Finite Group Databasebeta

← C2×#10594894 #11901159

Subgroups — C2×#10594894 #11901159

Order 1152.

3493 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×#924C211yesmaximal, characteristic, complemented
5C2×#63971C212yesmaximal, complemented
6C2×#63958C212yesmaximal, complemented
7C2×#63909C211yesmaximal, characteristic, complemented
8C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9C2×#63888C212yesmaximal, complemented
10#10594894C2116yesmaximal, direct product factor
11C2×#63886C212yesmaximal, complemented
12C2×#63856C211yesmaximal, characteristic, complemented
13C2×#5833—31nomaximal
14C2×#5629—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C2×C3×#235—28no—
21C2×C3×#235C2218yescomplemented
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×#626C2212yes—
28C22×#626C2212yes—
29C22×#624C2212yes—
30C22×D3×Dic3C2212yes—
31C2×#3799—28no—
32C2×#3799C2218yescomplemented
33#64139C2218yescomplemented
34C2×#3752C2212yes—
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C2×C3×#217C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C3×#924C2218yescomplemented
39C2×C3×Dic3⋊C4C2212yes—
40#63971C22116yescomplemented
41C2×#3724C2212yes—
42C2×Dic3⋊Dic3C2212yes—
43C2×#3722C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45#63958C22116yescomplemented
46#63909C2218yescomplemented
47D3×C4⋊Dic3C2218yescomplemented
48#63888C22116yescomplemented
49#63886C22116yescomplemented
50#63856C2218yescomplemented
51C22×C3×#41—31no—
52C22×#239—31no—
53C22×#235—31no—
54C22×#235D311yescharacteristic, complemented
55C2×C3×C22⋊Q8—31no—
56#5833—316no—
57C2×#946—31no—
58C2×#946—32no—
59C2×#939—32no—
60C2×#939—32no—
61C2×#938—32no—
62C2×#930—31no—
63C2×#930—31no—
64C2×#930—31no—
65C2×#930—61no—
66C22×C4⋊Dic3—31no—
67C2×#924—31no—
68C2×#924D311yescharacteristic, complemented
69#5629—316no—
70C2×#896—32no—
71C2×#895—32no—
72C2×#895—31no—
73C2×D3×C4⋊C4—31no—
74C2×#884—32no—
75C2×#884—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
84C2×#638—44no—
85C2×#638C2318yes—
86C22×C3⋊Dic3C2312yes—
87C2×C4⋊(C3⋊D3)—24no—
88C2×C4⋊(C3⋊D3)C2314yes—
89C2×C3×#67—24no—
90C2×C3×#67—24no—
91C2×C3×#67C2314yes—
92C2×C3×#67C2314yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C3×#235—232no—
98C2×C3×D12—24no—
99C2×C3×D12C2314yes—
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3D418yescomplemented
102C2×C3×C4×D3C2314yes—
103C2×C3×C4×D3C2314yes—
104C2×C3×Dic6—24no—
105C2×C3×Dic6—24no—
106C2×C3×Dic6C2314yes—
107C2×C3×Dic6C2314yes—
108C2×#626—28no—
109C2×#626—44no—
110C2×#626C2318yes—
111C2×#626C2318yes—
112C2×#624—28no—
113C2×#624C2318yes—
114C2×D3×Dic3—44no—
115C2×D3×Dic3C2318yes—
116#3799—232no—
117#3752C2318yes—
118C4⋊(C3⋊Dic3)C2314yes—
119C3×#217C2318yes—
120C3×C4⋊Dic3C2314yes—
121C3×Dic3⋊C4C2318yes—
122#3724C2318yes—
123Dic3⋊Dic3C2318yes—
124#3722C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126C2×#537—91noSylow
127C2×C3×#41—38no—
128C2×C3×#41—68no—
129C22×C3×Q8—31no—
130C22×C3×Q8—31no—
131C22×C3×D4—31no—
132C22×C3×D4—31no—
133C22×C3×D4—31no—
134C23×C3×C4—21no—
135C23×C3×C4—31no—
136C23×C3×C4—31no—
137C23×C3×C4C2×D311yescharacteristic
138C23×C3×C4C2×D311yescharacteristic
139C22×#67—32no—
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—62no—
144C22×#67C2×D311yescharacteristic
145C22×#67C2×D311yescharacteristic
146C23×Dic3—32no—
147C2×#239—38no—
148C2×#239—68no—
149C2×#235—28no—
150C2×#235—38no—
151C2×#235—68no—
152C2×#235C2×D318yescomplemented
153C22×D12—32no—
154C22×D12—31no—
155C22×D12—31no—
156C22×D12—32no—
157C22×D12—61no—
158C22×D12C2×D311yescharacteristic
159C22×C4×D3—32no—
160C22×C4×D3—32no—
161C22×C4×D3—32no—
162C22×C4×D3C2×D311yescharacteristic
163C22×C4×D3C2×D311yescharacteristic
164C22×Dic6C2×D311yescharacteristic
165C22×Dic6C2×D311yescharacteristic
166C3×C22⋊Q8—38no—
167C2×C3×C4⋊C4—32no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—32no—
170C2×#217—32no—
171C2×#217C2×D312yes—
172#946—38no—
173#946—316no—
174#939—316no—
175#939—316no—
176#938—316no—
177#930—38no—
178#930—38no—
179#930—38no—
180#930—68no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—62no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3—32no—
190C2×C4⋊Dic3—38no—
191C2×C4⋊Dic3—61no—
192C2×C4⋊Dic3C2×D311yescharacteristic
193#924—38no—
194#924C2×D318yescomplemented
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—32no—
198C2×Dic3⋊C4C2×D312yes—
199#896—316no—
200#895—316no—
201#895—38no—
202D3×C4⋊C4—38no—
203#884—316no—
204#884—316no—
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—22no—
216C22×C3×D3—22no—
217C22×C3×D3—22no—
218C22×C3×D3—22no—
219C22×C3×D3C2×D414yes—
220C22×C3×D3C2412yes—
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—28no—
232C3×#67—28no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—24no—
236C2×C3×Dic3C2×D414yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C3×D12—28no—
242C3×C4×D3—28no—
243C3×C4×D3C2×D4116yescomplemented
244C3×Dic6—28no—
245C3×Dic6—28no—
246#626—216no—
247#626—48no—
248#624—216no—
249D3×Dic3—48no—
250C22×#41—31no—
251C22×#41—91no—
252#537—916no—
253C2×C22⋊Q8—31no—
254C2×C22⋊Q8—92no—
255C2×C22⋊Q8—91no—
256C2×#121—92no—
257C2×#121—92no—
258C2×#121—91no—
259C2×#121—92no—
260C2×#121—91no—
261C22×C4⋊C4—91no—
262C24×C3—21no—
263C24×C3—31no—
264C24×C3—31no—
265C24×C3C22×D311yescharacteristic
266C24×C3C22×D311yescharacteristic
267C23×D3—32no—
268C23×D3—32no—
269C23×D3—62no—
270C23×D3C22×D311yescharacteristic
271C23×D3C22×D311yescharacteristic
272C3×#41—632no—
273C2×C3×Q8—34no—
274C2×C3×Q8—34no—
275C2×C3×Q8—64no—
276C2×C3×Q8—64no—
277C2×C3×D4—34no—
278C2×C3×D4—34no—
279C2×C3×D4—34no—
280C2×C3×D4—64no—
281C2×C3×D4—64no—
282C2×C3×D4—64no—
283C22×C3×C4—24no—
284C22×C3×C4—24no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—24no—
288C22×C3×C4—31no—
289C22×C3×C4—38no—
290C22×C3×C4—34no—
291C22×C3×C4—31no—
292C22×C3×C4—32no—
293C22×C3×C4—32no—
294C22×C3×C4—34no—
295C22×C3×C4—44no—
296C22×C3×C4—64no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D314yes—
299C22×C3×C4C22×D311yescharacteristic
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—68no—
310C2×#67—68no—
311C2×#67—124no—
312C2×#67—124no—
313C2×#67—124no—
314C2×#67—128no—
315C2×#67C22×D314yes—
316C2×#67C22×D314yes—
317C22×Dic3—32no—
318C22×Dic3—32no—
319C22×Dic3—38no—
320C22×Dic3—62no—
321C22×Dic3—124no—
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D312yes—
324C22×Dic3C22×D312yes—
325C22×Dic3C22×D311yescharacteristic
326#239—632no—
327#235—232no—
328#235—632no—
329C2×D12—24no—
330C2×D12—38no—
331C2×D12—34no—
332C2×D12—34no—
333C2×D12—38no—
334C2×D12—64no—
335C2×D12—68no—
336C2×D12—64no—
337C2×D12—64no—
338C2×D12—124no—
339C2×D12—124no—
340C2×D12C22×D314yes—
341C2×C4×D3—24no—
342C2×C4×D3—38no—
343C2×C4×D3—38no—
344C2×C4×D3—38no—
345C2×C4×D3—68no—
346C2×C4×D3—68no—
347C2×C4×D3—124no—
348C2×C4×D3#6718yescomplemented
349C2×C4×D3C22×D314yes—
350C2×C4×D3C22×D314yes—
351C2×Dic6—24no—
352C2×Dic6—24no—
353C2×Dic6C22×D314yes—
354C2×Dic6C22×D314yes—
355C3×C4⋊C4—34no—
356C3×C4⋊C4—38no—
357C3×C22⋊C4—38no—
358#217—38no—
359#217C22×D318yes—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—68no—
366C4⋊Dic3—34no—
367C4⋊Dic3—34no—
368C4⋊Dic3—38no—
369C4⋊Dic3—64no—
370C4⋊Dic3C22×D314yes—
371Dic3⋊C4—38no—
372Dic3⋊C4—38no—
373Dic3⋊C4—38no—
374Dic3⋊C4C22×D318yes—
375C22×C32—22no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—44no—
379C22×C32C22×D412yes—
380C22×C32H(5,𝔽2)12yes—
381C22×C322−1+412yes—
382C22×C32C2511yescharacteristic
383C2×C3⋊D3—24no—
384C2×C3⋊D3—24no—
385C2×C3⋊D3—24no—
386C2×C3⋊D3—48no—
387C2×C3×D3—28no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—22no—
393C2×C3×D3—44no—
394C2×C3×D3C22×D414yes—
395C32×C4—22no—
396C32×C4C22×D414yes—
397C3⋊Dic3—24no—
398C3×Dic3—24no—
399C3×Dic3—22no—
400C3×Dic3—24no—
401C3×Dic3C22×D414yes—
402C2×#41—38no—
403C2×#41—68no—
404C2×#41—98no—
405C2×#41—188no—
406C22×Q8—31no—
407C22×Q8—31no—
408C22×D4—31no—
409C22×D4—31no—
410C22×D4—31no—
411C22×D4—92no—
412C22×D4—92no—
413C22×D4—92no—
414C22×D4—91no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—92no—
418C23×C4—92no—
419C23×C4D3211yescharacteristic
420C22⋊Q8—38no—
421C22⋊Q8—916no—
422C22⋊Q8—98no—
423#121—916no—
424#121—916no—
425#121—98no—
426#121—916no—
427#121—98no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—32no—
430C2×C4⋊C4—98no—
431C2×C4⋊C4—92no—
432C2×C4⋊C4—92no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—32no—
435C2×C22⋊C4—92no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—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—32no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—62no—
453C23×C3—62no—
454C23×C3—62no—
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—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—34no—
467C22×D3—34no—
468C22×D3—64no—
469C22×D3—64no—
470C22×D3—64no—
471C22×D3—64no—
472C22×D3—64no—
473C22×D3—64no—
474C22×D3—64no—
475C22×D3—124no—
476C22×D3—124no—
477C22×D3—124no—
478C22×D3C2×#6714yes—
479C22×D3C23×D312yes—
480C22×D3C23×D312yes—
481C3×Q8—68no—
482C3×Q8—68no—
483C3×D4—68no—
484C3×D4—68no—
485C3×D4—68no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—28no—
489C2×C3×C4—28no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—24no—
493C2×C3×C4—34no—
494C2×C3×C4—32no—
495C2×C3×C4—316no—
496C2×C3×C4—32no—
497C2×C3×C4—34no—
498C2×C3×C4—34no—
499C2×C3×C4—48no—
500C2×C3×C4—42no—
501C2×C3×C4—62no—
502C2×C3×C4—64no—
503C2×C3×C4—64no—
504C2×C3×C4—68no—
505C2×C3×C4D3×D414yes—
506C2×C3×C4C2×#6714yes—
507C2×C3×C4C23×D312yes—
508C2×C3×C4C23×D312yes—
509C2×C3×C4C23×D312yes—
510C2×C3×C4C23×D312yes—
511#67—28no—
512#67—28no—
513#67—616no—
514#67—128no—
515#67—128no—
516#67—128no—
517#67—1216no—
518C2×Dic3—24no—
519C2×Dic3—24no—
520C2×Dic3—22no—
521C2×Dic3—34no—
522C2×Dic3—34no—
523C2×Dic3—64no—
524C2×Dic3—64no—
525C2×Dic3—64no—
526C2×Dic3—124no—
527C2×Dic3—128no—
528C2×Dic3C2×#6714yes—
529C2×Dic3C23×D312yes—
530C2×Dic3C23×D314yes—
531C2×Dic3C23×D314yes—
532C2×Dic3C23×D312yes—
533D12—28no—
534D12—616no—
535D12—68no—
536D12—68no—
537D12—128no—
538D12—128no—
539C4×D3—28no—
540C4×D3—616no—
541C4×D3—616no—
542C4×D3—128no—
543C4×D3C2×#67116yescomplemented
544Dic6—28no—
545Dic6—28no—
546C2×C32—42no—
547C2×C32#53714yescomplemented
548C2×C32C23×D411yescharacteristic
549C2×C32C2×H(5,𝔽2)11yescharacteristic
550C2×C32C2×2−1+411yescharacteristic
551C3⋊D3—44no—
552C3×D3—24no—
553C3×D3—42no—
554C24—31no—
555C24—31no—
556C24—92no—
557C24C2×D3211yescharacteristic
558#41—632no—
559#41—1832no—
560C2×Q8—34no—
561C2×Q8—34no—
562C2×Q8—64no—
563C2×Q8—64no—
564C2×D4—34no—
565C2×D4—34no—
566C2×D4—34no—
567C2×D4—64no—
568C2×D4—64no—
569C2×D4—64no—
570C2×D4—98no—
571C2×D4—98no—
572C2×D4—98no—
573C2×D4—94no—
574C2×D4—188no—
575C2×D4—184no—
576C2×D4—364no—
577C2×D4—364no—
578C22×C4—24no—
579C22×C4—31no—
580C22×C4—34no—
581C22×C4—38no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—31no—
585C22×C4—34no—
586C22×C4—64no—
587C22×C4—98no—
588C22×C4—98no—
589C22×C4—92no—
590C22×C4—188no—
591C22×C4—364no—
592C22×C4C2×D3214yes—
593C22×C4C2×D3211yescharacteristic
594C22×C4C2×D3211yescharacteristic
595C4⋊C4—34no—
596C4⋊C4—38no—
597C4⋊C4—98no—
598C4⋊C4—98no—
599C4⋊C4—94no—
600C22⋊C4—38no—
601C22⋊C4—98no—
602C22⋊C4—98no—
603C22⋊C4—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—34no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—48no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—62no—
622C22×C3—62no—
623C22×C3—68no—
624C22×C3—62no—
625C22×C3—62no—
626C22×C3—62no—
627C22×C3—124no—
628C22×C3C2×D3×D412yes—
629C22×C3#100712yes—
630C22×C3#100912yes—
631C22×C3#100912yes—
632C22×C3#101012yes—
633C22×C3C22×#6712yes—
634C22×C3C24×D311yescharacteristic
635C22×C3C24×D311yescharacteristic
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—28no—
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—22no—
642C2×D3—44no—
643C2×D3—64no—
644C2×D3—64no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—64no—
648C2×D3—64no—
649C2×D3—124no—
650C2×D3—124no—
651C2×D3—124no—
652C2×D3—128no—
653C2×D3—128no—
654C2×D3—248no—
655C2×D3C22×#6714yes—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—24no—
659C3×C4—34no—
660C3×C4—42no—
661C3×C4—62no—
662C3×C4—64no—
663C3×C4—64no—
664C3×C4C2×D3×D414yes—
665C3×C4C22×#6714yes—
666Dic3—24no—
667Dic3—24no—
668Dic3—22no—
669Dic3—64no—
670Dic3—64no—
671Dic3—124no—
672Dic3C22×#6714yes—
673C32C2×#53711yescharacteristic, complemented, Sylow
674C23—22no—
675C23—22no—
676C23—22no—
677C23—34no—
678C23—32no—
679C23—32no—
680C23—62no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—94no—
686C23—184no—
687C23—184no—
688C23—184no—
689C23C22×D3212yes—
690C23C22×D3211yescharacteristic
691Q8—68no—
692Q8—68no—
693D4—68no—
694D4—68no—
695D4—68no—
696D4—1816no—
697D4—188no—
698D4—368no—
699D4—368no—
700C2×C4—22no—
701C2×C4—28no—
702C2×C4—34no—
703C2×C4—32no—
704C2×C4—316no—
705C2×C4—34no—
706C2×C4—34no—
707C2×C4—32no—
708C2×C4—64no—
709C2×C4—62no—
710C2×C4—64no—
711C2×C4—68no—
712C2×C4—94no—
713C2×C4—1816no—
714C2×C4—184no—
715C2×C4—368no—
716C2×C4D3×#6714yes—
717C2×C4C22×D3212yes—
718C2×C4C22×D3212yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—24no—
722C2×C3—21no—
723C2×C3—44no—
724C2×C3—42no—
725C2×C3—42no—
726C2×C3—64no—
727C2×C3—122no—
728C2×C3#562914yescomplemented
729C2×C3#583314yescomplemented
730C2×C3C22×D3×D411yescharacteristic
731C2×C3C2×#100711yescharacteristic
732C2×C3C2×#100911yescharacteristic
733C2×C3C2×#100911yescharacteristic
734C2×C3C2×#101011yescharacteristic
735C2×C3C23×#6711yescharacteristic
736D3—24no—
737D3—42no—
738D3—124no—
739D3—124no—
740D3—244no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—34no—
745C22—44no—
746C22—62no—
747C22—62no—
748C22—68no—
749C22—62no—
750C22—62no—
751C22—62no—
752C22—124no—
753C22—184no—
754C22—184no—
755C22—184no—
756C22—368no—
757C22#6429712yes—
758C22#6430812yes—
759C22C2×D3×#6712yes—
760C22C23×D3211yescharacteristic
761C4—22no—
762C4—34no—
763C4—64no—
764C4—62no—
765C4—64no—
766C4—184no—
767C4C2×D3×#6714yes—
768C3—21no—
769C3C2×#562911yescharacteristic, complemented
770C3C2×#583311yescharacteristic, complemented
771C2—42no—
772C2—64no—
773C2—122no—
774C2—364no—
775C2#1059489414yesdirect product factor
776C2C2×#6429711yescharacteristic
777C2C2×#6430811yescharacteristic
778C2C22×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×#3799C2semidirect
3. C2×#64139C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63971C2semidirect
6. C2×#63958C2semidirect
7. C2×#63909C2semidirect
8. C2×D3×C4⋊Dic3C2semidirect
9. C2×#63888C2semidirect
10. #10594894C2direct (N × H)
11. C2×#63886C2semidirect
12. C2×#63856C2semidirect
21. C2×C3×#235C22semidirect
32. C2×#3799C22semidirect
33. #64139C22semidirect
38. C3×#924C22semidirect
40. #63971C22semidirect
45. #63958C22semidirect
46. #63909C22semidirect
47. D3×C4⋊Dic3C22semidirect
48. #63888C22semidirect
49. #63886C22semidirect
50. #63856C22semidirect
54. C22×#235D3semidirect
68. C2×#924D3semidirect
101. C2×C3×C4×D3D4semidirect
152. C2×#235C2×D3semidirect
194. #924C2×D3semidirect
243. C3×C4×D3C2×D4semidirect
348. C2×C4×D3#67semidirect
543. C4×D3C2×#67semidirect
547. C2×C32#537semidirect
673. C32C2×#537semidirect
728. C2×C3#5629semidirect
729. C2×C3#5833semidirect
769. C3C2×#5629semidirect
770. C3C2×#5833semidirect
775. C2#10594894direct (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×#9242
C2×#639712
C2×#639582
C2×#639092
C2×D3×C4⋊Dic32
C2×#638882
#105948942
C2×#638862
C2×#638562
C2×#58333
C2×#56293