Finite Group Databasebeta

← #11872742

Subgroups — #11872742

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic, complemented
2#10595218C211yesmaximal, characteristic, complemented
3#10592855C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6#10591456C211yesmaximal, characteristic, complemented
7#10591429C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10591425C211yesmaximal, characteristic, complemented
10#10591409C211yesmaximal, characteristic, complemented
11#10591400C211yesmaximal, characteristic, complemented
12#10590769C211yesmaximal, characteristic, complemented
13#10590746C211yesmaximal, characteristic, complemented
14#10590652C211yesmaximal, characteristic, complemented
15#10590647C211yesmaximal, characteristic, complemented
16#80317—31nomaximal
17#79874—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20#64147C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C3×#940C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27#63978—21no—
28#63974—21no—
29#63971—21no—
30#63969—21no—
31C2×#3722—21no—
32#63961—21no—
33#63952—21no—
34#63952—21no—
35#63916C2211yescharacteristic
36#63894C2211yescharacteristic
37#63894C2211yescharacteristic
38Dic3×D12C2211yescharacteristic, complemented
39#63874C2211yescharacteristic
40#63869C2211yescharacteristic, complemented
41#63849C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63659C2211yescharacteristic
44#63648C2211yescharacteristic
45#63647C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5719—31no—
62#5562—31no—
63#5545—31no—
64#5545—31no—
65C3×#459—31no—
66C3×#442—31no—
67#5156—31no—
68#5156—31no—
69#5156—31no—
70#5156—61no—
71#5152D311yescharacteristic, complemented
72#5150D311yescharacteristic, complemented
73Dic3×D8—31no—
74#5072—31no—
75C4×#213—31no—
76C4×#213—31no—
77#5009—31no—
78#4871—31no—
79#4866—31no—
80#4847—31no—
81#4840—31no—
82#4786—31no—
83#4785—31no—
84#4784—31no—
85#4779—31no—
86#4779—31no—
87#4773—31no—
88#4763—31no—
89#4756—31no—
90#4711—31no—
91#4709—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C2×C3×D12C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111C32×D8—22no—
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3753—22no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#213—22no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128#3724—21no—
129#3724D411yescharacteristic
130#3724D411yescharacteristic
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722D411yescharacteristic
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3714—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×C3×D8—21no—
146C2×C3×D8—31no—
147C2×C3×D8C2×D311yescharacteristic
148C2×C3×D8C2×D311yescharacteristic
149C3×#127—31no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153#940C2×D311yescharacteristic, complemented
154#939—61no—
155#939—61no—
156#938—31no—
157#938—31no—
158#938—31no—
159#938—61no—
160#935—61no—
161#935—61no—
162D4×Dic3—31no—
163D4×Dic3C2×D311yescharacteristic
164D4×Dic3C2×D311yescharacteristic
165D4×Dic3C2×D311yescharacteristic, complemented
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—61no—
170C2×#213C2×D311yescharacteristic
171#930—61no—
172#929—61no—
173C4×#67—61no—
174C4×#67—61no—
175C2×(C2×D3)⋊C4—61no—
176C2×(C2×D3)⋊C4—61no—
177C2×D24—31no—
178#895—31no—
179#893—31no—
180#893—31no—
181#892—31no—
182#892—31no—
183#890—31no—
184#884—61no—
185#883—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193#872—31no—
194#872—31no—
195#870—31no—
196C3×#106—31no—
197C3×C4⋊C8—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#97—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—61no—
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic, complemented
209#832C2×D311yescharacteristic, complemented
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214#821C2×D311yescharacteristic, complemented
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#818—31no—
221#817—31no—
222#817C2×D311yescharacteristic, complemented
223#815C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8C2×D311yescharacteristic, complemented
226C8×Dic3—31no—
227#809—31no—
228#809—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233C4⋊(C3⋊C8)—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C23×C32—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—24no—
239C22×C3⋊D3—81no—
240C22×C3⋊D3—81no—
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4C2411yescharacteristic
248#638—24no—
249#638—81no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yes—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C3×#67—81no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270#626—81no—
271#624—81no—
272#624—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—31no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—31no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C23×D3—61no—
294C23×D3—61no—
295C23×D3—121no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—121no—
316C2×#67—121no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—61no—
321D3×D4—62no—
322D3×D4—62no—
323D3×D4—62no—
324D3×D4—62no—
325D3×D4—122no—
326D3×D4—122no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—31no—
333C2×C4×D3—31no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C3×D8—22no—
341C3×D8—22no—
342C3×D8—42no—
343C3×D8—62no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356C3×C42—31no—
357#217—21no—
358#217—21no—
359#217—21no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—121no—
365#213—22no—
366#213—62no—
367#213—62no—
368#213—62no—
369#213—122no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3C22×D311yescharacteristic
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—62no—
406C22×C32—22no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—22no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—84no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3⋊Dic3—21no—
426C3⋊Dic3—41no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C22×D4—91no—
435C2×D8—31no—
436C2×D8—91no—
437C2×D8—91no—
438C2×D8D3211yescharacteristic
439#127—31no—
440#125—91no—
441#123—181no—
442#123—181no—
443#121—91no—
444#121—91no—
445#121—181no—
446#121—181no—
447C4×D4—31no—
448C4×D4—31no—
449C4×D4—31no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—91no—
457C2×C22⋊C4—181no—
458C2×C22⋊C4—181no—
459#107—91no—
460#107—91no—
461#106—31no—
462#106—91no—
463C4⋊C8—31no—
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—
473C22⋊C8—91no—
474C22⋊C8—91no—
475#97—31no—
476C4×C8—91no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—64no—
491C22×D3—64no—
492C22×D3—121no—
493C22×D3—124no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3—241no—
497C22×D3—241no—
498C22×D3—242no—
499C22×D3—242no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—241no—
513C3×D4—241no—
514C3×D4#23512yes—
515C3×D4#23712yes—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—241no—
525C2×C3×C4—241no—
526C2×C3×C4—241no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—64no—
530#67—64no—
531#67—81no—
532#67—81no—
533#67—124no—
534#67—241no—
535#67—241no—
536#67—241no—
537#67—242no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—81no—
547C2×Dic3—81no—
548C2×Dic3—81no—
549C2×Dic3—121no—
550C2×Dic3—241no—
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555D12—21no—
556D12—21no—
557D12—32no—
558D12—32no—
559D12—62no—
560D12—61no—
561D12—61no—
562D12—121no—
563D12—241no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—121no—
569C4×D3—121no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—61no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—121no—
585C2×C32—42no—
586C2×C32—81no—
587C2×C32#52511yescharacteristic
588C2×C32#57611yescharacteristic
589C2×C32#57611yescharacteristic
590C3⋊D3—41no—
591C3⋊D3—42no—
592C3×D3—81no—
593C24—181no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—91no—
598C2×D4—181no—
599C2×D4—181no—
600C2×D4—182no—
601C2×D4—182no—
602C2×D4—181no—
603C2×D4C2×D3211yescharacteristic
604C2×D4C2×D3211yescharacteristic
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—91no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612D8—22no—
613D8—62no—
614D8—182no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—91no—
619C2×C8C2×D3211yescharacteristic
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—31no—
641C42—181no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C2×D3×D411yescharacteristic
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—62no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—62no—
676C2×D3—61no—
677C2×D3—62no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—122no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3—244no—
688C2×D3—244no—
689C2×D3—248no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4C2×#23511yescharacteristic
700C3×C4C2×#23711yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4D3×#4111yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—21no—
706Dic3—21no—
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710Dic3—61no—
711Dic3—61no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716C32#312211yescharacteristic, complemented, Sylow
717C23—21no—
718C23—21no—
719C23—61no—
720C23—91no—
721C23—184no—
722C23—181no—
723C23—721no—
724C23—721no—
725D4—21no—
726D4—21no—
727D4—21no—
728D4—61no—
729D4—61no—
730D4—92no—
731D4—184no—
732D4—181no—
733D4—241no—
734D4—241no—
735D4—721no—
736D4—721no—
737D4#380412yes—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—91no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—241no—
750C2×C4—241no—
751C2×C4—241no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4—721no—
755C2×C4C22×D3211yescharacteristic
756C8—21no—
757C8—61no—
758C8—61no—
759C8—181no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—42no—
765C2×C3—82no—
766C2×C3—81no—
767C2×C3—81no—
768C2×C3—161no—
769C2×C3—241no—
770C2×C3#554711yescharacteristic
771C2×C3#560611yescharacteristic
772C2×C3#575711yescharacteristic
773C2×C3#577411yescharacteristic
774C2×C3#577411yescharacteristic
775C2×C3#577411yescharacteristic
776D3—81no—
777D3—122no—
778D3—121no—
779D3—122no—
780D3—121no—
781D3—122no—
782D3—242no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—181no—
793C22—182no—
794C22—181no—
795C22—181no—
796C22—361no—
797C22—361no—
798C22—724no—
799C22D32×D411yescharacteristic
800C4—61no—
801C4—61no—
802C4—61no—
803C4—61no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—181no—
808C4—361no—
809C4#6431211yescharacteristic
810C4C2×#380411yescharacteristic
811C3—21no—
812C3#7987411yescharacteristic, complemented
813C3#8031711yescharacteristic, complemented
814C2—42no—
815C2—81no—
816C2—241no—
817C2—361no—
818C2—362no—
819C2#1059473211yescharacteristic
820C2#1059473511yescharacteristic
821C2#1059513811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595223C2semidirect
2. #10595218C2semidirect
3. #10592855C2semidirect
4. C3×#5152C2semidirect
5. C3×#5150C2semidirect
6. #10591456C2semidirect
7. #10591429C2semidirect
8. Dic3×#213C2semidirect
9. #10591425C2semidirect
10. #10591409C2semidirect
11. #10591400C2semidirect
12. #10590769C2semidirect
13. #10590746C2semidirect
14. #10590652C2semidirect
15. #10590647C2semidirect
22. C3×#940C22semidirect
25. C3×D4×Dic3C22semidirect
38. Dic3×D12C22semidirect
40. #63869C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#821C22semidirect
50. C3×#817C22semidirect
51. C3×#815C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
71. #5152D3semidirect
72. #5150D3semidirect
153. #940C2×D3semidirect
165. D4×Dic3C2×D3semidirect
208. #832C2×D3semidirect
209. #832C2×D3semidirect
214. #821C2×D3semidirect
222. #817C2×D3semidirect
223. #815C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
716. C32#3122semidirect
812. C3#79874semidirect
813. C3#80317semidirect

Maximal subgroups

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

subgroupindex
#105952232
#105952182
#105928552
C3×#51522
C3×#51502
#105914562
#105914292
Dic3×#2132
#105914252
#105914092
#105914002
#105907692
#105907462
#105906522
#105906472
#803173
#798743