Finite Group Databasebeta

← (C2×D3)⋊#95 #69425

Subgroups — (C2×D3)⋊#95 #69425

Order 384.

1088 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D3C211yesmaximal, characteristic
2C22×(C2×D3)⋊C4C212yesmaximal
3C2×C3×#95C211yesmaximal, characteristic, complemented
4C2×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×C3⋊#95C212yesmaximal, complemented
6C22⋊#95—31nomaximal, Sylow
7C24×D3C2211yescharacteristic
8C23×C3×C4C2212yes—
9C23×C3×C4C2211yescharacteristic
10C23×Dic3C2212yes—
11C23×Dic3C2211yescharacteristic
12C22×C4×D3—24no—
13C22×C4×D3—22no—
14C22×C4×D3—22no—
15C22×C4×D3—24no—
16C22×C4×D3C414yescomplemented
17C2×(C2×D3)⋊C4—24no—
18C2×(C2×D3)⋊C4—24no—
19C2×(C2×D3)⋊C4C418yescomplemented
20C3×#95—22no—
21C3⋊#95—22no—
22C3⋊#95—24no—
23C24×C4—31no—
24C22×C22⋊C4—32no—
25C2×#95—32no—
26C2×#95—31no—
27C2×#95D311yescharacteristic, complemented
28C24×C3C2311yescharacteristic
29C23×D3—21no—
30C23×D3—22no—
31C23×D3—21no—
32C23×D3—22no—
33C23×D3—21no—
34C23×D3—21no—
35C23×D3C2×C414yes—
36C23×D3C2×C412yes—
37C23×D3D412yes—
38C23×D3D414yes—
39C23×D3Q812yes—
40C22×C3×C4—22no—
41C22×C3×C4—22no—
42C22×C3×C4—22no—
43C22×C3×C4—22no—
44C22×C3×C4—22no—
45C22×C3×C4—22no—
46C22×C3×C4—22no—
47C22×C3×C4—22no—
48C22×C3×C4C2×C412yes—
49C22×C3×C4C2×C414yescomplemented
50C22×C3×C4D412yes—
51C22×C3×C4D412yes—
52C22×Dic3—21no—
53C22×Dic3—22no—
54C22×Dic3—21no—
55C22×Dic3—22no—
56C22×Dic3—22no—
57C22×Dic3—22no—
58C22×Dic3—22no—
59C22×Dic3—22no—
60C22×Dic3—22no—
61C22×Dic3C2×C412yes—
62C22×Dic3C2×C414yescomplemented
63C22×Dic3D414yes—
64C2×C4×D3—216no—
65C2×C4×D3—216no—
66C2×C4×D3—28no—
67C2×C4×D3—28no—
68C2×C4×D3—28no—
69(C2×D3)⋊C4—216no—
70C25—31no—
71C23×C4—31no—
72C23×C4—32no—
73C23×C4—34no—
74C23×C4—64no—
75C23×C4—64no—
76C23×C4—62no—
77C23×C4—62no—
78C23×C4C2×D312yes—
79C23×C4C2×D311yescharacteristic
80C2×C22⋊C4—38no—
81C2×C22⋊C4—64no—
82C2×C22⋊C4—64no—
83#95—22no—
84#95—64no—
85#95—62no—
86C23×C3C22×C411yescharacteristic
87C23×C3C22×C412yes—
88C23×C3C2×D411yescharacteristic
89C23×C3C2×D412yes—
90C23×C3C2×D411yescharacteristic
91C23×C3C2×D412yes—
92C23×C3C2×D411yescharacteristic
93C23×C3C2×Q811yescharacteristic
94C23×C3#4112yes—
95C23×C3#4111yescharacteristic
96C23×C3#4111yescharacteristic
97C22×D3—22no—
98C22×D3—22no—
99C22×D3—22no—
100C22×D3—22no—
101C22×D3—24no—
102C22×D3—24no—
103C22×D3—24no—
104C22×D3—24no—
105C22×D3—24no—
106C22×D3—24no—
107C22×D3—24no—
108C22×D3—22no—
109C22×D3—22no—
110C22×D3—24no—
111C22×D3—22no—
112C22×D3—22no—
113C22×D3—24no—
114C22×D3—24no—
115C22×D3C4214yes—
116C22×D3C22⋊C418yes—
117C22×D3C22⋊C414yes—
118C22×D3C4⋊C414yes—
119C22×D3C4⋊C418yes—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—24no—
123C2×C3×C4—24no—
124C2×C3×C4—24no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—42no—
128C2×C3×C4—42no—
129C2×C3×C4—42no—
130C2×C3×C4—42no—
131C2×C3×C4C22⋊C414yescomplemented
132C2×Dic3—22no—
133C2×Dic3—22no—
134C2×Dic3—24no—
135C2×Dic3—24no—
136C2×Dic3—24no—
137C2×Dic3—24no—
138C2×Dic3—24no—
139C2×Dic3—42no—
140C2×Dic3—42no—
141C2×Dic3—42no—
142C2×Dic3—42no—
143C2×Dic3C22⋊C414yescomplemented
144C4×D3—232no—
145C24—34no—
146C24—32no—
147C24—32no—
148C24—34no—
149C24—32no—
150C24—61no—
151C24—62no—
152C24—62no—
153C24—61no—
154C24—61no—
155C24—61no—
156C24C22×D311yescharacteristic
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—32no—
166C22×C4—34no—
167C22×C4—34no—
168C22×C4—68no—
169C22×C4—68no—
170C22×C4—616no—
171C22×C4—616no—
172C22×C4—61no—
173C22×C4—62no—
174C22×C4—61no—
175C22×C4—68no—
176C22×C4—62no—
177C22×C4—62no—
178C22×C4—62no—
179C22×C4—62no—
180C22×C4—62no—
181C22×C4—62no—
182C22×C4C4×D312yes—
183C22×C4C4×D314yescomplemented
184C22×C4D1212yes—
185C22×C4#6712yes—
186C22⋊C4—616no—
187C22×C3C2×C4211yescharacteristic
188C22×C3C2×C22⋊C411yescharacteristic
189C22×C3C2×C22⋊C412yes—
190C22×C3C2×C22⋊C411yescharacteristic
191C22×C3C2×C22⋊C411yescharacteristic
192C22×C3C2×C4⋊C411yescharacteristic
193C22×C3C2×C4⋊C412yes—
194C22×C3#11711yescharacteristic
195C22×C3#11711yescharacteristic
196C22×C3C4×D412yes—
197C22×C3C4×D412yes—
198C22×C3C4×D412yes—
199C22×C3C4×D412yes—
200C22×C3#12012yes—
201C22×C3#12012yes—
202C22×C3#12112yes—
203C22×C3#12111yescharacteristic
204C22×C3#12111yescharacteristic
205C22×C3C22⋊Q812yes—
206C22×C3C22⋊Q811yescharacteristic
207C22×C3C22⋊Q811yescharacteristic
208C22×C3#12312yes—
209C22×C3#12312yes—
210C2×D3—24no—
211C2×D3—24no—
212C2×D3—24no—
213C2×D3—24no—
214C2×D3—24no—
215C2×D3—24no—
216C2×D3—28no—
217C2×D3—28no—
218C2×D3—28no—
219C2×D3—28no—
220C2×D3#9518yescomplemented
221C3×C4—24no—
222C3×C4—44no—
223Dic3—24no—
224Dic3—44no—
225C23—34no—
226C23—38no—
227C23—34no—
228C23—34no—
229C23—38no—
230C23—62no—
231C23—64no—
232C23—62no—
233C23—64no—
234C23—64no—
235C23—64no—
236C23—64no—
237C23—62no—
238C23—64no—
239C23—64no—
240C23—62no—
241C23—64no—
242C23—62no—
243C23—62no—
244C23—64no—
245C23—64no—
246C23—62no—
247C23—62no—
248C23C2×C4×D311yescharacteristic
249C23C2×C4×D312yes—
250C23C2×D1211yescharacteristic
251C23#23512yes—
252C23D3×D412yes—
253C23D3×D411yescharacteristic
254C23D3×D412yes—
255C23#23711yescharacteristic
256C23D3×Q811yescharacteristic
257C23#23911yescharacteristic
258C23C2×#6711yescharacteristic
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—34no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—632no—
272C2×C4—62no—
273C2×C4—64no—
274C2×C4—62no—
275C2×C4—64no—
276C2×C4—64no—
277C2×C4—64no—
278C2×C4—64no—
279C2×C4—122no—
280C2×C4—122no—
281C2×C4—122no—
282C2×C4—122no—
283C2×C4(C2×D3)⋊C414yescomplemented
284C2×C3C2×#9511yescharacteristic
285C2×C3C4×C22⋊C411yescharacteristic
286C2×C3C4×C22⋊C411yescharacteristic
287C2×C3#37911yescharacteristic
288C2×C3#38011yescharacteristic
289C2×C3#38011yescharacteristic
290C2×C3#38111yescharacteristic
291C2×C3#38512yes—
292C2×C3#38512yes—
293C2×C3#38612yes—
294C2×C3#38612yes—
295D3—28no—
296C22—38no—
297C22—64no—
298C22—68no—
299C22—64no—
300C22—64no—
301C22—68no—
302C22—64no—
303C22—64no—
304C22—68no—
305C22—64no—
306C22—68no—
307C22C42×D311yescharacteristic
308C22#87211yescharacteristic
309C22C4×D1212yes—
310C22D3×C22⋊C411yescharacteristic
311C22D3×C22⋊C412yes—
312C22D3×C22⋊C411yescharacteristic
313C22#67⋊C412yes—
314C22#88212yes—
315C22#88312yes—
316C22#88412yes—
317C22D3×C4⋊C411yescharacteristic
318C22D3×C4⋊C412yes—
319C22#89211yescharacteristic
320C22#89312yes—
321C22#89412yes—
322C22#89511yescharacteristic
323C22#89612yes—
324C22#89711yescharacteristic
325C22C2×(C2×D3)⋊C411yescharacteristic
326C22C4×#6712yes—
327C22#93712yes—
328C22#93811yescharacteristic
329C22#94611yescharacteristic
330C4—24no—
331C4—44no—
332C4—64no—
333C4—124no—
334C3C22⋊#9511yescharacteristic, complemented, Sylow
335C2—68no—
336C2D3×#9511yescharacteristic
337C2#466411yescharacteristic
338C2#466512yes—
339C2#466611yescharacteristic
340C2#466711yescharacteristic
341C2#466812yes—
342C2C4×(C2×D3)⋊C411yescharacteristic
343C2#495511yescharacteristic
344C2#495612yes—
345C2#498711yescharacteristic
346C2#498912yes—
subgroupG/H
center, FrattiniC24C22×D3
commutatorC22×C3C2×C42
FittingC2×C3×#95C2
socle, cosocleC24×C3C23
prime radicalC24×D3C22
hypercenterC2×#95D3
hypocenterC3C22⋊#95
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. C2×C3×#95C2semidirect
4. C2×C3⋊#95C2semidirect
5. C2×C3⋊#95C2semidirect
16. C22×C4×D3C4semidirect
19. C2×(C2×D3)⋊C4C4semidirect
27. C2×#95D3semidirect
49. C22×C3×C4C2×C4semidirect
62. C22×Dic3C2×C4semidirect
131. C2×C3×C4C22⋊C4semidirect
143. C2×Dic3C22⋊C4semidirect
183. C22×C4C4×D3semidirect
220. C2×D3#95semidirect
283. C2×C4(C2×D3)⋊C4semidirect
334. C3C22⋊#95semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D32
C22×(C2×D3)⋊C42
C2×C3×#952
C2×C3⋊#952
C22⋊#953