Finite Group Databasebeta

← C2×#10595229 #11902470

Subgroups — C2×#10595229 #11902470

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×#64147C211yesmaximal, characteristic, complemented
4C2×C3×#936C211yesmaximal, characteristic, complemented
5C2×#63977C212yesmaximal, complemented
6C2×#63971C212yesmaximal, complemented
7C2×#63969C212yesmaximal, complemented
8C2×D3×#217C212yesmaximal, complemented
9#10595229C2116yesmaximal, direct product factor
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×Dic3×D12C211yesmaximal, characteristic, complemented
12C2×#63856C211yesmaximal, characteristic, complemented
13C2×#5806—31nomaximal
14C2×#5676—31nomaximal
15C24×C3×D3C2212yes—
16C22×C32×D4C2211yescharacteristic
17C22×#638C2212yescomplemented
18C22×C4×C3⋊D3C2211yescharacteristic, complemented
19C22×C3×#67C2212yes—
20C2×C3×D3×D4—28no—
21C2×C3×D3×D4C2218yescomplemented
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic, complemented
25C22×#626C2211yescharacteristic
26C22×#626C2212yescomplemented
27C22×D3×Dic3C2212yescomplemented
28C22×D3×Dic3C2212yescomplemented
29C2×#3796—28no—
30C2×#3796C2218yescomplemented
31C2×#3757C2212yescomplemented
32#64147C2218yescomplemented
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C2×C3×#217C2212yescomplemented
35C2×C3×#217C2212yescomplemented
36C3×#936C2218yescomplemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38#63977C22116yescomplemented
39#63971C22116yescomplemented
40#63969C22116yescomplemented
41D3×#217C22116yescomplemented
42C2×#3724C2212yescomplemented
43C2×Dic3⋊Dic3C2211yescharacteristic, complemented
44C2×#3722C2211yescharacteristic, complemented
45C2×(C2×D3)⋊Dic3C2212yes—
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2212yescomplemented
48C4×#626C2218yescomplemented
49Dic3×D12C2218yescomplemented
50#63856C2218yescomplemented
51C23×C3×D4—31no—
52C22×#239—31no—
53C22×#237—31no—
54C22×D3×D4D311yescharacteristic, complemented
55C2×C3×#124—31no—
56C2×#953—32no—
57C22×#217—32no—
58C2×#946—31no—
59#5806—316no—
60C2×#939—32no—
61C2×#938—31no—
62C2×#938—31no—
63C2×#938—61no—
64C2×#936D311yescharacteristic, complemented
65C2×#935—32no—
66C2×D4×Dic3—31no—
67C2×C4×#67—31no—
68C2×#924—31no—
69#5676—316no—
70C2×#884—32no—
71C2×#883—32no—
72C2×#882—32no—
73C2×D3×C22⋊C4—32no—
74C2×C4×D12—31no—
75C2×C4×D12—31no—
76C24×C32C2312yes—
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3—28no—
79C23×C3×D3—28no—
80C23×C3×D3—44no—
81C23×C3×D3C2318yes—
82C23×C3×D3C2312yes—
83C23×C3×D3C2311yescharacteristic
84C2×C32×D4—24no—
85C2×C32×D4C2314yes—
86C22×C32×C4C2311yescharacteristic
87C2×#638—44no—
88C2×#638C2318yescomplemented
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2312yes—
91C2×C4×C3⋊D3—24no—
92C2×C4×C3⋊D3C2314yescomplemented
93C2×C3×#67—28no—
94C2×C3×#67C2318yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2311yescharacteristic
99C3×D3×D4—232no—
100C2×C3×D12D418yescomplemented
101C2×C3×D12C2314yes—
102C2×C3×C4×D3—24no—
103C2×C3×C4×D3C2314yes—
104C2×C3×Dic6—24no—
105C2×C3×Dic6C2314yescomplemented
106C2×#626—28no—
107C2×#626—24no—
108C2×#626C2314yes—
109C2×#626C2318yescomplemented
110C2×D3×Dic3—28no—
111C2×D3×Dic3—44no—
112C2×D3×Dic3C2318yescomplemented
113C2×D3×Dic3C2318yescomplemented
114#3796—232no—
115#3757C2318yescomplemented
116C4⋊(C3⋊Dic3)C2314yescomplemented
117C3×#217C2318yescomplemented
118C3×#217C2318yescomplemented
119C3×C4×Dic3C2314yescomplemented
120#3724C2318yescomplemented
121Dic3⋊Dic3C2314yescomplemented
122#3722C2314yescomplemented
123(C2×D3)⋊Dic3C2318yes—
124(C2×D3)⋊Dic3C2314yes—
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#546—91noSylow
127C25×C3—32no—
128C24×D3C2×D312yes—
129C22×C3×Q8—31no—
130C22×C3×D4—21no—
131C22×C3×D4—32no—
132C22×C3×D4—38no—
133C22×C3×D4—31no—
134C22×C3×D4—68no—
135C22×C3×D4C2×D311yescharacteristic
136C22×C3×D4C2×D311yescharacteristic
137C23×C3×C4—31no—
138C22×#67—32no—
139C22×#67—32no—
140C22×#67—32no—
141C22×#67—31no—
142C22×#67—62no—
143C22×#67C2×D312yes—
144C23×Dic3—32no—
145C23×Dic3—32no—
146C2×#239—38no—
147C2×#239—68no—
148C2×#237—38no—
149C2×#237—68no—
150C2×D3×D4—28no—
151C2×D3×D4C2×D318yescomplemented
152C22×D12—31no—
153C22×D12—32no—
154C22×D12C2×D311yescharacteristic
155C22×C4×D3—32no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—32no—
159C22×C4×D3—61no—
160C22×C4×D3C2×D311yescharacteristic
161C22×Dic6C2×D311yescharacteristic, complemented
162C3×#124—38no—
163C2×C3×C22⋊C4—32no—
164C2×C3×C22⋊C4—32no—
165C2×C3×C42—31no—
166#953—316no—
167C2×#217—32no—
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—31no—
171C2×#217—32no—
172C2×#217—316no—
173C2×#217—62no—
174C2×#217C2×D312yescomplemented
175C2×#217C2×D312yescomplemented
176#946—38no—
177#939—316no—
178#938—38no—
179#938—38no—
180#938—68no—
181#936C2×D318yescomplemented
182#935—316no—
183D4×Dic3—38no—
184C4×#67—38no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—61no—
194#924—38no—
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—31no—
198C2×C4×Dic3C2×D311yescharacteristic, complemented
199#884—316no—
200#883—316no—
201#882—316no—
202D3×C22⋊C4—316no—
203C4×D12—38no—
204C4×D12—38no—
205C23×C32—24no—
206C23×C32—24no—
207C23×C32—24no—
208C23×C32C2414yes—
209C23×C32C2411yescharacteristic
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3—22no—
213C22×C3⋊D3C2412yes—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—22no—
217C22×C3×D3—24no—
218C22×C3×D3—216no—
219C22×C3×D3—216no—
220C22×C3×D3—48no—
221C22×C3×D3—432no—
222C22×C3×D3C2×D418yes—
223C22×C3×D3#4114yescomplemented
224C22×C3×D3C2414yes—
225C22×C3×D3C2412yes—
226C32×D4—28no—
227C2×C32×C4C2×D414yes—
228C2×C32×C4C2412yes—
229#638—48no—
230C2×C3⋊Dic3—22no—
231C2×C3⋊Dic3—24no—
232C2×C3⋊Dic3C2414yes—
233C2×C3⋊Dic3C2412yes—
234C4×C3⋊D3—28no—
235C3×#67—216no—
236C2×C3×Dic3—24no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2414yes—
242C2×C3×Dic3C2412yes—
243C2×C3×Dic3C2412yes—
244C3×D12C2×D4116yescomplemented
245C3×C4×D3—28no—
246C3×Dic6—28no—
247#626—216no—
248#626—28no—
249D3×Dic3—216no—
250D3×Dic3—48no—
251C22×#41—91no—
252C23×D4—31no—
253#546—916no—
254C2×#124—31no—
255C2×#123—92no—
256C2×C22⋊Q8—91no—
257C2×#121—92no—
258C2×#121—91no—
259C2×#120—92no—
260C2×C4×D4—91no—
261C2×C4×D4—91no—
262C22×C22⋊C4—92no—
263C24×C3—22no—
264C24×C3—31no—
265C24×C3—32no—
266C24×C3—38no—
267C24×C3—68no—
268C24×C3—68no—
269C24×C3—124no—
270C24×C3C22×D312yes—
271C24×C3C22×D312yes—
272C23×D3—28no—
273C23×D3—28no—
274C23×D3—31no—
275C23×D3—31no—
276C23×D3—44no—
277C23×D3—61no—
278C23×D3C22×D318yes—
279C23×D3C22×D311yescharacteristic
280C23×D3C22×D312yes—
281C2×C3×Q8—34no—
282C2×C3×Q8—64no—
283C2×C3×D4—24no—
284C2×C3×D4—24no—
285C2×C3×D4—24no—
286C2×C3×D4—38no—
287C2×C3×D4—38no—
288C2×C3×D4—34no—
289C2×C3×D4—44no—
290C2×C3×D4—632no—
291C2×C3×D4—68no—
292C2×C3×D4C22×D314yes—
293C2×C3×D4C22×D314yes—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—32no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—34no—
300C22×C3×C4—64no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—28no—
304C2×#67—38no—
305C2×#67—38no—
306C2×#67—34no—
307C2×#67—38no—
308C2×#67—68no—
309C2×#67—68no—
310C2×#67—64no—
311C2×#67—124no—
312C2×#67—124no—
313C2×#67—128no—
314C2×#67C22×D318yes—
315C22×Dic3—32no—
316C22×Dic3—32no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—38no—
320C22×Dic3—38no—
321C22×Dic3—62no—
322C22×Dic3—61no—
323C22×Dic3—68no—
324C22×Dic3—124no—
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D312yes—
329#239—632no—
330#237—632no—
331D3×D4—232no—
332C2×D12—34no—
333C2×D12—38no—
334C2×D12—64no—
335C2×D12—68no—
336C2×D12#6718yescomplemented
337C2×D12C22×D314yes—
338C2×C4×D3—24no—
339C2×C4×D3—38no—
340C2×C4×D3—34no—
341C2×C4×D3—34no—
342C2×C4×D3—38no—
343C2×C4×D3—64no—
344C2×C4×D3—68no—
345C2×C4×D3—64no—
346C2×C4×D3—64no—
347C2×C4×D3—124no—
348C2×C4×D3—124no—
349C2×C4×D3C22×D314yes—
350C2×Dic6—24no—
351C2×Dic6C22×D314yescomplemented
352C3×C22⋊C4—38no—
353C3×C22⋊C4—38no—
354C3×C42—34no—
355#217—38no—
356#217—38no—
357#217—38no—
358#217—34no—
359#217—38no—
360#217—68no—
361#217C22×D318yescomplemented
362#217C22×D318yescomplemented
363(C2×D3)⋊C4—34no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—34no—
367(C2×D3)⋊C4—34no—
368C4⋊Dic3—34no—
369C4⋊Dic3—34no—
370C4⋊Dic3—34no—
371C4⋊Dic3—64no—
372Dic3⋊C4—38no—
373Dic3⋊C4—34no—
374Dic3⋊C4—38no—
375C4×Dic3C22×D314yescomplemented
376C22×C32—24no—
377C22×C32—24no—
378C22×C32—24no—
379C22×C32—48no—
380C22×C32C22×D412yes—
381C22×C32C2×#4112yes—
382C22×C32H(5,𝔽2)12yes—
383C22×C32C2511yescharacteristic
384C2×C3⋊D3—22no—
385C2×C3⋊D3—22no—
386C2×C3⋊D3—22no—
387C2×C3⋊D3—44no—
388C2×C3×D3—28no—
389C2×C3×D3—216no—
390C2×C3×D3—22no—
391C2×C3×D3—24no—
392C2×C3×D3—24no—
393C2×C3×D3—22no—
394C2×C3×D3—432no—
395C2×C3×D3C22×D418yes—
396C2×C3×D3C2×#4114yescomplemented
397C32×C4C22×D414yes—
398C3⋊Dic3—22no—
399C3⋊Dic3—24no—
400C3×Dic3—24no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C25—32no—
405C2×#41—98no—
406C2×#41—188no—
407C22×Q8—31no—
408C22×D4—32no—
409C22×D4—38no—
410C22×D4—31no—
411C22×D4—68no—
412C22×D4—91no—
413C22×D4—92no—
414C22×D4—92no—
415C22×D4D3211yescharacteristic
416C23×C4—31no—
417C23×C4—92no—
418C23×C4—92no—
419C23×C4—91no—
420#124—38no—
421#123—916no—
422C22⋊Q8—98no—
423#121—916no—
424#121—98no—
425#120—916no—
426C4×D4—98no—
427C4×D4—98no—
428C2×C4⋊C4—91no—
429C2×C4⋊C4—92no—
430C2×C4⋊C4—91no—
431C2×C22⋊C4—32no—
432C2×C22⋊C4—32no—
433C2×C22⋊C4—916no—
434C2×C22⋊C4—91no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—92no—
438C2×C22⋊C4—92no—
439C2×C42—31no—
440C23×C3—24no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—24no—
444C23×C3—24no—
445C23×C3—24no—
446C23×C3—24no—
447C23×C3—21no—
448C23×C3—38no—
449C23×C3—34no—
450C23×C3—32no—
451C23×C3—34no—
452C23×C3—44no—
453C23×C3—44no—
454C23×C3—44no—
455C23×C3—616no—
456C23×C3—616no—
457C23×C3—62no—
458C23×C3—64no—
459C23×C3—64no—
460C23×C3—62no—
461C23×C3—128no—
462C23×C3—1232no—
463C23×C3C23×D314yes—
464C23×C3C23×D314yes—
465C23×C3C23×D311yescharacteristic
466C23×C3C23×D311yescharacteristic
467C22×D3—24no—
468C22×D3—24no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—216no—
472C22×D3—216no—
473C22×D3—32no—
474C22×D3—32no—
475C22×D3—48no—
476C22×D3—432no—
477C22×D3—62no—
478C22×D3—64no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3—62no—
485C22×D3—122no—
486C22×D3—122no—
487C22×D3#23714yescomplemented
488C22×D3C2×#6718yes—
489C22×D3C23×D312yes—
490C22×D3C23×D314yes—
491C3×Q8—68no—
492C3×D4—28no—
493C3×D4—28no—
494C3×D4—316no—
495C3×D4—48no—
496C3×D4—616no—
497C2×C3×C4—22no—
498C2×C3×C4—24no—
499C2×C3×C4—32no—
500C2×C3×C4—34no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—64no—
507C2×C3×C4—68no—
508C2×C3×C4D3×D414yes—
509C2×C3×C4C2×#6714yes—
510C2×C3×C4C23×D312yes—
511C2×C3×C4C23×D312yes—
512#67—216no—
513#67—616no—
514#67—68no—
515#67—128no—
516#67—128no—
517#67—1216no—
518C2×Dic3—24no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—34no—
523C2×Dic3—34no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—64no—
527C2×Dic3—62no—
528C2×Dic3—616no—
529C2×Dic3—62no—
530C2×Dic3—64no—
531C2×Dic3—64no—
532C2×Dic3—62no—
533C2×Dic3—122no—
534C2×Dic3—124no—
535C2×Dic3—128no—
536C2×Dic3C23×D312yes—
537C2×Dic3C23×D312yes—
538C2×Dic3C23×D312yes—
539C2×Dic3C23×D314yes—
540D12—68no—
541D12—616no—
542D12C2×#67116yescomplemented
543C4×D3—28no—
544C4×D3—616no—
545C4×D3—68no—
546C4×D3—68no—
547C4×D3—128no—
548C4×D3—128no—
549Dic6—28no—
550C2×C32—44no—
551C2×C32#54614yescomplemented
552C2×C32C23×D411yescharacteristic
553C2×C32C22×#4111yescharacteristic
554C2×C32C2×H(5,𝔽2)11yescharacteristic
555C3⋊D3—42no—
556C3×D3—24no—
557C3×D3—28no—
558C24—31no—
559C24—32no—
560C24—38no—
561C24—68no—
562C24—68no—
563C24—91no—
564C24—124no—
565C24C2×D3212yes—
566#41—1832no—
567C2×Q8—34no—
568C2×Q8—64no—
569C2×D4—24no—
570C2×D4—38no—
571C2×D4—34no—
572C2×D4—38no—
573C2×D4—632no—
574C2×D4—68no—
575C2×D4—94no—
576C2×D4—98no—
577C2×D4—98no—
578C2×D4—188no—
579C2×D4—184no—
580C2×D4—364no—
581C2×D4C2×D3214yes—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—32no—
585C22×C4—31no—
586C22×C4—34no—
587C22×C4—64no—
588C22×C4—98no—
589C22×C4—98no—
590C22×C4—92no—
591C22×C4—91no—
592C22×C4—94no—
593C22×C4—188no—
594C22×C4—184no—
595C22×C4—364no—
596C22×C4C2×D3211yescharacteristic
597C4⋊C4—94no—
598C4⋊C4—98no—
599C4⋊C4—94no—
600C22⋊C4—38no—
601C22⋊C4—38no—
602C22⋊C4—94no—
603C22⋊C4—94no—
604C22⋊C4—98no—
605C22⋊C4—98no—
606C22⋊C4—98no—
607C42—34no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—24no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—21no—
618C22×C3—38no—
619C22×C3—34no—
620C22×C3—44no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—48no—
624C22×C3—48no—
625C22×C3—68no—
626C22×C3—616no—
627C22×C3—62no—
628C22×C3—64no—
629C22×C3—64no—
630C22×C3—62no—
631C22×C3—88no—
632C22×C3—1232no—
633C22×C3C2×D3×D412yes—
634C22×C3C2×#23712yes—
635C22×C3#100412yes—
636C22×C3D3×#4112yes—
637C22×C3#100912yes—
638C22×C3C22×#6712yes—
639C22×C3C24×D311yescharacteristic
640C22×C3C24×D311yescharacteristic
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—28no—
646C2×D3—216no—
647C2×D3—432no—
648C2×D3—64no—
649C2×D3—62no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—122no—
656C2×D3—122no—
657C2×D3—128no—
658C2×D3—124no—
659C2×D3—124no—
660C2×D3C2×#23714yescomplemented
661C2×D3C22×#6718yes—
662C3×C4—24no—
663C3×C4—62no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—64no—
667C3×C4C2×D3×D414yes—
668C3×C4C22×#6714yes—
669Dic3—24no—
670Dic3—22no—
671Dic3—22no—
672Dic3—22no—
673Dic3—62no—
674Dic3—64no—
675Dic3—64no—
676Dic3—62no—
677Dic3—122no—
678Dic3—124no—
679C32C2×#54611yescharacteristic, complemented, Sylow
680C23—24no—
681C23—24no—
682C23—24no—
683C23—34no—
684C23—38no—
685C23—32no—
686C23—34no—
687C23—616no—
688C23—616no—
689C23—64no—
690C23—64no—
691C23—62no—
692C23—62no—
693C23—92no—
694C23—128no—
695C23—1232no—
696C23—182no—
697C23—182no—
698C23—182no—
699C23C22×D3214yes—
700C23C22×D3211yescharacteristic
701Q8—68no—
702D4—28no—
703D4—316no—
704D4—616no—
705D4—1816no—
706D4—188no—
707D4—368no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—34no—
711C2×C4—32no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—64no—
716C2×C4—68no—
717C2×C4—94no—
718C2×C4—92no—
719C2×C4—1816no—
720C2×C4—184no—
721C2×C4—182no—
722C2×C4—188no—
723C2×C4—368no—
724C2×C4D3×#6714yes—
725C2×C4C22×D3212yes—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—24no—
730C2×C3—44no—
731C2×C3—44no—
732C2×C3—64no—
733C2×C3—68no—
734C2×C3—84no—
735C2×C3#567614yescomplemented
736C2×C3#580614yescomplemented
737C2×C3C22×D3×D411yescharacteristic
738C2×C3C22×#23711yescharacteristic
739C2×C3C2×#100411yescharacteristic
740C2×C3C2×D3×#4111yescharacteristic
741C2×C3C2×#100911yescharacteristic
742C2×C3C23×#6711yescharacteristic
743D3—24no—
744D3—28no—
745D3—124no—
746D3—122no—
747D3—122no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—34no—
752C22—38no—
753C22—48no—
754C22—64no—
755C22—64no—
756C22—62no—
757C22—62no—
758C22—68no—
759C22—616no—
760C22—1232no—
761C22—182no—
762C22—182no—
763C22—182no—
764C22—364no—
765C22D3×#23712yes—
766C22#6431412yes—
767C22C2×D3×#6712yes—
768C22C23×D3211yescharacteristic
769C4—62no—
770C4—62no—
771C4—62no—
772C4—64no—
773C4—184no—
774C4—182no—
775C4C2×D3×#6714yes—
776C3—21no—
777C3C2×#567611yescharacteristic, complemented
778C3C2×#580611yescharacteristic, complemented
779C2—44no—
780C2—64no—
781C2—68no—
782C2—362no—
783C2#1059522914yesdirect product factor
784C2C2×D3×#23711yescharacteristic
785C2C2×#6431411yescharacteristic
786C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C22×#3796C2semidirect
3. C2×#64147C2semidirect
4. C2×C3×#936C2semidirect
5. C2×#63977C2semidirect
6. C2×#63971C2semidirect
7. C2×#63969C2semidirect
8. C2×D3×#217C2semidirect
9. #10595229C2direct (N × H)
10. C2×C4×#626C2semidirect
11. C2×Dic3×D12C2semidirect
12. C2×#63856C2semidirect
17. C22×#638C22semidirect
18. C22×C4×C3⋊D3C22semidirect
21. C2×C3×D3×D4C22semidirect
24. C22×C3×Dic6C22semidirect
26. C22×#626C22semidirect
27. C22×D3×Dic3C22semidirect
28. C22×D3×Dic3C22semidirect
30. C2×#3796C22semidirect
31. C2×#3757C22semidirect
32. #64147C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
36. C3×#936C22semidirect
37. C2×C3×C4×Dic3C22semidirect
38. #63977C22semidirect
39. #63971C22semidirect
40. #63969C22semidirect
41. D3×#217C22semidirect
42. C2×#3724C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
44. C2×#3722C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. C4×#626C22semidirect
49. Dic3×D12C22semidirect
50. #63856C22semidirect
54. C22×D3×D4D3semidirect
64. C2×#936D3semidirect
88. C2×#638C23semidirect
92. C2×C4×C3⋊D3C23semidirect
100. C2×C3×D12D4semidirect
105. C2×C3×Dic6C23semidirect
109. C2×#626C23semidirect
112. C2×D3×Dic3C23semidirect
113. C2×D3×Dic3C23semidirect
115. #3757C23semidirect
116. C4⋊(C3⋊Dic3)C23semidirect
117. C3×#217C23semidirect
118. C3×#217C23semidirect
119. C3×C4×Dic3C23semidirect
120. #3724C23semidirect
121. Dic3⋊Dic3C23semidirect
122. #3722C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
151. C2×D3×D4C2×D3semidirect
161. C22×Dic6C2×D3semidirect
174. C2×#217C2×D3semidirect
175. C2×#217C2×D3semidirect
181. #936C2×D3semidirect
198. C2×C4×Dic3C2×D3semidirect
223. C22×C3×D3#41semidirect
244. C3×D12C2×D4semidirect
336. C2×D12#67semidirect
351. C2×Dic6C22×D3semidirect
361. #217C22×D3semidirect
362. #217C22×D3semidirect
375. C4×Dic3C22×D3semidirect
396. C2×C3×D3C2×#41semidirect
487. C22×D3#237semidirect
542. D12C2×#67semidirect
551. C2×C32#546semidirect
660. C2×D3C2×#237semidirect
679. C32C2×#546semidirect
735. C2×C3#5676semidirect
736. C2×C3#5806semidirect
777. C3C2×#5676semidirect
778. C3C2×#5806semidirect
783. C2#10595229direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C22×#37962
C2×#641472
C2×C3×#9362
C2×#639772
C2×#639712
C2×#639692
C2×D3×#2172
#105952292
C2×C4×#6262
C2×Dic3×D122
C2×#638562
C2×#58063
C2×#56763