Finite Group Databasebeta

← #30599652

Subgroups — #30599652

Order 15616.

348 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462717C211yesmaximal, characteristic
2#21461992C211yesmaximal, characteristic
3#21461392C212yesmaximal
4#21460714C212yesmaximal
5#21444141C211yesmaximal, characteristic
6#16840812—22no—
7#16840812—22no—
8#16840783—21no—
9#16840783C2212yes—
10#16840778—21no—
11C2×C4⋊#92420C2211yescharacteristic
12C2×#14519832C2211yescharacteristic
13#16840628—21no—
14#16840628—21no—
15#16840626—22no—
16#16840623—22no—
17C2×#14519742C2211yescharacteristic
18#16839812C2212yes—
19#16839488C411yescharacteristic
20#16839487C412yes—
21C61×#324C411yescharacteristic
22C22×#92420—21no—
23C22×#92420—21no—
24C4⋊#92420—21no—
25C4⋊#92420—21no—
26C4⋊#92420—21no—
27C4⋊#92420—21no—
28C4⋊#92420—22no—
29C4⋊#92420D412yes—
30C4⋊#92420D412yes—
31C22⋊#92420—22no—
32#14519832—22no—
33#14519832—22no—
34#14519832—22no—
35C4×#92420—22no—
36C22×Dic122Q811yescharacteristic
37#14519742—22no—
38#14519742—22no—
39C2×#11758196C2×C411yescharacteristic
40C2×#11758196Q811yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61C2311yescharacteristic
44#14519706—22no—
45C22⋊#92418C2×C412yes—
46C8×Dic61—22no—
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C22⋊C8×C61C2×C412yes—
49C22×C4×C61C4⋊C411yescharacteristic
50C22×C4×C61C4⋊C411yescharacteristic
51C22×C4×C61C22×C411yescharacteristic
52C22×Dic61C4⋊C411yescharacteristic
53C22×Dic61C4⋊C411yescharacteristic
54C22×Dic61C2×D411yescharacteristic
55C22×Dic61C2×Q811yescharacteristic
56C2×Dic122—22no—
57C2×Dic122—22no—
58C2×Dic122—41no—
59C2×#92420—22no—
60C2×#92420—22no—
61C2×#92420—22no—
62C2×#92420—41no—
63C2×#92420—41no—
64C2×#92420—42no—
65C2×#92420—41no—
66C2×C8×C61—22no—
67C4⋊C4×C61—22no—
68#11758196—22no—
69#11758196—22no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61C2×D412yes—
75C4×Dic61#4112yes—
76C2×#92418—22no—
77C23×C61C2×C4⋊C411yescharacteristic
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61#10812yes—
84C2×C4×C61C4×D412yes—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—41no—
94C2×Dic61#12011yescharacteristic
95C2×Dic61C22⋊Q812yes—
96C2×Dic61#12311yescharacteristic
97Dic122—44no—
98#92420—42no—
99#92420—42no—
100#92420—42no—
101#92420—81no—
102C8×C61—42no—
103#92418—42no—
104#8865—611nomaximal, Sylow
105C22×C61—21no—
106C22×C61—21no—
107C22×C61#38511yescharacteristic
108C22×C61C2×#10811yescharacteristic
109C22×C61#43011yescharacteristic
110C4×C61—22no—
111C4×C61—22no—
112C4×C61—41no—
113Dic61—22no—
114Dic61—21no—
115Dic61—41no—
116Dic61—41no—
117Dic61#45411yescharacteristic
118Dic61#45611yescharacteristic
119#2983—611no—
120#1985—611no—
121#1573—612no—
122#1461—611no—
123#1302—612no—
124C2×C61—21no—
125C2×C61—21no—
126C2×C61#185511yescharacteristic
127C2×C61#185711yescharacteristic
128C2×C61#186811yescharacteristic
129C2×C4×Q8—611no—
130#446—1222no—
131#446—1222no—
132#432—612no—
133#432—1221no—
134#431—612no—
135#431—1221no—
136C2×C4⋊C8—611no—
137C2×#97—611no—
138#336—1221no—
139#336—1221no—
140#335—1222no—
141#334—1222no—
142#324—611no—
143#324—612no—
144#324#692311yescharacteristic
145C61#886511yescharacteristic, complemented, Sylow
146C22×Q8—611no—
147C22×C8—1221no—
148C22×C8—1221no—
149C4×Q8—1222no—
150C4×Q8—1222no—
151C2×C4⋊C4—611no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4C2×#692311yescharacteristic
154C2×C42—611no—
155C2×C42—611no—
156C2×C42—611no—
157C4⋊C8—612no—
158C4⋊C8—612no—
159C4⋊C8—1222no—
160C4⋊C8—1222no—
161C4⋊C8—1221no—
162C4⋊C8—1221no—
163C4⋊C8—1221no—
164C4⋊C8—1221no—
165C22⋊C8—612no—
166C22⋊C8—1222no—
167C22⋊C8C2×#692312yes—
168#97—1222no—
169#97—1222no—
170#97—1222no—
171C4×C8—1222no—
172C4×C8—1222no—
173C2×Q8—1222no—
174C2×Q8—1222no—
175C2×Q8—2441no—
176C22×C4—611no—
177C22×C4—611no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4C4⋊#692311yescharacteristic
181C22×C4C4⋊#692311yescharacteristic
182C22×C4C22×#692311yescharacteristic
183C2×C8—22no—
184C2×C8—1222no—
185C2×C8—1222no—
186C2×C8—1222no—
187C2×C8—1222no—
188C2×C8—2441no—
189C2×C8—2442no—
190C2×C8—2441no—
191C2×C8—2441no—
192C4⋊C4—22no—
193C4⋊C4—1222no—
194C4⋊C4—1222no—
195C42—612no—
196C42—612no—
197C42—1221no—
198C42—1221no—
199C42—1221no—
200C42—1221no—
201C23C2×C4⋊#692311yescharacteristic
202Q8—2444no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—611no—
209C2×C4—612no—
210C2×C4—611no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—2441no—
220C2×C4#1451984712yes—
221C2×C4D4×#692312yes—
222C8—42no—
223C8—4881no—
224C8—2442no—
225C8—2442no—
226C8—2442no—
227C8—2442no—
228C22—21no—
229C22—21no—
230C22#1684070911yescharacteristic
231C22C2×#1451984711yescharacteristic
232C22#1684077711yescharacteristic
233C4—22no—
234C4—22no—
235C4—41no—
236C4—611no—
237C4—611no—
238C4—1222no—
239C4—1221no—
240C4—2441no—
241C4—2441no—
242C2—21no—
243C2—21no—
244C2#2146177211yescharacteristic
245C2#2146177511yescharacteristic
246C2#2146179111yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#324C4
socleC22×C61#385
prime radicalC23×C61C2×C4⋊C4
cosocleC2×C4×Dic61C23
hypercenter#324#6923
hypocenterC61#8865
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
145. C61#8865semidirect

Maximal subgroups

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

subgroupindex
#214627172
#214619922
#214613922
#214607142
#214441412
#886561