Finite Group Databasebeta

← #11870512

Subgroups — #11870512

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C211yesmaximal, characteristic, complemented
2C4×D3×D12C211yesmaximal, characteristic
3C4×#3755C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic
6#10591565C211yesmaximal, characteristic, complemented
7#10591564C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10590596C211yesmaximal, characteristic
10#10590466C211yesmaximal, characteristic, complemented
11#10590465C211yesmaximal, characteristic, complemented
12#10590439C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14C4×#3715C211yesmaximal, characteristic, complemented
15#10590261C211yesmaximal, characteristic, complemented
16#83351—31nomaximal
17#79651—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C32×C4×Q8C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#944C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×#897C2211yescharacteristic
27C3×#896—21no—
28C3×#889—21no—
29C3×#888C2211yescharacteristic, complemented
30C3×C4×D12C2211yescharacteristic
31C3×#872—21no—
32C3×C42×D3C2211yescharacteristic
33C3×C4×Dic6—21no—
34C3×C4×Dic6C2211yescharacteristic, complemented
35D3×(C2×D3)⋊C4—21no—
36C4×#626—21no—
37#63894C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63880—21no—
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63662C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic, complemented
46C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#533—31no—
62#5578D311yescharacteristic, complemented
63C4×D3×D4—31no—
64C2×C4×D12—31no—
65C3×C4×SD16—31no—
66#5169—31no—
67#5162—31no—
68#5084—31no—
69#5084—31no—
70#5083—31no—
71#5083—31no—
72#5046—31no—
73#5046—31no—
74#5043—31no—
75#5043—31no—
76C4×#215—31no—
77C4×#215—31no—
78C4×#215—31no—
79C4×#215—31no—
80C4×#215—61no—
81C4×#215D311yescharacteristic, complemented
82C4×#214—31no—
83#4925—31no—
84#4870—31no—
85#4862—31no—
86#4818—31no—
87#4805—31no—
88#4776—31no—
89#4761—31no—
90C4×#204—31no—
91#4685—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3D411yescharacteristic
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107D3×D12—22no—
108D3×D12—22no—
109C4×D32—44no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114#3755—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#215—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3D411yescharacteristic
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140#3717—22no—
141#3715—22no—
142#3101—91noSylow
143C2×D3×D4—31no—
144C22×D12—31no—
145C22×C4×D3—61no—
146C22×C4×D3—61no—
147C2×C3×SD16—31no—
148C3×C4⋊Q8—31no—
149C3×C4⋊Q8—31no—
150C3×#125—61no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—61no—
154C3×C4×Q8—21no—
155C3×C4×Q8—31no—
156C3×C4×Q8—61no—
157C3×C4×Q8C2×D311yescharacteristic, complemented
158C3×C4×Q8C2×D311yescharacteristic, complemented
159C3×C4×D4—31no—
160C3×#117—61no—
161C2×C3×C42—31no—
162#946C2×D311yescharacteristic
163#944C2×D311yescharacteristic, complemented
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—61no—
169C2×#215C2×D311yescharacteristic
170D4×Dic3—31no—
171C2×#214—31no—
172C4×#67—61no—
173C2×(C2×D3)⋊C4—61no—
174C2×C4⋊Dic3—31no—
175C2×#204—31no—
176#897C2×D311yescharacteristic
177#896—21no—
178#893—31no—
179D3×C4⋊C4—31no—
180#889—21no—
181#888C2×D311yescharacteristic, complemented
182#67⋊C4—61no—
183D3×C22⋊C4—61no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×D12—61no—
190C4×D12—61no—
191C4×D12C2×D311yescharacteristic
192#872—21no—
193C42×D3C2×D311yescharacteristic
194C4×Dic6—21no—
195C4×Dic6C2×D311yescharacteristic, complemented
196C3×#106—31no—
197C3×#103—31no—
198C3×#102—31no—
199C3×C4×C8—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—61no—
205#835C2×D311yescharacteristic, complemented
206#832—31no—
207#830—31no—
208#830—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#817—31no—
213#816—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216#810—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—61no—
222#809C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—61no—
229#808C2×D311yescharacteristic, complemented
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C4×C3⋊C8C2×D311yescharacteristic, complemented
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—42no—
241C2×D32—42no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)#4112yes—
252C4×C3⋊D3—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12#4112yes—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—41no—
264C3×C4×D3—42no—
265C3×C4×D3SD1614yescomplemented
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269#626—24no—
270#624—42no—
271D3×Dic3—42no—
272D3×Dic3—42no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#533—31no—
278C2×C4×D4—91no—
279#483—91no—
280#483—91no—
281#476—91no—
282#476—91no—
283#461—91no—
284#461—91no—
285#450—91no—
286#450—91no—
287C4×SD16—31no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#431—91no—
292C23×D3—61no—
293C23×D3—61no—
294C2×C3×Q8—21no—
295C2×C3×Q8—31no—
296C2×C3×Q8—61no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C2×#67—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307D3×D4—62no—
308D3×D4—62no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—61no—
312C2×D12—62no—
313C2×D12—61no—
314C2×D12—62no—
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—121no—
324C2×C4×D3—124no—
325C2×C4×D3—124no—
326C2×C4×D3#6711yescharacteristic
327C2×C4×D3#6711yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—21no—
330C2×Dic6C22×D311yescharacteristic
331C3×SD16—62no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—41no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—21no—
352C3×C42—21no—
353C3×C42—21no—
354C3×C42—31no—
355C3×C42—31no—
356C3×C42—31no—
357C3×C42—41no—
358C3×C42—61no—
359C3×C42C22×D311yescharacteristic
360C3×C42C22×D311yescharacteristic
361#217—61no—
362#215—22no—
363#215—62no—
364#215—62no—
365#215—62no—
366#215—64no—
367#215—62no—
368#214—62no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3#6711yescharacteristic
393C4×Dic3#6711yescharacteristic
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403#204—62no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—22no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3C2×SD1612yes—
414D32—48no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×SD1612yes—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×SD1612yes—
428C22×D4—91no—
429C23×C4—181no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×SD16—91no—
433C2×SD16—91no—
434C4⋊Q8—31no—
435C4⋊Q8—31no—
436#125—61no—
437C22⋊Q8—31no—
438C22⋊Q8—31no—
439C22⋊Q8—61no—
440C4×Q8—31no—
441C4×Q8—61no—
442C4×Q8D3211yescharacteristic, complemented
443C4×D4—31no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—181no—
448C4×D4—181no—
449#117—61no—
450C2×C4⋊C4—91no—
451C2×C22⋊C4—181no—
452C2×C42—31no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—91no—
458C4⋊C8—91no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469C4×C8—31no—
470C4×C8—91no—
471C23×C3—31no—
472C23×C3—61no—
473C22×D3—21no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3—122no—
480C22×D3—122no—
481C22×D3—122no—
482C22×D3—122no—
483C22×D3C2×#6711yescharacteristic
484C3×Q8—22no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—122no—
493C3×D4—32no—
494C3×D4—61no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—34no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—121no—
514C2×C3×C4—122no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—64no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—122no—
529C2×Dic3—122no—
530C2×Dic3C2×#6711yescharacteristic
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533D12—21no—
534D12—32no—
535D12—32no—
536D12—62no—
537D12—64no—
538D12—61no—
539D12—61no—
540D12—121no—
541D12#23512yes—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—41no—
545C4×D3—42no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—242no—
553C4×D3#21514yescomplemented
554Dic6—21no—
555Dic6—21no—
556Dic6—42no—
557C3×C8—61no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—62no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—121no—
567C2×C32#52511yescharacteristic
568C2×C32C22×SD1611yescharacteristic
569C2×C32#57511yescharacteristic
570C3⋊D3—42no—
571C3×D3—22no—
572C3×D3—42no—
573C24—181no—
574C2×Q8—31no—
575C2×Q8—61no—
576C2×Q8C2×D3211yescharacteristic
577C2×D4—31no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4—182no—
581C2×D4—182no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—364no—
591SD16—62no—
592SD16—182no—
593SD16—182no—
594SD16—182no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—91no—
598C2×C8—91no—
599C4⋊C4—21no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—91no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—21no—
618C42—31no—
619C42—31no—
620C42—31no—
621C42—61no—
622C42C2×D3211yescharacteristic
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—62no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C22×#6711yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—122no—
640C2×D3—128no—
641C2×D3—128no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—241no—
647C2×D3—241no—
648C2×D3C2×#21512yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—22no—
654C3×C4—32no—
655C3×C4—41no—
656C3×C4—42no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4D3×SD1612yes—
668C3×C4C2×#21512yes—
669C3×C4C2×#23511yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672C3×C4D3×#4111yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3C2×#21512yes—
682C32#310111yescharacteristic, complemented, Sylow
683C23—31no—
684C23—61no—
685C23—184no—
686C23—181no—
687C23—362no—
688C23—362no—
689Q8—21no—
690Q8—21no—
691Q8—61no—
692Q8—61no—
693Q8—122no—
694D4—32no—
695D4—61no—
696D4—92no—
697D4—184no—
698D4—181no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—34no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—121no—
711C2×C4—122no—
712C2×C4—181no—
713C2×C4—362no—
714C2×C4—362no—
715C2×C4—362no—
716C2×C4—362no—
717C2×C4D3×#6711yescharacteristic
718C2×C4D3×#6711yescharacteristic
719C2×C4C22×D3211yescharacteristic
720C8—61no—
721C8—61no—
722C8—181no—
723C8—181no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—62no—
728C2×C3—122no—
729C2×C3#554711yescharacteristic
730C2×C3C2×D3×SD1611yescharacteristic
731C2×C3#576811yescharacteristic
732C2×C3C22×#21511yescharacteristic
733C2×C3#582211yescharacteristic
734C2×C3#582811yescharacteristic
735D3—22no—
736D3—42no—
737D3—122no—
738D3—122no—
739D3—242no—
740C22—32no—
741C22—61no—
742C22—61no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—182no—
747C22—368no—
748C22—361no—
749C22—361no—
750C22C2×D3×#6711yescharacteristic
751C4—21no—
752C4—32no—
753C4—41no—
754C4—41no—
755C4—61no—
756C4—61no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4—361no—
761C4D3×#21512yes—
762C4D3×#23511yescharacteristic
763C4#6430611yescharacteristic
764C3—21no—
765C3#7965111yescharacteristic, complemented
766C3#8335111yescharacteristic, complemented
767C2—62no—
768C2—122no—
769C2—362no—
770C2#1059506011yescharacteristic
771C2C2×D3×#21511yescharacteristic
772C2#1059545311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4×Q8D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5578C2semidirect
3. C4×#3755C2semidirect
4. C3×C4×#215C2semidirect
6. #10591565C2semidirect
7. #10591564C2semidirect
8. #10591549C2semidirect
10. #10590466C2semidirect
11. #10590465C2semidirect
12. #10590439C2semidirect
13. C4×#3717C2semidirect
14. C4×#3715C2semidirect
15. #10590261C2semidirect
20. C32×C4×Q8C22semidirect
24. C3×#944C22semidirect
29. C3×#888C22semidirect
34. C3×C4×Dic6C22semidirect
43. #63662C22semidirect
45. #63635C22semidirect
46. C4×C3⋊(C3⋊C8)C22semidirect
47. C3×#835C22semidirect
49. C3×#808C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
62. #5578D3semidirect
81. C4×#215D3semidirect
157. C3×C4×Q8C2×D3semidirect
158. C3×C4×Q8C2×D3semidirect
163. #944C2×D3semidirect
181. #888C2×D3semidirect
195. C4×Dic6C2×D3semidirect
205. #835C2×D3semidirect
229. #808C2×D3semidirect
235. C4×C3⋊C8C2×D3semidirect
265. C3×C4×D3SD16semidirect
442. C4×Q8D32semidirect
553. C4×D3#215semidirect
682. C32#3101semidirect
765. C3#79651semidirect
766. C3#83351semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
C4×D3×D122
C4×#37552
C3×C4×#2152
#105916512
#105915652
#105915642
#105915492
#105905962
#105904662
#105904652
#105904392
C4×#37172
C4×#37152
#105902612
#833513
#796513