Finite Group Databasebeta

← #30598961

Subgroups — #30598961

Order 15616.

478 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 128 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
1#21461673C212yesmaximal
2C2×#16840625C211yesmaximal, characteristic, complemented
3C2×#16840624C211yesmaximal, characteristic, complemented
4#21460649C212yesmaximal, complemented
5C2×#16839812C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C4⋊#92420C2212yes—
8C2×C22⋊#92420—22no—
9#16840628—22no—
10#16840625—22no—
11#16840624—22no—
12C22×C4×Dic61C2211yescharacteristic
13#16839812—22no—
14#16839812—22no—
15C2×#14519706C411yescharacteristic
16C2×#14519706C411yescharacteristic
17C2×C22⋊#92418C411yescharacteristic
18C2×C8×Dic61C2211yescharacteristic
19C2×C8×Dic61C2211yescharacteristic
20C2×C22⋊C8×C61C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C4⋊#92420—22no—
26C4⋊#92420—22no—
27C22⋊#92420—44no—
28C23×Dic61D411yescharacteristic
29C23×Dic61Q811yescharacteristic
30C22×#92418C2×C411yescharacteristic
31C22×#92418C2×C411yescharacteristic
32C2×C4×Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61C2×C411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61Q811yescharacteristic
39C2×C4×Dic61C2311yescharacteristic
40#14519706—22no—
41#14519706—22no—
42C22⋊#92418—22no—
43C8×Dic61—21no—
44C8×Dic61—21no—
45C8×Dic61D412yes—
46C8×Dic61D412yes—
47C23×C4×C61C2×C411yescharacteristic
48C22×C8×C61C2×C411yescharacteristic
49C22×C8×C61C2×C411yescharacteristic
50C22⋊C8×C61—22no—
51C24×C61C4⋊C411yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61C4⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61—22no—
59C22×Dic61—22no—
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—22no—
65C22×Dic61—22no—
66C22×Dic61C4⋊C411yescharacteristic
67C22×Dic61C4⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×Q811yescharacteristic
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C2×C8×C61—22no—
77C2×C8×C61—21no—
78C2×C8×C61—22no—
79C2×C8×C61C22⋊C412yes—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—21no—
84C4×Dic61—21no—
85C4×Dic61—21no—
86C4×Dic61C2×D411yescharacteristic
87C4×Dic61C2×D411yescharacteristic
88C4×Dic61#4111yescharacteristic
89C4×Dic61#4111yescharacteristic
90C2×#92418—22no—
91C2×#92418—21no—
92C2×#92418—22no—
93C2×#92418C22⋊C412yes—
94C23×C61—21no—
95C23×C61—22no—
96C23×C61—22no—
97C23×C61—21no—
98C23×C61#10812yes—
99C23×C61C2×C4⋊C411yescharacteristic
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—42no—
105C2×C4×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61#11711yescharacteristic
107C2×C4×C61#13112yes—
108C2×C4×C61#13112yes—
109C2×Dic61—24no—
110C2×Dic61—24no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—22no—
117C2×Dic61—42no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61#10812yes—
121C2×Dic61#12111yescharacteristic
122C2×Dic61#12111yescharacteristic
123C2×Dic61C22⋊Q811yescharacteristic
124C2×Dic61C22⋊Q811yescharacteristic
125C2×Dic61AGL(1,ℤ/8)12yes—
126C2×Dic61#13712yes—
127#92420—82no—
128#92420—82no—
129C8×C61—22no—
130C8×C61—41no—
131#92418—22no—
132#92418—41no—
133#8600—611nomaximal, Sylow
134C22×C61—22no—
135C22×C61—24no—
136C22×C61—41no—
137C22×C61—41no—
138C22×C61—42no—
139C22×C61#38011yescharacteristic
140C22×C61#42412yes—
141C22×C61#42812yes—
142C22×C61C2×#10811yescharacteristic
143C22×C61C2×#10811yescharacteristic
144C4×C61—41no—
145C4×C61#40811yescharacteristic
146C4×C61#40811yescharacteristic
147C4×C61#43312yes—
148Dic61—22no—
149Dic61—21no—
150Dic61—21no—
151Dic61—41no—
152Dic61#46812yes—
153Dic61#46911yescharacteristic
154Dic61#47011yescharacteristic
155C2×#431—611no—
156#1797—612no—
157C2×#335—611no—
158C2×#334—611no—
159#1277—612no—
160C2×C61—42no—
161C2×C61#157312yes—
162C2×C61#157412yes—
163C2×C61#179811yescharacteristic
164C2×C61#180911yescharacteristic
165C2×C61#181011yescharacteristic
166C22×C42—611no—
167#431—1222no—
168#431—1222no—
169C2×C4⋊C8—611no—
170C2×C4⋊C8—611no—
171C2×C4⋊C8—612no—
172C2×C4⋊C8—612no—
173C2×C22⋊C8—611no—
174C2×C22⋊C8—1222no—
175C2×C22⋊C8#692311yescharacteristic
176C2×C4×C8—611no—
177C2×C4×C8—611no—
178#336—1222no—
179#335—1222no—
180#334—1222no—
181C61#860011yescharacteristic, complemented, Sylow
182C23×C4—611no—
183C23×C4—611no—
184C23×C4C2×#692311yescharacteristic
185C22×C8—611no—
186C22×C8—611no—
187C22×C8—1222no—
188C22×C8—1222no—
189C22×C8C2×#692311yescharacteristic
190C22×C8C2×#692311yescharacteristic
191C2×C42—611no—
192C2×C42—611no—
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—1221no—
196C2×C42—1221no—
197C2×C42—1221no—
198C2×C42—1221no—
199C4⋊C8—1222no—
200C4⋊C8—1222no—
201C4⋊C8—1222no—
202C4⋊C8—1222no—
203C4⋊C8—1222no—
204C4⋊C8—1222no—
205C22⋊C8—22no—
206C22⋊C8—1222no—
207C22⋊C8—2444no—
208C4×C8—612no—
209C4×C8—612no—
210C4×C8—1221no—
211C4×C8—1221no—
212C24C4⋊#692311yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1222no—
224C22×C4—1222no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—1222no—
228C22×C4—1222no—
229C22×C4C4⋊#692311yescharacteristic
230C22×C4C22×#692311yescharacteristic
231C2×C8—22no—
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—612no—
235C2×C8—1222no—
236C2×C8—1221no—
237C2×C8—1222no—
238C2×C8—2442no—
239C2×C8—2442no—
240C2×C8—2442no—
241C2×C8—2442no—
242C2×C8—2442no—
243C2×C8—2442no—
244C2×C8C22⋊#692312yes—
245C42—611no—
246C42—611no—
247C42—611no—
248C42—611no—
249C42—1221no—
250C42—1221no—
251C42—1221no—
252C42—1221no—
253C42—1221no—
254C42—1221no—
255C23—21no—
256C23—22no—
257C23—22no—
258C23—21no—
259C23#1451984812yes—
260C23C2×C4⋊#692311yescharacteristic
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—611no—
267C2×C4—611no—
268C2×C4—612no—
269C2×C4—612no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—612no—
273C2×C4—1224no—
274C2×C4—1224no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1222no—
281C2×C4—2442no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4C2×C22⋊#692311yescharacteristic
285C2×C4#1451985611yescharacteristic
286C2×C4#1451986412yes—
287C2×C4#1451986412yes—
288C8—22no—
289C8—41no—
290C8—1222no—
291C8—4882no—
292C8—4882no—
293C8—2441no—
294C22—24no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22#1684070411yescharacteristic
300C22#1684076812yes—
301C22#1684077312yes—
302C22D61⋊#10811yescharacteristic
303C22C2×#1451984811yescharacteristic
304C4—41no—
305C4—612no—
306C4—611no—
307C4—611no—
308C4—1222no—
309C4—1221no—
310C4—1221no—
311C4—2441no—
312C4#1684073511yescharacteristic
313C4#1684073611yescharacteristic
314C4#1684078612yes—
315C2—42no—
316C2#2146139412yes—
317C2#2146139512yes—
318C2#2146167711yescharacteristic
319C2#2146169711yescharacteristic
320C2#2146169911yescharacteristic
subgroupG/H
centerC23C2×C4⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC23×C61C2×C4⋊C4
prime radicalC24×C61C4⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#8600
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16840625C2semidirect
3. C2×#16840624C2semidirect
4. #21460649C2semidirect
181. C61#8600semidirect

Maximal subgroups

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

subgroupindex
#214616732
C2×#168406252
C2×#168406242
#214606492
C2×#168398122
#860061