Finite Group Databasebeta

← C2×#21460792 #30604711

Subgroups — C2×#21460792 #30604711

Order 15616.

444 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 88 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×#16840659C211yesmaximal, characteristic
2C2×#16840630C211yesmaximal, characteristic
3#21460792C214yesmaximal, direct product factor
4C2×#16840021C211yesmaximal, characteristic
5C2×#14519856—21no—
6C2×#14519851—21no—
7#16840659—21no—
8#16840659C2212yes—
9#16840630—21no—
10#16840630C2212yes—
11C22×Dic244C411yescharacteristic, complemented
12C22×#11758189C2211yescharacteristic
13C2×#14519757—21no—
14#16840021—21no—
15#16840021—21no—
16#16840021C412yescomplemented
17#16840021C2212yes—
18C2×#14519700—21no—
19C2×#106×C61C411yescharacteristic, complemented
20#14519856—22no—
21#14519856—22no—
22#14519856—41no—
23#14519856—41no—
24C2×C4⋊#6923—41no—
25C2×C22⋊#6923—41no—
26C2×C4×#6923—22no—
27#14519851—22no—
28#14519851—41no—
29C2×#11758187—41no—
30C22×Dic122—21no—
31C22×C4×D61D411yescharacteristic
32C2×Dic244—21no—
33C2×Dic244—41no—
34C2×Dic244—41no—
35C2×Dic244C2×C412yescomplemented
36C2×#11758189—41no—
37C2×#11758189—41no—
38C2×#11758189C2×C411yescharacteristic
39C2×#11758189D411yescharacteristic
40C2×#11758189D411yescharacteristic
41C2×#11758189C2311yescharacteristic
42C22×#92418D411yescharacteristic
43#14519757—22no—
44#14519757—22no—
45#14519757—41no—
46#14519757—41no—
47C2×C4⋊Dic61—41no—
48C2×#11758198—41no—
49#14519700—22no—
50#14519700—22no—
51C22×C8×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53#106×C61—21no—
54#106×C61C2×C412yescomplemented
55C23×D61D811yescharacteristic
56C22×#6923—42no—
57C22×C4×C61—41no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×Dic61—41no—
60C22×Dic61SD1611yescharacteristic
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C4×D61C22⋊C411yescharacteristic
66C2×C4×D61D811yescharacteristic
67C2×C4×D61SD1611yescharacteristic
68C2×C4×D61C2×D411yescharacteristic
69C2×Dic122—22no—
70C2×Dic122—41no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C22⋊#6923—42no—
76C22⋊#6923—42no—
77C4⋊#6923—42no—
78C4⋊#6923—42no—
79C4×#6923—24no—
80C4×#6923—42no—
81C2×C8×C61—21no—
82C2×C8×C61—21no—
83C2×C8×C61C22⋊C411yescharacteristic
84C2×C8×C61C22×C411yescharacteristic
85C4⋊C4×C61—22no—
86C4⋊C4×C61—41no—
87#11758198—42no—
88#11758198—42no—
89C4⋊Dic61—42no—
90C4⋊Dic61—42no—
91C2×#92418—21no—
92C2×#92418—21no—
93C2×#92418C22⋊C411yescharacteristic
94C2×#92418C2×D411yescharacteristic
95Dic244—42no—
96Dic244—42no—
97#11758189—41no—
98#11758189—41no—
99#11758189—41no—
100#11758189—41no—
101#11758187—42no—
102C23×C61#10211yescharacteristic
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—42no—
106C22×D61#10211yescharacteristic
107C22×D61C2×D811yescharacteristic
108C2×#6923—44no—
109C2×#6923—84no—
110C2×C4×C61—42no—
111C2×C4×C61—82no—
112C2×C4×C61#9911yescharacteristic
113C2×C4×C61#9911yescharacteristic
114C2×C4×C61#10211yescharacteristic
115C2×C4×C61#10411yescharacteristic
116C2×C4×C61#10411yescharacteristic
117C2×C4×C61C2×C22⋊C411yescharacteristic
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—42no—
121C2×Dic61—81no—
122C2×Dic61—81no—
123C2×Dic61#10211yescharacteristic
124C2×Dic61C2×SD1611yescharacteristic
125C4×D61—21no—
126C4×D61—21no—
127C4×D61—21no—
128C4×D61—21no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—21no—
132C4×D61—21no—
133Dic122—42no—
134Dic122—42no—
135Dic122—81no—
136Dic122—81no—
137C8×C61—21no—
138C8×C61—21no—
139#92418—21no—
140#92418—21no—
141C2×#1340—611nomaximal, Sylow
142C22×C61—22no—
143C22×C61#32711yescharacteristic
144C22×C61#32711yescharacteristic
145C22×C61C2×#10211yescharacteristic
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—42no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—81no—
152#6923—84no—
153C4×C61—82no—
154C4×C61#32711yescharacteristic
155C4×C61#32711yescharacteristic
156C4×C61C2×#9911yescharacteristic
157C4×C61C2×#10411yescharacteristic
158Dic61—21no—
159Dic61—21no—
160Dic61—82no—
161C2×#470—611no—
162C2×#349—611no—
163C2×H(3,ℤ/4)—611no—
164#1340—614no—
165C2×C61—21no—
166C2×C61—21no—
167C2×C61#134012yescomplemented
168C2×C61C2×#32711yescharacteristic
169D61—41no—
170D61—41no—
171C22×Q16—611no—
172C22×M16—611no—
173C2×C22⋊Q8—1221no—
174C2×#117—1221no—
175C2×M32—1221no—
176#470—612no—
177#470—612no—
178#470—1221no—
179#470—1221no—
180C2×#106#692311yescharacteristic, complemented
181C2×#103—1221no—
182#349—612no—
183#349—1221no—
184H(3,ℤ/4)—612no—
185H(3,ℤ/4)—1221no—
186C61C2×#134011yescharacteristic, complemented, Sylow
187C22×Q8—1221no—
188C23×C4—611no—
189C2×Q16—612no—
190C2×Q16—1221no—
191C2×Q16—2441no—
192C2×Q16—2441no—
193C2×M16—611no—
194C2×M16—611no—
195C2×M16—611no—
196C2×M16—611no—
197C2×M16—2441no—
198C2×M16—2441no—
199C22×C8—611no—
200C22×C8C2×#692311yescharacteristic
201C22⋊Q8—1222no—
202C22⋊Q8—1222no—
203C22⋊Q8—2441no—
204C22⋊Q8—2441no—
205#117—1222no—
206#117—1222no—
207#117—2441no—
208#117—2441no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—2441no—
211C2×C4⋊C4—2441no—
212C2×C22⋊C4—2441no—
213C2×C22⋊C4—2441no—
214C2×C42—1222no—
215M32—1222no—
216M32—2441no—
217C2×C16—2441no—
218#106—21no—
219#106C2×#692312yescomplemented
220#103—1222no—
221#103—1222no—
222C24—611no—
223C2×Q8—1222no—
224C2×Q8—2441no—
225C2×Q8—2441no—
226C2×Q8—2441no—
227C2×Q8—2441no—
228C2×Q8—2441no—
229C22×C4—41no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—2442no—
240C22×C4—2441no—
241C22×C4C22⋊#692311yescharacteristic
242Q16—2442no—
243Q16—2442no—
244M16—2441no—
245M16—2441no—
246M16—2441no—
247M16—2441no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—611no—
251C2×C8—611no—
252C2×C8—1221no—
253C2×C8—1221no—
254C2×C8C22⋊#692311yescharacteristic
255C2×C8C22×#692311yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—2442no—
259C4⋊C4—2442no—
260C4⋊C4—2442no—
261C4⋊C4—2442no—
262C22⋊C4—2442no—
263C22⋊C4—2442no—
264C22⋊C4—2442no—
265C22⋊C4—2442no—
266C42—1224no—
267C42—2442no—
268C16—2442no—
269C23—611no—
270C23—611no—
271C23—1221no—
272C23—1221no—
273C23—2442no—
274C23#1451983911yescharacteristic
275Q8—4881no—
276Q8—4881no—
277Q8—2442no—
278Q8—2442no—
279C2×C4—42no—
280C2×C4—82no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—4884no—
294C2×C4—4881no—
295C2×C4—4881no—
296C2×C4—2444no—
297C2×C4—2442no—
298C2×C4#1451983611yescharacteristic
299C2×C4#1451983611yescharacteristic
300C2×C4#1451983911yescharacteristic
301C2×C4#1451984211yescharacteristic
302C2×C4#1451984211yescharacteristic
303C2×C4C2×C22⋊#692311yescharacteristic
304C8—21no—
305C8—21no—
306C8—1221no—
307C8—1221no—
308C22—22no—
309C22—1221no—
310C22—1221no—
311C22—4881no—
312C22—2441no—
313C22—2441no—
314C22—2442no—
315C22#1684061411yescharacteristic
316C22#1684061411yescharacteristic
317C22C2×#1451983911yescharacteristic
318C4—82no—
319C4—1221no—
320C4—1221no—
321C4—4884no—
322C4—4882no—
323C4#1684061411yescharacteristic
324C4#1684061411yescharacteristic
325C4C2×#1451983611yescharacteristic
326C4C2×#1451984211yescharacteristic
327C2—21no—
328C2—21no—
329C2—2441no—
330C2—2441no—
331C2#2146079212yesdirect product factor
332C2C2×#1684061411yescharacteristic
subgroupG/H
centerC22#16840614
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×#106×C61C4
socleC22×C61#327
prime radicalC23×D61D8
cosocleC2×#11758189C23
hypercenterC2×#106#6923
hypocenterC61C2×#1340
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #21460792C2direct (N × H)
11. C22×Dic244C4semidirect
16. #16840021C4semidirect
19. C2×#106×C61C4semidirect
35. C2×Dic244C2×C4semidirect
54. #106×C61C2×C4semidirect
167. C2×C61#1340semidirect
180. C2×#106#6923semidirect
186. C61C2×#1340semidirect
219. #106C2×#6923semidirect
331. C2#21460792direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406592
C2×#168406302
#214607922
C2×#168400212
C2×#134061