6—42no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—41no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—62no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C2×C32—42no—
594C2×C32#52511yescharacteristic
595C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
596C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
597C3⋊D3—81no—
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—81no—
601C24—61no—
602#41—364no—
603C2×Q8—61no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—62no—
609C2×D4—62no—
610C2×D4—91no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4C2×D3211yescharacteristic
615C22×C4—31no—
616C22×C4—61no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4—364no—
626D8—62no—
627D8—62no—
628D8—182no—
629D8—182no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8C2×D3211yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4C2×D3211yescharacteristic
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—91no—
650C42—91no—
651C42—91no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—42no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—62no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—128no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3C2×D3×D411yescharacteristic
673C22×C3C2×D3×D411yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—22no—
677C2×D3—48no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—122no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3#91112yes—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—32no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4C2×#23711yescharacteristic
704C3×C4C2×#23711yescharacteristic
705C3×C4C2×#23911yescharacteristic
706C3×C4D3×#4111yescharacteristic
707Dic3—21no—
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719Dic3—241no—
720Dic3#91412yes—
721C32#310911yescharacteristic, complemented, Sylow
722C23—21no—
723C23—31no—
724C23—64no—
725C23—61no—
726C23—61no—
727C23—122no—
728C23—122no—
729C23—181no—
730Q8—122no—
731D4—21no—
732D4—32no—
733D4—64no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—122no—
738D4—181no—
739D4—181no—
740D4—362no—
741D4—362no—
742D4—362no—
743D4#379612yescomplemented
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—122no—
755C2×C4—182no—
756C2×C4—182no—
757C2×C4—181no—
758C2×C4—362no—
759C2×C4—362no—
760C2×C4—362no—
761C2×C4—362no—
762C2×C4—362no—
763C2×C4—362no—
764C2×C4C22×D3211yescharacteristic
765C8—21no—
766C8—61no—
767C8—61no—
768C8—181no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—42no—
773C2×C3—42no—
774C2×C3—62no—
775C2×C3—82no—
776C2×C3—122no—
777C2×C3—241no—
778C2×C3#558611yescharacteristic
779C2×C3#562711yescharacteristic
780C2×C3C2×#91111yescharacteristic
781C2×C3C2×#91411yescharacteristic
782C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
783C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
784D3—22no—
785D3—42no—
786D3—81no—
787D3—242no—
788D3—241no—
789D3—241no—
790C22—22no—
791C22—32no—
792C22—41no—
793C22—41no—
794C22—61no—
795C22—61no—
796C22—62no—
797C22—128no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—361no—
804C22—361no—
805C22—361no—
806C22D32×D411yescharacteristic
807C4—32no—
808C4—41no—
809C4—61no—
810C4—61no—
811C4—121no—
812C4—121no—
813C4—181no—
814C4—181no—
815C4—361no—
816C4C2×#379611yescharacteristic
817C4D3×#23711yescharacteristic
818C3—21no—
819C3#7999011yescharacteristic, complemented
820C3#8104611yescharacteristic, complemented
821C2—42no—
822C2—62no—
823C2—122no—
824C2—241no—
825C2—721no—
826C2#1059405511yescharacteristic
827C2D3×#91111yescharacteristic
828C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3109
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D3×D4×Dic3C2semidirect
2. #10594369C2semidirect
3. #10592484C2semidirect
4. C3×#4773C2semidirect
5. C3×#4761C2semidirect
6. #10591481C2semidirect
7. #10591448C2semidirect
8. #10591436C2semidirect
9. #10590781C2semidirect
10. #10590753C2semidirect
11. #10590677C2semidirect
12. #10590661C2semidirect
13. #10590465C2semidirect
14. #10590462C2semidirect
15. #10590441C2semidirect
23. #64102C22semidirect
28. C3×#888C22semidirect
32. #63911C22semidirect
36. #63898C22semidirect
44. #63648C22semidirect
45. #63642C22semidirect
46. #63635C22semidirect
49. C3×#817C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#808C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
60. #63555C22semidirect
87. #4773D3semidirect
89. #4761D3semidirect
189. #888C2×D3semidirect
219. #817C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
235. #808C2×D3semidirect
246. C32×D4#41semidirect
267. C3×D12#41semidirect
513. C3×D4#237semidirect
514. C3×D4#239semidirect
570. D12#237semidirect
721. C32#3109semidirect
743. D4#3796semidirect
819. C3#79990semidirect
820. C3#81046semidirect

Maximal subgroups

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

subgroupindex
D3×D4×Dic32
#105943692
#105924842
C3×#47732
C3×#47612
#105914812
#105914482
#105914362
#105907812
#105907532
#105906772
#105906612
#105904652
#105904622
#105904412
#810463
#799903