Finite Group Databasebeta

← C2×#10595007 #11902723

Subgroups — C2×#10595007 #11902723

Order 1152.

3685 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64139C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63979C212yesmaximal, complemented
6C2×#63958C212yesmaximal, complemented
7C2×#63911C211yesmaximal, characteristic, complemented
8C2×#63908C211yesmaximal, characteristic, complemented
9C2×#63906C212yesmaximal, complemented
10#10595007C2116yesmaximal, direct product factor
11C2×#63904C212yesmaximal, complemented
12C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
13C2×#5834—31nomaximal
14C2×#5553—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2212yes—
20C2×C3×#235—28no—
21C2×C3×#235C2218yescomplemented
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2212yes—
25C22×C3×Dic6C2211yescharacteristic
26C22×#626C2212yes—
27C22×#626C2212yes—
28C22×#626C2212yes—
29C22×#625C2212yes—
30C22×#624C2212yes—
31C2×#3799—28no—
32C2×#3799C2218yescomplemented
33#64139C2218yescomplemented
34C2×#3752C2212yes—
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C3×C4×#67C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41#63979C22116yescomplemented
42C2×Dic3⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44#63958C22116yescomplemented
45C2×Dic32C2212yes—
46#63911C2218yescomplemented
47#63908C2218yescomplemented
48#63906C22116yescomplemented
49#63904C22116yescomplemented
50Dic3×Dic6C2218yescomplemented
51C22×C3×#41—31no—
52C22×#239—31no—
53C22×#235—31no—
54C22×#235D311yescharacteristic, complemented
55C2×C3×C4×D4—31no—
56#5834—316no—
57C2×Q8×Dic3—31no—
58C2×#940—32no—
59C2×#940—32no—
60C2×#940—31no—
61C2×#938—31no—
62C2×#938—32no—
63C2×#930—31no—
64C2×#930—31no—
65C2×#930—31no—
66C2×#930—32no—
67C2×#930—61no—
68C2×C4×#67—32no—
69C2×C4×#67D311yescharacteristic, complemented
70#5553—316no—
71C2×#893—32no—
72C2×#884—32no—
73C2×#884—32no—
74C2×#874—31no—
75C2×C4×Dic6—31no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2312yes—
80C22×C32×C4—24no—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2314yes—
83C22×C32×C4C2311yescharacteristic
84C2×#638—44no—
85C2×#638C2318yes—
86C22×C3⋊Dic3C2312yes—
87C2×C4⋊(C3⋊D3)—24no—
88C2×C4⋊(C3⋊D3)C2314yes—
89C2×C3×#67—28no—
90C2×C3×#67—24no—
91C2×C3×#67C2314yes—
92C2×C3×#67C2318yes—
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2311yescharacteristic
97C3×#235—232no—
98C2×C3×D12—24no—
99C2×C3×D12C2314yes—
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3—28no—
102C2×C3×C4×D3C2314yes—
103C2×C3×C4×D3C2318yes—
104C2×C3×Dic6D418yescomplemented
105C2×C3×Dic6C2314yes—
106C2×#626—28no—
107C2×#626—28no—
108C2×#626—44no—
109C2×#626C2318yes—
110C2×#626C2318yes—
111C2×#626C2318yes—
112C2×#625—44no—
113C2×#625C2318yes—
114C2×#624—28no—
115C2×#624C2318yes—
116#3799—232no—
117#3752C2318yes—
118C4⋊(C3⋊Dic3)C2314yes—
119C3×#217C2314yes—
120C3×(C2×D3)⋊C4C2314yes—
121C3×Dic3⋊C4C2314yes—
122C3×C4×Dic3C2314yes—
123Dic3⋊Dic3C2318yes—
124(C2×D3)⋊Dic3C2318yes—
125Dic32C2318yes—
126C2×#550—91noSylow
127C2×C3×#41—38no—
128C2×C3×#41—68no—
129C22×C3×Q8—31no—
130C22×C3×D4—32no—
131C22×C3×D4—31no—
132C22×C3×D4—31no—
133C23×C3×C4—21no—
134C23×C3×C4—31no—
135C23×C3×C4—32no—
136C23×C3×C4C2×D311yescharacteristic
137C23×C3×C4C2×D311yescharacteristic
138C22×#67—32no—
139C22×#67—32no—
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—32no—
144C22×#67—32no—
145C22×#67—62no—
146C22×#67C2×D312yes—
147C22×#67C2×D311yescharacteristic
148C2×#239—38no—
149C2×#239—68no—
150C2×#235—28no—
151C2×#235—38no—
152C2×#235—68no—
153C2×#235C2×D318yescomplemented
154C22×D12—32no—
155C22×D12—32no—
156C22×D12—31no—
157C22×D12—31no—
158C22×D12—32no—
159C22×D12—61no—
160C22×D12C2×D311yescharacteristic
161C22×C4×D3—32no—
162C22×C4×D3—32no—
163C22×C4×D3C2×D312yes—
164C22×C4×D3C2×D311yescharacteristic
165C22×Dic6C2×D311yescharacteristic
166C3×C4×D4—38no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C42—31no—
171C2×#217—32no—
172C2×#217C2×D311yescharacteristic
173Q8×Dic3—38no—
174#940—316no—
175#940—316no—
176#940—38no—
177#938—38no—
178#938—316no—
179#930—38no—
180#930—38no—
181#930—38no—
182#930—316no—
183#930—68no—
184C4×#67—316no—
185C4×#67C2×D318yescomplemented
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—62no—
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—32no—
194C2×C4⋊Dic3—61no—
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4C2×D311yescharacteristic
197C2×C4×Dic3—32no—
198C2×C4×Dic3—32no—
199C2×C4×Dic3C2×D311yescharacteristic
200#893—316no—
201#884—316no—
202#884—316no—
203#874—38no—
204C4×Dic6—38no—
205C23×C32—22no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32C2412yes—
209C23×C32C2411yescharacteristic
210C22×C3⋊D3—24no—
211C22×C3⋊D3—24no—
212C22×C3⋊D3—24no—
213C22×C3⋊D3C2414yes—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—24no—
217C22×C3×D3—22no—
218C22×C3×D3—22no—
219C22×C3×D3—24no—
220C22×C3×D3C2414yes—
221C22×C3×D3C2412yes—
222C2×C32×C4—22no—
223C2×C32×C4—28no—
224C2×C32×C4C2×D414yes—
225C2×C32×C4C2412yes—
226C2×C32×C4C2412yes—
227#638—48no—
228C2×C3⋊Dic3—24no—
229C2×C3⋊Dic3C2414yes—
230C4⋊(C3⋊D3)—28no—
231C3×#67—216no—
232C3×#67—28no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3C2×D418yes—
236C2×C3×Dic3#4114yescomplemented
237C2×C3×Dic3C2412yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C3×D12—28no—
242C3×C4×D3—28no—
243C3×C4×D3—216no—
244C3×Dic6C2×D4116yescomplemented
245#626—216no—
246#626—216no—
247#626—48no—
248#625—48no—
249#624—216no—
250C22×#41—31no—
251C22×#41—91no—
252#550—916no—
253C2×#127—91no—
254C2×#127—92no—
255C2×#121—92no—
256C2×#121—92no—
257C2×#121—91no—
258C2×#121—91no—
259C2×C4×Q8—91no—
260C2×C4×D4—31no—
261C2×C4×D4—92no—
262C24×C3—21no—
263C24×C3—32no—
264C24×C3—31no—
265C24×C3C22×D311yescharacteristic
266C24×C3C22×D311yescharacteristic
267C23×D3—32no—
268C23×D3—32no—
269C23×D3—62no—
270C23×D3C22×D312yes—
271C23×D3C22×D311yescharacteristic
272C3×#41—632no—
273C2×C3×Q8—38no—
274C2×C3×Q8—34no—
275C2×C3×D4—38no—
276C2×C3×D4—34no—
277C2×C3×D4—34no—
278C2×C3×D4—64no—
279C2×C3×D4—68no—
280C2×C3×D4—64no—
281C22×C3×C4—24no—
282C22×C3×C4—24no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—24no—
286C22×C3×C4—31no—
287C22×C3×C4—32no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—38no—
291C22×C3×C4—34no—
292C22×C3×C4—44no—
293C22×C3×C4—68no—
294C22×C3×C4—64no—
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D314yes—
298C22×C3×C4C22×D314yes—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C2×#67—24no—
302C2×#67—28no—
303C2×#67—38no—
304C2×#67—38no—
305C2×#67—38no—
306C2×#67—38no—
307C2×#67—38no—
308C2×#67—38no—
309C2×#67—38no—
310C2×#67—68no—
311C2×#67—68no—
312C2×#67—68no—
313C2×#67—124no—
314C2×#67—124no—
315C2×#67—124no—
316C2×#67—124no—
317C2×#67—124no—
318C2×#67—128no—
319C2×#67C22×D318yes—
320C2×#67C22×D314yes—
321C22×Dic3—32no—
322C22×Dic3—32no—
323C22×Dic3—62no—
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D312yes—
328#239—632no—
329#235—232no—
330#235—632no—
331C2×D12—24no—
332C2×D12—38no—
333C2×D12—38no—
334C2×D12—34no—
335C2×D12—34no—
336C2×D12—38no—
337C2×D12—64no—
338C2×D12—68no—
339C2×D12—68no—
340C2×D12—64no—
341C2×D12—64no—
342C2×D12—124no—
343C2×D12—124no—
344C2×D12C22×D314yes—
345C2×C4×D3—24no—
346C2×C4×D3—28no—
347C2×C4×D3—38no—
348C2×C4×D3—38no—
349C2×C4×D3—68no—
350C2×C4×D3—68no—
351C2×C4×D3C22×D318yes—
352C2×C4×D3C22×D314yes—
353C2×Dic6#6718yescomplemented
354C2×Dic6C22×D314yes—
355C3×C4⋊C4—34no—
356C3×C22⋊C4—34no—
357C3×C22⋊C4—34no—
358C3×C42—34no—
359#217—38no—
360#217C22×D314yes—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—68no—
365(C2×D3)⋊C4C22×D314yes—
366C4⋊Dic3—34no—
367C4⋊Dic3—34no—
368C4⋊Dic3—38no—
369C4⋊Dic3—64no—
370Dic3⋊C4—38no—
371Dic3⋊C4C22×D314yes—
372C4×Dic3—38no—
373C4×Dic3—38no—
374C4×Dic3C22×D314yes—
375C22×C32—22no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—44no—
379C22×C32C22×D412yes—
380C22×C32C2×#4112yes—
381C22×C32H(5,𝔽2)12yes—
382C22×C32C2511yescharacteristic
383C2×C3⋊D3—24no—
384C2×C3⋊D3—24no—
385C2×C3⋊D3—24no—
386C2×C3⋊D3—48no—
387C2×C3×D3—22no—
388C2×C3×D3—24no—
389C2×C3×D3—24no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—24no—
393C2×C3×D3—44no—
394C2×C3×D3—48no—
395C32×C4—22no—
396C32×C4C22×D414yes—
397C3⋊Dic3—24no—
398C3×Dic3—22no—
399C3×Dic3—22no—
400C3×Dic3C22×D418yes—
401C3×Dic3C2×#4114yescomplemented
402C2×#41—38no—
403C2×#41—68no—
404C2×#41—98no—
405C2×#41—188no—
406C22×Q8—31no—
407C22×D4—31no—
408C22×D4—32no—
409C22×D4—31no—
410C22×D4—92no—
411C22×D4—92no—
412C22×D4—92no—
413C22×D4—92no—
414C22×D4—92no—
415C22×D4—91no—
416C23×C4—31no—
417C23×C4—32no—
418C23×C4—92no—
419C23×C4D3211yescharacteristic
420#127—98no—
421#127—916no—
422#121—916no—
423#121—916no—
424#121—98no—
425#121—98no—
426C4×Q8—98no—
427C4×D4—38no—
428C4×D4—916no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—92no—
431C2×C4⋊C4—91no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—92no—
435C2×C22⋊C4—92no—
436C2×C42—31no—
437C2×C42—92no—
438C23×C3—24no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—21no—
447C23×C3—34no—
448C23×C3—32no—
449C23×C3—42no—
450C23×C3—42no—
451C23×C3—64no—
452C23×C3—64no—
453C23×C3—62no—
454C23×C3—64no—
455C23×C3—62no—
456C23×C3—62no—
457C23×C3C23×D312yes—
458C23×C3C23×D312yes—
459C23×C3C23×D311yescharacteristic
460C23×C3C23×D311yescharacteristic
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—24no—
464C22×D3—24no—
465C22×D3—22no—
466C22×D3—24no—
467C22×D3—34no—
468C22×D3—34no—
469C22×D3—64no—
470C22×D3—64no—
471C22×D3—64no—
472C22×D3—64no—
473C22×D3—64no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—124no—
477C22×D3—124no—
478C22×D3—124no—
479C22×D3C23×D314yes—
480C22×D3C23×D312yes—
481C3×Q8—316no—
482C3×D4—68no—
483C3×D4—616no—
484C3×D4—68no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—28no—
488C2×C3×C4—28no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—24no—
492C2×C3×C4—38no—
493C2×C3×C4—34no—
494C2×C3×C4—32no—
495C2×C3×C4—34no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—48no—
499C2×C3×C4—42no—
500C2×C3×C4—616no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—68no—
504C2×C3×C4D3×D414yes—
505C2×C3×C4C2×#6714yes—
506C2×C3×C4C23×D312yes—
507C2×C3×C4C23×D312yes—
508C2×C3×C4C23×D312yes—
509C2×C3×C4C23×D312yes—
510#67—28no—
511#67—216no—
512#67—616no—
513#67—616no—
514#67—128no—
515#67—128no—
516#67—128no—
517#67—128no—
518#67—128no—
519#67—1216no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—34no—
523C2×Dic3—34no—
524C2×Dic3—64no—
525C2×Dic3—64no—
526C2×Dic3—64no—
527C2×Dic3—124no—
528C2×Dic3#23514yescomplemented
529C2×Dic3C2×#6718yes—
530C2×Dic3C23×D312yes—
531C2×Dic3C23×D312yes—
532C2×Dic3C23×D312yes—
533C2×Dic3C23×D314yes—
534D12—28no—
535D12—616no—
536D12—616no—
537D12—68no—
538D12—68no—
539D12—128no—
540D12—128no—
541C4×D3—28no—
542C4×D3—216no—
543C4×D3—616no—
544C4×D3—616no—
545Dic6C2×#67116yescomplemented
546C2×C32—42no—
547C2×C32#55014yescomplemented
548C2×C32C23×D411yescharacteristic
549C2×C32C22×#4111yescharacteristic
550C2×C32C2×H(5,𝔽2)11yescharacteristic
551C3⋊D3—44no—
552C3×D3—44no—
553C3×D3—42no—
554C24—31no—
555C24—32no—
556C24—92no—
557C24C2×D3211yescharacteristic
558#41—632no—
559#41—1832no—
560C2×Q8—34no—
561C2×Q8—38no—
562C2×D4—34no—
563C2×D4—38no—
564C2×D4—34no—
565C2×D4—68no—
566C2×D4—64no—
567C2×D4—64no—
568C2×D4—98no—
569C2×D4—98no—
570C2×D4—98no—
571C2×D4—98no—
572C2×D4—98no—
573C2×D4—94no—
574C2×D4—188no—
575C2×D4—188no—
576C2×D4—184no—
577C2×D4—364no—
578C2×D4—364no—
579C2×D4—364no—
580C22×C4—24no—
581C22×C4—31no—
582C22×C4—32no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—34no—
586C22×C4—38no—
587C22×C4—68no—
588C22×C4—64no—
589C22×C4—98no—
590C22×C4—92no—
591C22×C4—188no—
592C22×C4C2×D3214yes—
593C22×C4C2×D3211yescharacteristic
594C22×C4C2×D3211yescharacteristic
595C4⋊C4—34no—
596C4⋊C4—98no—
597C4⋊C4—94no—
598C22⋊C4—34no—
599C22⋊C4—34no—
600C22⋊C4—98no—
601C22⋊C4—98no—
602C42—34no—
603C42—98no—
604C22×C3—24no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—21no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—48no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3—64no—
621C22×C3—64no—
622C22×C3—62no—
623C22×C3—62no—
624C22×C3—64no—
625C22×C3—62no—
626C22×C3—128no—
627C22×C3—124no—
628C22×C3C2×#23512yes—
629C22×C3C2×D3×D412yes—
630C22×C3D3×#4112yes—
631C22×C3#100912yes—
632C22×C3#100912yes—
633C22×C3C22×#6712yes—
634C22×C3C24×D311yescharacteristic
635C22×C3C24×D311yescharacteristic
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—24no—
639C2×D3—24no—
640C2×D3—22no—
641C2×D3—24no—
642C2×D3—44no—
643C2×D3—48no—
644C2×D3—64no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—64no—
648C2×D3—64no—
649C2×D3—64no—
650C2×D3—124no—
651C2×D3—124no—
652C2×D3—124no—
653C2×D3—128no—
654C2×D3—128no—
655C2×D3—248no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—24no—
659C3×C4—38no—
660C3×C4—34no—
661C3×C4—42no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4C2×D3×D414yes—
665C3×C4C22×#6714yes—
666Dic3—22no—
667Dic3—22no—
668Dic3—64no—
669Dic3—64no—
670Dic3—124no—
671Dic3C2×#23514yescomplemented
672Dic3C22×#6718yes—
673C32C2×#55011yescharacteristic, complemented, Sylow
674C23—22no—
675C23—22no—
676C23—22no—
677C23—32no—
678C23—34no—
679C23—62no—
680C23—64no—
681C23—64no—
682C23—62no—
683C23—64no—
684C23—62no—
685C23—94no—
686C23—184no—
687C23—184no—
688C23—184no—
689C23C22×D3212yes—
690C23C22×D3211yescharacteristic
691Q8—316no—
692D4—616no—
693D4—68no—
694D4—68no—
695D4—1816no—
696D4—1816no—
697D4—188no—
698D4—368no—
699D4—368no—
700D4—368no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—34no—
704C2×C4—38no—
705C2×C4—32no—
706C2×C4—34no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—616no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—68no—
713C2×C4—94no—
714C2×C4—1816no—
715C2×C4—184no—
716C2×C4D3×#6714yes—
717C2×C4C22×D3212yes—
718C2×C4C22×D3212yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—24no—
723C2×C3—44no—
724C2×C3—42no—
725C2×C3—42no—
726C2×C3—122no—
727C2×C3—124no—
728C2×C3#555314yescomplemented
729C2×C3#583414yescomplemented
730C2×C3C22×#23511yescharacteristic
731C2×C3C22×D3×D411yescharacteristic
732C2×C3C2×D3×#4111yescharacteristic
733C2×C3C2×#100911yescharacteristic
734C2×C3C2×#100911yescharacteristic
735C2×C3C23×#6711yescharacteristic
736D3—44no—
737D3—42no—
738D3—124no—
739D3—124no—
740D3—244no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22—62no—
746C22—64no—
747C22—64no—
748C22—62no—
749C22—64no—
750C22—62no—
751C22—124no—
752C22—128no—
753C22—184no—
754C22—184no—
755C22—184no—
756C22—368no—
757C22D3×#23512yes—
758C22#6430812yes—
759C22C2×D3×#6712yes—
760C22C23×D3211yescharacteristic
761C4—22no—
762C4—34no—
763C4—38no—
764C4—62no—
765C4—62no—
766C4—184no—
767C4C2×D3×#6714yes—
768C3—21no—
769C3C2×#555311yescharacteristic, complemented
770C3C2×#583411yescharacteristic, complemented
771C2—42no—
772C2—122no—
773C2—124no—
774C2—364no—
775C2#1059500714yesdirect product factor
776C2C2×D3×#23511yescharacteristic
777C2C2×#6430811yescharacteristic
778C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×#3799C2semidirect
3. C2×#64139C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63979C2semidirect
6. C2×#63958C2semidirect
7. C2×#63911C2semidirect
8. C2×#63908C2semidirect
9. C2×#63906C2semidirect
10. #10595007C2direct (N × H)
11. C2×#63904C2semidirect
12. C2×Dic3×Dic6C2semidirect
21. C2×C3×#235C22semidirect
32. C2×#3799C22semidirect
33. #64139C22semidirect
37. C3×C4×#67C22semidirect
41. #63979C22semidirect
44. #63958C22semidirect
46. #63911C22semidirect
47. #63908C22semidirect
48. #63906C22semidirect
49. #63904C22semidirect
50. Dic3×Dic6C22semidirect
54. C22×#235D3semidirect
69. C2×C4×#67D3semidirect
104. C2×C3×Dic6D4semidirect
153. C2×#235C2×D3semidirect
185. C4×#67C2×D3semidirect
236. C2×C3×Dic3#41semidirect
244. C3×Dic6C2×D4semidirect
353. C2×Dic6#67semidirect
401. C3×Dic3C2×#41semidirect
528. C2×Dic3#235semidirect
545. Dic6C2×#67semidirect
547. C2×C32#550semidirect
671. Dic3C2×#235semidirect
673. C32C2×#550semidirect
728. C2×C3#5553semidirect
729. C2×C3#5834semidirect
769. C3C2×#5553semidirect
770. C3C2×#5834semidirect
775. C2#10595007direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#37992
C2×#641392
C2×C3×C4×#672
C2×#639792
C2×#639582
C2×#639112
C2×#639082
C2×#639062
#105950072
C2×#639042
C2×Dic3×Dic62
C2×#58343
C2×#55533