Finite Group Databasebeta

← #11895754

Subgroups — #11895754

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596010C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic, complemented
3C3×#5015C211yesmaximal, characteristic, complemented
4C3×#5014C211yesmaximal, characteristic, complemented
5#10591486C211yesmaximal, characteristic, complemented
6#10591486C211yesmaximal, characteristic, complemented
7#10591436C211yesmaximal, characteristic, complemented
8#10591435C211yesmaximal, characteristic, complemented
9#10590554C211yesmaximal, characteristic, complemented
10#10590552C211yesmaximal, characteristic, complemented
11#10590474C211yesmaximal, characteristic, complemented
12#10590472C211yesmaximal, characteristic, complemented
13#10590275C211yesmaximal, characteristic, complemented
14#10590271C211yesmaximal, characteristic, complemented
15#10590255C211yesmaximal, characteristic, complemented
16#80321—31nomaximal
17#79851—31nomaximal
18C2×#3795—21no—
19C32×C4×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22#64133—21no—
23C2×#3750—21no—
24#64099C2211yescharacteristic
25#64097C2211yescharacteristic
26#64087—21no—
27#64087—21no—
28#64079C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#874C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35#63914C2211yescharacteristic
36#63914C2211yescharacteristic
37#63908—21no—
38#63898C2211yescharacteristic
39#63898C2211yescharacteristic
40#63885—21no—
41#63885—21no—
42C3×#832C2211yescharacteristic
43C3×#809C2211yescharacteristic
44C3×#809C2211yescharacteristic
45C3×#809C2211yescharacteristic
46C3×#808C2211yescharacteristic
47C3×C4⋊(C3⋊C8)C2211yescharacteristic
48C3×#803C2211yescharacteristic
49#63575C2211yescharacteristic
50#63573C2211yescharacteristic
51#63572C2211yescharacteristic
52#63572C2211yescharacteristic
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5718—31no—
62#5553—31no—
63#5539—31no—
64#5539—31no—
65#5539—61no—
66C3×#459—31no—
67C3×#442—31no—
68#5152—31no—
69#5150—31no—
70#5150—31no—
71#5150—31no—
72#5150—31no—
73Dic3×D8—31no—
74#5071—31no—
75#5015D311yescharacteristic, complemented
76#5014D311yescharacteristic, complemented
77#5009—31no—
78#4871—31no—
79#4870—31no—
80#4847—31no—
81#4828—31no—
82#4785—31no—
83#4766—31no—
84#4764—31no—
85#4764—31no—
86#4761—31no—
87#4760—31no—
88#4760—31no—
89#4756—31no—
90#4713—31no—
91#4701—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C22×C3⋊Dic3—21no—
95C22×C3⋊Dic3—21no—
96C2×#634—21no—
97C2×#634D411yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×#625—21no—
105C2×#625—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—44no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114#3757—21no—
115#3757—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)D411yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750—21no—
122#3750—21no—
123#3750—21no—
124#3750D411yescharacteristic
125#3750D411yescharacteristic
126C4×C3⋊Dic3C2311yescharacteristic
127C4×C3⋊Dic3C2311yescharacteristic
128C3×#213—22no—
129C3×#213—22no—
130C3×#213—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3366—91noSylow
140C2×#237—61no—
141C2×#235—61no—
142C2×C3×D8—31no—
143C2×C3×D8—31no—
144C2×C3×D8—31no—
145C3×#127—31no—
146C3×C4×D4—21no—
147C3×C4×D4—31no—
148C3×C4×D4C2×D311yescharacteristic
149C3×C4×D4C2×D311yescharacteristic
150#940—31no—
151#940—31no—
152#940—31no—
153#940—31no—
154#939—61no—
155#939—61no—
156#938—61no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165C2×#213C2×D311yescharacteristic
166C2×#213C2×D311yescharacteristic
167C2×#213C2×D311yescharacteristic
168#930—61no—
169#924—61no—
170#924—61no—
171#924—62no—
172C2×Dic3⋊C4—61no—
173C2×Dic3⋊C4—61no—
174C2×Dic3⋊C4—62no—
175#893—31no—
176#893—31no—
177#890—31no—
178#890—31no—
179#890—61no—
180#888—31no—
181#888—31no—
182#888—61no—
183#884—61no—
184#884—61no—
185#878—61no—
186#878—61no—
187#878—61no—
188#878—61no—
189#878—62no—
190#878—62no—
191#874C2×D311yescharacteristic
192C4×D12C2×D311yescharacteristic
193#870—31no—
194#870—31no—
195#870—61no—
196C4×Dic6—31no—
197C4×Dic6—31no—
198C4×Dic6—61no—
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#97—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832C2×D311yescharacteristic
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#818—31no—
220#817—31no—
221#815—31no—
222#815—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229#809C2×D311yescharacteristic
230#809C2×D311yescharacteristic
231#809C2×D311yescharacteristic
232#808—31no—
233#808C2×D311yescharacteristic
234#807—31no—
235C4⋊(C3⋊C8)C2×D311yescharacteristic
236#803C2×D311yescharacteristic
237C23×C32—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C32×D4—21no—
242C32×D4#4112yescomplemented
243C2×C32×C4—21no—
244C2×C32×C4—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
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
256#634—22no—
257#634—81no—
258C2×C3×Dic3—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12—81no—
267C3×C4×D3—42no—
268#625—42no—
269#625—42no—
270#625—81no—
271#625—81no—
272D3×Dic3—42no—
273D3×Dic3—42no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#554—91no—
279#550—91no—
280#490—91no—
281#490—91no—
282#486—91no—
283#478—91no—
284#478—91no—
285#476—91no—
286#459—31no—
287#459—91no—
288#459—91no—
289#446—91no—
290#442—31no—
291#442—91no—
292C4×D8—91no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—22no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—62no—
320C22×Dic3—62no—
321#237—124no—
322#235—124no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12C22×D311yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—62no—
337C3×D8—62no—
338C3×D8—62no—
339C3×D8—62no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—22no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—62no—
362#217—62no—
363#213—22no—
364#213—22no—
365#213—22no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—62no—
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—62no—
393Dic3⋊C4—62no—
394Dic3⋊C4—62no—
395Dic3⋊C4—62no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410C22×C32—22no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C42−1+411yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3⋊Dic3AGL(1,ℤ/8)12yes—
434C3×Dic3—41no—
435C2×#41—181no—
436C2×D8—31no—
437C2×D8—31no—
438C2×D8—31no—
439C4⋊Q8—91no—
440#127—31no—
441#127—91no—
442#127—91no—
443#125—91no—
444#125—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448#121—181no—
449#121—181no—
450#121—181no—
451C4×Q8—91no—
452C4×D4—31no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4D3211yescharacteristic
458C2×C4⋊C4—181no—
459#107—91no—
460#106—31no—
461#106—91no—
462C4⋊C8—31no—
463C4⋊C8—91no—
464C4⋊C8—91no—
465#102—31no—
466#102—31no—
467#102—31no—
468#102—31no—
469#102—91no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#97—31no—
476#97—91no—
477C4×C8—91no—
478C23×C3—22no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C3×D4—22no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—22no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—122no—
498C3×D4—241no—
499C3×D4#23512yescomplemented
500C3×D4#23712yescomplemented
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—61no—
508C2×C3×C4—81no—
509C2×C3×C4—81no—
510C2×C3×C4—82no—
511C2×C3×C4—122no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—122no—
519#67—122no—
520#67—122no—
521#67—122no—
522#67—241no—
523#67—241no—
524#67—241no—
525#67—241no—
526C2×Dic3—21no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—62no—
540C2×Dic3—62no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—122no—
546C2×Dic3—122no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3—124no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3—242no—
553D12—21no—
554D12—21no—
555D12—21no—
556D12—21no—
557D12—21no—
558D12—21no—
559D12—42no—
560D12—81no—
561C4×D3—42no—
562C4×D3—122no—
563C4×D3—122no—
564Dic6—62no—
565Dic6—62no—
566Dic6—122no—
567Dic6—241no—
568Dic6—241no—
569Dic6—242no—
570C3×C8—61no—
571C3×C8—61no—
572C3×C8—61no—
573C3×C8—61no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C2×C32—42no—
579C2×C32#54811yescharacteristic
580C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
581C2×C32#57611yescharacteristic
582C3×D3—81no—
583C3×D3—81no—
584C3×D3—81no—
585#41—364no—
586C2×Q8—91no—
587C2×Q8—181no—
588C2×D4—31no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—181no—
594C2×D4—181no—
595C2×D4—181no—
596C2×D4—181no—
597C2×D4C2×D3211yescharacteristic
598C22×C4—21no—
599C22×C4—61no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604D8—62no—
605D8—62no—
606D8—62no—
607C2×C8—31no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—31no—
611C4⋊C4—31no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4C2×D3211yescharacteristic
623C22⋊C4—21no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—91no—
630C42—91no—
631C42C2×D3211yescharacteristic
632C22×C3—24no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C2×D3×D411yescharacteristic
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—121no—
674C3×C4C2×#23511yescharacteristic
675C3×C4C2×#23711yescharacteristic
676C3×C4#101011yescharacteristic
677C3×C4#101011yescharacteristic
678Dic3—32no—
679Dic3—32no—
680Dic3—41no—
681Dic3—62no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—122no—
692Dic3—122no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697C32#336611yescharacteristic, complemented, Sylow
698C23—21no—
699C23—61no—
700C23—61no—
701C23—61no—
702Q8—182no—
703Q8—721no—
704D4—21no—
705D4—61no—
706D4—61no—
707D4—61no—
708D4—61no—
709D4—61no—
710D4—61no—
711D4—122no—
712D4—241no—
713D4—362no—
714D4—362no—
715D4—721no—
716D4—721no—
717D4#379512yescomplemented
718C2×C4—21no—
719C2×C4—61no—
720C2×C4—81no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—122no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—362no—
729C2×C4—362no—
730C2×C4—362no—
731C2×C4—721no—
732C2×C4#381111yescharacteristic
733C2×C4#381111yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—61no—
736C8—61no—
737C8—61no—
738C8—61no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—44no—
743C2×C3—42no—
744C2×C3—42no—
745C2×C3—241no—
746C2×C3—241no—
747C2×C3—241no—
748C2×C3#555211yescharacteristic
749C2×C3#559811yescharacteristic
750C2×C3#575711yescharacteristic
751C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
752C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
753C2×C3#577411yescharacteristic
754D3—81no—
755D3—81no—
756D3—81no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22C2×#381111yescharacteristic
770C4—21no—
771C4—21no—
772C4—41no—
773C4—92no—
774C4—121no—
775C4—181no—
776C4—181no—
777C4—181no—
778C4—361no—
779C4—361no—
780C4C2×#379511yescharacteristic
781C4#6429811yescharacteristic
782C3—21no—
783C3#7985111yescharacteristic, complemented
784C3#8032111yescharacteristic, complemented
785C2—42no—
786C2—241no—
787C2—241no—
788C2—241no—
789C2#1059491811yescharacteristic
790C2#1059510211yescharacteristic
791C2#1059545811yescharacteristic
subgroupG/H
centerC22C2×#3811
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. #10596010C2semidirect
2. #10593906C2semidirect
3. C3×#5015C2semidirect
4. C3×#5014C2semidirect
5. #10591486C2semidirect
6. #10591486C2semidirect
7. #10591436C2semidirect
8. #10591435C2semidirect
9. #10590554C2semidirect
10. #10590552C2semidirect
11. #10590474C2semidirect
12. #10590472C2semidirect
13. #10590275C2semidirect
14. #10590271C2semidirect
15. #10590255C2semidirect
75. #5015D3semidirect
76. #5014D3semidirect
242. C32×D4#41semidirect
499. C3×D4#235semidirect
500. C3×D4#237semidirect
697. C32#3366semidirect
717. D4#3795semidirect
783. C3#79851semidirect
784. C3#80321semidirect

Maximal subgroups

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

subgroupindex
#105960102
#105939062
C3×#50152
C3×#50142
#105914862
#105914362
#105914352
#105905542
#105905522
#105904742
#105904722
#105902752
#105902712
#105902552
#803213
#798513