Finite Group Databasebeta

← #30599574

Subgroups — #30599574

Order 15616.

386 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461989C211yesmaximal, characteristic
3#21461372C212yesmaximal
4#21460652C212yesmaximal
5#21445614C211yesmaximal, characteristic
6#16840812—22no—
7#16840812—22no—
8#16840783—22no—
9#16840778C2212yes—
10C2×C4⋊#92420C2211yescharacteristic
11C2×C4×#92420C2211yescharacteristic
12#16840628—22no—
13#16840626—22no—
14#16840624—22no—
15C2×#14519742C2211yescharacteristic
16C2×#14519695C412yes—
17M16×Dic61C2212yes—
18#16839531C411yescharacteristic
19C61×#343C411yescharacteristic
20C22×#92420—21no—
21C22×#92420—21no—
22C4⋊#92420—22no—
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C4⋊#92420D412yes—
26C4⋊#92420D412yes—
27C22⋊#92420—22no—
28#14519832—24no—
29C4×#92420—22no—
30C4×#92420—22no—
31C22×Dic122C2×C411yescharacteristic
32C2×#11758194C2×C412yes—
33#14519742—22no—
34#14519742—22no—
35C2×#11758196Q812yes—
36C2×C4×Dic61D412yes—
37C2×C4×Dic61C2311yescharacteristic
38#14519695—24no—
39#14519687—22no—
40C8×Dic61—22no—
41C2×M16×C61C2×C412yes—
42C2×C4⋊C4×C61C2×C411yescharacteristic
43C22×C4×C61C4⋊C412yes—
44C22×C4×C61C22×C411yescharacteristic
45C22×Dic61C4⋊C412yes—
46C22×Dic61C2×D411yescharacteristic
47C22×Dic61C2×Q811yescharacteristic
48C2×Dic122—22no—
49C2×Dic122—22no—
50C2×Dic122—21no—
51C2×Dic122—21no—
52C2×#92420—22no—
53C2×#92420—22no—
54C2×#92420—22no—
55C2×#92420—41no—
56C2×#92420—41no—
57C2×#92420—42no—
58C2×#92420—41no—
59M16×C61—22no—
60M16×C61—22no—
61C2×C8×C61—22no—
62C4⋊C4×C61—22no—
63#11758196—24no—
64C4×Dic61—22no—
65C4×Dic61—22no—
66C4×Dic61C2×D412yes—
67C4×Dic61#4112yes—
68#11758194—22no—
69#11758194M1614yes—
70C2×#92418—22no—
71C23×C61C2×C4⋊C411yescharacteristic
72C2×C4×C61—22no—
73C2×C4×C61—42no—
74C2×C4×C61C4×D412yes—
75C2×C4×C61C2×M1612yes—
76C2×C4×C61#13111yescharacteristic
77C2×C4×C61#13111yescharacteristic
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—41no—
84C2×Dic61#12011yescharacteristic
85C2×Dic61C22⋊Q812yes—
86C2×Dic61#12311yescharacteristic
87Dic122—42no—
88Dic122—42no—
89#92420—42no—
90#92420—42no—
91#92420—42no—
92#92420—81no—
93C8×C61—42no—
94#92418—24no—
95#8838—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61#38511yescharacteristic
99C22×C61#42311yescharacteristic
100C22×C61#42411yescharacteristic
101C4×C61—42no—
102C4×C61#43512yes—
103C4×C61#43612yes—
104Dic61—21no—
105Dic61—22no—
106Dic61—42no—
107Dic61#45411yescharacteristic
108Dic61#45611yescharacteristic
109#2983—611no—
110#1984—611no—
111C4×#101—611no—
112#1565—612no—
113#1278—612no—
114C2×C61—21no—
115C2×C61—21no—
116C2×C61#185111yescharacteristic
117C2×C61#185711yescharacteristic
118C2×C61#185811yescharacteristic
119C2×C4×Q8—611no—
120#446—1222no—
121#446—1222no—
122#432—1222no—
123#431—612no—
124C2×C4⋊C8—611no—
125C2×#101—612no—
126C4×M16—612no—
127C2×C4×C8—611no—
128#343—611no—
129#343#692311yescharacteristic
130#336—1222no—
131#335—1222no—
132#334—1222no—
133C61#883811yescharacteristic, complemented, Sylow
134C22×Q8—611no—
135C2×M16—612no—
136C2×M16C2×#692312yes—
137C22×C8—1221no—
138C22×C8—1221no—
139C4×Q8—1222no—
140C4×Q8—1222no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4C2×#692311yescharacteristic
143C2×C42—611no—
144C2×C42—612no—
145C4⋊C8—612no—
146C4⋊C8—612no—
147C4⋊C8—1222no—
148C4⋊C8—1222no—
149C4⋊C8—1222no—
150#101—1224no—
151C22⋊C8—1222no—
152#97—1222no—
153#97—1224no—
154C4×C8—1222no—
155C4×C8—1222no—
156C4×C8—1222no—
157C2×Q8—1222no—
158C2×Q8—1222no—
159C2×Q8—1221no—
160C2×Q8—1221no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—612no—
164C22×C4C4⋊#692312yes—
165C22×C4C22×#692311yescharacteristic
166M16—22no—
167M16—22no—
168M16—614no—
169M16—1222no—
170C2×C8—22no—
171C2×C8—1222no—
172C2×C8—1222no—
173C2×C8—1222no—
174C2×C8—1222no—
175C2×C8—2441no—
176C2×C8—2442no—
177C2×C8—2441no—
178C2×C8—2441no—
179C4⋊C4—22no—
180C4⋊C4—1224no—
181C42—612no—
182C42—612no—
183C42—1222no—
184C42—1222no—
185C23C2×C4⋊#692311yescharacteristic
186Q8—2442no—
187Q8—2442no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—611no—
191C2×C4—612no—
192C2×C4—611no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—2441no—
199C2×C4D4×#692312yes—
200C2×C4D61⋊M1612yes—
201C2×C4#1451986411yescharacteristic
202C2×C4#1451986511yescharacteristic
203C8—42no—
204C8—1224no—
205C8—4881no—
206C8—2442no—
207C8—2442no—
208C8—2442no—
209C22—21no—
210C22—21no—
211C22#1684070911yescharacteristic
212C22#1684076711yescharacteristic
213C22#1684076911yescharacteristic
214C4—42no—
215C4—611no—
216C4—611no—
217C4—1221no—
218C4—1222no—
219C4—2442no—
220C4#1684079212yes—
221C4#1684079512yes—
222C2—21no—
223C2—21no—
224C2#2146176711yescharacteristic
225C2#2146177511yescharacteristic
226C2#2146177611yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#343C4
socleC22×C61#385
prime radicalC23×C61C2×C4⋊C4
cosocleC2×C4×Dic61C23
hypercenter#343#6923
hypocenterC61#8838
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
133. C61#8838semidirect

Maximal subgroups

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

subgroupindex
#214627172
#214619892
#214613722
#214606522
#214456142
#883861