Finite Group Databasebeta

← C2×#10595390 #11903344

Subgroups — C2×#10595390 #11903344

Order 1152.

2625 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic, complemented
2C2×C3×#947C212yesmaximal, complemented
3#10595390C2116yesmaximal, direct product factor
4C2×#63913C212yesmaximal, complemented
5C2×#63902C212yesmaximal, complemented
6C2×#63885C214yesmaximal, complemented
7C2×#63877C214yesmaximal, complemented
8C2×#5670—32nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C3×D12C2212yes—
12C22×#625C2212yes—
13C22×#625C2212yes—
14C22×D3×Dic3C2214yes—
15#64153C2218yescomplemented
16C2×#3750C2214yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C3×#947C22116yescomplemented
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×(C2×D3)⋊C4C2214yes—
21C2×C3×C4×Dic3C2212yes—
22C2×#3724C2212yes—
23C2×(C2×D3)⋊Dic3C2214yes—
24C2×Dic32C2212yes—
25#63913C22116yescomplemented
26#63902C22116yescomplemented
27#63885C22132yescomplemented
28#63877C22132yescomplemented
29C2×C3×#124—32no—
30C2×#947D312yescomplemented
31C2×#944—32no—
32C2×#944—61no—
33C2×#939—34no—
34#5670—332no—
35C2×#885—34no—
36C2×#884—34no—
37C2×#67⋊C4—34no—
38C2×#877—34no—
39C2×#872—34no—
40C23×C3×D3C2314yes—
41C2×C32×Q8—42no—
42C2×C32×Q8C2314yes—
43C22×C32×C4C2312yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3C2312yes—
46C22×C3⋊Dic3C2312yes—
47C2×#634—42no—
48C2×#634C2314yes—
49C22×C3×Dic3C2314yes—
50C2×C3×D12—44no—
51C2×C3×D12C2318yes—
52C2×#625—28no—
53C2×#625—44no—
54C2×#625C2318yes—
55C2×#625C2318yes—
56C2×D3×Dic3—216no—
57C2×D3×Dic3C23116yes—
58#3750C23116yes—
59C4×C3⋊Dic3C2314yes—
60C3×(C2×D3)⋊C4C23116yes—
61C3×(C2×D3)⋊C4C23116yes—
62C3×C4×Dic3C2318yes—
63#3724C2318yes—
64(C2×D3)⋊Dic3C23116yes—
65Dic32C2318yes—
66C2×#555—91noSylow
67C22×C3×Q8—21no—
68C22×C3×Q8C2×D312yes—
69C22×C3×D4—32no—
70C22×#67—34no—
71C22×#67—34no—
72C23×Dic3—34no—
73C22×D12C2×D312yes—
74C22×C4×D3—34no—
75C22×Dic6—32no—
76C22×Dic6—61no—
77C3×#124—316no—
78C2×C3×C22⋊C4—34no—
79C2×C3×C22⋊C4—34no—
80C2×C3×C42—32no—
81C2×#217—34no—
82#947C2×D3116yescomplemented
83#944—316no—
84#944—68no—
85#939—332no—
86C2×(C2×D3)⋊C4—34no—
87C2×(C2×D3)⋊C4C2×D314yes—
88C2×(C2×D3)⋊C4C2×D314yes—
89C2×Dic3⋊C4—34no—
90C2×Dic3⋊C4—34no—
91C2×Dic3⋊C4—34no—
92C2×Dic3⋊C4—64no—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—61no—
96C2×C4×Dic3C2×D312yes—
97#885—332no—
98#884—332no—
99#67⋊C4—332no—
100#877—332no—
101#872—332no—
102C23×C32C2411yescharacteristic
103C22×C3×D3—28no—
104C22×C3×D3—28no—
105C22×C3×D3—28no—
106C22×C3×D3C2418yes—
107C32×Q8—44no—
108C2×C32×C4—22no—
109C2×C32×C4—24no—
110C2×C32×C4C2414yes—
111C2×C32×C4C2412yes—
112C2×C3⋊Dic3—24no—
113C2×C3⋊Dic3#4118yes—
114C2×C3⋊Dic3C2414yes—
115C2×C3⋊Dic3C2414yes—
116#634—44no—
117C2×C3×Dic3—28no—
118C2×C3×Dic3C2418yes—
119C3×D12—48no—
120#625—216no—
121#625—48no—
122D3×Dic3—232no—
123#555—916no—
124C2×C4⋊Q8—91no—
125C2×#124—32no—
126C2×#124—92no—
127C2×#121—94no—
128C2×C4×D4—92no—
129C2×#117—94no—
130C24×C3—34no—
131C23×D3C22×D314yes—
132C2×C3×Q8—24no—
133C2×C3×Q8—44no—
134C2×C3×Q8—44no—
135C2×C3×Q8C22×D318yes—
136C2×C3×D4—38no—
137C2×C3×D4—124no—
138C22×C3×C4—21no—
139C22×C3×C4—22no—
140C22×C3×C4—34no—
141C22×C3×C4C22×D312yes—
142C22×C3×C4C22×D312yes—
143C22×C3×C4C22×D312yes—
144C2×#67—316no—
145C2×#67—316no—
146C2×#67—616no—
147C2×#67—128no—
148C22×Dic3—34no—
149C22×Dic3—34no—
150C22×Dic3—316no—
151C22×Dic3—62no—
152C22×Dic3—62no—
153C22×Dic3—616no—
154C22×Dic3C22×D314yes—
155C2×D12—44no—
156C2×D12C22×D318yes—
157C2×C4×D3—316no—
158C2×C4×D3—616no—
159C2×Dic6—38no—
160C2×Dic6—64no—
161C2×Dic6—124no—
162C2×Dic6—124no—
163C3×C22⋊C4—316no—
164C3×C22⋊C4—316no—
165C3×C42—38no—
166#217—316no—
167(C2×D3)⋊C4—316no—
168(C2×D3)⋊C4C22×D3116yes—
169(C2×D3)⋊C4C22×D3116yes—
170Dic3⋊C4—316no—
171Dic3⋊C4—316no—
172Dic3⋊C4—316no—
173Dic3⋊C4—616no—
174C4×Dic3—38no—
175C4×Dic3—316no—
176C4×Dic3—64no—
177C4×Dic3C22×D318yes—
178C22×C32C2×#4114yes—
179C22×C32H(5,𝔽2)12yes—
180C22×C32C2511yescharacteristic
181C2×C3×D3—28no—
182C2×C3×D3—28no—
183C2×C3×D3—28no—
184C2×C3×D3—416no—
185C32×C4—22no—
186C32×C4—24no—
187C3⋊Dic3—24no—
188C3⋊Dic3C2×#4118yes—
189C3×Dic3—28no—
190C22×Q8—91no—
191C22×Q8D3211yescharacteristic
192C22×D4—32no—
193C22×D4—92no—
194C22×D4—92no—
195C23×C4—94no—
196C4⋊Q8—98no—
197#124—316no—
198#124—916no—
199#121—932no—
200C4×D4—916no—
201#117—932no—
202C2×C4⋊C4—92no—
203C2×C4⋊C4—94no—
204C2×C22⋊C4—34no—
205C2×C22⋊C4—34no—
206C2×C22⋊C4—94no—
207C2×C42—32no—
208C2×C42—92no—
209C2×C42—91no—
210C23×C3—21no—
211C23×C3—38no—
212C23×C3—68no—
213C23×C3—68no—
214C23×C3—68no—
215C23×C3C23×D312yes—
216C22×D3—28no—
217C22×D3—28no—
218C22×D3—28no—
219C22×D3C23×D318yes—
220C3×Q8—48no—
221C3×Q8—48no—
222C3×D4—128no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—22no—
228C2×C3×C4—24no—
229C2×C3×C4—38no—
230C2×C3×C4—44no—
231C2×C3×C4—68no—
232C2×C3×C4C23×D314yes—
233C2×C3×C4C23×D314yes—
234C2×C3×C4C23×D314yes—
235#67—632no—
236#67—1216no—
237C2×Dic3—28no—
238C2×Dic3—316no—
239C2×Dic3—38no—
240C2×Dic3—38no—
241C2×Dic3—68no—
242C2×Dic3—64no—
243C2×Dic3—64no—
244C2×Dic3—632no—
245C2×Dic3—68no—
246C2×Dic3—124no—
247C2×Dic3C23×D318yes—
248D12—48no—
249C4×D3—632no—
250Dic6—128no—
251Dic6—128no—
252C2×C32#55514yescomplemented
253C2×C32C22×#4112yes—
254C2×C32C2×H(5,𝔽2)11yescharacteristic
255C3×D3—48no—
256C24—34no—
257C2×Q8—42no—
258C2×Q8—94no—
259C2×Q8—362no—
260C2×Q8C2×D3214yes—
261C2×D4—38no—
262C2×D4—98no—
263C2×D4—98no—
264C2×D4—124no—
265C2×D4—188no—
266C2×D4—364no—
267C22×C4—34no—
268C22×C4—916no—
269C22×C4—92no—
270C22×C4—92no—
271C22×C4—1816no—
272C22×C4C2×D3212yes—
273C22×C4C2×D3211yescharacteristic
274C4⋊C4—98no—
275C4⋊C4—916no—
276C22⋊C4—316no—
277C22⋊C4—316no—
278C22⋊C4—916no—
279C42—38no—
280C42—98no—
281C42—94no—
282C22×C3—24no—
283C22×C3—22no—
284C22×C3—21no—
285C22×C3—68no—
286C22×C3—68no—
287C22×C3—68no—
288C22×C3—1216no—
289C22×C3#100414yes—
290C22×C3D3×#4118yes—
291C22×C3C24×D312yes—
292C2×D3—28no—
293C2×D3—28no—
294C2×D3—28no—
295C2×D3—416no—
296C3×C4—24no—
297C3×C4—24no—
298C3×C4—24no—
299C3×C4—24no—
300C3×C4—44no—
301C3×C4—68no—
302Dic3—28no—
303Dic3—316no—
304Dic3—68no—
305Dic3—68no—
306Dic3—124no—
307C32C2×#55511yescharacteristic, complemented, Sylow
308C23—38no—
309C23—68no—
310C23—68no—
311C23—68no—
312C23C22×D3211yescharacteristic
313Q8—44no—
314Q8—364no—
315D4—128no—
316D4—1816no—
317D4—368no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—38no—
321C2×C4—68no—
322C2×C4—98no—
323C2×C4—94no—
324C2×C4—94no—
325C2×C4—1832no—
326C2×C4—184no—
327C2×C4C22×D3214yes—
328C2×C4C22×D3212yes—
329C2×C3—24no—
330C2×C3—22no—
331C2×C3—21no—
332C2×C3—128no—
333C2×C3#567018yescomplemented
334C2×C3C2×#100412yes—
335C2×C3C2×D3×#4114yes—
336D3—48no—
337C22—68no—
338C22—68no—
339C22—68no—
340C22—1216no—
341C22#6431914yes—
342C22#6433012yes—
343C22C23×D3211yescharacteristic
344C4—24no—
345C4—22no—
346C4—68no—
347C4—98no—
348C4—184no—
349C3—21no—
350C3C2×#567012yescomplemented
351C2—128no—
352C2#1059539014yesdirect product factor
353C2C2×#6431912yes—
354C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#555
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64153C2semidirect
2. C2×C3×#947C2semidirect
3. #10595390C2direct (N × H)
4. C2×#63913C2semidirect
5. C2×#63902C2semidirect
6. C2×#63885C2semidirect
7. C2×#63877C2semidirect
15. #64153C22semidirect
18. C3×#947C22semidirect
25. #63913C22semidirect
26. #63902C22semidirect
27. #63885C22semidirect
28. #63877C22semidirect
30. C2×#947D3semidirect
82. #947C2×D3semidirect
252. C2×C32#555semidirect
307. C32C2×#555semidirect
333. C2×C3#5670semidirect
350. C3C2×#5670semidirect
352. C2#10595390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#9472
#105953902
C2×#639132
C2×#639022
C2×#638852
C2×#638772
C2×#56703