Finite Group Databasebeta

← C2×C22⋊C4×#92418 #29677583

Subgroups — C2×C22⋊C4×#92418 #29677583

Order 15616.

2046 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×#92418C211yesmaximal, characteristic
2C22×C22⋊#92418C211yesmaximal, characteristic
3C22×C4×#92418C212yesmaximal, complemented
4C22⋊C4×#92418C218yesmaximal, direct product factor
5C2×#16839517C212yesmaximal, complemented
6C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
7C23×#92418—28no—
8C23×#92418C418yescomplemented
9C23×#92418C2211yescharacteristic
10C23×#92418C2212yes—
11C23×#92418C2214yes—
12C23×#92418C2211yescharacteristic
13C2×C22⋊#92418C418yescomplemented
14C2×C22⋊#92418C2214yes—
15C2×C4×#92418—28no—
16C2×C4×#92418C2218yescomplemented
17#16839517C2218yescomplemented
18C24×C4×C61C2211yescharacteristic
19C22×C22⋊C4×C61C412yes—
20C22×C42×C61C2212yes—
21C4×C22⋊C4×C61C414yes—
22C4×C22⋊C4×C61C2214yes—
23C2×#95×C61C412yes—
24C22×#92418—24no—
25C22×#92418—24no—
26C22×#92418—24no—
27C22×#92418—232no—
28C22×#92418—216no—
29C22×#92418C2×C418yes—
30C22×#92418C2×C414yes—
31C22×#92418C2×C414yes—
32C22×#92418C2×C4116yescomplemented
33C22×#92418D418yes—
34C22×#92418C2314yes—
35C22×#92418C2312yes—
36C22×#92418C2312yes—
37C22⋊#92418C2×C4116yescomplemented
38C4×#92418—216no—
39C25×C61C2×C411yescharacteristic
40C23×C4×C61—24no—
41C23×C4×C61—24no—
42C23×C4×C61C2×C414yes—
43C23×C4×C61C2×C414yes—
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61C2×C412yes—
46C23×C4×C61C2×C414yes—
47C23×C4×C61C2312yes—
48C23×C4×C61C2311yescharacteristic
49C2×C22⋊C4×C61C8116yescomplemented
50C2×C22⋊C4×C61C2×C418yes—
51C2×C42×C61—24no—
52C2×C42×C61—24no—
53C2×C42×C61C2×C414yes—
54C2×C42×C61C2314yes—
55#95×C61C2×C418yes—
56C24×C61—24no—
57C24×C61—24no—
58C24×C61C4214yes—
59C24×C61C2×C818yes—
60C24×C61C22×C412yes—
61C24×C61C22×C411yescharacteristic
62C22×C4×C61—28no—
63C22×C4×C61—24no—
64C22×C4×C61—28no—
65C22×C4×C61—28no—
66C22×C4×C61—28no—
67C22×C4×C61—28no—
68C22×C4×C61—216no—
69C22×C4×C61—24no—
70C22×C4×C61—24no—
71C22×C4×C61C4214yes—
72C22×C4×C61C4218yes—
73C22×C4×C61C2×C8116yescomplemented
74C22×C4×C61C22×C412yes—
75C22×C4×C61C22×C414yes—
76C22×C4×C61C22×C414yes—
77C22×C4×C61C22×C418yes—
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C22×C412yes—
80C22×C4×C61C22×C412yes—
81C22×C4×C61C2×D414yes—
82C22×C4×C61#4114yes—
83C22×C4×C61C2411yescharacteristic
84C22⋊C4×C61C2×C8132yescomplemented
85C42×C61—28no—
86C42×C61—24no—
87C42×C61—24no—
88C2×#92418—28no—
89C2×#92418—216no—
90C2×#92418—24no—
91C2×#92418—24no—
92C2×#92418—24no—
93C2×#92418—232no—
94C2×#92418C22⋊C4116yesdirect product factor
95C2×#92418C22×C418yes—
96C2×#92418C22×C414yes—
97C2×#92418C22×C414yes—
98C2×#92418C2×D418yes—
99C23×C61—24no—
100C23×C61—24no—
101C23×C61—28no—
102C23×C61—28no—
103C23×C61—232no—
104C23×C61C4×C8116yescomplemented
105C23×C61C2×C4214yes—
106C23×C61C2×C4212yes—
107C23×C61C4×D414yes—
108C23×C61C22×C818yes—
109C23×C61C22×C814yes—
110C23×C61#13114yes—
111C23×C61C23×C411yescharacteristic
112C2×C4×C61—28no—
113C2×C4×C61—24no—
114C2×C4×C61—28no—
115C2×C4×C61—28no—
116C2×C4×C61—232no—
117C2×C4×C61—24no—
118C2×C4×C61—24no—
119C2×C4×C61—28no—
120C2×C4×C61—216no—
121C2×C4×C61C2×C4214yes—
122C2×C4×C61C2×C4212yes—
123C2×C4×C61C2×C22⋊C414yes—
124C2×C4×C61#11714yes—
125C2×C4×C61C4×D418yes—
126C2×C4×C61C4×D414yes—
127C2×C4×C61C22×C8116yescomplemented
128C2×C4×C61C23×C411yescharacteristic
129C2×C4×C61C23×C411yescharacteristic
130C2×C4×C61C22×D412yes—
131C2×C4×C61C2×#4112yes—
132#92418—24no—
133#92418—28no—
134#92418C2×C22⋊C418yesdirect product factor
135C2×C8×C22⋊C4—611nomaximal, Sylow
136C22×C61—24no—
137C22×C61—216no—
138C22×C61—232no—
139C22×C61—24no—
140C22×C61C4×C22⋊C414yes—
141C22×C61C2×C4×C814yes—
142C22×C61C2×C4×C818yescomplemented
143C22×C61#40514yes—
144C22×C61C8×D4116yes—
145C22×C61C22×C4211yescharacteristic
146C22×C61C2×C4×D412yes—
147C22×C61C23×C812yes—
148C22×C61C2×#13112yes—
149C4×C61—216no—
150C4×C61—24no—
151C4×C61C4×C22⋊C414yes—
152C4×C61C22×C22⋊C411yescharacteristic
153C4×C61C2×#11711yescharacteristic
154C4×C61C2×C4×D412yes—
155C24×C8—611no—
156C22×C22⋊C8—611no—
157C22×C4×C8—612no—
158C2×C4×C22⋊C4D6111yescharacteristic
159C8×C22⋊C4—618no—
160C2×#336—612no—
161C2×C61—28no—
162C2×C61C8×C22⋊C418yescomplemented
163C2×C61C2×C4×C22⋊C411yescharacteristic
164C2×C61C22×C4×C811yescharacteristic
165C2×C61C2×#40511yescharacteristic
166C2×C61C2×C8×D414yes—
167C24×C4C2×D6111yescharacteristic
168C23×C8—611no—
169C23×C8—618no—
170C23×C8—614no—
171C23×C8—612no—
172C23×C8—611no—
173C23×C8—1228no—
174C22×C22⋊C4Dic6112yes—
175C22×C42C2×D6112yes—
176C2×C22⋊C8—618no—
177C2×C22⋊C8—614no—
178C2×C4×C8—618no—
179C2×C4×C8—1228no—
180C4×C22⋊C4Dic6114yes—
181C4×C22⋊C4C2×D6114yes—
182C2×#95Dic6112yes—
183#336—618no—
184C61C2×C8×C22⋊C411yescharacteristic, complemented, Sylow
185C25C2×Dic6111yescharacteristic
186C23×C4—24no—
187C23×C4—24no—
188C23×C4C4×D6114yes—
189C23×C4C4×D6114yes—
190C23×C4C2×Dic6114yes—
191C23×C4C2×Dic6111yescharacteristic
192C23×C4C2×Dic6112yes—
193C23×C4C22×D6112yes—
194C23×C4C22×D6111yescharacteristic
195C22×C8—614no—
196C22×C8—618no—
197C22×C8—612no—
198C22×C8—614no—
199C22×C8—6116no—
200C22×C8—618no—
201C22×C8—612no—
202C22×C8—614no—
203C22×C8—12216no—
204C22×C8—12232no—
205C22×C8—1224no—
206C22×C8—1224no—
207C22×C8—1224no—
208C2×C22⋊C4#92418116yesdirect product factor
209C2×C22⋊C4C2×Dic6118yes—
210C2×C42—24no—
211C2×C42—24no—
212C2×C42C2×Dic6114yes—
213C2×C42C22×D6114yes—
214C22⋊C8—6116no—
215C4×C8—12216no—
216#95C2×Dic6118yes—
217C24—24no—
218C24—24no—
219C24C2×#9241818yes—
220C24C4×Dic6114yes—
221C24C22×Dic6112yes—
222C24C22×Dic6111yescharacteristic
223C22×C4—28no—
224C22×C4—24no—
225C22×C4—28no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—28no—
229C22×C4—28no—
230C22×C4—216no—
231C22×C4—28no—
232C22×C4C2×#92418116yescomplemented
233C22×C4C4×Dic6114yes—
234C22×C4C4×Dic6118yes—
235C22×C4C2×C4×D6114yes—
236C22×C4C2×C4×D6114yes—
237C22×C4C2×C4×D6112yes—
238C22×C4C2×C4×D6112yes—
239C22×C4D4×D6114yes—
240C22×C4#1175822414yes—
241C22×C4C22×Dic6112yes—
242C22×C4C22×Dic6118yes—
243C22×C4C22×Dic6111yescharacteristic
244C22×C4C23×D6111yescharacteristic
245C2×C8—614no—
246C2×C8—618no—
247C2×C8—6116no—
248C2×C8—618no—
249C2×C8—614no—
250C2×C8—12232no—
251C2×C8—1224no—
252C2×C8—1224no—
253C2×C8—1224no—
254C2×C8—1228no—
255C2×C8—12216no—
256C22⋊C4C2×#92418132yesdirect product factor
257C42—24no—
258C42—24no—
259C42—28no—
260C23—24no—
261C23—28no—
262C23—24no—
263C23—232no—
264C23—28no—
265C23C4×#92418116yescomplemented
266C23C2×C4×Dic6114yes—
267C23C2×C4×Dic6112yes—
268C23D4×Dic6114yes—
269C23C22×#9241818yes—
270C23C22×#9241814yes—
271C23#1451978414yes—
272C23C23×Dic6111yescharacteristic
273C2×C4—28no—
274C2×C4—24no—
275C2×C4—28no—
276C2×C4—232no—
277C2×C4—28no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—28no—
281C2×C4—216no—
282C2×C4C2×C4×Dic6114yes—
283C2×C4C2×C4×Dic6112yes—
284C2×C4C22⋊C4×D6114yes—
285C2×C4#1451973314yes—
286C2×C4#1451973718yes—
287C2×C4D4×Dic6114yes—
288C2×C4C22×#92418116yescomplemented
289C2×C4C22×C4×D6111yescharacteristic
290C2×C4C22×C4×D6111yescharacteristic
291C2×C4C2×D4×D6112yes—
292C2×C4C2×#1175822412yes—
293C8—618no—
294C8—1224no—
295C8—1228no—
296C22—24no—
297C22—216no—
298C22—24no—
299C22—232no—
300C22C22⋊C4×Dic6114yes—
301C22C2×C4×#9241814yes—
302C22C2×C4×#9241818yescomplemented
303C22#1683971814yes—
304C22D4×#92418116yes—
305C22C22×C4×Dic6111yescharacteristic
306C22C2×D4×Dic6112yes—
307C22C23×#9241812yes—
308C22C2×#1451978412yes—
309C4—216no—
310C4—24no—
311C4C22⋊C4×Dic6114yes—
312C4C2×C22⋊C4×D6111yescharacteristic
313C4C2×#1451973311yescharacteristic
314C4C2×#1451973712yes—
315C2—28no—
316C2C22⋊C4×#9241818yesdirect product factor
317C2C2×C22⋊C4×Dic6111yescharacteristic
318C2C22×C4×#9241811yescharacteristic
319C2C2×#1683971811yescharacteristic
320C2C2×D4×#9241814yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC2×C61C22×C4×C8
FrattiniC22×C4C23×D61
FittingC2×C4×C22⋊C4×C61C2
socleC24×C61C22×C4
prime radicalC25×C61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C2×C8×C22⋊C4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4×#92418C2semidirect
4. C22⋊C4×#92418C2direct (N × H)
5. C2×#16839517C2semidirect
8. C23×#92418C4semidirect
13. C2×C22⋊#92418C4semidirect
16. C2×C4×#92418C22semidirect
17. #16839517C22semidirect
32. C22×#92418C2×C4semidirect
37. C22⋊#92418C2×C4semidirect
49. C2×C22⋊C4×C61C8semidirect
73. C22×C4×C61C2×C8semidirect
84. C22⋊C4×C61C2×C8semidirect
94. C2×#92418C22⋊C4direct (N × H)
104. C23×C61C4×C8semidirect
127. C2×C4×C61C22×C8semidirect
134. #92418C2×C22⋊C4direct (N × H)
142. C22×C61C2×C4×C8semidirect
162. C2×C61C8×C22⋊C4semidirect
184. C61C2×C8×C22⋊C4semidirect
208. C2×C22⋊C4#92418direct (N × H)
232. C22×C4C2×#92418semidirect
256. C22⋊C4C2×#92418direct (N × H)
265. C23C4×#92418semidirect
288. C2×C4C22×#92418semidirect
302. C22C2×C4×#92418semidirect
316. C2C22⋊C4×#92418direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#924182
C22×C22⋊#924182
C22×C4×#924182
C22⋊C4×#924182
C2×#168395172
C2×C4×C22⋊C4×C612
C2×C8×C22⋊C461