Finite Group Databasebeta

← C2×#10595429 #11900328

Subgroups — C2×#10595429 #11900328

Order 1152.

4105 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C4×D32C211yesmaximal, characteristic
3C2×C3×#946C212yesmaximal, complemented
4#10595429C2116yesmaximal, direct product factor
5C2×#63921C212yesmaximal
6C2×#63900C211yesmaximal, characteristic, complemented
7C2×#63896C214yesmaximal, complemented
8C2×#63883C212yesmaximal, complemented
9C2×#63857C212yesmaximal, complemented
10C2×D3×C22⋊Q8—32nomaximal
11C23×D32C2211yescharacteristic
12C22×C32×Q8C2211yescharacteristic, complemented
13C2×Q8×C3⋊D3—28no—
14C2×Q8×C3⋊D3C2218yescomplemented
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C22×#634C2212yescomplemented
19C22×C3×C4×D3C2212yes—
20C22×#624C2211yescharacteristic
21C22×#624C2212yes—
22C22×D3×Dic3C2212yes—
23C2×C4×D32—28no—
24C2×C4×D32C2218yes—
25C3×#946C22116yescomplemented
26C2×C3×(C2×D3)⋊C4C2214yes—
27C2×C3×C4⋊Dic3C2212yescomplemented
28C2×C3×Dic3⋊C4C2214yescomplemented
29C2×#3724C2212yescomplemented
30C2×Dic3⋊Dic3C2214yescomplemented
31C2×(C2×D3)⋊Dic3C2214yes—
32#63921C22116yes—
33#63900C2218yescomplemented
34#63896C22132yescomplemented
35#63883C22116yescomplemented
36#63857C22116yescomplemented
37C22×D3×Q8—32no—
38C22×D3×Q8—61no—
39C23×C4×D3—32no—
40C2×C3×C22⋊Q8—32no—
41C2×#946D312yescomplemented
42C2×#924—32no—
43D3×C22⋊Q8—332no—
44C2×#897—32no—
45C2×#896—34no—
46C2×D3×C4⋊C4—32no—
47C2×D3×C4⋊C4—34no—
48C2×D3×C22⋊C4—34no—
49C2×#878—34no—
50C23×C3⋊D3C2311yescharacteristic
51C23×C3×D3C2312yes—
52C22×D32—24no—
53C22×D32—24no—
54C22×D32Q818yescomplemented
55C22×D32C2314yes—
56C2×C32×Q8—24no—
57C2×C32×Q8C2314yescomplemented
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2312yes—
61C22×C3⋊Dic3C2311yescharacteristic
62Q8×C3⋊D3—232no—
63C2×C4×C3⋊D3—28no—
64C2×C4×C3⋊D3D418yes—
65C2×C4×C3⋊D3C2318yes—
66C2×C4×C3⋊D3C2314yes—
67C2×#634—24no—
68C2×#634—28no—
69C2×#634C2314yescomplemented
70C2×#634C2318yescomplemented
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2314yes—
73C2×C3×C4×D3—28no—
74C2×C3×C4×D3C2318yes—
75C2×#624—24no—
76C2×#624—28no—
77C2×#624C2314yes—
78C2×#624C2318yes—
79C2×D3×Dic3—28no—
80C2×D3×Dic3C2318yes—
81C4×D32—232no—
82C3×(C2×D3)⋊C4C23116yes—
83C3×C4⋊Dic3C2318yescomplemented
84C3×Dic3⋊C4C23116yescomplemented
85#3724C2318yescomplemented
86Dic3⋊Dic3C23116yescomplemented
87(C2×D3)⋊Dic3C23116yes—
88C22×C22⋊Q8—91noSylow
89C24×D3—32no—
90C22×C3×Q8—21no—
91C22×C3×Q8C2×D312yescomplemented
92C23×C3×C4—32no—
93C23×Dic3—32no—
94C2×D3×Q8—316no—
95C2×D3×Q8—68no—
96C2×D3×Q8—616no—
97C2×D3×Q8—616no—
98C22×C4×D3—32no—
99C22×C4×D3—32no—
100C22×C4×D3—34no—
101C22×C4×D3—32no—
102C22×C4×D3—34no—
103C22×C4×D3—316no—
104C22×C4×D3—61no—
105C22×C4×D3—62no—
106C22×C4×D3—616no—
107C22×C4×D3C2×D312yes—
108C22×Dic6—34no—
109C22×Dic6—32no—
110C22×Dic6—61no—
111C22×Dic6—62no—
112C3×C22⋊Q8—316no—
113C2×C3×C4⋊C4—34no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C22⋊C4—34no—
116C2×#217—34no—
117#946C2×D3116yescomplemented
118C2×(C2×D3)⋊C4—34no—
119C2×(C2×D3)⋊C4C2×D314yes—
120C2×C4⋊Dic3—34no—
121C2×C4⋊Dic3C2×D312yescomplemented
122#924—316no—
123C2×Dic3⋊C4—34no—
124C2×Dic3⋊C4—34no—
125C2×Dic3⋊C4C2×D314yescomplemented
126#897—316no—
127#896—332no—
128D3×C4⋊C4—316no—
129D3×C4⋊C4—332no—
130D3×C22⋊C4—332no—
131#878—332no—
132C23×C32C2411yescharacteristic
133C22×C3⋊D3C2×D414yes—
134C22×C3⋊D3C2×Q814yes—
135C22×C3⋊D3#4114yes—
136C22×C3⋊D3C2412yes—
137C22×C3×D3—24no—
138C22×C3×D3—24no—
139C22×C3×D3C2×Q818yescomplemented
140C22×C3×D3C2414yes—
141C2×D32—232no—
142C2×D32—28no—
143C2×D32—28no—
144C2×D32C2×Q8116yescomplemented
145C32×Q8—28no—
146C2×C32×C4—24no—
147C2×C32×C4C2×D414yes—
148C2×C32×C4C2414yes—
149C2×C32×C4C2412yes—
150C2×C3⋊Dic3—24no—
151C2×C3⋊Dic3C2×D414yes—
152C2×C3⋊Dic3C2414yes—
153C2×C3⋊Dic3C2412yes—
154C4×C3⋊D3—216no—
155C4×C3⋊D3C2×D4116yes—
156#634—28no—
157#634—216no—
158C2×C3×Dic3—24no—
159C2×C3×Dic3—28no—
160C2×C3×Dic3C2418yes—
161C2×C3×Dic3C2414yes—
162C3×C4×D3—216no—
163#624—28no—
164#624—216no—
165D3×Dic3—216no—
166C23×Q8—91no—
167C24×C4—91no—
168C2×C22⋊Q8—32no—
169C2×C22⋊Q8—94no—
170C2×C22⋊Q8—92no—
171C2×C22⋊Q8—916no—
172C22×C4⋊C4—92no—
173C22×C4⋊C4—91no—
174C22×C22⋊C4—92no—
175C24×C3—32no—
176C23×D3—32no—
177C23×D3—316no—
178C23×D3—38no—
179C23×D3—61no—
180C23×D3—68no—
181C23×D3—68no—
182C23×D3C22×D312yes—
183C2×C3×Q8—28no—
184C2×C3×Q8—28no—
185C2×C3×Q8—24no—
186C2×C3×Q8C22×D318yescomplemented
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—32no—
190C22×C3×C4—34no—
191C22×C3×C4—38no—
192C22×C3×C4—68no—
193C22×C3×C4C22×D314yes—
194C22×C3×C4C22×D312yes—
195C22×Dic3—32no—
196C22×Dic3—34no—
197C22×Dic3—38no—
198C22×Dic3—61no—
199C22×Dic3—62no—
200C22×Dic3—68no—
201C22×Dic3C22×D314yes—
202C22×Dic3C22×D312yes—
203D3×Q8—664no—
204D3×Q8—664no—
205C2×C4×D3—28no—
206C2×C4×D3—316no—
207C2×C4×D3—38no—
208C2×C4×D3—38no—
209C2×C4×D3—316no—
210C2×C4×D3—316no—
211C2×C4×D3—38no—
212C2×C4×D3—68no—
213C2×C4×D3—64no—
214C2×C4×D3—68no—
215C2×C4×D3—664no—
216C2×C4×D3—616no—
217C2×C4×D3—68no—
218C2×C4×D3—68no—
219C2×C4×D3—616no—
220C2×C4×D3—616no—
221C2×C4×D3C22×D318yes—
222C2×Dic6—316no—
223C2×Dic6—38no—
224C2×Dic6—64no—
225C2×Dic6—68no—
226C2×Dic6—616no—
227C2×Dic6—616no—
228C2×Dic6—68no—
229C2×Dic6—68no—
230C3×C4⋊C4—316no—
231C3×C4⋊C4—38no—
232C3×C22⋊C4—316no—
233#217—316no—
234(C2×D3)⋊C4—316no—
235(C2×D3)⋊C4C22×D3116yes—
236C4⋊Dic3—316no—
237C4⋊Dic3C22×D318yescomplemented
238Dic3⋊C4—316no—
239Dic3⋊C4—316no—
240Dic3⋊C4C22×D3116yescomplemented
241C22×C32C22×D412yes—
242C22×C32C22×Q812yes—
243C22×C32C2×#4112yes—
244C22×C32C2511yescharacteristic
245C2×C3⋊D3C22⋊Q8116yescomplemented
246C2×C3⋊D3C22×D414yes—
247C2×C3⋊D3C22×Q814yes—
248C2×C3⋊D3C2×#4114yes—
249C2×C3×D3—216no—
250C2×C3×D3—24no—
251C2×C3×D3—24no—
252C2×C3×D3C22×Q818yescomplemented
253D32—232no—
254C32×C4—24no—
255C32×C4C22×D414yes—
256C3⋊Dic3—24no—
257C3⋊Dic3C22×D414yes—
258C3×Dic3—24no—
259C3×Dic3—28no—
260C25—91no—
261C22×Q8—98no—
262C22×Q8—92no—
263C22×Q8—91no—
264C22×Q8—188no—
265C22×Q8D3211yescharacteristic, complemented
266C23×C4—32no—
267C23×C4—92no—
268C23×C4—91no—
269C23×C4—98no—
270C23×C4—92no—
271C23×C4—91no—
272C23×C4—92no—
273C23×C4—188no—
274C22⋊Q8—316no—
275C22⋊Q8—932no—
276C22⋊Q8—916no—
277C2×C4⋊C4—34no—
278C2×C4⋊C4—32no—
279C2×C4⋊C4—916no—
280C2×C4⋊C4—98no—
281C2×C4⋊C4—92no—
282C2×C4⋊C4—94no—
283C2×C22⋊C4—34no—
284C2×C22⋊C4—916no—
285C2×C22⋊C4—94no—
286C23×C3—21no—
287C23×C3—38no—
288C23×C3—34no—
289C23×C3—64no—
290C23×C3—64no—
291C23×C3C23×D312yes—
292C22×D3—24no—
293C22×D3—24no—
294C22×D3—38no—
295C22×D3—38no—
296C22×D3—38no—
297C22×D3—34no—
298C22×D3—332no—
299C22×D3—64no—
300C22×D3—64no—
301C22×D3—64no—
302C22×D3—62no—
303C22×D3—616no—
304C22×D3—616no—
305C22×D3—664no—
306C22×D3D3×Q818yescomplemented
307C22×D3C23×D314yes—
308C3×Q8—216no—
309C3×Q8—216no—
310C2×C3×C4—28no—
311C2×C3×C4—28no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—24no—
315C2×C3×C4—34no—
316C2×C3×C4—38no—
317C2×C3×C4—64no—
318C2×C3×C4—68no—
319C2×C3×C4—616no—
320C2×C3×C4D3×D418yes—
321C2×C3×C4C23×D318yes—
322C2×C3×C4C23×D314yes—
323C2×Dic3—24no—
324C2×Dic3—28no—
325C2×Dic3—38no—
326C2×Dic3—34no—
327C2×Dic3—38no—
328C2×Dic3—64no—
329C2×Dic3—62no—
330C2×Dic3—64no—
331C2×Dic3—616no—
332C2×Dic3—68no—
333C2×Dic3—68no—
334C2×Dic3C23×D318yes—
335C2×Dic3C23×D314yes—
336C4×D3—216no—
337C4×D3—332no—
338C4×D3—616no—
339C4×D3—632no—
340C4×D3—616no—
341C4×D3—616no—
342C4×D3—632no—
343C4×D3—632no—
344Dic6—632no—
345Dic6—632no—
346Dic6—616no—
347Dic6—616no—
348C2×C32C2×C22⋊Q814yescomplemented
349C2×C32C23×D411yescharacteristic
350C2×C32C23×Q811yescharacteristic
351C2×C32C22×#4111yescharacteristic
352C3⋊D3C2×C22⋊Q818yescomplemented
353C3×D3—28no—
354C24—32no—
355C24—94no—
356C24—98no—
357C24—91no—
358C24—184no—
359C24—184no—
360C2×Q8—24no—
361C2×Q8—98no—
362C2×Q8—94no—
363C2×Q8—188no—
364C2×Q8—1832no—
365C2×Q8—184no—
366C2×Q8C2×D3214yescomplemented
367C22×C4—34no—
368C22×C4—32no—
369C22×C4—38no—
370C22×C4—68no—
371C22×C4—98no—
372C22×C4—94no—
373C22×C4—98no—
374C22×C4—91no—
375C22×C4—94no—
376C22×C4—98no—
377C22×C4—92no—
378C22×C4—98no—
379C22×C4—188no—
380C22×C4—1832no—
381C22×C4—184no—
382C22×C4—188no—
383C22×C4—188no—
384C22×C4C2×D3212yes—
385C22×C4C2×D3211yescharacteristic
386C4⋊C4—316no—
387C4⋊C4—38no—
388C4⋊C4—98no—
389C4⋊C4—916no—
390C22⋊C4—316no—
391C22⋊C4—916no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—38no—
397C22×C3—64no—
398C22×C3—64no—
399C22×C3—616no—
400C22×C3C2×D3×D414yes—
401C22×C3C2×D3×Q814yes—
402C22×C3D3×#4114yes—
403C22×C3C24×D312yes—
404C2×D3—24no—
405C2×D3—24no—
406C2×D3—216no—
407C2×D3—38no—
408C2×D3—38no—
409C2×D3—38no—
410C2×D3—332no—
411C2×D3—64no—
412C2×D3—616no—
413C2×D3—64no—
414C2×D3—64no—
415C2×D3—664no—
416C2×D3C2×D3×Q818yescomplemented
417C3×C4—28no—
418C3×C4—28no—
419C3×C4—24no—
420C3×C4—64no—
421C3×C4—68no—
422C3×C4C2×D3×D418yes—
423Dic3—24no—
424Dic3—28no—
425Dic3—38no—
426Dic3—64no—
427Dic3—68no—
428Dic3—68no—
429C32C22×C22⋊Q811yescharacteristic, complemented, Sylow
430C23—38no—
431C23—34no—
432C23—64no—
433C23—64no—
434C23—916no—
435C23—94no—
436C23—94no—
437C23—94no—
438C23—92no—
439C23—188no—
440C23—188no—
441C23—1832no—
442C23C22×D3211yescharacteristic
443Q8—28no—
444Q8—1816no—
445Q8—188no—
446C2×C4—24no—
447C2×C4—38no—
448C2×C4—34no—
449C2×C4—68no—
450C2×C4—64no—
451C2×C4—616no—
452C2×C4—94no—
453C2×C4—92no—
454C2×C4—916no—
455C2×C4—94no—
456C2×C4—1816no—
457C2×C4—188no—
458C2×C4—1816no—
459C2×C4—1816no—
460C2×C4—184no—
461C2×C4#381114yes—
462C2×C4C22×D3214yes—
463C2×C4C22×D3212yes—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—24no—
468C2×C3—68no—
469C2×C3D3×C22⋊Q818yescomplemented
470C2×C3C22×D3×D412yes—
471C2×C3C22×D3×Q812yes—
472C2×C3C2×D3×#4112yes—
473D3—28no—
474D3—316no—
475D3—68no—
476C22—38no—
477C22—64no—
478C22—64no—
479C22—616no—
480C22—94no—
481C22—94no—
482C22—94no—
483C22—916no—
484C22—1832no—
485C22D32×Q812yes—
486C22#6431912yes—
487C22C2×#381112yes—
488C22C23×D3211yescharacteristic
489C4—24no—
490C4—68no—
491C4—64no—
492C4—94no—
493C4—184no—
494C4C2×#381114yes—
495C3—21no—
496C3C2×D3×C22⋊Q812yescomplemented
497C2—68no—
498C2—98no—
499C2#1059542914yesdirect product factor
500C2C2×D32×Q811yescharacteristic
501C2C2×#6431911yescharacteristic
502C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC23×D32C22
hypercenterC22×Q8D32
hypocenterC32C22×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×C3⋊D3C2semidirect
3. C2×C3×#946C2semidirect
4. #10595429C2direct (N × H)
6. C2×#63900C2semidirect
7. C2×#63896C2semidirect
8. C2×#63883C2semidirect
9. C2×#63857C2semidirect
12. C22×C32×Q8C22semidirect
14. C2×Q8×C3⋊D3C22semidirect
17. C22×#634C22semidirect
18. C22×#634C22semidirect
25. C3×#946C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
29. C2×#3724C22semidirect
30. C2×Dic3⋊Dic3C22semidirect
33. #63900C22semidirect
34. #63896C22semidirect
35. #63883C22semidirect
36. #63857C22semidirect
41. C2×#946D3semidirect
54. C22×D32Q8semidirect
57. C2×C32×Q8C23semidirect
69. C2×#634C23semidirect
70. C2×#634C23semidirect
83. C3×C4⋊Dic3C23semidirect
84. C3×Dic3⋊C4C23semidirect
85. #3724C23semidirect
86. Dic3⋊Dic3C23semidirect
91. C22×C3×Q8C2×D3semidirect
117. #946C2×D3semidirect
121. C2×C4⋊Dic3C2×D3semidirect
125. C2×Dic3⋊C4C2×D3semidirect
139. C22×C3×D3C2×Q8semidirect
144. C2×D32C2×Q8semidirect
186. C2×C3×Q8C22×D3semidirect
237. C4⋊Dic3C22×D3semidirect
240. Dic3⋊C4C22×D3semidirect
245. C2×C3⋊D3C22⋊Q8semidirect
252. C2×C3×D3C22×Q8semidirect
265. C22×Q8D32semidirect
306. C22×D3D3×Q8semidirect
348. C2×C32C2×C22⋊Q8semidirect
352. C3⋊D3C2×C22⋊Q8semidirect
366. C2×Q8C2×D32semidirect
416. C2×D3C2×D3×Q8semidirect
429. C32C22×C22⋊Q8semidirect
469. C2×C3D3×C22⋊Q8semidirect
496. C3C2×D3×C22⋊Q8semidirect
499. C2#10595429direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C22×C4×D322
C2×C3×#9462
#105954292
C2×#639212
C2×#639002
C2×#638962
C2×#638832
C2×#638572
C2×D3×C22⋊Q83