Finite Group Databasebeta

← C2×#10595039 #11901331

Subgroups — C2×#10595039 #11901331

Order 1152.

3009 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C212yesmaximal, complemented
3C2×#63982C211yesmaximal, characteristic, complemented
4C2×#63981C212yesmaximal, complemented
5C2×#63980C211yesmaximal, characteristic, complemented
6#10595039C2116yesmaximal, direct product factor
7C2×#63906C212yesmaximal, complemented
8C2×#63868C212yesmaximal, complemented
9C2×#63852C212yesmaximal, complemented
10C2×#63850C212yesmaximal, complemented
11C2×#5560—32nomaximal
12C24×C3⋊D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×C4×D3C2212yescomplemented
17C22×#627C2211yescharacteristic, complemented
18C22×#626C2212yes—
19C22×#626C2212yes—
20C22×#625C2211yescharacteristic, complemented
21C2×#3752C2212yes—
22C2×#3752C2212yes—
23C2×#3752C2218yescomplemented
24C2×C3×#217C2212yes—
25C3×C4×#67C22116yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yescomplemented
27C2×C3×Dic3⋊C4C2212yescomplemented
28C2×C3×C4×Dic3C2212yescomplemented
29#63982C2218yescomplemented
30#63981C22116yescomplemented
31#63980C2218yescomplemented
32C2×#3724C2211yescharacteristic, complemented
33C2×#3724C2211yescharacteristic, complemented
34C2×Dic3⋊Dic3C2212yescomplemented
35C2×#3722C2212yes—
36C2×#3722C2212yes—
37C2×(C2×D3)⋊Dic3C2212yescomplemented
38#63906C22116yescomplemented
39#63868C22116yescomplemented
40#63852C22116yescomplemented
41#63850C22116yescomplemented
42C2×C3×C4×D4—32no—
43C2×#939—32no—
44C2×#937—32no—
45C2×#930—32no—
46C2×#929—32no—
47C2×C4×#67D312yescomplemented
48C22×(C2×D3)⋊C4—32no—
49C22×(C2×D3)⋊C4—61no—
50#5560—332no—
51C2×#898—32no—
52C2×#894—32no—
53C2×#885—32no—
54C2×#884—32no—
55C2×#882—32no—
56C2×#878—32no—
57C2×#876—32no—
58C2×#875—32no—
59C24×C32C2311yescharacteristic
60C23×C3⋊D3—24no—
61C23×C3⋊D3—42no—
62C23×C3⋊D3—42no—
63C23×C3⋊D3C2312yes—
64C23×C3⋊D3C2314yes—
65C23×C3×D3C2312yes—
66C22×C32×C4—42no—
67C22×C32×C4C2312yes—
68C22×C32×C4C2314yes—
69C22×C3⋊Dic3—42no—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2314yes—
73C2×C3×#67—28no—
74C2×C3×#67C2318yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C2×C3×C4×D3—44no—
79C2×C3×C4×D3C2318yescomplemented
80C2×#627—42no—
81C2×#627C2314yescomplemented
82C2×#626—44no—
83C2×#626—44no—
84C2×#626C2318yes—
85C2×#626C2318yes—
86C2×#625—42no—
87C2×#625C2314yescomplemented
88#3752C2318yes—
89#3752C2318yes—
90C3×#217C2318yes—
91C3×(C2×D3)⋊C4C2318yescomplemented
92C3×Dic3⋊C4C2318yescomplemented
93C3×C4×Dic3C2318yescomplemented
94#3724C2314yescomplemented
95#3724C2314yescomplemented
96Dic3⋊Dic3C2318yescomplemented
97#3722C2318yes—
98#3722C2318yes—
99(C2×D3)⋊Dic3C2318yescomplemented
100C2×#538—91noSylow
101C24×D3—32no—
102C24×D3—61no—
103C22×C3×D4—32no—
104C23×C3×C4—21no—
105C23×C3×C4—32no—
106C23×C3×C4C2×D312yes—
107C22×#67—32no—
108C22×#67—32no—
109C22×#67—32no—
110C22×#67C2×D312yes—
111C23×Dic3—32no—
112C23×Dic3—61no—
113C22×D12—32no—
114C22×D12—32no—
115C22×C4×D3C2×D312yescomplemented
116C22×Dic6—32no—
117C3×C4×D4—316no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C22⋊C4—32no—
120C2×C3×C22⋊C4—32no—
121C2×C3×C42—32no—
122C2×#217—32no—
123C2×#217C2×D312yes—
124#939—316no—
125#937—316no—
126#930—316no—
127#929—316no—
128C4×#67C2×D3116yescomplemented
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—316no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—62no—
140C2×(C2×D3)⋊C4—62no—
141C2×(C2×D3)⋊C4—68no—
142C2×(C2×D3)⋊C4C2×D312yescomplemented
143C2×C4⋊Dic3—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4C2×D312yescomplemented
148C2×C4×Dic3C2×D312yescomplemented
149#898—316no—
150#894—316no—
151#885—316no—
152#884—316no—
153#882—316no—
154#878—316no—
155#876—316no—
156#875—316no—
157C23×C32—22no—
158C23×C32—22no—
159C23×C32#4114yes—
160C23×C32C2412yes—
161C23×C32C2411yescharacteristic
162C22×C3⋊D3—28no—
163C22×C3⋊D3—24no—
164C22×C3⋊D3—24no—
165C22×C3⋊D3—24no—
166C22×C3⋊D3—44no—
167C22×C3⋊D3—44no—
168C22×C3⋊D3—416no—
169C22×C3⋊D3C2414yes—
170C22×C3×D3—24no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3C2414yes—
174C2×C32×C4—24no—
175C2×C32×C4—44no—
176C2×C32×C4C2414yes—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—44no—
180C2×C3⋊Dic3C2412yes—
181C2×C3⋊Dic3C2412yes—
182C3×#67—216no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—24no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2414yes—
188C2×C3×Dic3C2414yes—
189C3×C4×D3—48no—
190#627—44no—
191#626—48no—
192#626—48no—
193#625—44no—
194#538—916no—
195C2×#126—92no—
196C2×#124—92no—
197C2×#123—92no—
198C2×C22⋊Q8—91no—
199C2×#121—92no—
200C2×#121—91no—
201C2×#120—92no—
202C2×C4×D4—32no—
203C22×C22⋊C4—91no—
204C24×C3—21no—
205C24×C3—32no—
206C24×C3C22×D312yes—
207C23×D3—32no—
208C23×D3—32no—
209C23×D3—38no—
210C23×D3—62no—
211C23×D3—64no—
212C23×D3—68no—
213C23×D3—68no—
214C23×D3—124no—
215C23×D3—124no—
216C23×D3—124no—
217C23×D3—124no—
218C23×D3C22×D312yes—
219C2×C3×D4—38no—
220C2×C3×D4—68no—
221C22×C3×C4—22no—
222C22×C3×C4—24no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—38no—
227C22×C3×C4—44no—
228C22×C3×C4—44no—
229C22×C3×C4—124no—
230C22×C3×C4C22×D312yes—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D318yes—
233C2×#67—28no—
234C2×#67—38no—
235C2×#67—38no—
236C2×#67—38no—
237C2×#67—124no—
238C2×#67—124no—
239C2×#67—124no—
240C2×#67C22×D318yes—
241C22×Dic3—32no—
242C22×Dic3—32no—
243C22×Dic3—38no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—64no—
247C22×Dic3—124no—
248C22×Dic3—124no—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D312yes—
252C2×D12—38no—
253C2×D12—38no—
254C2×D12—124no—
255C2×D12—124no—
256C2×C4×D3—44no—
257C2×C4×D3C22×D318yescomplemented
258C2×Dic6—38no—
259C2×Dic6—124no—
260C3×C4⋊C4—38no—
261C3×C22⋊C4—38no—
262C3×C22⋊C4—38no—
263C3×C42—38no—
264#217—38no—
265#217C22×D318yes—
266(C2×D3)⋊C4—38no—
267(C2×D3)⋊C4—38no—
268(C2×D3)⋊C4—38no—
269(C2×D3)⋊C4—38no—
270(C2×D3)⋊C4—38no—
271(C2×D3)⋊C4—38no—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4—38no—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—68no—
276(C2×D3)⋊C4—68no—
277(C2×D3)⋊C4C22×D318yescomplemented
278C4⋊Dic3—38no—
279Dic3⋊C4—38no—
280Dic3⋊C4—38no—
281Dic3⋊C4—38no—
282Dic3⋊C4C22×D318yescomplemented
283C4×Dic3C22×D318yescomplemented
284C22×C32—28no—
285C22×C32—22no—
286C22×C32—22no—
287C22×C32C2×#4114yes—
288C22×C32C2×#4112yes—
289C22×C32H(5,𝔽2)12yes—
290C22×C32H(5,𝔽2)12yes—
291C22×C32C2511yescharacteristic
292C2×C3⋊D3—24no—
293C2×C3⋊D3—24no—
294C2×C3⋊D3—24no—
295C2×C3⋊D3—416no—
296C2×C3⋊D3—48no—
297C2×C3×D3—24no—
298C2×C3×D3—24no—
299C2×C3×D3—24no—
300C2×C3×D3—48no—
301C32×C4—24no—
302C3⋊Dic3—22no—
303C3⋊Dic3—22no—
304C3×Dic3—24no—
305C3×Dic3—24no—
306C3×Dic3—24no—
307C25—91no—
308C22×Q8—91no—
309C22×D4—32no—
310C22×D4—92no—
311C22×D4—92no—
312C22×D4—91no—
313C23×C4—32no—
314C23×C4—91no—
315C23×C4D3211yescharacteristic
316#126—916no—
317#124—916no—
318#123—916no—
319C22⋊Q8—98no—
320#121—916no—
321#121—98no—
322#120—916no—
323C4×D4—316no—
324C2×C4⋊C4—32no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—91no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—92no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4—98no—
336C2×C42—32no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—22no—
342C23×C3—21no—
343C23×C3—24no—
344C23×C3—34no—
345C23×C3—64no—
346C23×C3—64no—
347C23×C3—64no—
348C23×C3#23518yes—
349C23×C3C23×D314yes—
350C23×C3C23×D312yes—
351C22×D3—24no—
352C22×D3—24no—
353C22×D3—24no—
354C22×D3—34no—
355C22×D3—34no—
356C22×D3—64no—
357C22×D3—616no—
358C22×D3—68no—
359C22×D3—616no—
360C22×D3—64no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—124no—
367C22×D3—124no—
368C22×D3—128no—
369C22×D3—128no—
370C22×D3—128no—
371C22×D3—128no—
372C22×D3—1232no—
373C22×D3—1232no—
374C22×D3C23×D314yes—
375C3×D4—616no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—34no—
380C2×C3×C4—34no—
381C2×C3×C4—34no—
382C2×C3×C4—44no—
383C2×C3×C4—48no—
384C2×C3×C4—48no—
385C2×C3×C4—64no—
386C2×C3×C4—64no—
387C2×C3×C4—64no—
388C2×C3×C4—128no—
389C2×C3×C4C23×D314yes—
390C2×C3×C4C23×D314yes—
391#67—216no—
392#67—128no—
393#67—128no—
394#67—128no—
395C2×Dic3—24no—
396C2×Dic3—24no—
397C2×Dic3—24no—
398C2×Dic3—34no—
399C2×Dic3—34no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—64no—
403C2×Dic3—64no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—128no—
407C2×Dic3—128no—
408C2×Dic3C23×D314yes—
409C2×Dic3C23×D314yes—
410C2×Dic3C23×D314yes—
411D12—128no—
412D12—128no—
413C4×D3—48no—
414Dic6—128no—
415C2×C32—24no—
416C2×C32#53814yescomplemented
417C2×C32C22×#4111yescharacteristic
418C2×C32C2×H(5,𝔽2)11yescharacteristic
419C2×C32C2×H(5,𝔽2)11yescharacteristic
420C3⋊D3—44no—
421C3×D3—44no—
422C24—32no—
423C24—92no—
424C24—94no—
425C24—184no—
426C24—362no—
427C24—362no—
428C24C2×D3211yescharacteristic
429C2×Q8—94no—
430C2×Q8—362no—
431C2×D4—38no—
432C2×D4—68no—
433C2×D4—98no—
434C2×D4—98no—
435C2×D4—94no—
436C2×D4—364no—
437C2×D4—364no—
438C2×D4—362no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—32no—
442C22×C4—38no—
443C22×C4—42no—
444C22×C4—91no—
445C22×C4—91no—
446C22×C4—94no—
447C22×C4—124no—
448C22×C4—362no—
449C22×C4C2×D3212yes—
450C22×C4C2×D3214yes—
451C4⋊C4—38no—
452C4⋊C4—98no—
453C4⋊C4—94no—
454C4⋊C4—94no—
455C22⋊C4—38no—
456C22⋊C4—38no—
457C22⋊C4—98no—
458C22⋊C4—98no—
459C22⋊C4—98no—
460C22⋊C4—98no—
461C22⋊C4—98no—
462C42—38no—
463C22×C3—24no—
464C22×C3—24no—
465C22×C3—216no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—216no—
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—64no—
475C22×C3—64no—
476C22×C3—64no—
477C22×C3—128no—
478C22×C3C2×#23518yes—
479C22×C3C2×#23514yes—
480C22×C3#100414yes—
481C22×C3#100914yes—
482C22×C3C24×D312yes—
483C2×D3—24no—
484C2×D3—24no—
485C2×D3—24no—
486C2×D3—48no—
487C2×D3—68no—
488C2×D3—64no—
489C2×D3—64no—
490C2×D3—64no—
491C2×D3—64no—
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—124no—
495C2×D3—124no—
496C2×D3—1232no—
497C2×D3—1232no—
498C2×D3—1216no—
499C2×D3—128no—
500C2×D3—128no—
501C3×C4—24no—
502C3×C4—24no—
503C3×C4—44no—
504C3×C4—64no—
505C3×C4—64no—
506C3×C4—64no—
507Dic3—24no—
508Dic3—24no—
509Dic3—24no—
510Dic3—64no—
511Dic3—64no—
512Dic3—122no—
513Dic3—122no—
514C32C2×#53811yescharacteristic, complemented, Sylow
515C23—22no—
516C23—22no—
517C23—34no—
518C23—64no—
519C23—64no—
520C23—64no—
521C23—94no—
522C23—188no—
523C23—184no—
524C23—184no—
525C23—184no—
526C23—364no—
527C23—364no—
528C23—3616no—
529C23#379814yes—
530C23C22×D3212yes—
531C23C22×D3211yescharacteristic
532Q8—364no—
533D4—616no—
534D4—368no—
535D4—368no—
536D4—364no—
537C2×C4—24no—
538C2×C4—34no—
539C2×C4—34no—
540C2×C4—34no—
541C2×C4—44no—
542C2×C4—64no—
543C2×C4—64no—
544C2×C4—64no—
545C2×C4—92no—
546C2×C4—92no—
547C2×C4—128no—
548C2×C4—182no—
549C2×C4—182no—
550C2×C4—364no—
551C2×C4C22×D3214yes—
552C2×C3—28no—
553C2×C3—28no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—24no—
558C2×C3—124no—
559C2×C3#556018yescomplemented
560C2×C3C22×#23512yes—
561C2×C3C2×#100412yes—
562C2×C3C2×#100912yes—
563D3—44no—
564D3—128no—
565D3—124no—
566D3—124no—
567C22—22no—
568C22—22no—
569C22—28no—
570C22—64no—
571C22—64no—
572C22—64no—
573C22—128no—
574C22—184no—
575C22—184no—
576C22—184no—
577C22—3616no—
578C22—368no—
579C22C2×#379814yes—
580C22C2×#379812yes—
581C22#6430812yes—
582C22#6433012yes—
583C22C23×D3211yescharacteristic
584C4—24no—
585C4—64no—
586C4—64no—
587C4—64no—
588C4—182no—
589C4—182no—
590C3—21no—
591C3C2×#556012yescomplemented
592C2—24no—
593C2—124no—
594C2—364no—
595C2#1059503914yesdirect product factor
596C2C22×#379811yescharacteristic
597C2C2×#6430811yescharacteristic
598C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3752C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×#63982C2semidirect
4. C2×#63981C2semidirect
5. C2×#63980C2semidirect
6. #10595039C2direct (N × H)
7. C2×#63906C2semidirect
8. C2×#63868C2semidirect
9. C2×#63852C2semidirect
10. C2×#63850C2semidirect
16. C22×C3×C4×D3C22semidirect
17. C22×#627C22semidirect
20. C22×#625C22semidirect
23. C2×#3752C22semidirect
25. C3×C4×#67C22semidirect
26. C2×C3×(C2×D3)⋊C4C22semidirect
27. C2×C3×Dic3⋊C4C22semidirect
28. C2×C3×C4×Dic3C22semidirect
29. #63982C22semidirect
30. #63981C22semidirect
31. #63980C22semidirect
32. C2×#3724C22semidirect
33. C2×#3724C22semidirect
34. C2×Dic3⋊Dic3C22semidirect
37. C2×(C2×D3)⋊Dic3C22semidirect
38. #63906C22semidirect
39. #63868C22semidirect
40. #63852C22semidirect
41. #63850C22semidirect
47. C2×C4×#67D3semidirect
79. C2×C3×C4×D3C23semidirect
81. C2×#627C23semidirect
87. C2×#625C23semidirect
91. C3×(C2×D3)⋊C4C23semidirect
92. C3×Dic3⋊C4C23semidirect
93. C3×C4×Dic3C23semidirect
94. #3724C23semidirect
95. #3724C23semidirect
96. Dic3⋊Dic3C23semidirect
99. (C2×D3)⋊Dic3C23semidirect
115. C22×C4×D3C2×D3semidirect
128. C4×#67C2×D3semidirect
142. C2×(C2×D3)⋊C4C2×D3semidirect
147. C2×Dic3⋊C4C2×D3semidirect
148. C2×C4×Dic3C2×D3semidirect
257. C2×C4×D3C22×D3semidirect
277. (C2×D3)⋊C4C22×D3semidirect
282. Dic3⋊C4C22×D3semidirect
283. C4×Dic3C22×D3semidirect
416. C2×C32#538semidirect
514. C32C2×#538semidirect
559. C2×C3#5560semidirect
591. C3C2×#5560semidirect
595. C2#10595039direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37522
C2×C3×C4×#672
C2×#639822
C2×#639812
C2×#639802
#105950392
C2×#639062
C2×#638682
C2×#638522
C2×#638502
C2×#55603