Finite Group Databasebeta

← C2×#10591061 #11858718

Subgroups — C2×#10591061 #11858718

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#830C212yesmaximal
3C2×#63572C212yesmaximal, complemented
4#10591061C218yesmaximal, direct product factor
5C2×#63553C212yesmaximal, complemented
6C2×#4718—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C411yescharacteristic
9C23×C3⋊Dic3C411yescharacteristic
10C2×C4×C3⋊Dic3C411yescharacteristic
11C2×C4×C3⋊Dic3C414yes—
12C2×C4×C3⋊Dic3C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2214yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2214yes—
17C3×#830C2218yes—
18#63572C2218yescomplemented
19#63553C2218yescomplemented
20C22×C4×Dic3—32no—
21C22×C4×Dic3—61no—
22C2×C3×C22⋊C8—32no—
23C2×#830D312yes—
24C2×Dic3⋊C8—34no—
25C2×C8×Dic3—34no—
26#4718—316no—
27C24×C32C2×C411yescharacteristic
28C22×C32×C4—24no—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2×C412yes—
31C22×C32×C4C2312yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—24no—
34C22×C3⋊Dic3C818yescomplemented
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C414yes—
37C22×C3⋊Dic3C2×C411yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3C2×C414yes—
40C22×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3C2×C414yes—
42C4×C3⋊Dic3C2×C412yes—
43C4×C3⋊Dic3C2×C414yes—
44C4×C3⋊Dic3C2×C412yes—
45C4×C3⋊Dic3C2312yes—
46C4×C3⋊Dic3C2312yes—
47C2×C3×C3⋊C8—28no—
48C2×C3×C3⋊C8C2318yes—
49C2×#431—91noSylow
50C23×C3×C4—21no—
51C23×C3×C4C2×D312yes—
52C23×Dic3—32no—
53C23×Dic3—32no—
54C23×Dic3—61no—
55C23×Dic3—61no—
56C22×C3×C8—34no—
57C2×C4×Dic3—32no—
58C2×C4×Dic3—38no—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—38no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—32no—
63C2×C4×Dic3—61no—
64C2×C4×Dic3—61no—
65C2×C4×Dic3—64no—
66C2×C4×Dic3—64no—
67C2×C4×Dic3—61no—
68C2×C4×Dic3—61no—
69C22×C3⋊C8C2×D314yes—
70C3×C22⋊C8—38no—
71#830C2×D318yes—
72Dic3⋊C8—316no—
73C8×Dic3—316no—
74C23×C32—22no—
75C23×C32—22no—
76C23×C32C2×C814yes—
77C23×C32C22×C412yes—
78C23×C32C22×C411yescharacteristic
79C2×C32×C4—22no—
80C2×C32×C4—24no—
81C2×C32×C4—24no—
82C2×C32×C4C22×C412yes—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4#4114yes—
85C2×C32×C4C2411yescharacteristic
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—28no—
88C2×C3⋊Dic3C2×C814yes—
89C2×C3⋊Dic3C2×C814yes—
90C2×C3⋊Dic3C2×C8116yescomplemented
91C2×C3⋊Dic3M1614yes—
92C2×C3⋊Dic3C22×C412yes—
93C2×C3⋊Dic3C22×C412yes—
94C2×C3⋊Dic3C22×C412yes—
95C2×C3⋊Dic3C22×C412yes—
96C3×C3⋊C8—28no—
97C22×C42—91no—
98#431—98no—
99C2×C4⋊C8—92no—
100C2×C22⋊C8—32no—
101C2×C4×C8—92no—
102C24×C3—21no—
103C24×C3C4×D312yes—
104C22×C3×C4—28no—
105C22×C3×C4—28no—
106C22×C3×C4—21no—
107C22×C3×C4—22no—
108C22×C3×C4—22no—
109C22×C3×C4—21no—
110C22×C3×C4C4×D312yes—
111C22×C3×C4C4×D314yes—
112C22×C3×C4C22×D314yes—
113C22×C3×C4C22×D312yes—
114C22×Dic3—316no—
115C22×Dic3—32no—
116C22×Dic3—32no—
117C22×Dic3—38no—
118C22×Dic3—32no—
119C22×Dic3—38no—
120C22×Dic3—32no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—64no—
124C22×Dic3—61no—
125C22×Dic3—64no—
126C22×Dic3—61no—
127C22×Dic3—68no—
128C22×Dic3—68no—
129C22×Dic3—68no—
130C2×C3×C8—38no—
131C2×C3×C8—68no—
132C4×Dic3—38no—
133C4×Dic3—34no—
134C4×Dic3—38no—
135C4×Dic3—34no—
136C4×Dic3—34no—
137C4×Dic3—34no—
138C4×Dic3—64no—
139C4×Dic3—62no—
140C4×Dic3—64no—
141C4×Dic3—62no—
142C4×Dic3—62no—
143C4×Dic3—62no—
144C2×C3⋊C8—28no—
145C2×C3⋊C8C22×D318yes—
146C22×C32—22no—
147C22×C32—22no—
148C22×C32—28no—
149C22×C32#11712yes—
150C22×C32C22×C814yes—
151C22×C32C22×C812yes—
152C22×C32C2×M1612yes—
153C22×C32C23×C411yescharacteristic
154C32×C4—22no—
155C32×C4#11712yes—
156C32×C4C2×#4112yes—
157C3⋊Dic3—22no—
158C3⋊Dic3C22×C814yes—
159C3⋊Dic3C22×C814yes—
160C3⋊Dic3C2×M1614yes—
161C23×C4—91no—
162C23×C4—91no—
163C23×C4D3211yescharacteristic
164C22×C8—34no—
165C2×C42—91no—
166C2×C42—94no—
167C2×C42—91no—
168C2×C42—94no—
169C2×C42—91no—
170C2×C42—91no—
171C4⋊C8—98no—
172C22⋊C8—38no—
173C4×C8—98no—
174C23×C3—24no—
175C23×C3—24no—
176C23×C3—24no—
177C23×C3—24no—
178C23×C3—24no—
179C23×C3—22no—
180C23×C3—21no—
181C23×C3D3×C818yes—
182C23×C3C2×C4×D314yes—
183C23×C3C2×C4×D312yes—
184C2×C3×C4—24no—
185C2×C3×C4—28no—
186C2×C3×C4—28no—
187C2×C3×C4—24no—
188C2×C3×C4—28no—
189C2×C3×C4—28no—
190C2×C3×C4—21no—
191C2×C3×C4—24no—
192C2×C3×C4—22no—
193C2×C3×C4—21no—
194C2×C3×C4C2×C4×D314yes—
195C2×C3×C4C2×C4×D312yes—
196C2×C3×C4#23718yes—
197C2×C3×C4C23×D312yes—
198C2×Dic3—38no—
199C2×Dic3—38no—
200C2×Dic3—332no—
201C2×Dic3—38no—
202C2×Dic3—34no—
203C2×Dic3—34no—
204C2×Dic3—34no—
205C2×Dic3—34no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—616no—
209C2×Dic3—64no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—616no—
215C2×Dic3—616no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C3×C8—68no—
219C3⋊C8—28no—
220C2×C32—24no—
221C2×C32#43114yescomplemented
222C2×C32C2×#11711yescharacteristic
223C2×C32C23×C811yescharacteristic
224C2×C32C22×M1611yescharacteristic
225C24#62411yescharacteristic
226C22×C4—24no—
227C22×C4—98no—
228C22×C4—94no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—94no—
233C22×C4—91no—
234C22×C4—184no—
235C22×C4#62411yescharacteristic
236C22×C4#62412yes—
237C22×C4C2×D3212yes—
238C22×C4C2×D3211yescharacteristic
239C2×C8—38no—
240C2×C8—68no—
241C42—92no—
242C42—92no—
243C42—94no—
244C42—92no—
245C42—94no—
246C42—92no—
247C22×C3—24no—
248C22×C3—24no—
249C22×C3—216no—
250C22×C3—24no—
251C22×C3—216no—
252C22×C3—24no—
253C22×C3—21no—
254C22×C3—24no—
255C22×C3—22no—
256C22×C3—22no—
257C22×C3—22no—
258C22×C3#87714yes—
259C22×C3C2×D3×C818yes—
260C22×C3C2×D3×C814yes—
261C22×C3D3×M1614yes—
262C22×C3C22×C4×D312yes—
263C3×C4—24no—
264C3×C4—24no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4#87714yes—
268C3×C4C2×#23714yes—
269Dic3—38no—
270Dic3—38no—
271Dic3—38no—
272Dic3—64no—
273Dic3—64no—
274Dic3—64no—
275Dic3—64no—
276Dic3—64no—
277C32C2×#43111yescharacteristic, complemented, Sylow
278C23—22no—
279C23—22no—
280C23#371014yes—
281C23C2×#62412yes—
282C23C2×#62411yescharacteristic
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—92no—
287C2×C4—92no—
288C2×C4—92no—
289C2×C4—916no—
290C2×C4—94no—
291C2×C4—94no—
292C2×C4—94no—
293C2×C4—92no—
294C2×C4—188no—
295C2×C4—182no—
296C2×C4#380514yes—
297C2×C4C2×#62412yes—
298C2×C4C2×#62411yescharacteristic
299C2×C4C22×D3211yescharacteristic
300C8—68no—
301C2×C3—28no—
302C2×C3—28no—
303C2×C3—24no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3#471818yescomplemented
308C2×C3C2×#87712yes—
309C2×C3C22×D3×C812yes—
310C2×C3C2×D3×M1612yes—
311C22—28no—
312C22—22no—
313C22—22no—
314C22C2×#371014yes—
315C22C2×#371012yes—
316C22#6381812yes—
317C22#6395712yes—
318C22C22×#62411yescharacteristic
319C4—22no—
320C4—94no—
321C4—94no—
322C4—94no—
323C4—182no—
324C4#6395712yes—
325C4C2×#380512yes—
326C3—21no—
327C3C2×#471812yescomplemented
328C2—24no—
329C2#1059106114yesdirect product factor
330C2C22×#371011yescharacteristic
331C2C2×#6381811yescharacteristic
332C2C2×#6395711yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C23×C8
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#431
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63572C2semidirect
4. #10591061C2direct (N × H)
5. C2×#63553C2semidirect
18. #63572C22semidirect
19. #63553C22semidirect
34. C22×C3⋊Dic3C8semidirect
90. C2×C3⋊Dic3C2×C8semidirect
221. C2×C32#431semidirect
277. C32C2×#431semidirect
307. C2×C3#4718semidirect
327. C3C2×#4718semidirect
329. C2#10591061direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C2×C3×#8302
C2×#635722
#105910612
C2×#635532
C2×#47183