Finite Group Databasebeta

← #11865782

Subgroups — #11865782

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic, complemented
3#10594954C211yesmaximal, characteristic, complemented
4C2×#63829C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591577C211yesmaximal, characteristic, complemented
7#10591575C211yesmaximal, characteristic, complemented
8#10591568C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10591441C211yesmaximal, characteristic, complemented
11#10591439C211yesmaximal, characteristic, complemented
12#10591432C211yesmaximal, characteristic, complemented
13#10591429C211yesmaximal, characteristic, complemented
14C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10591083C211yesmaximal, characteristic, complemented
16#83296—31nomaximal
17#78861—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21#64159—24no—
22C2×#3756C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26C22×C3⋊(C3⋊C8)C2211yescharacteristic
27C3×#947C2211yescharacteristic
28C3×#944C2211yescharacteristic
29C3×#940C2211yescharacteristic
30C3×#939—21no—
31C3×#939—21no—
32C3×#936C2211yescharacteristic
33C3×C4×#67—21no—
34C3×C4×#67—21no—
35C3×#926C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C22×C3×C3⋊C8C2211yescharacteristic
38#63952—21no—
39#63952—21no—
40#63894C2211yescharacteristic
41#63894C2211yescharacteristic
42C4×#624—21no—
43#63874—21no—
44#63844C2211yescharacteristic
45#63844C2211yescharacteristic
46C2×#3719C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48#63829—24no—
49C2×#3716C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×#835C2211yescharacteristic
53C3×#832C2211yescharacteristic
54C3×#832C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic
63C3×#532—31no—
64#5832D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—31no—
68C2×#950—61no—
69C2×#904—31no—
70#5522—31no—
71C4×#235—31no—
72C3×#416—31no—
73#5233—31no—
74#5233D311yescharacteristic, complemented
75C2×Dic3⋊C8—31no—
76#5090—31no—
77#5083—31no—
78#5075—31no—
79#5072—31no—
80#5057—31no—
81#5057—31no—
82#5054—31no—
83#5054—31no—
84#5002—31no—
85C2×C4⋊(C3⋊C8)—31no—
86#4819—31no—
87#4818—31no—
88#4798—31no—
89#4795—31no—
90#4787—31no—
91#4786—31no—
92#4767—31no—
93#4762—31no—
94C32×#41—22no—
95C32×#41—22no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C22×C32×C4C2311yescharacteristic
101C2×#638—21no—
102#3828—22no—
103#3828D414yescomplemented
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3D411yescharacteristic
111C22×C3×Dic3D411yescharacteristic
112C3×#235—22no—
113C3×#235—22no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×Dic6C2311yescharacteristic
117C2×#624—21no—
118C2×#624—21no—
119#3756—22no—
120#3755—22no—
121#3754—22no—
122#3753—22no—
123C2×C3⋊(C3⋊C8)—22no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#217—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3724—21no—
144#3724—21no—
145#3722—21no—
146#3722—21no—
147Dic32—21no—
148Dic32—21no—
149#3719—22no—
150#3717—22no—
151#3716—22no—
152#3714—22no—
153#3035—91noSylow
154C2×C3×#41—21no—
155C2×C3×#41—31no—
156C2×C3×#41C2×D311yescharacteristic
157C2×C3×#41C2×D311yescharacteristic
158C2×#235—31no—
159C2×#235—31no—
160C2×#235—61no—
161C2×#235C2×D311yescharacteristic
162C22×C3×C8—31no—
163C3×C4⋊Q8—31no—
164C3×#127—31no—
165C3×#124—31no—
166C3×#124—31no—
167C3×#121—61no—
168C3×#121—61no—
169C3×C4×D4—61no—
170C3×C4×D4—61no—
171C3×#117—31no—
172C2×C3×C42—31no—
173#950—64no—
174#950—64no—
175#950—64no—
176#950—68no—
177#947C2×D311yescharacteristic
178#944C2×D311yescharacteristic
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—61no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—61no—
187#940C2×D311yescharacteristic
188#939—21no—
189#939—21no—
190#936C2×D311yescharacteristic
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—61no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—61no—
199C4×#67—21no—
200C4×#67—21no—
201C4×#67—61no—
202C4×#67—61no—
203#926C2×D311yescharacteristic
204C2×C4×Dic3C2×D311yescharacteristic
205C22×C3⋊C8—31no—
206C22×C3⋊C8—31no—
207C22×C3⋊C8—61no—
208C22×C3⋊C8C2×D311yescharacteristic
209C2×Dic12—31no—
210#904—64no—
211C2×D24—31no—
212C2×#204—31no—
213C2×#204—31no—
214#893—31no—
215#893—31no—
216#887—31no—
217#887—31no—
218#67⋊C4—61no—
219#67⋊C4—61no—
220C4×D12—31no—
221C4×D12—31no—
222#872—61no—
223#872—61no—
224C42×D3—61no—
225C42×D3—61no—
226C4×Dic6—31no—
227C4×Dic6—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#102—31no—
231C3×#102—31no—
232#835—31no—
233#835—31no—
234#835C2×D311yescharacteristic
235#835C2×D311yescharacteristic
236#832—31no—
237#832—31no—
238#832C2×D311yescharacteristic
239#832C2×D311yescharacteristic
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244#810—31no—
245#810—31no—
246#809—31no—
247#809—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C23×C32—21no—
253C23×C32C2×D411yescharacteristic
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C32×Q8—21no—
257C32×Q8—21no—
258C32×D4—21no—
259C32×D4—21no—
260C32×D4—42no—
261C2×C32×C4—21no—
262C2×C32×C4—42no—
263C2×C32×C4C2×D412yes—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4#4112yes—
266C2×C32×C4C2411yescharacteristic
267#638—24no—
268C2×C3⋊Dic3—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)C2×D412yes—
271C4×C3⋊D3—24no—
272#634—21no—
273#634C2×D412yes—
274C3×#67—42no—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—41no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#624—42no—
292#624—42no—
293C3⋊(C3⋊C8)—21no—
294C3⋊(C3⋊C8)—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8—21no—
297C2×#135—91no—
298C2×#135—91no—
299#532—31no—
300C4×#41—91no—
301#464—91no—
302#464—91no—
303#463—91no—
304#463—91no—
305#462—91no—
306#461—91no—
307#460—91no—
308#459—91no—
309C2×C4⋊C8—91no—
310#416—31no—
311#416—91no—
312C3×#41—24no—
313C3×#41—22no—
314C3×#41—22no—
315C3×#41—22no—
316C3×#41—22no—
317C3×#41—42no—
318C3×#41—62no—
319C3×#41—62no—
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—41no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—41no—
340C22×C3×C4—61no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—121no—
349C22×Dic3#6711yescharacteristic
350C22×Dic3#6711yescharacteristic
351#235—22no—
352#235—22no—
353#235—34no—
354#235—34no—
355#235—64no—
356#235—62no—
357#235—62no—
358#235—122no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—61no—
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—121no—
371C2×Dic6—31no—
372C2×Dic6—31no—
373C2×Dic6—61no—
374C2×Dic6C22×D311yescharacteristic
375C2×C3×C8—31no—
376C2×C3×C8—31no—
377C2×C3×C8—62no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C42—31no—
388C3×C42—31no—
389C3×C42—31no—
390C3×C42—31no—
391C3×C42—61no—
392#217—21no—
393#217—21no—
394#217—21no—
395#216—62no—
396#216—62no—
397#216—62no—
398#216—64no—
399#215—62no—
400#215—62no—
401#215—62no—
402#215—64no—
403#214—62no—
404#214—62no—
405#214—62no—
406#214—64no—
407#213—62no—
408#213—62no—
409#213—62no—
410#213—64no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417C4⋊Dic3C22×D311yescharacteristic
418C4⋊Dic3C22×D311yescharacteristic
419Dic3⋊C4—21no—
420Dic3⋊C4—21no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425C4×Dic3—21no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C4×Dic3#6711yescharacteristic
431C4×Dic3#6711yescharacteristic
432C4×Dic3C22×D311yescharacteristic
433C4×Dic3C22×D311yescharacteristic
434C2×C3⋊C8—22no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8—64no—
442C2×C3⋊C8—62no—
443C2×C3⋊C8—62no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446Dic12—62no—
447D24—62no—
448#204—62no—
449#204—62no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32#12112yes—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—22no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C32×C4—41no—
464C32×C4#12112yes—
465C32×C4C22×D411yescharacteristic
466C32×C4C2×#4111yescharacteristic
467C3⋊Dic3—22no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3—41no—
474C3×Dic3#13512yescomplemented
475C2×#41—31no—
476C2×#41—91no—
477C2×#41D3211yescharacteristic
478#135—184no—
479#135—184no—
480C2×Q16—91no—
481C2×Q16—91no—
482C2×SD16—91no—
483C2×SD16—91no—
484C2×SD16—91no—
485C2×SD16—91no—
486C2×D8—91no—
487C2×D8—91no—
488C22×C8—31no—
489C22×C8—91no—
490C4⋊Q8—31no—
491#127—31no—
492#124—31no—
493#124—31no—
494#121—61no—
495#121—61no—
496C4×Q8—91no—
497C4×Q8—91no—
498C4×D4—61no—
499C4×D4—61no—
500C4×D4—91no—
501C4×D4—91no—
502C4×D4—181no—
503C4×D4—181no—
504#117—31no—
505#117—181no—
506C2×C42—31no—
507C2×C42—181no—
508C4⋊C8—91no—
509C4⋊C8—91no—
510C4⋊C8—91no—
511C4⋊C8—91no—
512#103—31no—
513#103—31no—
514#103—91no—
515#103—91no—
516#102—31no—
517#102—31no—
518#102—91no—
519#102—91no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—41no—
524C23×C3—61no—
525C23×C3D3×D411yescharacteristic
526C23×C3C2×#6711yescharacteristic
527C22×D3—21no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—121no—
531C3×Q8—22no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—41no—
537C3×Q8—61no—
538C3×Q8—61no—
539C3×D4—22no—
540C3×D4—21no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—41no—
545C3×D4—44no—
546C3×D4—42no—
547C3×D4—42no—
548C3×D4—61no—
549C3×D4—61no—
550C3×D4—122no—
551C3×D4—122no—
552C3×D4—122no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—41no—
564C2×C3×C4—44no—
565C2×C3×C4—42no—
566C2×C3×C4—42no—
567C2×C3×C4—62no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—121no—
572C2×C3×C4—122no—
573C2×C3×C4#23512yes—
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4D3×D412yes—
576C2×C3×C4D3×D412yes—
577C2×C3×C4#23712yes—
578C2×C3×C4C2×#6711yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—42no—
582#67—42no—
583#67—42no—
584#67—64no—
585#67—64no—
586#67—124no—
587C2×Dic3—22no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—41no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—121no—
595C2×Dic3C2×#6711yescharacteristic
596C2×Dic3C2×#6711yescharacteristic
597C2×Dic3C2×#6711yescharacteristic
598C2×Dic3C2×#6711yescharacteristic
599D12—21no—
600D12—21no—
601D12—32no—
602D12—32no—
603D12—62no—
604D12—61no—
605D12—61no—
606D12—121no—
607C4×D3—42no—
608C4×D3—64no—
609C4×D3—64no—
610C4×D3—124no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—122no—
614C4×D3—122no—
615Dic6—21no—
616Dic6—21no—
617Dic6—32no—
618Dic6—32no—
619Dic6—62no—
620Dic6—61no—
621Dic6—61no—
622Dic6—121no—
623C3×C8—61no—
624C3×C8—61no—
625C3⋊C8—21no—
626C3⋊C8—21no—
627C3⋊C8—62no—
628C3⋊C8—62no—
629C3⋊C8—61no—
630C3⋊C8—61no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C2×C32—22no—
634C2×C32—81no—
635C2×C32C2×#12111yescharacteristic
636C2×C32C2×#13511yescharacteristic
637C2×C32#57511yescharacteristic
638C3⋊D3—42no—
639C3×D3—81no—
640#41—22no—
641#41—22no—
642#41—62no—
643#41—62no—
644#41—94no—
645#41—182no—
646C2×Q8—31no—
647C2×Q8—91no—
648C2×Q8C2×D3211yescharacteristic
649C2×D4—21no—
650C2×D4—31no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—91no—
655C2×D4—181no—
656C2×D4C2×D3211yescharacteristic
657C22×C4—21no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—61no—
661C22×C4—181no—
662C22×C4—181no—
663C22×C4—181no—
664C22×C4C2×D3211yescharacteristic
665Q16—182no—
666Q16—182no—
667SD16—182no—
668SD16—182no—
669SD16—182no—
670SD16—182no—
671D8—182no—
672D8—182no—
673C2×C8—31no—
674C2×C8—31no—
675C2×C8—62no—
676C2×C8—91no—
677C2×C8—91no—
678C2×C8—182no—
679C4⋊C4—31no—
680C4⋊C4—31no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—181no—
684C4⋊C4—181no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—61no—
688C22⋊C4—61no—
689C22⋊C4—61no—
690C22⋊C4—181no—
691C22⋊C4—181no—
692C42—31no—
693C42—31no—
694C42—31no—
695C42—31no—
696C42—61no—
697C42—181no—
698C42—181no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—22no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—42no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3#88412yes—
720C22×C3#93812yes—
721C22×C3C2×D3×D411yescharacteristic
722C22×C3C22×#6711yescharacteristic
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—122no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—241no—
734C2×D3—241no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—22no—
738C3×C4—32no—
739C3×C4—42no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—121no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4#88412yes—
749C3×C4#93812yes—
750C3×C4C2×#23511yescharacteristic
751C3×C4C2×D3×D411yescharacteristic
752C3×C4C2×D3×D411yescharacteristic
753C3×C4C2×#23711yescharacteristic
754Dic3—21no—
755Dic3—21no—
756Dic3—21no—
757Dic3—41no—
758Dic3—41no—
759Dic3—41no—
760Dic3—62no—
761Dic3—62no—
762Dic3—122no—
763Dic3#95012yescomplemented
764C32#303511yescharacteristic, complemented, Sylow
765C23—21no—
766C23—61no—
767C23—181no—
768C23D3×#6711yescharacteristic
769Q8—21no—
770Q8—21no—
771Q8—61no—
772Q8—61no—
773Q8—92no—
774Q8—181no—
775D4—21no—
776D4—21no—
777D4—42no—
778D4—61no—
779D4—61no—
780D4—92no—
781D4—122no—
782D4—122no—
783D4—122no—
784D4—184no—
785D4—181no—
786C2×C4—21no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—42no—
792C2×C4—62no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—121no—
797C2×C4—122no—
798C2×C4—181no—
799C2×C4—184no—
800C2×C4—362no—
801C2×C4—362no—
802C2×C4#380412yes—
803C2×C4D3×#6711yescharacteristic
804C2×C4#381112yes—
805C2×C4C22×D3211yescharacteristic
806C8—61no—
807C8—61no—
808C8—181no—
809C8—181no—
810C2×C3—22no—
811C2×C3—22no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—42no—
816C2×C3—82no—
817C2×C3—81no—
818C2×C3—81no—
819C2×C3—241no—
820C2×C3C2×#88411yescharacteristic
821C2×C3D3×#13511yescharacteristic
822C2×C3#576811yescharacteristic
823C2×C3C2×#93811yescharacteristic
824C2×C3C2×#95011yescharacteristic
825C2×C3#582211yescharacteristic
826D3—81no—
827D3—122no—
828D3—122no—
829D3—242no—
830C22—21no—
831C22—21no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—182no—
839C22—361no—
840C22—361no—
841C22#6395812yes—
842C22C2×D3×#6711yescharacteristic
843C4—32no—
844C4—41no—
845C4—61no—
846C4—61no—
847C4—61no—
848C4—121no—
849C4—121no—
850C4—121no—
851C4—182no—
852C4#6395812yes—
853C4C2×#380411yescharacteristic
854C4C2×#381111yescharacteristic
855C3—21no—
856C3#7886111yescharacteristic, complemented
857C3#8329611yescharacteristic, complemented
858C2—22no—
859C2—81no—
860C2—241no—
861C2—362no—
862C2D3×#95011yescharacteristic
863C2#1059545311yescharacteristic
864C2C2×#6395811yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64159C2semidirect
2. C3×#5832C2semidirect
3. #10594954C2semidirect
4. C2×#63829C2semidirect
5. C3×#5233C2semidirect
6. #10591577C2semidirect
7. #10591575C2semidirect
8. #10591568C2semidirect
9. #10591565C2semidirect
10. #10591441C2semidirect
11. #10591439C2semidirect
12. #10591432C2semidirect
13. #10591429C2semidirect
14. C2×Dic3⋊(C3⋊C8)C2semidirect
15. #10591083C2semidirect
64. #5832D3semidirect
74. #5233D3semidirect
103. #3828D4semidirect
474. C3×Dic3#135semidirect
763. Dic3#950semidirect
764. C32#3035semidirect
856. C3#78861semidirect
857. C3#83296semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C3×#58322
#105949542
C2×#638292
C3×#52332
#105915772
#105915752
#105915682
#105915652
#105914412
#105914392
#105914322
#105914292
C2×Dic3⋊(C3⋊C8)2
#105910832
#832963
#788613