Finite Group Databasebeta

← C2×#10595006 #11902721

Subgroups — C2×#10595006 #11902721

Order 1152.

3685 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C2×#63979C212yesmaximal, complemented
6C2×#63970C212yesmaximal, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63914C211yesmaximal, characteristic, complemented
9C2×#63906C212yesmaximal, complemented
10#10595006C2116yesmaximal, direct product factor
11C2×#63879C212yesmaximal, complemented
12C2×#63843C211yesmaximal, characteristic, complemented
13C2×#5834—31nomaximal
14C2×#5599—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yes—
20C2×C3×#235—28no—
21C2×C3×#235C2218yescomplemented
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2212yes—
25C22×C3×Dic6C2211yescharacteristic
26C22×#626C2212yes—
27C22×#626C2212yes—
28C22×#625C2212yes—
29C22×#625C2212yes—
30C22×D3×Dic3C2212yes—
31C2×#3796—28no—
32C2×#3796C2218yescomplemented
33C2×#3757C2211yescharacteristic
34C4×#638C2218yescomplemented
35C2×#3752C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38C3×#930C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2212yes—
40C2×C3×C4⋊Dic3C2211yescharacteristic
41#63979C22116yescomplemented
42#63970C22116yescomplemented
43C2×Dic3⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×Dic32C2212yes—
46#63916C2218yescomplemented
47#63914C2218yescomplemented
48#63906C22116yescomplemented
49#63879C22116yescomplemented
50#63843C2218yescomplemented
51C22×C3×#41—31no—
52C22×#239—31no—
53C22×#237—31no—
54C22×#235D311yescharacteristic, complemented
55C2×C3×#121—31no—
56#5834—316no—
57C2×Q8×Dic3—31no—
58C2×#940—32no—
59C2×#940—32no—
60C2×#940—31no—
61C2×#940—31no—
62C2×#939—32no—
63C2×#938—32no—
64C2×#938—31no—
65C2×#930—32no—
66C2×#930D311yescharacteristic, complemented
67C2×C4×#67—31no—
68C2×C4×#67—31no—
69C2×C4×#67—32no—
70C2×C4×#67—61no—
71#5599—316no—
72C2×#895—31no—
73C2×#887—31no—
74C2×#884—32no—
75C2×#67⋊C4—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C23×C3×D3C2312yes—
80C22×C32×C4—24no—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2314yes—
83C22×C32×C4C2311yescharacteristic
84C2×#638—24no—
85C2×#638C2314yes—
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C2×C4×C3⋊D3—24no—
90C2×C4×C3⋊D3C2314yes—
91C2×C3×#67—28no—
92C2×C3×#67—44no—
93C2×C3×#67C2318yes—
94C2×C3×#67C2318yes—
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2312yes—
97C3×#235—232no—
98C2×C3×D12—24no—
99C2×C3×D12—24no—
100C2×C3×D12C2314yes—
101C2×C3×D12C2314yes—
102C2×C3×C4×D3—28no—
103C2×C3×C4×D3C2318yes—
104C2×C3×Dic6D418yescomplemented
105C2×C3×Dic6C2314yes—
106C2×#626—28no—
107C2×#626—44no—
108C2×#626C2318yes—
109C2×#626C2318yes—
110C2×#625—28no—
111C2×#625—44no—
112C2×#625C2318yes—
113C2×#625C2318yes—
114C2×D3×Dic3—28no—
115C2×D3×Dic3C2318yes—
116#3796—232no—
117#3757C2314yes—
118#3752C2314yes—
119#3750C2314yes—
120C4×C3⋊Dic3C2314yes—
121C3×(C2×D3)⋊C4C2318yes—
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—32no—
132C22×C3×D4—31no—
133C22×C3×D4—31no—
134C23×C3×C4—21no—
135C23×C3×C4—32no—
136C23×C3×C4C2×D311yescharacteristic
137C23×C3×C4C2×D311yescharacteristic
138C22×#67—31no—
139C22×#67—31no—
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—32no—
144C22×#67—32no—
145C22×#67—32no—
146C22×#67—61no—
147C22×#67C2×D312yes—
148C22×#67C2×D312yes—
149C23×Dic3—32no—
150C2×#239—38no—
151C2×#239—68no—
152C2×#237—38no—
153C2×#237—68no—
154C2×#235—28no—
155C2×#235C2×D318yescomplemented
156C22×D12—32no—
157C22×D12—32no—
158C22×D12C2×D311yescharacteristic
159C22×D12C2×D311yescharacteristic
160C22×C4×D3—32no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—61no—
164C22×C4×D3C2×D312yes—
165C22×Dic6C2×D311yescharacteristic
166C3×#121—38no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—32no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—32no—
172C2×#217—61no—
173Q8×Dic3—38no—
174#940—316no—
175#940—316no—
176#940—38no—
177#940—38no—
178#939—316no—
179#938—316no—
180#938—38no—
181#930—316no—
182#930C2×D318yescomplemented
183C4×#67—38no—
184C4×#67—38no—
185C4×#67—316no—
186C4×#67—68no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4C2×D312yes—
192C2×C4⋊Dic3—32no—
193C2×C4⋊Dic3C2×D311yescharacteristic
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—61no—
198C2×C4×Dic3—31no—
199C2×C4×Dic3—31no—
200C2×C4×Dic3—32no—
201C2×C4×Dic3—32no—
202C2×C4×Dic3—61no—
203#895—38no—
204#887—38no—
205#884—316no—
206#67⋊C4—316no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32—22no—
210C23×C32C2412yes—
211C23×C32C2411yescharacteristic
212C22×C3⋊D3—22no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3—22no—
215C22×C3⋊D3C2412yes—
216C22×C3×D3—24no—
217C22×C3×D3—24no—
218C22×C3×D3—24no—
219C22×C3×D3—24no—
220C22×C3×D3—24no—
221C22×C3×D3—24no—
222C22×C3×D3C2414yes—
223C22×C3×D3C2414yes—
224C2×C32×C4—22no—
225C2×C32×C4—28no—
226C2×C32×C4C2×D414yes—
227C2×C32×C4C2412yes—
228C2×C32×C4C2412yes—
229#638—28no—
230C2×C3⋊Dic3—22no—
231C2×C3⋊Dic3—22no—
232C2×C3⋊Dic3#4114yescomplemented
233C2×C3⋊Dic3C2412yes—
234C2×C3⋊Dic3C2412yes—
235C2×C3⋊Dic3C2412yes—
236C4×C3⋊D3—28no—
237C3×#67—216no—
238C3×#67—48no—
239C2×C3×Dic3—24no—
240C2×C3×Dic3C2×D418yes—
241C2×C3×Dic3C2414yes—
242C2×C3×Dic3C2414yes—
243C3×D12—28no—
244C3×D12—28no—
245C3×C4×D3—216no—
246C3×Dic6C2×D4116yescomplemented
247#626—216no—
248#626—48no—
249#625—216no—
250#625—48no—
251D3×Dic3—216no—
252C22×#41—31no—
253C22×#41—91no—
254#550—916no—
255C2×#127—92no—
256C2×#127—91no—
257C2×#121—31no—
258C2×#121—92no—
259C2×#121—91no—
260C2×#121—92no—
261C2×C4×Q8—91no—
262C2×C4×D4—92no—
263C2×C4×D4—91no—
264C24×C3—21no—
265C24×C3—32no—
266C24×C3—32no—
267C24×C3C22×D311yescharacteristic
268C24×C3C22×D311yescharacteristic
269C23×D3—31no—
270C23×D3—31no—
271C23×D3—61no—
272C23×D3C22×D312yes—
273C23×D3C22×D312yes—
274C3×#41—632no—
275C2×C3×Q8—38no—
276C2×C3×Q8—34no—
277C2×C3×D4—38no—
278C2×C3×D4—38no—
279C2×C3×D4—34no—
280C2×C3×D4—34no—
281C2×C3×D4—68no—
282C2×C3×D4—64no—
283C2×C3×D4—64no—
284C2×C3×D4—124no—
285C22×C3×C4—24no—
286C22×C3×C4—24no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—24no—
290C22×C3×C4—32no—
291C22×C3×C4—32no—
292C22×C3×C4—38no—
293C22×C3×C4—44no—
294C22×C3×C4—68no—
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—28no—
302C2×#67—34no—
303C2×#67—34no—
304C2×#67—38no—
305C2×#67—38no—
306C2×#67—38no—
307C2×#67—38no—
308C2×#67—38no—
309C2×#67—38no—
310C2×#67—44no—
311C2×#67—64no—
312C2×#67—68no—
313C2×#67—68no—
314C2×#67—64no—
315C2×#67—64no—
316C2×#67—68no—
317C2×#67—68no—
318C2×#67—124no—
319C2×#67—124no—
320C2×#67—124no—
321C2×#67C22×D318yes—
322C2×#67C22×D318yes—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—38no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—68no—
334C22×Dic3C22×D312yes—
335C22×Dic3C22×D312yes—
336#239—632no—
337#237—632no—
338#235—232no—
339C2×D12—24no—
340C2×D12—24no—
341C2×D12—38no—
342C2×D12—38no—
343C2×D12—68no—
344C2×D12—124no—
345C2×D12C22×D314yes—
346C2×D12C22×D314yes—
347C2×C4×D3—28no—
348C2×C4×D3—38no—
349C2×C4×D3—34no—
350C2×C4×D3—34no—
351C2×C4×D3—64no—
352C2×C4×D3—68no—
353C2×C4×D3—64no—
354C2×C4×D3—64no—
355C2×C4×D3—124no—
356C2×C4×D3C22×D318yes—
357C2×Dic6#6718yescomplemented
358C2×Dic6C22×D314yes—
359C3×C4⋊C4—34no—
360C3×C22⋊C4—38no—
361#217—34no—
362#217—34no—
363#217—38no—
364#217—64no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—34no—
367(C2×D3)⋊C4—34no—
368(C2×D3)⋊C4—64no—
369(C2×D3)⋊C4C22×D318yes—
370C4⋊Dic3—38no—
371C4⋊Dic3C22×D314yes—
372Dic3⋊C4—34no—
373Dic3⋊C4—34no—
374Dic3⋊C4—38no—
375Dic3⋊C4—64no—
376C4×Dic3—34no—
377C4×Dic3—34no—
378C4×Dic3—38no—
379C4×Dic3—38no—
380C4×Dic3—64no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32—22no—
384C22×C32—44no—
385C22×C32C22×D412yes—
386C22×C32C2×#4112yes—
387C22×C32H(5,𝔽2)12yes—
388C22×C32C2511yescharacteristic
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—44no—
393C2×C3×D3—24no—
394C2×C3×D3—24no—
395C2×C3×D3—24no—
396C2×C3×D3—24no—
397C2×C3×D3—24no—
398C2×C3×D3—24no—
399C2×C3×D3—48no—
400C2×C3×D3—48no—
401C32×C4—22no—
402C32×C4C22×D414yes—
403C3⋊Dic3—22no—
404C3⋊Dic3—22no—
405C3⋊Dic3C2×#4114yescomplemented
406C3×Dic3—24no—
407C3×Dic3C22×D418yes—
408C2×#41—38no—
409C2×#41—68no—
410C2×#41—98no—
411C2×#41—188no—
412C22×Q8—31no—
413C22×D4—32no—
414C22×D4—32no—
415C22×D4—31no—
416C22×D4—31no—
417C22×D4—92no—
418C22×D4—92no—
419C22×D4—92no—
420C22×D4—91no—
421C22×D4—92no—
422C23×C4—32no—
423C23×C4—92no—
424C23×C4—91no—
425C23×C4D3211yescharacteristic
426#127—916no—
427#127—98no—
428#121—38no—
429#121—916no—
430#121—98no—
431#121—916no—
432C4×Q8—98no—
433C4×D4—916no—
434C4×D4—98no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—92no—
437C2×C4⋊C4—91no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C42—92no—
443C2×C42—91no—
444C23×C3—24no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—21no—
453C23×C3—34no—
454C23×C3—34no—
455C23×C3—42no—
456C23×C3—42no—
457C23×C3—64no—
458C23×C3—64no—
459C23×C3—64no—
460C23×C3—64no—
461C23×C3—64no—
462C23×C3—64no—
463C23×C3C23×D312yes—
464C23×C3C23×D312yes—
465C23×C3C23×D311yescharacteristic
466C23×C3C23×D311yescharacteristic
467C22×D3—24no—
468C22×D3—24no—
469C22×D3—24no—
470C22×D3—24no—
471C22×D3—24no—
472C22×D3—24no—
473C22×D3—32no—
474C22×D3—32no—
475C22×D3—62no—
476C22×D3—64no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—122no—
484C22×D3—122no—
485C22×D3C23×D314yes—
486C22×D3C23×D314yes—
487C3×Q8—316no—
488C3×D4—616no—
489C3×D4—68no—
490C3×D4—68no—
491C3×D4—128no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—28no—
495C2×C3×C4—28no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—24no—
499C2×C3×C4—38no—
500C2×C3×C4—34no—
501C2×C3×C4—34no—
502C2×C3×C4—48no—
503C2×C3×C4—42no—
504C2×C3×C4—616no—
505C2×C3×C4—64no—
506C2×C3×C4D3×D414yes—
507C2×C3×C4C2×#6714yes—
508C2×C3×C4C23×D312yes—
509C2×C3×C4C23×D312yes—
510C2×C3×C4C23×D312yes—
511C2×C3×C4C23×D312yes—
512#67—216no—
513#67—48no—
514#67—616no—
515#67—616no—
516#67—68no—
517#67—68no—
518#67—616no—
519#67—616no—
520#67—128no—
521#67—128no—
522#67—128no—
523C2×Dic3—24no—
524C2×Dic3—34no—
525C2×Dic3—34no—
526C2×Dic3—32no—
527C2×Dic3—32no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—64no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—616no—
541C2×Dic3—122no—
542C2×Dic3—122no—
543C2×Dic3C2×#6718yes—
544C2×Dic3C23×D314yes—
545C2×Dic3C23×D314yes—
546D12—28no—
547D12—28no—
548D12—616no—
549D12—128no—
550C4×D3—216no—
551C4×D3—616no—
552C4×D3—68no—
553C4×D3—68no—
554C4×D3—128no—
555Dic6C2×#67116yescomplemented
556C2×C32—42no—
557C2×C32#55014yescomplemented
558C2×C32C23×D411yescharacteristic
559C2×C32C22×#4111yescharacteristic
560C2×C32C2×H(5,𝔽2)11yescharacteristic
561C3⋊D3—42no—
562C3×D3—44no—
563C3×D3—44no—
564C24—32no—
565C24—32no—
566C24—91no—
567C24C2×D3211yescharacteristic
568#41—632no—
569#41—1832no—
570C2×Q8—34no—
571C2×Q8—38no—
572C2×D4—38no—
573C2×D4—38no—
574C2×D4—34no—
575C2×D4—34no—
576C2×D4—68no—
577C2×D4—64no—
578C2×D4—64no—
579C2×D4—98no—
580C2×D4—98no—
581C2×D4—98no—
582C2×D4—94no—
583C2×D4—98no—
584C2×D4—124no—
585C2×D4—188no—
586C2×D4—184no—
587C2×D4—188no—
588C2×D4—364no—
589C2×D4—364no—
590C22×C4—24no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—38no—
594C22×C4—68no—
595C22×C4—98no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—91no—
599C22×C4—94no—
600C22×C4—188no—
601C22×C4—184no—
602C22×C4C2×D3214yes—
603C22×C4C2×D3211yescharacteristic
604C22×C4C2×D3211yescharacteristic
605C4⋊C4—34no—
606C4⋊C4—98no—
607C4⋊C4—94no—
608C22⋊C4—38no—
609C22⋊C4—98no—
610C22⋊C4—94no—
611C22⋊C4—94no—
612C42—98no—
613C42—94no—
614C22×C3—24no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—48no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—64no—
631C22×C3—64no—
632C22×C3—64no—
633C22×C3—64no—
634C22×C3—64no—
635C22×C3—64no—
636C22×C3—128no—
637C22×C3—128no—
638C22×C3C2×D3×D412yes—
639C22×C3#100412yes—
640C22×C3D3×#4112yes—
641C22×C3D3×#4112yes—
642C22×C3#100912yes—
643C22×C3C22×#6712yes—
644C22×C3C24×D311yescharacteristic
645C22×C3C24×D311yescharacteristic
646C2×D3—24no—
647C2×D3—24no—
648C2×D3—24no—
649C2×D3—24no—
650C2×D3—24no—
651C2×D3—24no—
652C2×D3—48no—
653C2×D3—48no—
654C2×D3—64no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—122no—
662C2×D3—122no—
663C2×D3—128no—
664C2×D3—124no—
665C2×D3—124no—
666C3×C4—22no—
667C3×C4—22no—
668C3×C4—24no—
669C3×C4—38no—
670C3×C4—42no—
671C3×C4—64no—
672C3×C4C2×D3×D414yes—
673C3×C4C22×#6714yes—
674Dic3—24no—
675Dic3—34no—
676Dic3—34no—
677Dic3—64no—
678Dic3—62no—
679Dic3—62no—
680Dic3—62no—
681Dic3—62no—
682Dic3—122no—
683Dic3—122no—
684Dic3C22×#6718yes—
685C32C2×#55011yescharacteristic, complemented, Sylow
686C23—22no—
687C23—22no—
688C23—22no—
689C23—34no—
690C23—34no—
691C23—64no—
692C23—64no—
693C23—64no—
694C23—64no—
695C23—64no—
696C23—64no—
697C23—92no—
698C23—182no—
699C23—182no—
700C23—182no—
701C23C22×D3212yes—
702C23C22×D3211yescharacteristic
703Q8—316no—
704D4—616no—
705D4—68no—
706D4—68no—
707D4—128no—
708D4—1816no—
709D4—188no—
710D4—1816no—
711D4—368no—
712D4—368no—
713C2×C4—22no—
714C2×C4—28no—
715C2×C4—38no—
716C2×C4—34no—
717C2×C4—34no—
718C2×C4—616no—
719C2×C4—64no—
720C2×C4—94no—
721C2×C4—92no—
722C2×C4—92no—
723C2×C4—92no—
724C2×C4—1816no—
725C2×C4—182no—
726C2×C4—182no—
727C2×C4—188no—
728C2×C4D3×#6714yes—
729C2×C4C22×D3212yes—
730C2×C4C22×D3212yes—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—24no—
735C2×C3—44no—
736C2×C3—42no—
737C2×C3—42no—
738C2×C3—124no—
739C2×C3—124no—
740C2×C3#559914yescomplemented
741C2×C3#583414yescomplemented
742C2×C3C22×D3×D411yescharacteristic
743C2×C3C2×#100411yescharacteristic
744C2×C3C2×D3×#4111yescharacteristic
745C2×C3C2×D3×#4111yescharacteristic
746C2×C3C2×#100911yescharacteristic
747C2×C3C23×#6711yescharacteristic
748D3—44no—
749D3—44no—
750D3—124no—
751D3—122no—
752D3—122no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—64no—
758C22—64no—
759C22—64no—
760C22—64no—
761C22—64no—
762C22—64no—
763C22—128no—
764C22—128no—
765C22—182no—
766C22—182no—
767C22—182no—
768C22—364no—
769C22#6430612yes—
770C22#6430712yes—
771C22C2×D3×#6712yes—
772C22C23×D3211yescharacteristic
773C4—22no—
774C4—38no—
775C4—64no—
776C4—94no—
777C4—182no—
778C4—182no—
779C4C2×D3×#6714yes—
780C3—21no—
781C3C2×#559911yescharacteristic, complemented
782C3C2×#583411yescharacteristic, complemented
783C2—42no—
784C2—124no—
785C2—124no—
786C2—362no—
787C2#1059500614yesdirect product factor
788C2C2×#6430611yescharacteristic
789C2C2×#6430711yescharacteristic
790C2C22×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×#3796C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C3×#930C2semidirect
5. C2×#63979C2semidirect
6. C2×#63970C2semidirect
7. C2×#63916C2semidirect
8. C2×#63914C2semidirect
9. C2×#63906C2semidirect
10. #10595006C2direct (N × H)
11. C2×#63879C2semidirect
12. C2×#63843C2semidirect
21. C2×C3×#235C22semidirect
32. C2×#3796C22semidirect
34. C4×#638C22semidirect
38. C3×#930C22semidirect
41. #63979C22semidirect
42. #63970C22semidirect
46. #63916C22semidirect
47. #63914C22semidirect
48. #63906C22semidirect
49. #63879C22semidirect
50. #63843C22semidirect
54. C22×#235D3semidirect
66. C2×#930D3semidirect
104. C2×C3×Dic6D4semidirect
155. C2×#235C2×D3semidirect
182. #930C2×D3semidirect
232. C2×C3⋊Dic3#41semidirect
246. C3×Dic6C2×D4semidirect
357. C2×Dic6#67semidirect
405. C3⋊Dic3C2×#41semidirect
555. Dic6C2×#67semidirect
557. C2×C32#550semidirect
685. C32C2×#550semidirect
740. C2×C3#5599semidirect
741. C2×C3#5834semidirect
781. C3C2×#5599semidirect
782. C3C2×#5834semidirect
787. C2#10595006direct (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×#37962
C2×C4×#6382
C2×C3×#9302
C2×#639792
C2×#639702
C2×#639162
C2×#639142
C2×#639062
#105950062
C2×#638792
C2×#638432
C2×#58343
C2×#55993