Finite Group Databasebeta

← C4×#10625060 #15675953

Subgroups — C4×#10625060 #15675953

Order 2944.

484 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
1C2×#10625060C211yesmaximal, characteristic
2#13092314C211yesmaximal, characteristic
3#13092312C211yesmaximal, characteristic
4#13092303C211yesmaximal, characteristic
5#13092302C211yesmaximal, characteristic
6#13092299C211yesmaximal, characteristic
7#13092298C211yesmaximal, characteristic
8#13092281C211yesmaximal, characteristic
9C4×Dic23⋊C4C211yesmaximal, characteristic
10C4×Dic23⋊C4C211yesmaximal, characteristic
11C4×Dic23⋊C4C211yesmaximal, characteristic
12C4×Dic23⋊C4C211yesmaximal, characteristic
13C4×C4⋊Dic23C211yesmaximal, characteristic
14C42×Dic23C211yesmaximal, characteristic
15C4×C4⋊C4×C23C211yesmaximal, characteristic
16C2×C4⋊C4×C23C2211yescharacteristic
17C2×C4⋊C4×C23C2211yescharacteristic
18C2×C42×C23C2211yescharacteristic
19C2×C42×C23C2211yescharacteristic
20C2×C42×C23C2211yescharacteristic
21C2×C4⋊Dic23C2211yescharacteristic
22C2×C4⋊Dic23C2211yescharacteristic
23C2×Dic23⋊C4C2211yescharacteristic
24C2×Dic23⋊C4C2211yescharacteristic
25C2×Dic23⋊C4C2211yescharacteristic
26C2×Dic23⋊C4C2211yescharacteristic
27C2×Dic23⋊C4C2211yescharacteristic
28C2×Dic23⋊C4C2211yescharacteristic
29C2×Dic23⋊C4C2211yescharacteristic
30C2×Dic23⋊C4C2211yescharacteristic
31C2×C4×Dic23C2211yescharacteristic
32C2×C4×Dic23C2211yescharacteristic
33C2×C4×Dic23C2211yescharacteristic
34C2×C4×Dic23C2211yescharacteristic
35C2×C4×Dic23C2211yescharacteristic
36C2×C4×Dic23C2211yescharacteristic
37C2×C4×Dic23C2211yescharacteristic
38C2×C4×Dic23C2211yescharacteristic
39#10625060C418yesdirect product factor
40C23×#95C2211yescharacteristic
41C23×#95C2211yescharacteristic
42C23⋊#95C2211yescharacteristic
43C23⋊#95C2211yescharacteristic
44C23⋊#95C2211yescharacteristic
45C23⋊#95C2211yescharacteristic
46C23⋊#95C2211yescharacteristic
47C23⋊#95C2211yescharacteristic
48C23⋊#95C2211yescharacteristic
49C23⋊#95C2211yescharacteristic
50C23⋊#95C2211yescharacteristic
51C23⋊#95C2211yescharacteristic
52C22×C4×C23C2311yescharacteristic
53C22×C4×C23C2311yescharacteristic
54C22×C4×C23C2311yescharacteristic
55C22×C4×C23C2311yescharacteristic
56C22×C4×C23C2311yescharacteristic
57C22×C4×C23C2311yescharacteristic
58C22×C4×C23C2311yescharacteristic
59C22×Dic23C2311yescharacteristic
60C22×Dic23C2311yescharacteristic
61C22×Dic23C2311yescharacteristic
62C22×Dic23C2311yescharacteristic
63C22×Dic23C2311yescharacteristic
64C22×Dic23C2311yescharacteristic
65C22×Dic23C2311yescharacteristic
66C22×Dic23C2311yescharacteristic
67C4⋊C4×C23—22no—
68C4⋊C4×C23C2×C414yes—
69C42×C23—22no—
70C42×C23—22no—
71C42×C23—22no—
72C4⋊Dic23—22no—
73C4⋊Dic23C2×C414yes—
74Dic23⋊C4—22no—
75Dic23⋊C4—22no—
76Dic23⋊C4—22no—
77Dic23⋊C4—22no—
78Dic23⋊C4C2×C414yes—
79Dic23⋊C4C2×C414yes—
80Dic23⋊C4C2×C414yes—
81Dic23⋊C4C2×C414yes—
82C4×Dic23—22no—
83C4×Dic23—22no—
84C4×Dic23—22no—
85C4×Dic23—22no—
86C4×Dic23—22no—
87C4×Dic23—22no—
88C4×Dic23C2×C414yes—
89C4×Dic23Q814yes—
90C23×C23C2411yescharacteristic
91C2×C4×C23—21no—
92C2×C4×C23—21no—
93C2×C4×C23—21no—
94C2×C4×C23—21no—
95C2×C4×C23—21no—
96C2×C4×C23—21no—
97C2×C4×C23—21no—
98C2×C4×C23—21no—
99C2×C4×C23—21no—
100C2×C4×C23—21no—
101C2×C4×C23—21no—
102C2×C4×C23—21no—
103C2×C4×C23—21no—
104C2×C4×C23—21no—
105C2×C4×C23C22×C412yes—
106C2×C4×C23C22×C412yes—
107C2×C4×C23C22×C412yes—
108C2×C4×C23C2×Q812yes—
109C2×C4×C23#4112yes—
110C2×C4×C23#4112yes—
111C2×C4×C23#4112yes—
112C2×Dic23—21no—
113C2×Dic23—21no—
114C2×Dic23—21no—
115C2×Dic23—21no—
116C2×Dic23—21no—
117C2×Dic23—21no—
118C2×Dic23—21no—
119C2×Dic23—21no—
120C2×Dic23—21no—
121C2×Dic23—21no—
122C2×Dic23—21no—
123C2×Dic23—21no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23C22×C412yes—
129C2×Dic23C22×C412yes—
130C2×Dic23C22×C412yes—
131C2×Dic23C22×C412yes—
132C2×Dic23C2×Q812yes—
133C2×Dic23C2×Q812yes—
134C2×Dic23#4112yes—
135C2×Dic23#4112yes—
136C4×#125—231nomaximal, Sylow
137C22×C23C23×C411yescharacteristic
138C22×C23C22×Q811yescharacteristic
139C22×C23C2×#4111yescharacteristic
140C22×C23C2×#4111yescharacteristic
141C22×C23C2×#4111yescharacteristic
142C22×C23C2×#4111yescharacteristic
143C22×C23C2×#4111yescharacteristic
144C4×C23—22no—
145C4×C23—22no—
146C4×C23—22no—
147C4×C23—22no—
148C4×C23—41no—
149C4×C23—41no—
150C4×C23#12514yescomplemented
151Dic23—22no—
152Dic23—22no—
153Dic23—22no—
154Dic23—22no—
155Dic23—22no—
156Dic23—41no—
157Dic23—41no—
158Dic23C4×Q814yes—
159C2×#125—231no—
160#389—231no—
161#389—231no—
162#387—231no—
163#387—231no—
164#387—231no—
165#387—231no—
166#382—231no—
167C4×C4⋊C4—231no—
168C4×C4⋊C4—231no—
169C4×C4⋊C4—231no—
170C4×C4⋊C4—231no—
171C4×C4⋊C4—231no—
172C4×C4⋊C4D2311yescharacteristic
173C43—231no—
174C2×C23C2×C4×Q811yescharacteristic
175C2×C23C4×#4111yescharacteristic
176C2×C23C4×#4111yescharacteristic
177C2×C23C2×#12511yescharacteristic
178C2×C23#52911yescharacteristic
179C2×C23#52911yescharacteristic
180C2×C23#53311yescharacteristic
181#125—238no—
182C2×C4⋊C4—231no—
183C2×C4⋊C4—231no—
184C2×C4⋊C4—231no—
185C2×C4⋊C4—231no—
186C2×C4⋊C4—231no—
187C2×C4⋊C4—231no—
188C2×C4⋊C4—231no—
189C2×C4⋊C4—231no—
190C2×C4⋊C4—231no—
191C2×C4⋊C4—231no—
192C2×C4⋊C4C2×D2311yescharacteristic
193C2×C4⋊C4C2×D2311yescharacteristic
194C2×C42—231no—
195C2×C42—231no—
196C2×C42—231no—
197C2×C42—231no—
198C2×C42—231no—
199C2×C42—231no—
200C2×C42—231no—
201C2×C42—231no—
202C2×C42C2×D2311yescharacteristic
203C2×C42C2×D2311yescharacteristic
204C2×C42C2×D2311yescharacteristic
205#95—231no—
206#95—231no—
207#95—231no—
208#95—231no—
209#95—231no—
210#95—231no—
211#95—231no—
212#95—231no—
213#95—231no—
214#95—231no—
215#95C2×D2311yescharacteristic
216#95C2×D2311yescharacteristic
217C23C4×#12511yescharacteristic, complemented, Sylow
218C22×C4—231no—
219C22×C4—231no—
220C22×C4—231no—
221C22×C4—231no—
222C22×C4—231no—
223C22×C4—231no—
224C22×C4—231no—
225C22×C4—231no—
226C22×C4C22×D2311yescharacteristic
227C22×C4C22×D2311yescharacteristic
228C22×C4C22×D2311yescharacteristic
229C22×C4C22×D2311yescharacteristic
230C22×C4C22×D2311yescharacteristic
231C22×C4C22×D2311yescharacteristic
232C22×C4C22×D2311yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—234no—
235C4⋊C4—234no—
236C4⋊C4—234no—
237C4⋊C4—234no—
238C4⋊C4—234no—
239C4⋊C4—462no—
240C4⋊C4—462no—
241C4⋊C4—462no—
242C4⋊C4—462no—
243C4⋊C4—462no—
244C4⋊C4C4×D2314yes—
245C42—22no—
246C42—22no—
247C42—22no—
248C42—234no—
249C42—234no—
250C42—462no—
251C42—462no—
252C42—462no—
253C42—462no—
254C42—462no—
255C42—462no—
256C23C23×D2311yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—232no—
272C2×C4—232no—
273C2×C4—232no—
274C2×C4—232no—
275C2×C4—232no—
276C2×C4—232no—
277C2×C4—232no—
278C2×C4—232no—
279C2×C4—461no—
280C2×C4—461no—
281C2×C4—461no—
282C2×C4—461no—
283C2×C4—461no—
284C2×C4—461no—
285C2×C4—461no—
286C2×C4—461no—
287C2×C4—461no—
288C2×C4—461no—
289C2×C4—461no—
290C2×C4—461no—
291C2×C4—461no—
292C2×C4—461no—
293C2×C4—461no—
294C2×C4—461no—
295C2×C4C2×C4×D2312yes—
296C2×C4C2×C4×D2312yes—
297C2×C4C2×C4×D2312yes—
298C2×C4#6728812yes—
299C2×C4#6728812yes—
300C2×C4#6729012yes—
301C2×C4Q8×D2312yes—
302C22C22×C4×D2311yescharacteristic
303C22C2×#6728811yescharacteristic
304C22C2×#6728811yescharacteristic
305C22C2×#6729011yescharacteristic
306C22C2×Q8×D2311yescharacteristic
307C22#41×D2311yescharacteristic
308C22#41×D2311yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—234no—
316C4—462no—
317C4—462no—
318C4—462no—
319C4—462no—
320C4—462no—
321C4—921no—
322C4—921no—
323C4#1062506014yesdirect product factor
324C2C4×Q8×D2311yescharacteristic
325C2C4×#6729011yescharacteristic
326C2C4×#6728811yescharacteristic
327C2C2×#1062506011yescharacteristic
328C2#1309294511yescharacteristic
329C2#1309294711yescharacteristic
330C2#1309297111yescharacteristic
subgroupG/H
centerC22×C4C22×D23
commutatorC22×C23C23×C4
FrattiniC23C23×D23
FittingC4×C4⋊C4×C23C2
socle, prime radical, cosocleC23×C23C24
hypercenterC4×C4⋊C4D23
hypocenterC23C4×#125
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
39. #10625060C4direct (N × H)
150. C4×C23#125semidirect
217. C23C4×#125semidirect
323. C4#10625060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106250602
#130923142
#130923122
#130923032
#130923022
#130922992
#130922982
#130922812
C4×Dic23⋊C42
C4×C4⋊Dic232
C42×Dic232
C4×C4⋊C4×C232
C4×#12523