Finite Group Databasebeta

← C23×#3241 #15670860

Subgroups — C23×#3241 #15670860

Order 2944.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#544C211yesmaximal, characteristic, complemented
2C23×#540C211yesmaximal, characteristic
3C23×#501C211yesmaximal, characteristic, complemented
4C23×#499C211yesmaximal, characteristic, complemented
5C23×#490C211yesmaximal, characteristic, complemented
6C23×#486C211yesmaximal, characteristic, complemented
7C23×#482C211yesmaximal, characteristic, complemented
8C23×#482C211yesmaximal, characteristic, complemented
9C23×#481C211yesmaximal, characteristic, complemented
10C23×#480C211yesmaximal, characteristic, complemented
11C23×#478C211yesmaximal, characteristic, complemented
12C23×#478C211yesmaximal, characteristic, complemented
13C23×#476C211yesmaximal, characteristic, complemented
14C23×#474C211yesmaximal, characteristic, complemented
15C23×#433C211yesmaximal, characteristic, complemented
16C23×C4⋊Q8—21no—
17C23×C4⋊Q8C2211yescharacteristic
18C23×C4⋊Q8C2211yescharacteristic
19C23×#127C2211yescharacteristic
20C23×#125—21no—
21C23×#125C2211yescharacteristic
22C23×#125C2211yescharacteristic
23C23×#125C2211yescharacteristic
24C23×#123—21no—
25C23×#123—21no—
26C23×C22⋊Q8—21no—
27C23×C22⋊Q8—21no—
28C23×#121—21no—
29C23×#121—21no—
30C23×#121C2211yescharacteristic
31C23×#121C2211yescharacteristic
32C4×D4×C23C2211yescharacteristic
33C4×D4×C23C2211yescharacteristic
34C23×#117C2211yescharacteristic
35C23×#117C2211yescharacteristic
36C2×C4⋊C4×C23C2211yescharacteristic
37C23×#107C2211yescharacteristic
38C23×#107C2211yescharacteristic
39C23×#107C2211yescharacteristic
40C23×#107C2211yescharacteristic
41C23×#106C2211yescharacteristic
42C23×#106C2211yescharacteristic
43C23×#106C2211yescharacteristic
44C23×#106C2211yescharacteristic
45C23×C4⋊C8C2211yescharacteristic
46C23×C4⋊C8C2211yescharacteristic
47C23×#102C2211yescharacteristic
48C23×#102C2211yescharacteristic
49C23×#102C2211yescharacteristic
50C23×#102C2211yescharacteristic
51C23×#102C2211yescharacteristic
52C23×#102C2211yescharacteristic
53C23×#102C2211yescharacteristic
54C23×#102C2211yescharacteristic
55C23×C22⋊C8C2211yescharacteristic
56C23×C22⋊C8C2211yescharacteristic
57C23×#97C2211yescharacteristic
58C4×C8×C23C2211yescharacteristic
59C2×Q8×C23—21no—
60C2×Q8×C23—21no—
61C2×D4×C23—21no—
62C2×D4×C23—21no—
63C2×D4×C23—21no—
64C2×D4×C23—21no—
65C2×D4×C23C2311yescharacteristic
66C2×D4×C23C2311yescharacteristic
67C22×C4×C23—21no—
68C22×C4×C23—21no—
69C22×C4×C23—21no—
70C22×C4×C23C2311yescharacteristic
71C2×C8×C23C2311yescharacteristic
72C2×C8×C23C2311yescharacteristic
73C2×C8×C23C2311yescharacteristic
74C2×C8×C23C2311yescharacteristic
75C4⋊C4×C23—21no—
76C4⋊C4×C23—21no—
77C4⋊C4×C23—21no—
78C4⋊C4×C23—21no—
79C4⋊C4×C23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23—21no—
82C4⋊C4×C23—21no—
83C4⋊C4×C23—21no—
84C4⋊C4×C23D411yescharacteristic
85C4⋊C4×C23D411yescharacteristic
86C4⋊C4×C23C2311yescharacteristic
87C4⋊C4×C23C2311yescharacteristic
88C4⋊C4×C23C2311yescharacteristic
89C4⋊C4×C23C2311yescharacteristic
90C4⋊C4×C23C2311yescharacteristic
91C4⋊C4×C23C2311yescharacteristic
92C22⋊C4×C23—21no—
93C22⋊C4×C23—21no—
94C22⋊C4×C23—21no—
95C22⋊C4×C23—21no—
96C22⋊C4×C23—21no—
97C22⋊C4×C23D411yescharacteristic
98C22⋊C4×C23D411yescharacteristic
99C42×C23—21no—
100C42×C23C2311yescharacteristic
101C42×C23C2311yescharacteristic
102C23×C23—21no—
103C23×C23—21no—
104C23×C23C2×D411yescharacteristic
105Q8×C23—81no—
106Q8×C23—81no—
107D4×C23—21no—
108D4×C23—21no—
109D4×C23—21no—
110D4×C23—21no—
111D4×C23—81no—
112D4×C23—81no—
113D4×C23—81no—
114D4×C23—81no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—81no—
124C2×C4×C23—81no—
125C2×C4×C23—81no—
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2×D411yescharacteristic
131C2×C4×C23C2411yescharacteristic
132C8×C23—21no—
133C8×C23—21no—
134C8×C23—21no—
135C8×C23—21no—
136#3241C2311yesmaximal, characteristic, direct product factor, Sylow
137C22×C23—21no—
138C22×C23—21no—
139C22×C23—21no—
140C22×C23—41no—
141C22×C23—41no—
142C22×C23—41no—
143C22×C23—41no—
144C22×C23—41no—
145C22×C23—41no—
146C22×C23C22×D411yescharacteristic
147C4×C23—21no—
148C4×C23—21no—
149C4×C23—21no—
150C4×C23—21no—
151C4×C23—21no—
152C4×C23—41no—
153C4×C23—41no—
154C4×C23—41no—
155C4×C23—41no—
156C4×C23—41no—
157C4×C23—41no—
158C4×C232−1+411yescharacteristic
159C4×C232−1+411yescharacteristic
160#544C2×C2311yescharacteristic, complemented
161#540C2×C2311yescharacteristic
162#501C2×C2311yescharacteristic, complemented
163#499C2×C2311yescharacteristic, complemented
164#490C2×C2311yescharacteristic, complemented
165#486C2×C2311yescharacteristic, complemented
166#482C2×C2311yescharacteristic, complemented
167#482C2×C2311yescharacteristic, complemented
168#481C2×C2311yescharacteristic, complemented
169#480C2×C2311yescharacteristic, complemented
170#478C2×C2311yescharacteristic, complemented
171#478C2×C2311yescharacteristic, complemented
172#476C2×C2311yescharacteristic, complemented
173#474C2×C2311yescharacteristic, complemented
174#433C2×C2311yescharacteristic, complemented
175C2×C23—41no—
176C2×C23—81no—
177C2×C23—81no—
178C2×C23#53611yescharacteristic
179C2×C23#57611yescharacteristic
180C2×C23#57711yescharacteristic
181C4⋊Q8—21no—
182C4⋊Q8C22×C2311yescharacteristic
183C4⋊Q8C22×C2311yescharacteristic
184#127C22×C2311yescharacteristic
185#125—21no—
186#125C22×C2311yescharacteristic
187#125C22×C2311yescharacteristic
188#125C22×C2311yescharacteristic
189#123—21no—
190#123—21no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193#121—21no—
194#121—21no—
195#121C22×C2311yescharacteristic
196#121C22×C2311yescharacteristic
197C4×D4C22×C2311yescharacteristic
198C4×D4C22×C2311yescharacteristic
199#117C22×C2311yescharacteristic
200#117C22×C2311yescharacteristic
201C2×C4⋊C4C22×C2311yescharacteristic
202#107C22×C2311yescharacteristic
203#107C22×C2311yescharacteristic
204#107C22×C2311yescharacteristic
205#107C22×C2311yescharacteristic
206#106C22×C2311yescharacteristic
207#106C22×C2311yescharacteristic
208#106C22×C2311yescharacteristic
209#106C22×C2311yescharacteristic
210C4⋊C8C22×C2311yescharacteristic
211C4⋊C8C22×C2311yescharacteristic
212#102C22×C2311yescharacteristic
213#102C22×C2311yescharacteristic
214#102C22×C2311yescharacteristic
215#102C22×C2311yescharacteristic
216#102C22×C2311yescharacteristic
217#102C22×C2311yescharacteristic
218#102C22×C2311yescharacteristic
219#102C22×C2311yescharacteristic
220C22⋊C8C22×C2311yescharacteristic
221C22⋊C8C22×C2311yescharacteristic
222#97C22×C2311yescharacteristic
223C4×C8C22×C2311yescharacteristic
224C23#324111yescharacteristic, direct product factor, Sylow
225C2×Q8—21no—
226C2×Q8—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C23×C2311yescharacteristic
232C2×D4C23×C2311yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C23×C2311yescharacteristic
237C2×C8C23×C2311yescharacteristic
238C2×C8C23×C2311yescharacteristic
239C2×C8C23×C2311yescharacteristic
240C2×C8C23×C2311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4D4×C2311yescharacteristic
251C4⋊C4D4×C2311yescharacteristic
252C4⋊C4C23×C2311yescharacteristic
253C4⋊C4C23×C2311yescharacteristic
254C4⋊C4C23×C2311yescharacteristic
255C4⋊C4C23×C2311yescharacteristic
256C4⋊C4C23×C2311yescharacteristic
257C4⋊C4C23×C2311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4D4×C2311yescharacteristic
264C22⋊C4D4×C2311yescharacteristic
265C42—21no—
266C42C23×C2311yescharacteristic
267C42C23×C2311yescharacteristic
268C23—21no—
269C23—21no—
270C23C2×D4×C2311yescharacteristic
271Q8—81no—
272Q8—81no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C2311yescharacteristic
293C2×C4C2×D4×C2311yescharacteristic
294C2×C4C2×D4×C2311yescharacteristic
295C2×C4C2×D4×C2311yescharacteristic
296C2×C4C2×D4×C2311yescharacteristic
297C2×C4C24×C2311yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×D4×C2311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4C23×2−1+411yescharacteristic
324C4C23×2−1+411yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2C23×#53611yescharacteristic
329C2C23×#57611yescharacteristic
330C2C23×#57711yescharacteristic
subgroupG/H
center, socleC22×C23C22×D4
commutator, Frattini, cosocleC2×C4C24×C23
prime radicalC23×#540C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#544C2semidirect
3. C23×#501C2semidirect
4. C23×#499C2semidirect
5. C23×#490C2semidirect
6. C23×#486C2semidirect
7. C23×#482C2semidirect
8. C23×#482C2semidirect
9. C23×#481C2semidirect
10. C23×#480C2semidirect
11. C23×#478C2semidirect
12. C23×#478C2semidirect
13. C23×#476C2semidirect
14. C23×#474C2semidirect
15. C23×#433C2semidirect
136. #3241C23direct (N × H)
160. #544C2×C23semidirect
162. #501C2×C23semidirect
163. #499C2×C23semidirect
164. #490C2×C23semidirect
165. #486C2×C23semidirect
166. #482C2×C23semidirect
167. #482C2×C23semidirect
168. #481C2×C23semidirect
169. #480C2×C23semidirect
170. #478C2×C23semidirect
171. #478C2×C23semidirect
172. #476C2×C23semidirect
173. #474C2×C23semidirect
174. #433C2×C23semidirect
224. C23#3241direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5442
C23×#5402
C23×#5012
C23×#4992
C23×#4902
C23×#4862
C23×#4822
C23×#4812
C23×#4802
C23×#4782
C23×#4762
C23×#4742
C23×#4332
#324123