Finite Group Databasebeta

← C2×C47×#2923 #26099818

Subgroups — C2×C47×#2923 #26099818

Order 12032.

2134 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C47C211yesmaximal, characteristic
2C47×#2923C2116yesmaximal, direct product factor
3C2×C47×#433C214yesmaximal, complemented
4C2×C47×#432C214yesmaximal, complemented
5C2×C47×#424C212yesmaximal, complemented
6C2×C47×#408C212yesmaximal
7C2×C4×M16×C47C211yesmaximal, characteristic, complemented
8C22×#97×C47C211yesmaximal, characteristic, complemented
9C22×#41×C47C2211yescharacteristic
10C22×M16×C47C2212yes—
11C23×C8×C47C2212yes—
12C4×#41×C47C418yes—
13C4×#41×C47C2218yes—
14C2×C4×Q8×C47C412yes—
15C2×C4×D4×C47C414yes—
16C2×C4×D4×C47C412yes—
17C2×#117×C47C2211yescharacteristic
18C2×#117×C47C2212yes—
19C22×C42×C47C2211yescharacteristic
20C22×C42×C47C2212yes—
21C47×#433C22132yescomplemented
22C47×#432C22132yescomplemented
23C47×#424C22116yescomplemented
24C2×C4⋊C8×C47C2218yes—
25C47×#408C22116yes—
26C2×C22⋊C8×C47C2218yes—
27C4×M16×C47C2218yescomplemented
28C2×#97×C47C2212yes—
29C2×#97×C47C2212yes—
30C2×#97×C47C2212yes—
31C2×#97×C47C2218yescomplemented
32C2×C4×C8×C47C2212yes—
33C2×#41×C47—28no—
34C2×#41×C47C2×C414yes—
35C2×#41×C47C2314yes—
36C22×Q8×C47C2×C411yescharacteristic
37C22×D4×C47C2×C412yes—
38C22×D4×C47C2×C411yescharacteristic
39C23×C4×C47C2×C414yes—
40C23×C4×C47C2×C412yes—
41C23×C4×C47C2312yes—
42C23×C4×C47C2311yescharacteristic
43C2×M16×C47—28no—
44C2×M16×C47C2318yes—
45C22×C8×C47—28no—
46C22×C8×C47C2318yes—
47C22×C8×C47C2314yes—
48C22×C8×C47C2314yes—
49C4×Q8×C47C2×C4116yes—
50C4×D4×C47C2×C4132yes—
51C4×D4×C47C2×C4116yes—
52#117×C47C2×C418yes—
53#117×C47C2×C414yes—
54#117×C47C2314yes—
55#117×C47C2318yes—
56C2×C4⋊C4×C47C2×C414yes—
57C2×C4⋊C4×C47C2×C412yes—
58C2×C22⋊C4×C47C2×C414yes—
59C2×C22⋊C4×C47C2×C412yes—
60C2×C42×C47C2×C414yes—
61C2×C42×C47C2×C412yes—
62C2×C42×C47C2×C418yes—
63C2×C42×C47C2×C414yes—
64C2×C42×C47C2314yes—
65C2×C42×C47C2318yes—
66C2×C42×C47C2311yescharacteristic
67C2×C42×C47C2311yescharacteristic
68C2×C42×C47C2312yes—
69C4⋊C8×C47C23132yes—
70C22⋊C8×C47C23132yes—
71#97×C47C2318yes—
72#97×C47C2318yes—
73#97×C47C2318yes—
74C4×C8×C47C2318yes—
75C24×C47C22×C412yes—
76C24×C47C22×C411yescharacteristic
77#41×C47—216no—
78#41×C47—216no—
79C2×Q8×C47—24no—
80C2×Q8×C47C22×C414yes—
81C2×D4×C47—28no—
82C2×D4×C47—24no—
83C2×D4×C47C22×C418yes—
84C2×D4×C47C22×C414yes—
85C22×C4×C47—28no—
86C22×C4×C47—44no—
87C22×C4×C47—48no—
88C22×C4×C47C22×C412yes—
89C22×C4×C47C22×C412yes—
90C22×C4×C47C22×C414yes—
91C22×C4×C47C22×C412yes—
92C22×C4×C47C22×C414yes—
93C22×C4×C47C22×C4116yes—
94C22×C4×C47C22×C418yes—
95C22×C4×C47C22×C411yescharacteristic
96C22×C4×C47C22×C412yes—
97C22×C4×C47#4118yes—
98C22×C4×C47C2414yes—
99C22×C4×C47C2412yes—
100C22×C4×C47C2411yescharacteristic
101M16×C47—216no—
102C2×C8×C47—28no—
103C2×C8×C47—216no—
104C2×C8×C47—28no—
105C2×C8×C47C2418yes—
106C2×C8×C47C2418yes—
107C4⋊C4×C47C22×C4116yes—
108C4⋊C4×C47C22×C418yes—
109C22⋊C4×C47C22×C4116yes—
110C22⋊C4×C47C22×C418yes—
111C42×C47C22×C412yes—
112C42×C47C22×C412yes—
113C42×C47C22×C414yes—
114C42×C47C22×C4116yes—
115C42×C47C22×C418yes—
116C42×C47C2414yes—
117C42×C47C2412yes—
118C42×C47C2412yes—
119C23×C47—24no—
120C23×C47—24no—
121C23×C47—28no—
122C23×C47#11714yes—
123C23×C47C23×C414yes—
124C23×C47C23×C412yes—
125C23×C47C23×C411yescharacteristic
126Q8×C47—28no—
127D4×C47—216no—
128D4×C47—28no—
129C2×C4×C47—24no—
130C2×C4×C47—24no—
131C2×C4×C47—24no—
132C2×C4×C47—28no—
133C2×C4×C47—28no—
134C2×C4×C47—28no—
135C2×C4×C47—48no—
136C2×C4×C47—416no—
137C2×C4×C47#11714yes—
138C2×C4×C47#11718yes—
139C2×C4×C47C23×C414yes—
140C2×C4×C47C23×C414yes—
141C2×C4×C47C23×C418yes—
142C2×C4×C47C23×C414yes—
143C2×C4×C47C23×C411yescharacteristic
144C2×C4×C47C23×C412yes—
145C2×C4×C47C2×#4114yes—
146C2×C4×C47C2×#4118yes—
147C2×C4×C47C2511yescharacteristic
148C8×C47—28no—
149C8×C47—28no—
150C2×#2923C4711yesmaximal, characteristic, direct product factor, Sylow
151C22×C47—28no—
152C22×C47—24no—
153C22×C47—24no—
154C22×C47—28no—
155C22×C47—48no—
156C22×C47C2×#11714yes—
157C22×C47C2×#11712yes—
158C22×C47#56814yes—
159C22×C47C24×C411yescharacteristic
160C4×C47—24no—
161C4×C47—24no—
162C4×C47—24no—
163C4×C47—28no—
164C4×C47C2×#11712yes—
165C4×C47C2×#11714yes—
166C4×C47C22×#4112yes—
167C2×C4×#41C2×C4711yescharacteristic
168#2923C2×C47116yesdirect product factor
169C2×#433C2×C4714yescomplemented
170C2×#432C2×C4714yescomplemented
171C2×#424C2×C4712yescomplemented
172C2×#408C2×C4712yes—
173C2×C4×M16C2×C4711yescharacteristic, complemented
174C22×#97C2×C4711yescharacteristic, complemented
175C2×C47—24no—
176C2×C47—44no—
177C2×C47#292314yesdirect product factor
178C2×C47C22×#11711yescharacteristic
179C2×C47C2×#56812yes—
180C22×#41C22×C4711yescharacteristic
181C22×M16C22×C4712yes—
182C23×C8C22×C4712yes—
183C4×#41C4×C4718yes—
184C4×#41C22×C4718yes—
185C2×C4×Q8C4×C4712yes—
186C2×C4×D4C4×C4714yes—
187C2×C4×D4C4×C4712yes—
188C2×#117C22×C4711yescharacteristic
189C2×#117C22×C4712yes—
190C22×C42C22×C4711yescharacteristic
191C22×C42C22×C4712yes—
192#433C22×C47132yescomplemented
193#432C22×C47132yescomplemented
194#424C22×C47116yescomplemented
195C2×C4⋊C8C22×C4718yes—
196#408C22×C47116yes—
197C2×C22⋊C8C22×C4718yes—
198C4×M16C22×C4718yescomplemented
199C2×#97C22×C4712yes—
200C2×#97C22×C4712yes—
201C2×#97C22×C4712yes—
202C2×#97C22×C4718yescomplemented
203C2×C4×C8C22×C4712yes—
204C47C2×#292311yescharacteristic, direct product factor, Sylow
205C2×#41—28no—
206C2×#41C2×C4×C4714yes—
207C2×#41C23×C4714yes—
208C22×Q8C2×C4×C4711yescharacteristic
209C22×D4C2×C4×C4712yes—
210C22×D4C2×C4×C4711yescharacteristic
211C23×C4C2×C4×C4714yes—
212C23×C4C2×C4×C4712yes—
213C23×C4C23×C4712yes—
214C23×C4C23×C4711yescharacteristic
215C2×M16—28no—
216C2×M16C23×C4718yes—
217C22×C8—28no—
218C22×C8C23×C4714yes—
219C22×C8C23×C4718yes—
220C22×C8C23×C4714yes—
221C4×Q8C2×C4×C47116yes—
222C4×D4C2×C4×C47132yes—
223C4×D4C2×C4×C47116yes—
224#117C2×C4×C4718yes—
225#117C2×C4×C4714yes—
226#117C23×C4714yes—
227#117C23×C4718yes—
228C2×C4⋊C4C2×C4×C4714yes—
229C2×C4⋊C4C2×C4×C4712yes—
230C2×C22⋊C4C2×C4×C4714yes—
231C2×C22⋊C4C2×C4×C4712yes—
232C2×C42C2×C4×C4714yes—
233C2×C42C2×C4×C4712yes—
234C2×C42C2×C4×C4718yes—
235C2×C42C2×C4×C4714yes—
236C2×C42C23×C4711yescharacteristic
237C2×C42C23×C4712yes—
238C2×C42C23×C4714yes—
239C2×C42C23×C4718yes—
240C2×C42C23×C4711yescharacteristic
241C4⋊C8C23×C47132yes—
242C22⋊C8C23×C47132yes—
243#97C23×C4718yes—
244#97C23×C4718yes—
245#97C23×C4718yes—
246C4×C8C23×C4718yes—
247C24C22×C4×C4712yes—
248C24C22×C4×C4711yescharacteristic
249#41—216no—
250#41—216no—
251C2×Q8—24no—
252C2×Q8C22×C4×C4714yes—
253C2×D4—28no—
254C2×D4—24no—
255C2×D4C22×C4×C4718yes—
256C2×D4C22×C4×C4714yes—
257C22×C4—28no—
258C22×C4—44no—
259C22×C4—48no—
260C22×C4C22×C4×C4712yes—
261C22×C4C22×C4×C4712yes—
262C22×C4C22×C4×C4714yes—
263C22×C4C22×C4×C4712yes—
264C22×C4C22×C4×C4714yes—
265C22×C4C22×C4×C47116yes—
266C22×C4C22×C4×C4718yes—
267C22×C4C22×C4×C4711yescharacteristic
268C22×C4C22×C4×C4712yes—
269C22×C4#41×C4718yes—
270C22×C4C24×C4714yes—
271C22×C4C24×C4712yes—
272C22×C4C24×C4711yescharacteristic
273M16—216no—
274C2×C8—28no—
275C2×C8—216no—
276C2×C8—28no—
277C2×C8C24×C4718yes—
278C2×C8C24×C4718yes—
279C4⋊C4C22×C4×C47116yes—
280C4⋊C4C22×C4×C4718yes—
281C22⋊C4C22×C4×C47116yes—
282C22⋊C4C22×C4×C4718yes—
283C42C22×C4×C4712yes—
284C42C22×C4×C4712yes—
285C42C22×C4×C4714yes—
286C42C22×C4×C47116yes—
287C42C22×C4×C4718yes—
288C42C24×C4712yes—
289C42C24×C4712yes—
290C42C24×C4714yes—
291C23—24no—
292C23—24no—
293C23—28no—
294C23#117×C4714yes—
295C23C23×C4×C4714yes—
296C23C23×C4×C4712yes—
297C23C23×C4×C4711yescharacteristic
298Q8—28no—
299D4—216no—
300D4—28no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—48no—
308C2×C4—416no—
309C2×C4#117×C4714yes—
310C2×C4#117×C4718yes—
311C2×C4C23×C4×C4714yes—
312C2×C4C23×C4×C4714yes—
313C2×C4C23×C4×C4714yes—
314C2×C4C23×C4×C4718yes—
315C2×C4C23×C4×C4711yescharacteristic
316C2×C4C23×C4×C4712yes—
317C2×C4C2×#41×C4714yes—
318C2×C4C2×#41×C4718yes—
319C2×C4C25×C4711yescharacteristic
320C8—28no—
321C8—28no—
322C22—24no—
323C22—28no—
324C22—28no—
325C22—24no—
326C22—48no—
327C22C2×#117×C4714yes—
328C22C2×#117×C4712yes—
329C22C47×#56814yes—
330C22C24×C4×C4711yescharacteristic
331C4—24no—
332C4—24no—
333C4—28no—
334C4—24no—
335C4C2×#117×C4712yes—
336C4C2×#117×C4714yes—
337C4C22×#41×C4712yes—
338C2—24no—
339C2—44no—
340C2C47×#292314yesdirect product factor
341C2C22×#117×C4711yescharacteristic
342C2C2×C47×#56812yes—
subgroupG/H
centerC22×C4×C47C24
commutatorC22C24×C4×C47
Frattini, cosocleC2×C4C25×C47
socleC23×C47C23×C4
prime radicalC22×#41×C47C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2923C2direct (N × H)
3. C2×C47×#433C2semidirect
4. C2×C47×#432C2semidirect
5. C2×C47×#424C2semidirect
7. C2×C4×M16×C47C2semidirect
8. C22×#97×C47C2semidirect
21. C47×#433C22semidirect
22. C47×#432C22semidirect
23. C47×#424C22semidirect
27. C4×M16×C47C22semidirect
31. C2×#97×C47C22semidirect
150. C2×#2923C47direct (N × H)
168. #2923C2×C47direct (N × H)
169. C2×#433C2×C47semidirect
170. C2×#432C2×C47semidirect
171. C2×#424C2×C47semidirect
173. C2×C4×M16C2×C47semidirect
174. C22×#97C2×C47semidirect
177. C2×C47#2923direct (N × H)
192. #433C22×C47semidirect
193. #432C22×C47semidirect
194. #424C22×C47semidirect
198. C4×M16C22×C47semidirect
202. C2×#97C22×C47semidirect
204. C47C2×#2923direct (N × H)
340. C2C47×#2923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#41×C472
C47×#29232
C2×C47×#4332
C2×C47×#4322
C2×C47×#4242
C2×C47×#4082
C2×C4×M16×C472
C22×#97×C472
C2×#292347