Finite Group Databasebeta

← #30603962

Subgroups — #30603962

Order 15616.

398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 90 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
1D61⋊(C22⋊C16)C212yesmaximal, complemented
2#21460757C212yesmaximal, complemented
3#21460742C212yesmaximal, complemented
4#21454515C211yesmaximal, characteristic
5C2×D61⋊C16—22no—
6#16840657—22no—
7C22⋊#11758187C2214yes—
8C2×#14519783C411yescharacteristic
9C22×C8×D61C2211yescharacteristic
10#16840274C411yescharacteristic
11#16839835—22no—
12C8×D244—22no—
13#16839789C2211yescharacteristic
14#16839730C2211yescharacteristic
15#16839725C411yescharacteristic
16C61×#405C411yescharacteristic
17D61⋊C16—44no—
18C2×#11758187—24no—
19C2×#11758222C2×C411yescharacteristic
20C22×C4×D61C2×C411yescharacteristic
21#14519783—42no—
22C2×#11758194C2×C411yescharacteristic
23C2×#11758189—21no—
24C22×#92418C2311yescharacteristic
25C2×C8×D61—21no—
26C2×C8×D61—42no—
27C2×C8×D61D412yes—
28C2×C8×D61D412yes—
29#14519761—21no—
30#14519757C812yes—
31#14519752C812yes—
32#14519747—21no—
33C4×D244—22no—
34C4⋊#92418—22no—
35#14519689—22no—
36#14519689—22no—
37C2×M16×C61C2×C411yescharacteristic
38C22×C8×C61C2×C411yescharacteristic
39#117×C61C2×C411yescharacteristic
40#97×C61—21no—
41C4×C8×C61—21no—
42C23×D61M1611yescharacteristic
43C22×C4×C61C22×C411yescharacteristic
44C2×C22⋊D61—21no—
45C22×Dic61M1611yescharacteristic
46#11758222—41no—
47#11758222—41no—
48C2×D244—22no—
49C2×D244C2×C811yescharacteristic
50C2×C4×D61—21no—
51C2×C4×D61—41no—
52C2×C4×D61—41no—
53C2×C4×D61C22⋊C412yes—
54C2×C4×D61C2×C812yes—
55C2×Dic122C2×C811yescharacteristic
56M16×C61—41no—
57C2×C8×C61—22no—
58C2×C8×C61—21no—
59C2×C8×C61C22⋊C411yescharacteristic
60C2×C8×C61C22⋊C411yescharacteristic
61C4⋊C4×C61C2×C812yes—
62C22⋊C4×C61—21no—
63C42×C61—21no—
64#11758198—22no—
65#11758198—22no—
66C4⋊Dic61—22no—
67#11758194—41no—
68C2×#92418—21no—
69C2×#92418—41no—
70C2×#92418C2×D412yes—
71#11758189—42no—
72C8×D61—24no—
73C8×D61—42no—
74C8×D61—42no—
75#11758187—44no—
76C23×C61C2×M1611yescharacteristic
77C22×D61—24no—
78C22×D61—21no—
79C22×D61—41no—
80C22×D61C22⋊C812yes—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61C2×C22⋊C411yescharacteristic
85C2×C4×C61C22×C811yescharacteristic
86C22⋊D61—42no—
87C2×Dic61—21no—
88C2×Dic61—41no—
89C2×Dic61C22⋊C812yes—
90D244—41no—
91D244—44no—
92C4×D61—22no—
93C4×D61—22no—
94C4×D61—42no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—41no—
98C8×C61—21no—
99C8×C61—41no—
100C8×C61#9912yes—
101#92418—22no—
102#92418—41no—
103#11468—611nomaximal, Sylow
104C22×C61—22no—
105C22×C61—21no—
106C22×C61C2×C22⋊C811yescharacteristic
107C2×D61—22no—
108C2×D61—22no—
109C2×D61—44no—
110C2×D61—42no—
111C2×D61—41no—
112C2×D61#35014yes—
113C4×C61—21no—
114C4×C61—42no—
115C4×C61C2×#9911yescharacteristic
116C4×C61#41311yescharacteristic
117Dic61—22no—
118Dic61—41no—
119#2929—611no—
120C2×C22⋊C16—612no—
121#1323—612no—
122#1315—612no—
123C2×C61—41no—
124C2×C61#145911yescharacteristic
125C2×C61C2×#35012yes—
126D61—24no—
127D61—81no—
128C2×#131—611no—
129C23×C8—611no—
130#525—611no—
131C22×C16—1222no—
132#435—1222no—
133C8×D4—1222no—
134#424—611no—
135#408—611no—
136#407—611no—
137#405#692311yescharacteristic
138C22⋊C16—614no—
139C22⋊C16—1222no—
140C61#1146811yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C23×C4—611no—
143#131—2442no—
144C2×M16—611no—
145C2×M16—1221no—
146C2×M16C2×#692311yescharacteristic
147C22×C8—611no—
148C22×C8—612no—
149C22×C8—612no—
150C22×C8—1221no—
151C22×C8—2442no—
152C22×C8C2×#692311yescharacteristic
153#123—1221no—
154C22⋊Q8—612no—
155#121—612no—
156#120—1221no—
157C4×D4—1222no—
158#117C2×#692311yescharacteristic
159C2×C16—1224no—
160C2×C16—2444no—
161C4⋊C8—1222no—
162C22⋊C8—1222no—
163C22⋊C8—1222no—
164#97—21no—
165C4×C8—21no—
166C24—611no—
167#41—2441no—
168#41—2441no—
169C2×Q8—611no—
170C2×D4—611no—
171C2×D4—1222no—
172C2×D4—1221no—
173C22×C4—611no—
174C22×C4—612no—
175C22×C4—612no—
176C22×C4—1221no—
177C22×C4—2441no—
178C22×C4—2441no—
179C22×C4C22×#692311yescharacteristic
180M16—41no—
181M16—2442no—
182M16—2441no—
183C2×C8—22no—
184C2×C8—21no—
185C2×C8—612no—
186C2×C8—1224no—
187C2×C8—1221no—
188C2×C8—2442no—
189C2×C8—2441no—
190C2×C8—2442no—
191C2×C8C22⋊#692311yescharacteristic
192C2×C8C22⋊#692311yescharacteristic
193C4⋊C4—1222no—
194C4⋊C4D61⋊C812yes—
195C22⋊C4—21no—
196C22⋊C4—1222no—
197C22⋊C4—1222no—
198C42—21no—
199C16—2444no—
200C23—612no—
201C23—1224no—
202C23—1221no—
203C23—2441no—
204C23D61⋊M1611yescharacteristic
205Q8—2441no—
206D4—2441no—
207D4—2444no—
208D4—2442no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—612no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—2442no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4C2×C22⋊#692311yescharacteristic
221C2×C4C2×D61⋊C811yescharacteristic
222C8—21no—
223C8—41no—
224C8—1222no—
225C8—2441no—
226C8#1451983612yes—
227C22—22no—
228C22—21no—
229C22—614no—
230C22—1222no—
231C22—1222no—
232C22—2444no—
233C22—2442no—
234C22—2441no—
235C22D61⋊(C22⋊C8)11yescharacteristic
236C4—21no—
237C4—42no—
238C4—1222no—
239C4—2441no—
240C4C2×#1451983611yescharacteristic
241C4#1684074811yescharacteristic
242C2—41no—
243C2—1224no—
244C2—4881no—
245C2#2146105611yescharacteristic
246C2D61⋊#35012yes—
subgroupG/H
centerC2×C8C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#405C4
socleC22×C61C2×C22⋊C8
prime radical#16840274C4
cosocleC22×#92418C23
hypercenter#405#6923
hypocenterC61#11468
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
1. D61⋊(C22⋊C16)C2semidirect
2. #21460757C2semidirect
3. #21460742C2semidirect
140. C61#11468semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214607572
#214607422
#214545152
#1146861