Finite Group Databasebeta

← #30598990

Subgroups — #30598990

Order 15616.

372 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461368C211yesmaximal, characteristic, complemented
2C2×#16840623C211yesmaximal, characteristic, complemented
3#21461116C212yesmaximal
4#21460665C212yesmaximal, complemented
5#21454462C211yesmaximal, characteristic
6#16840778C2212yes—
7C2×C4⋊#92420C2212yes—
8#16840626—21no—
9#16840624—21no—
10#16840623—21no—
11#16840623—21no—
12#16840612—22no—
13#16840610—22no—
14#16840230C2211yescharacteristic
15#16839822—21no—
16#16839822—21no—
17#16839814—21no—
18#16839814—21no—
19#16839789C411yescharacteristic
20#16839730C411yescharacteristic
21#16839728C411yescharacteristic
22M16×Dic61C2211yescharacteristic
23C2×C8×Dic61C2211yescharacteristic
24C61×#424C411yescharacteristic
25C22×#92420—22no—
26C4⋊#92420—22no—
27C4⋊#92420—22no—
28C4⋊#92420—22no—
29C22⋊#92420—22no—
30C4×#92420—22no—
31C2×#11758222C2×C411yescharacteristic
32C2×#11758194C2×C411yescharacteristic
33C22×#92418C2×C411yescharacteristic
34#14519742D411yescharacteristic
35#14519742Q811yescharacteristic
36#14519739D411yescharacteristic
37#14519739Q811yescharacteristic
38#14519737—21no—
39#14519737—21no—
40#14519734—21no—
41C2×C4×Dic61C2311yescharacteristic
42C42×D61—21no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45#14519689—21no—
46#14519689—21no—
47#14519689—21no—
48#14519689—21no—
49#14519687—21no—
50C8×Dic61—21no—
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C8×Dic61D411yescharacteristic
54C8×Dic61D411yescharacteristic
55C2×M16×C61C2×C411yescharacteristic
56C22×C8×C61C2×C411yescharacteristic
57#117×C61C2×C411yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C22×C4×C61C22×C411yescharacteristic
61C2×C22⋊D61—21no—
62C22×Dic61#4111yescharacteristic
63C22×Dic61#4111yescharacteristic
64#11758222—22no—
65#11758222—22no—
66C2×D244C4⋊C411yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×Dic122C4⋊C411yescharacteristic
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—82no—
74M16×C61—22no—
75C2×C8×C61—22no—
76C2×C8×C61—21no—
77C2×C8×C61C22⋊C411yescharacteristic
78C2×C8×C61C22⋊C411yescharacteristic
79C4⋊C4×C61C4⋊C411yescharacteristic
80C4⋊C4×C61C4⋊C411yescharacteristic
81C22⋊C4×C61—21no—
82C42×C61—21no—
83#11758198—21no—
84#11758198—21no—
85#11758196—21no—
86#11758196—21no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61C2×D411yescharacteristic
90C4×Dic61C2×D411yescharacteristic
91C4×Dic61C2×D411yescharacteristic
92C4×Dic61C2×Q811yescharacteristic
93#11758194—22no—
94C2×#92418—22no—
95C2×#92418—21no—
96C2×#92418C22⋊C411yescharacteristic
97C2×#92418C22⋊C411yescharacteristic
98C23×C61#11711yescharacteristic
99C22×D61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61C2×C4⋊C411yescharacteristic
104C2×C4×C61#13112yes—
105C2×C4×C61#13112yes—
106C22⋊D61—42no—
107C2×Dic61—22no—
108C2×Dic61—21no—
109C2×Dic61—41no—
110C2×Dic61#12111yescharacteristic
111C2×Dic61#12111yescharacteristic
112C2×Dic61C22⋊Q811yescharacteristic
113C2×Dic61C22⋊Q811yescharacteristic
114D244—22no—
115C4×D61—42no—
116C4×D61—41no—
117C4×D61—41no—
118C4×D61—42no—
119Dic122—22no—
120#92420—82no—
121#92420—82no—
122C8×C61—21no—
123C8×C61—21no—
124C8×C61—41no—
125#92418—21no—
126#92418—21no—
127#92418—41no—
128#8607—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—21no—
131C22×C61#38011yescharacteristic
132C22×C61#43312yes—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—41no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61#40811yescharacteristic
139C4×C61#40811yescharacteristic
140C4×C61#42412yes—
141Dic61—21no—
142Dic61—21no—
143Dic61—21no—
144Dic61—41no—
145Dic61#47112yes—
146#2922—611no—
147#1564—611no—
148C2×#334—611no—
149#1477—612no—
150#1283—612no—
151C2×C61—22no—
152C2×C61#179811yescharacteristic
153C2×C61#181411yescharacteristic
154C2×C61#181511yescharacteristic
155D61—81no—
156C4×#41—611no—
157#433—1221no—
158#433—1221no—
159#431—612no—
160#431—1221no—
161#431—1221no—
162#424—611no—
163#424#692311yescharacteristic
164C2×C4⋊C8—612no—
165#408—611no—
166#408—611no—
167C4×M16—611no—
168C2×C4×C8—611no—
169#335—1221no—
170#334—1221no—
171#334—1221no—
172#334—1221no—
173Q8⋊C8—1222no—
174D4⋊C8—1222no—
175C61#860711yescharacteristic, complemented, Sylow
176C2×#41—611no—
177C2×M16—611no—
178C2×M16C2×#692311yescharacteristic
179C22×C8—611no—
180C22×C8—1222no—
181C22×C8C2×#692311yescharacteristic
182C4×Q8—611no—
183C4×Q8—611no—
184C4×D4—611no—
185C4×D4—611no—
186C4×D4—1221no—
187C4×D4—1221no—
188#117—1221no—
189#117C2×#692311yescharacteristic
190C2×C42—611no—
191C2×C42—1221no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—1221no—
195C4⋊C8—1221no—
196C4⋊C8—1222no—
197C4⋊C8—1222no—
198C4⋊C8—1222no—
199C22⋊C8—1221no—
200C22⋊C8—1221no—
201C22⋊C8—1221no—
202C22⋊C8—1221no—
203C22⋊C8—1222no—
204#97—1221no—
205C4×C8—611no—
206C4×C8—611no—
207C4×C8—611no—
208C4×C8—611no—
209C4×C8—1221no—
210C4×C8—1222no—
211#41—1222no—
212#41—1222no—
213C2×Q8—611no—
214C2×D4—611no—
215C2×D4—1221no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—1221no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4C22×#692311yescharacteristic
222M16—22no—
223M16—1222no—
224C2×C8—22no—
225C2×C8—21no—
226C2×C8—611no—
227C2×C8—611no—
228C2×C8—1222no—
229C2×C8—1221no—
230C2×C8—4882no—
231C2×C8—2442no—
232C2×C8—2442no—
233C2×C8C22⋊#692311yescharacteristic
234C2×C8C22⋊#692311yescharacteristic
235C4⋊C4—1221no—
236C4⋊C4—1221no—
237C4⋊C4C4⋊#692311yescharacteristic
238C4⋊C4C4⋊#692311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—1221no—
241C22⋊C4—1221no—
242C42—21no—
243C42—611no—
244C42—611no—
245C42—611no—
246C42—611no—
247C42—1221no—
248C42—1221no—
249C23—1221no—
250C23#1451985611yescharacteristic
251Q8—1222no—
252D4—1222no—
253D4—2442no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—2442no—
263C2×C4—2442no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4C2×C22⋊#692311yescharacteristic
268C2×C4C2×C4⋊#692311yescharacteristic
269C2×C4#1451986412yes—
270C2×C4#1451986512yes—
271C8—21no—
272C8—21no—
273C8—41no—
274C8—1221no—
275C8—1221no—
276C8—4882no—
277C8—4882no—
278C8—2441no—
279C22—21no—
280C22—21no—
281C22—2441no—
282C22—2441no—
283C22—2441no—
284C22#1684070411yescharacteristic
285C22#1684078712yes—
286C4—41no—
287C4—41no—
288C4—612no—
289C4—1221no—
290C4—1221no—
291C4—1221no—
292C4—2441no—
293C4#1684073511yescharacteristic
294C4#1684073711yescharacteristic
295C4#1684076912yes—
296C2—22no—
297C2—4881no—
298C2#2146167811yescharacteristic
299C2#2146170511yescharacteristic
300C2#2146170711yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC22×C61#380
prime radicalC2×#11758222C2×C4
cosocleC2×C4×Dic61C23
hypercenter#424#6923
hypocenterC61#8607
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #21461368C2semidirect
2. C2×#16840623C2semidirect
4. #21460665C2semidirect
175. C61#8607semidirect

Maximal subgroups

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

subgroupindex
#214613682
C2×#168406232
#214611162
#214606652
#214544622
#860761