Finite Group Databasebeta

← #30598956

Subgroups — #30598956

Order 15616.

478 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 132 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#21461674C212yesmaximal
2C2×#16840624C211yesmaximal, characteristic, complemented
3C2×#16840623C211yesmaximal, characteristic, complemented
4#21460649C212yesmaximal, complemented
5C2×#16839814C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C4⋊#92420C2212yes—
8C2×#14519834—22no—
9#16840628—22no—
10#16840624—22no—
11#16840623—22no—
12C2×C42×D61C2211yescharacteristic
13#16839814—22no—
14#16839814—22no—
15C2×C4⋊#92418C411yescharacteristic
16C2×#14519689C411yescharacteristic
17C2×#14519689C411yescharacteristic
18C2×C8×Dic61C2211yescharacteristic
19C2×C8×Dic61C2211yescharacteristic
20C2×C4⋊C8×C61C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C4⋊#92420—22no—
26C4⋊#92420—22no—
27#14519834—44no—
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61Q811yescharacteristic
31C22×#92418C2×C411yescharacteristic
32C22×#92418C2×C411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61Q811yescharacteristic
35C2×C4×Dic61C2311yescharacteristic
36C42×D61—21no—
37C42×D61—21no—
38C42×D61—21no—
39C42×D61—21no—
40C4⋊#92418—22no—
41#14519689—22no—
42#14519689—22no—
43C8×Dic61—21no—
44C8×Dic61—21no—
45C8×Dic61D412yes—
46C8×Dic61D412yes—
47C22×C8×C61C2×C411yescharacteristic
48C22×C8×C61C2×C411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50C4⋊C8×C61—22no—
51C23×D61C4⋊C411yescharacteristic
52C22×C4×C61C4⋊C411yescharacteristic
53C22×C4×C61C4⋊C411yescharacteristic
54C22×C4×C61C22×C411yescharacteristic
55C22×Dic61C4⋊C411yescharacteristic
56C22×Dic61C2×D411yescharacteristic
57C22×Dic61C2×Q811yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—22no—
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—42no—
68C2×C4×D61SD1614yes—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×C8×C61—22no—
76C2×C8×C61—21no—
77C2×C8×C61—22no—
78C2×C8×C61C22⋊C412yes—
79C42×C61—21no—
80C42×C61—21no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—21no—
84C4×Dic61—21no—
85C4×Dic61C2×D411yescharacteristic
86C4×Dic61C2×D411yescharacteristic
87C4×Dic61#4111yescharacteristic
88C4×Dic61#4111yescharacteristic
89C2×#92418—22no—
90C2×#92418—21no—
91C2×#92418—22no—
92C2×#92418C22⋊C412yes—
93C23×C61C2×C4⋊C411yescharacteristic
94C22×D61—21no—
95C22×D61—22no—
96C22×D61—21no—
97C22×D61—22no—
98C22×D61#10612yes—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61#10612yes—
104C2×C4×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61#11711yescharacteristic
106C2×C4×C61#13112yes—
107C2×C4×C61#13112yes—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61#12111yescharacteristic
112C2×Dic61#12111yescharacteristic
113C2×Dic61C22⋊Q811yescharacteristic
114C2×Dic61C22⋊Q811yescharacteristic
115C2×Dic61C2×SD1612yes—
116C2×Dic61#13512yes—
117C4×D61—24no—
118C4×D61—24no—
119C4×D61—42no—
120C4×D61—42no—
121C4×D61—41no—
122C4×D61—41no—
123C4×D61—42no—
124#92420—82no—
125#92420—82no—
126C8×C61—22no—
127C8×C61—41no—
128#92418—22no—
129#92418—41no—
130#8598—611nomaximal, Sylow
131C22×C61#38011yescharacteristic
132C22×C61#42412yes—
133C22×C61C2×#10611yescharacteristic
134C22×C61#42711yescharacteristic
135C22×C61#43012yes—
136C2×D61—22no—
137C2×D61—24no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—42no—
141C4×C61—22no—
142C4×C61—41no—
143C4×C61#40811yescharacteristic
144C4×C61#40811yescharacteristic
145C4×C61#43312yes—
146Dic61—21no—
147Dic61—21no—
148Dic61—41no—
149Dic61#46512yes—
150Dic61#46512yes—
151C2×#431—611no—
152#1797—612no—
153C2×#334—611no—
154C2×#334—611no—
155#1277—612no—
156C2×C61#157012yes—
157C2×C61#157212yes—
158C2×C61#179811yescharacteristic
159C2×C61#180711yescharacteristic
160C2×C61#181111yescharacteristic
161D61—42no—
162C22×C42—611no—
163#431—1222no—
164#431—1222no—
165C2×C4⋊C8—612no—
166C2×C4⋊C8—612no—
167C2×C4⋊C8—611no—
168C2×C4⋊C8#692311yescharacteristic
169C2×C22⋊C8—611no—
170C2×C22⋊C8—611no—
171C2×C22⋊C8—1222no—
172C2×C4×C8—611no—
173C2×C4×C8—611no—
174#336—1222no—
175#334—1222no—
176#334—1222no—
177C61#859811yescharacteristic, complemented, Sylow
178C23×C4—611no—
179C23×C4—611no—
180C23×C4—611no—
181C22×C8—611no—
182C22×C8—611no—
183C22×C8—1222no—
184C22×C8—1222no—
185C22×C8C2×#692311yescharacteristic
186C22×C8C2×#692311yescharacteristic
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—1221no—
191C2×C42—1221no—
192C2×C42—1221no—
193C2×C42—1221no—
194C2×C42C2×#692311yescharacteristic
195C4⋊C8—22no—
196C4⋊C8—1222no—
197C4⋊C8—1222no—
198C4⋊C8—1222no—
199C4⋊C8—1222no—
200C4⋊C8—1222no—
201C22⋊C8—1222no—
202C22⋊C8—1222no—
203C22⋊C8—2444no—
204C4×C8—612no—
205C4×C8—612no—
206C4×C8—1221no—
207C4×C8—1221no—
208C24—611no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—614no—
212C22×C4—611no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1222no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4—1221no—
220C22×C4—1222no—
221C22×C4—1222no—
222C22×C4—2442no—
223C22×C4C4⋊#692311yescharacteristic
224C22×C4C4⋊#692311yescharacteristic
225C22×C4C22×#692311yescharacteristic
226C2×C8—22no—
227C2×C8—21no—
228C2×C8—22no—
229C2×C8—612no—
230C2×C8—1222no—
231C2×C8—1221no—
232C2×C8—1222no—
233C2×C8—2442no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C2×C8—2442no—
239C2×C8C22⋊#692312yes—
240C42—21no—
241C42—21no—
242C42—611no—
243C42—611no—
244C42—611no—
245C42—611no—
246C42—1221no—
247C42—1221no—
248C42—1221no—
249C42—1221no—
250C23—612no—
251C23—1221no—
252C23—1222no—
253C23—1221no—
254C23—1222no—
255C23C2×C4⋊#692311yescharacteristic
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—612no—
263C2×C4—612no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—1224no—
267C2×C4—1224no—
268C2×C4—1222no—
269C2×C4—1221no—
270C2×C4—1222no—
271C2×C4—2442no—
272C2×C4—2442no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2442no—
276C2×C4#1451984512yes—
277C2×C4C2×C22⋊#692311yescharacteristic
278C2×C4#1451985611yescharacteristic
279C2×C4#1451986412yes—
280C2×C4#1451986512yes—
281C8—22no—
282C8—41no—
283C8—1222no—
284C8—4882no—
285C8—4882no—
286C8—2441no—
287C22—1224no—
288C22—1222no—
289C22—2442no—
290C22—2441no—
291C22—2441no—
292C22#1684070411yescharacteristic
293C22#1684076912yes—
294C22C2×#1451984511yescharacteristic
295C22#1684077211yescharacteristic
296C22#1684077712yes—
297C4—22no—
298C4—41no—
299C4—612no—
300C4—612no—
301C4—1221no—
302C4—1221no—
303C4—2441no—
304C4#1684073511yescharacteristic
305C4#1684073711yescharacteristic
306C4#1684078712yes—
307C2—2442no—
308C2#2146138712yes—
309C2#2146139112yes—
310C2#2146167811yescharacteristic
311C2#2146169511yescharacteristic
312C2#2146170011yescharacteristic
subgroupG/H
centerC23C2×C4⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊C8×C61C4
socleC23×C61C2×C4⋊C4
prime radicalC23×D61C4⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊C8#6923
hypocenterC61#8598
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16840624C2semidirect
3. C2×#16840623C2semidirect
4. #21460649C2semidirect
177. C61#8598semidirect

Maximal subgroups

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

subgroupindex
#214616742
C2×#168406242
C2×#168406232
#214606492
C2×#168398142
#859861