Finite Group Databasebeta

← C2×#21460804 #30604751

Subgroups — C2×#21460804 #30604751

Order 15616.

544 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840642C211yesmaximal, characteristic
2C2×#16840608C211yesmaximal, characteristic
3#21460804C214yesmaximal, direct product factor
4C2×#16839694C211yesmaximal, characteristic
5C22×#11758217—21no—
6C2×C22⋊#92420—21no—
7#16840642—21no—
8#16840642C2212yes—
9#16840608—21no—
10#16840608C2212yes—
11C22×C4⋊Dic61—21no—
12C22×C4⋊Dic61C411yescharacteristic
13C22×#11758196C2211yescharacteristic
14#16839694—21no—
15#16839694—21no—
16#16839694C412yes—
17#16839694C2212yes—
18C2×#14519684—21no—
19C2×#95×C61C411yescharacteristic
20C2×#11758217—24no—
21C2×#11758217—22no—
22C2×#11758217—41no—
23C2×#11758217—42no—
24C22×#92420—41no—
25C22×#92420—41no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C23×Dic61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61—22no—
34C2×C4⋊Dic61—42no—
35C2×C4⋊Dic61—42no—
36C2×C4⋊Dic61—41no—
37C2×C4⋊Dic61—41no—
38C2×C4⋊Dic61C2×C412yes—
39C2×#11758196—41no—
40C2×#11758196—41no—
41C2×#11758196C2×C411yescharacteristic
42C2×#11758196D411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×#11758196C2311yescharacteristic
45#14519684—22no—
46#14519684—22no—
47C23×C4×C61—21no—
48C23×C4×C61C2×C411yescharacteristic
49#95×C61—21no—
50#95×C61C2×C412yes—
51C24×C61C22⋊C411yescharacteristic
52C22×C4×C61—24no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—22no—
56C22×C4×C61—42no—
57C22×C4×C61—42no—
58C22×C4×C61—42no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—22no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—22no—
67C22×Dic61—42no—
68C22×Dic61—41no—
69C22×Dic61—41no—
70C22×Dic61—42no—
71C22×Dic61—42no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61D812yes—
75C22×Dic61SD1612yes—
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78#11758217—24no—
79#11758217—44no—
80#11758217—42no—
81C2×#92420—44no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—82no—
85C4⋊Dic61—42no—
86C4⋊Dic61—44no—
87C4⋊Dic61—42no—
88C4⋊Dic61—42no—
89C4⋊Dic61—42no—
90#11758196—41no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94C23×C61—22no—
95C23×C61—22no—
96C23×C61#9911yescharacteristic
97C23×C61#9911yescharacteristic
98C23×C61#10212yes—
99C23×C61#10412yes—
100C23×C61C2×C22⋊C411yescharacteristic
101C2×C4×C61—24no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—48no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—22no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—42no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126C2×Dic61—42no—
127C2×Dic61—81no—
128C2×Dic61—82no—
129C2×Dic61—82no—
130C2×Dic61#10212yes—
131C2×Dic61C2×D811yescharacteristic
132C2×Dic61C2×SD1611yescharacteristic
133#92420—44no—
134#92420—82no—
135C2×#1346—611nomaximal, Sylow
136C22×C61—24no—
137C22×C61—24no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#32712yes—
143C22×C61#32712yes—
144C22×C61#35212yes—
145C22×C61#35612yes—
146C22×C61C2×#9911yescharacteristic
147C22×C61C2×#10211yescharacteristic
148C22×C61C2×#10411yescharacteristic
149C4×C61—44no—
150C4×C61—41no—
151C4×C61—41no—
152Dic61—21no—
153Dic61—22no—
154Dic61—21no—
155Dic61—41no—
156Dic61—41no—
157Dic61—82no—
158C2×#398—611no—
159C2×#343—611no—
160C2×#324—611no—
161#1346—614no—
162C2×C61—21no—
163C2×C61—22no—
164C2×C61—21no—
165C2×C61#134614yescomplemented
166C2×C61C2×#32711yescharacteristic
167C2×C61C2×#35211yescharacteristic
168C2×C61C2×#35611yescharacteristic
169C22×M16—1221no—
170C22×C4⋊C4—611no—
171C22×C4⋊C4—611no—
172C22×C4⋊C4—1221no—
173C2×C22⋊C8—1221no—
174#398—612no—
175#398—612no—
176#398—1221no—
177#398—1221no—
178C2×#95—1221no—
179C2×#95#692311yescharacteristic
180#343—612no—
181#343—1221no—
182#324—612no—
183#324—1221no—
184C61C2×#134611yescharacteristic, complemented, Sylow
185C23×C4—21no—
186C23×C4—611no—
187C23×C4—611no—
188C23×C4—1221no—
189C23×C4C2×#692311yescharacteristic
190C2×M16—1222no—
191C2×M16—1224no—
192C2×M16—2442no—
193C2×M16—2441no—
194C22×C8—2441no—
195C22×C8—2441no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—612no—
201C2×C4⋊C4—1222no—
202C2×C4⋊C4—1222no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—2441no—
205C2×C4⋊C4—2441no—
206C2×C4⋊C4—2441no—
207C2×C4⋊C4—2441no—
208C2×C4⋊C4—2442no—
209C2×C4⋊C4—2442no—
210C22⋊C8—1222no—
211C22⋊C8—2441no—
212#95—21no—
213#95—1222no—
214#95—1222no—
215#95C2×#692312yes—
216C24C22⋊#692311yescharacteristic
217C22×C4—24no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—612no—
225C22×C4—612no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—1222no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—1222no—
236C22×C4—2441no—
237C22×C4—2441no—
238C22×C4—2442no—
239C22×C4—2442no—
240C22×C4—2442no—
241C22×C4C22⋊#692311yescharacteristic
242C22×C4C22×#692311yescharacteristic
243M16—1224no—
244M16—2442no—
245M16—2444no—
246C2×C8—4882no—
247C2×C8—2442no—
248C2×C8—2442no—
249C2×C8—2444no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2442no—
255C4⋊C4—2442no—
256C4⋊C4—2444no—
257C4⋊C4—2442no—
258C4⋊C4—2442no—
259C23—22no—
260C23—22no—
261C23#1451983611yescharacteristic
262C23#1451983611yescharacteristic
263C23#1451983912yes—
264C23#1451984212yes—
265C23C2×C22⋊#692311yescharacteristic
266C2×C4—24no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—48no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—612no—
277C2×C4—611no—
278C2×C4—611no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1222no—
284C2×C4—1222no—
285C2×C4—1222no—
286C2×C4—1222no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—4882no—
290C2×C4—4882no—
291C2×C4—4881no—
292C2×C4—2442no—
293C2×C4—2442no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4—2441no—
297C2×C4—2441no—
298C8—4882no—
299C8—2444no—
300C22—21no—
301C22—21no—
302C22—24no—
303C22—24no—
304C22—21no—
305C22—21no—
306C22#1684061412yes—
307C22#1684061412yes—
308C22#1684066512yes—
309C22#1684067312yes—
310C22C2×#1451983611yescharacteristic
311C22C2×#1451983911yescharacteristic
312C22C2×#1451984211yescharacteristic
313C4—44no—
314C4—41no—
315C4—41no—
316C4—1221no—
317C4—1222no—
318C4—1221no—
319C4—4882no—
320C4—2441no—
321C4—2441no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2#2146080414yesdirect product factor
326C2C2×#1684061411yescharacteristic
327C2C2×#1684066511yescharacteristic
328C2C2×#1684067311yescharacteristic
subgroupG/H
centerC23#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#95×C61C4
socleC23×C61#99
prime radicalC24×C61C22⋊C4
cosocleC2×#11758196C23
hypercenterC2×#95#6923
hypocenterC61C2×#1346
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #21460804C2direct (N × H)
165. C2×C61#1346semidirect
184. C61C2×#1346semidirect
325. C2#21460804direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406422
C2×#168406082
#214608042
C2×#168396942
C2×#134661