Finite Group Databasebeta

← C2×#10595004 #11901161

Subgroups — C2×#10595004 #11901161

Order 1152.

3441 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64133C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C2×#63970C212yesmaximal, complemented
6C2×#63970C212yesmaximal, complemented
7C2×#63908C211yesmaximal, characteristic, complemented
8#10595004C2116yesmaximal, direct product factor
9C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10C2×#63887C212yesmaximal, complemented
11C2×#63885C212yesmaximal, complemented
12C2×#63857C211yesmaximal, characteristic, complemented
13C2×#5833—31nomaximal
14C2×#5608—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2212yes—
20C2×C3×#235—28no—
21C2×C3×#235C2218yescomplemented
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×#625C2212yes—
28C22×#625C2212yes—
29C22×D3×Dic3C2212yes—
30C22×D3×Dic3C2212yes—
31C2×#3795—28no—
32C2×#3795C2218yescomplemented
33C2×#3757C2212yes—
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35#64133C2218yescomplemented
36C2×#3750C2212yes—
37C3×#930C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2212yes—
39C2×C3×C4⋊Dic3C2211yescharacteristic
40#63970C22116yescomplemented
41#63970C22116yescomplemented
42C2×Dic3⋊Dic3C2212yes—
43C2×Dic3⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×(C2×D3)⋊Dic3C2212yes—
46#63908C2218yescomplemented
47D3×C4⋊Dic3C2218yescomplemented
48#63887C22116yescomplemented
49#63885C22116yescomplemented
50#63857C2218yescomplemented
51C22×C3×#41—31no—
52C22×#237—31no—
53C22×#235—31no—
54C22×#235D311yescharacteristic, complemented
55C2×C3×#121—31no—
56#5833—316no—
57C2×#946—32no—
58C2×#939—32no—
59C2×#939—32no—
60C2×#939—32no—
61C2×#938—32no—
62C2×#938—32no—
63C2×#938—31no—
64C2×#930—31no—
65C2×#930D311yescharacteristic, complemented
66C22×C4⋊Dic3—31no—
67C2×#924—31no—
68C2×#924—31no—
69C2×#924—31no—
70C2×#924—61no—
71#5608—316no—
72C2×#897—31no—
73C2×D3×C4⋊C4—31no—
74C2×#884—32no—
75C2×#878—32no—
76C24×C32C2311yescharacteristic
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×C32×C4—24no—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2314yes—
83C22×C32×C4C2311yescharacteristic
84C22×C3⋊Dic3C2312yes—
85C22×C3⋊Dic3C2312yes—
86C2×#634—24no—
87C2×#634C2314yes—
88C2×C3×#67—24no—
89C2×C3×#67—24no—
90C2×C3×#67—44no—
91C2×C3×#67C2314yes—
92C2×C3×#67C2314yes—
93C2×C3×#67C2318yes—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C3×#235—232no—
98C2×C3×D12—24no—
99C2×C3×D12—24no—
100C2×C3×D12C2314yes—
101C2×C3×D12C2314yes—
102C2×C3×C4×D3—24no—
103C2×C3×C4×D3D418yescomplemented
104C2×C3×C4×D3C2314yes—
105C2×C3×C4×D3C2314yes—
106C2×C3×Dic6—24no—
107C2×C3×Dic6C2314yes—
108C2×#625—28no—
109C2×#625—44no—
110C2×#625C2318yes—
111C2×#625C2318yes—
112C2×D3×Dic3—28no—
113C2×D3×Dic3—44no—
114C2×D3×Dic3C2318yes—
115C2×D3×Dic3C2318yes—
116#3795—232no—
117#3757C2318yes—
118C4⋊(C3⋊Dic3)C2314yes—
119#3750C2318yes—
120C3×(C2×D3)⋊C4C2318yes—
121C3×C4⋊Dic3C2314yes—
122Dic3⋊Dic3C2318yes—
123Dic3⋊Dic3C2318yes—
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126C2×#537—91noSylow
127C2×C3×#41—38no—
128C2×C3×#41—68no—
129C22×C3×Q8—31no—
130C22×C3×D4—31no—
131C22×C3×D4—31no—
132C22×C3×D4—32no—
133C22×C3×D4—31no—
134C22×C3×D4—31no—
135C23×C3×C4—21no—
136C23×C3×C4—31no—
137C23×C3×C4—31no—
138C23×C3×C4C2×D311yescharacteristic
139C23×C3×C4C2×D311yescharacteristic
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—32no—
144C22×#67C2×D311yescharacteristic
145C22×#67C2×D311yescharacteristic
146C22×#67C2×D312yes—
147C23×Dic3—32no—
148C23×Dic3—32no—
149C2×#237—38no—
150C2×#237—68no—
151C2×#235—28no—
152C2×#235—38no—
153C2×#235—68no—
154C2×#235C2×D318yescomplemented
155C22×D12C2×D311yescharacteristic
156C22×D12C2×D311yescharacteristic
157C22×C4×D3—32no—
158C22×C4×D3—32no—
159C22×C4×D3C2×D311yescharacteristic
160C22×C4×D3C2×D311yescharacteristic
161C22×Dic6—31no—
162C22×Dic6—31no—
163C22×Dic6—61no—
164C22×Dic6C2×D311yescharacteristic
165C3×#121—38no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—32no—
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—32no—
171C2×#217—32no—
172C2×#217—62no—
173#946—316no—
174#939—316no—
175#939—316no—
176#939—316no—
177#938—316no—
178#938—316no—
179#938—38no—
180#930—38no—
181#930C2×D318yescomplemented
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4C2×D312yes—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—32no—
188C2×C4⋊Dic3—32no—
189C2×C4⋊Dic3—38no—
190C2×C4⋊Dic3—61no—
191C2×C4⋊Dic3C2×D311yescharacteristic
192#924—38no—
193#924—38no—
194#924—38no—
195#924—68no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—32no—
198C2×Dic3⋊C4—32no—
199C2×Dic3⋊C4—32no—
200C2×Dic3⋊C4—62no—
201#897—38no—
202D3×C4⋊C4—38no—
203#884—316no—
204#878—316no—
205C23×C32—22no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32C2412yes—
209C23×C32C2411yescharacteristic
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—24no—
217C22×C3×D3—22no—
218C22×C3×D3C2×D414yes—
219C22×C3×D3C2412yes—
220C22×C3×D3C2414yes—
221C22×C3×D3C2412yes—
222C2×C32×C4—22no—
223C2×C32×C4—28no—
224C2×C32×C4C2×D414yes—
225C2×C32×C4C2412yes—
226C2×C32×C4C2412yes—
227C2×C3⋊Dic3—24no—
228C2×C3⋊Dic3—24no—
229C2×C3⋊Dic3C2414yes—
230C2×C3⋊Dic3C2414yes—
231#634—28no—
232C3×#67—28no—
233C3×#67—28no—
234C3×#67—48no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—24no—
237C2×C3×Dic3C2×D414yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C3×D12—28no—
242C3×D12—28no—
243C3×C4×D3—28no—
244C3×C4×D3C2×D4116yescomplemented
245C3×Dic6—28no—
246#625—216no—
247#625—48no—
248D3×Dic3—216no—
249D3×Dic3—48no—
250C22×#41—31no—
251C22×#41—91no—
252#537—916no—
253C2×C22⋊Q8—92no—
254C2×C22⋊Q8—91no—
255C2×C22⋊Q8—91no—
256C2×#121—31no—
257C2×#121—92no—
258C2×#121—91no—
259C2×#121—92no—
260C2×#121—92no—
261C22×C4⋊C4—91no—
262C24×C3—21no—
263C24×C3—31no—
264C24×C3—31no—
265C24×C3—32no—
266C24×C3C22×D311yescharacteristic
267C24×C3C22×D311yescharacteristic
268C23×D3C22×D311yescharacteristic
269C23×D3C22×D312yes—
270C23×D3C22×D311yescharacteristic
271C3×#41—632no—
272C2×C3×Q8—34no—
273C2×C3×Q8—64no—
274C2×C3×D4—34no—
275C2×C3×D4—34no—
276C2×C3×D4—38no—
277C2×C3×D4—34no—
278C2×C3×D4—34no—
279C2×C3×D4—64no—
280C2×C3×D4—64no—
281C2×C3×D4—64no—
282C2×C3×D4—64no—
283C2×C3×D4—124no—
284C22×C3×C4—24no—
285C22×C3×C4—24no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—24no—
289C22×C3×C4—31no—
290C22×C3×C4—38no—
291C22×C3×C4—34no—
292C22×C3×C4—31no—
293C22×C3×C4—32no—
294C22×C3×C4—34no—
295C22×C3×C4—44no—
296C22×C3×C4—64no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D314yes—
300C22×C3×C4C22×D314yes—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—38no—
306C2×#67—38no—
307C2×#67—38no—
308C2×#67—38no—
309C2×#67—44no—
310C2×#67—68no—
311C2×#67—68no—
312C2×#67—124no—
313C2×#67—124no—
314C2×#67C22×D314yes—
315C2×#67C22×D314yes—
316C2×#67C22×D318yes—
317C22×Dic3—32no—
318C22×Dic3—32no—
319C22×Dic3—32no—
320C22×Dic3—32no—
321C22×Dic3—38no—
322C22×Dic3—38no—
323C22×Dic3—62no—
324C22×Dic3—62no—
325C22×Dic3—68no—
326C22×Dic3—124no—
327C22×Dic3C22×D312yes—
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330#237—632no—
331#235—232no—
332#235—632no—
333C2×D12—24no—
334C2×D12—24no—
335C2×D12C22×D314yes—
336C2×D12C22×D314yes—
337C2×C4×D3—24no—
338C2×C4×D3—38no—
339C2×C4×D3—38no—
340C2×C4×D3—68no—
341C2×C4×D3—124no—
342C2×C4×D3#6718yescomplemented
343C2×C4×D3C22×D314yes—
344C2×C4×D3C22×D314yes—
345C2×Dic6—24no—
346C2×Dic6—34no—
347C2×Dic6—34no—
348C2×Dic6—64no—
349C2×Dic6—64no—
350C2×Dic6—64no—
351C2×Dic6—124no—
352C2×Dic6C22×D314yes—
353C3×C4⋊C4—34no—
354C3×C22⋊C4—38no—
355#217—38no—
356#217—38no—
357#217—38no—
358#217—38no—
359#217—68no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4C22×D318yes—
363C4⋊Dic3—34no—
364C4⋊Dic3—34no—
365C4⋊Dic3—38no—
366C4⋊Dic3—38no—
367C4⋊Dic3—64no—
368C4⋊Dic3C22×D314yes—
369Dic3⋊C4—38no—
370Dic3⋊C4—38no—
371Dic3⋊C4—38no—
372Dic3⋊C4—38no—
373Dic3⋊C4—68no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—22no—
377C22×C32—44no—
378C22×C32C22×D412yes—
379C22×C32H(5,𝔽2)12yes—
380C22×C322−1+412yes—
381C22×C32C2511yescharacteristic
382C2×C3×D3—28no—
383C2×C3×D3—22no—
384C2×C3×D3—22no—
385C2×C3×D3—24no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—24no—
389C2×C3×D3—22no—
390C2×C3×D3—24no—
391C2×C3×D3—44no—
392C2×C3×D3—48no—
393C2×C3×D3C22×D414yes—
394C32×C4—22no—
395C32×C4C22×D414yes—
396C3⋊Dic3—24no—
397C3⋊Dic3—24no—
398C3×Dic3—22no—
399C3×Dic3—24no—
400C3×Dic3C22×D414yes—
401C2×#41—38no—
402C2×#41—68no—
403C2×#41—98no—
404C2×#41—188no—
405C22×Q8—31no—
406C22×Q8—91no—
407C22×D4—31no—
408C22×D4—31no—
409C22×D4—32no—
410C22×D4—31no—
411C22×D4—31no—
412C22×D4—92no—
413C22×D4—92no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—92no—
417C23×C4—92no—
418C23×C4D3211yescharacteristic
419C22⋊Q8—916no—
420C22⋊Q8—98no—
421C22⋊Q8—98no—
422#121—38no—
423#121—916no—
424#121—98no—
425#121—916no—
426#121—916no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—98no—
429C2×C4⋊C4—92no—
430C2×C4⋊C4—92no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—92no—
433C2×C22⋊C4—32no—
434C2×C22⋊C4—92no—
435C2×C22⋊C4—92no—
436C2×C22⋊C4—92no—
437C23×C3—24no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—21no—
446C23×C3—34no—
447C23×C3—32no—
448C23×C3—32no—
449C23×C3—34no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—62no—
453C23×C3—62no—
454C23×C3—62no—
455C23×C3—62no—
456C23×C3—64no—
457C23×C3—64no—
458C23×C3—62no—
459C23×C3—64no—
460C23×C3C23×D312yes—
461C23×C3C23×D312yes—
462C23×C3C23×D311yescharacteristic
463C23×C3C23×D311yescharacteristic
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—24no—
467C22×D3—24no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—24no—
471C22×D3—22no—
472C22×D3C2×#6714yes—
473C22×D3C23×D312yes—
474C22×D3C23×D314yes—
475C22×D3C23×D312yes—
476C3×Q8—68no—
477C3×D4—68no—
478C3×D4—68no—
479C3×D4—68no—
480C3×D4—68no—
481C3×D4—128no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—28no—
485C2×C3×C4—28no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—24no—
489C2×C3×C4—34no—
490C2×C3×C4—32no—
491C2×C3×C4—316no—
492C2×C3×C4—32no—
493C2×C3×C4—34no—
494C2×C3×C4—48no—
495C2×C3×C4—42no—
496C2×C3×C4—62no—
497C2×C3×C4—64no—
498C2×C3×C4—68no—
499C2×C3×C4D3×D414yes—
500C2×C3×C4C2×#6714yes—
501C2×C3×C4C23×D312yes—
502C2×C3×C4C23×D312yes—
503C2×C3×C4C23×D312yes—
504C2×C3×C4C23×D312yes—
505#67—28no—
506#67—28no—
507#67—48no—
508#67—616no—
509#67—616no—
510#67—128no—
511#67—128no—
512C2×Dic3—24no—
513C2×Dic3—22no—
514C2×Dic3—34no—
515C2×Dic3—34no—
516C2×Dic3—34no—
517C2×Dic3—34no—
518C2×Dic3—64no—
519C2×Dic3—64no—
520C2×Dic3—64no—
521C2×Dic3—64no—
522C2×Dic3—64no—
523C2×Dic3—64no—
524C2×Dic3—616no—
525C2×Dic3—124no—
526C2×Dic3—124no—
527C2×Dic3—128no—
528C2×Dic3C2×#6714yes—
529C2×Dic3C23×D314yes—
530C2×Dic3C23×D312yes—
531C2×Dic3C23×D312yes—
532D12—28no—
533D12—28no—
534C4×D3—28no—
535C4×D3—616no—
536C4×D3—128no—
537C4×D3C2×#67116yescomplemented
538Dic6—28no—
539Dic6—68no—
540Dic6—68no—
541Dic6—128no—
542C2×C32—42no—
543C2×C32#53714yescomplemented
544C2×C32C23×D411yescharacteristic
545C2×C32C2×H(5,𝔽2)11yescharacteristic
546C2×C32C2×2−1+411yescharacteristic
547C3×D3—24no—
548C3×D3—44no—
549C3×D3—42no—
550C24—31no—
551C24—32no—
552C24—31no—
553C24C2×D3211yescharacteristic
554#41—632no—
555#41—1832no—
556C2×Q8—34no—
557C2×Q8—64no—
558C2×Q8—94no—
559C2×Q8—184no—
560C2×D4—34no—
561C2×D4—34no—
562C2×D4—38no—
563C2×D4—34no—
564C2×D4—34no—
565C2×D4—64no—
566C2×D4—64no—
567C2×D4—64no—
568C2×D4—64no—
569C2×D4—98no—
570C2×D4—98no—
571C2×D4—124no—
572C2×D4—188no—
573C2×D4—364no—
574C22×C4—24no—
575C22×C4—31no—
576C22×C4—34no—
577C22×C4—38no—
578C22×C4—32no—
579C22×C4—31no—
580C22×C4—34no—
581C22×C4—64no—
582C22×C4—98no—
583C22×C4—98no—
584C22×C4—92no—
585C22×C4—92no—
586C22×C4—188no—
587C22×C4—364no—
588C22×C4C2×D3214yes—
589C22×C4C2×D3211yescharacteristic
590C22×C4C2×D3211yescharacteristic
591C4⋊C4—34no—
592C4⋊C4—98no—
593C4⋊C4—98no—
594C4⋊C4—94no—
595C4⋊C4—98no—
596C22⋊C4—38no—
597C22⋊C4—98no—
598C22⋊C4—98no—
599C22⋊C4—98no—
600C22×C3—24no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—21no—
611C22×C3—34no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—48no—
615C22×C3—44no—
616C22×C3—44no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—68no—
620C22×C3—62no—
621C22×C3—62no—
622C22×C3—64no—
623C22×C3—62no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—128no—
627C22×C3—124no—
628C22×C3C2×D3×D412yes—
629C22×C3#100412yes—
630C22×C3#100912yes—
631C22×C3#101012yes—
632C22×C3#101012yes—
633C22×C3C22×#6712yes—
634C22×C3C24×D311yescharacteristic
635C22×C3C24×D311yescharacteristic
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—28no—
639C2×D3—24no—
640C2×D3—24no—
641C2×D3—22no—
642C2×D3—24no—
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—44no—
646C2×D3—48no—
647C2×D3C22×#6714yes—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—24no—
651C3×C4—34no—
652C3×C4—42no—
653C3×C4—62no—
654C3×C4—64no—
655C3×C4C2×D3×D414yes—
656C3×C4C22×#6714yes—
657Dic3—24no—
658Dic3—22no—
659Dic3—64no—
660Dic3—64no—
661Dic3—64no—
662Dic3—64no—
663Dic3—124no—
664Dic3—124no—
665Dic3C22×#6714yes—
666C32C2×#53711yescharacteristic, complemented, Sylow
667C23—22no—
668C23—22no—
669C23—22no—
670C23—34no—
671C23—32no—
672C23—34no—
673C23—32no—
674C23—62no—
675C23—62no—
676C23—64no—
677C23—62no—
678C23—64no—
679C23—62no—
680C23—62no—
681C23—64no—
682C23C22×D3212yes—
683C23C22×D3211yescharacteristic
684Q8—68no—
685Q8—188no—
686D4—68no—
687D4—68no—
688D4—68no—
689D4—68no—
690D4—128no—
691D4—1816no—
692D4—368no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—34no—
696C2×C4—32no—
697C2×C4—316no—
698C2×C4—34no—
699C2×C4—32no—
700C2×C4—64no—
701C2×C4—62no—
702C2×C4—68no—
703C2×C4—94no—
704C2×C4—94no—
705C2×C4—1816no—
706C2×C4—184no—
707C2×C4—184no—
708C2×C4—368no—
709C2×C4D3×#6714yes—
710C2×C4C22×D3212yes—
711C2×C4C22×D3212yes—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—24no—
716C2×C3—44no—
717C2×C3—42no—
718C2×C3—42no—
719C2×C3—64no—
720C2×C3—122no—
721C2×C3—124no—
722C2×C3#560814yescomplemented
723C2×C3#583314yescomplemented
724C2×C3C22×D3×D411yescharacteristic
725C2×C3C2×#100411yescharacteristic
726C2×C3C2×#100911yescharacteristic
727C2×C3C2×#101011yescharacteristic
728C2×C3C2×#101011yescharacteristic
729C2×C3C23×#6711yescharacteristic
730D3—24no—
731D3—44no—
732D3—42no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—34no—
737C22—44no—
738C22—62no—
739C22—62no—
740C22—68no—
741C22—64no—
742C22—62no—
743C22—64no—
744C22—62no—
745C22—62no—
746C22—64no—
747C22—128no—
748C22—124no—
749C22#6429812yes—
750C22#6430712yes—
751C22C2×D3×#6712yes—
752C22C23×D3211yescharacteristic
753C4—22no—
754C4—34no—
755C4—64no—
756C4—62no—
757C4—184no—
758C4—184no—
759C4C2×D3×#6714yes—
760C3—21no—
761C3C2×#560811yescharacteristic, complemented
762C3C2×#583311yescharacteristic, complemented
763C2—42no—
764C2—64no—
765C2—124no—
766C2—122no—
767C2#1059500414yesdirect product factor
768C2C2×#6429811yescharacteristic
769C2C2×#6430711yescharacteristic
770C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#537
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×#3795C2semidirect
3. C2×#64133C2semidirect
4. C2×C3×#930C2semidirect
5. C2×#63970C2semidirect
6. C2×#63970C2semidirect
7. C2×#63908C2semidirect
8. #10595004C2direct (N × H)
9. C2×D3×C4⋊Dic3C2semidirect
10. C2×#63887C2semidirect
11. C2×#63885C2semidirect
12. C2×#63857C2semidirect
21. C2×C3×#235C22semidirect
32. C2×#3795C22semidirect
35. #64133C22semidirect
37. C3×#930C22semidirect
40. #63970C22semidirect
41. #63970C22semidirect
46. #63908C22semidirect
47. D3×C4⋊Dic3C22semidirect
48. #63887C22semidirect
49. #63885C22semidirect
50. #63857C22semidirect
54. C22×#235D3semidirect
65. C2×#930D3semidirect
103. C2×C3×C4×D3D4semidirect
154. C2×#235C2×D3semidirect
181. #930C2×D3semidirect
244. C3×C4×D3C2×D4semidirect
342. C2×C4×D3#67semidirect
537. C4×D3C2×#67semidirect
543. C2×C32#537semidirect
666. C32C2×#537semidirect
722. C2×C3#5608semidirect
723. C2×C3#5833semidirect
761. C3C2×#5608semidirect
762. C3C2×#5833semidirect
767. C2#10595004direct (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×#37952
C2×#641332
C2×C3×#9302
C2×#639702
C2×#639082
#105950042
C2×D3×C4⋊Dic32
C2×#638872
C2×#638852
C2×#638572
C2×#58333
C2×#56083