Finite Group Databasebeta

← #30608403

Subgroups — #30608403

Order 15616.

318 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 56 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#21462111C212yesmaximal
2#21460963C212yesmaximal, complemented
3#21460962C211yesmaximal, characteristic, complemented
4#21460961C211yesmaximal, characteristic, complemented
5#21456163C211yesmaximal, characteristic
6#16840749—22no—
7#16840673C2212yes—
8#16840673C2212yes—
9#16840670—22no—
10#16840318C411yescharacteristic
11#16840310C2211yescharacteristic
12#16840132C2211yescharacteristic
13#16840131C2211yescharacteristic
14#16840126C411yescharacteristic
15#16840120—22no—
16#16839755—22no—
17#97×D61C411yescharacteristic
18C61×#490C411yescharacteristic
19C2×#11758217—42no—
20#14519838—22no—
21#14519838—22no—
22#14519837—42no—
23C2×#11758224D412yes—
24C2×C8×D61—21no—
25#14519777C2311yescharacteristic
26#14519776—21no—
27#14519769C2×C411yescharacteristic
28#14519764D412yes—
29#14519755—41no—
30#14519748—41no—
31#14519742—41no—
32D4×Dic61—41no—
33#14519735—21no—
34C42×D61C2×C411yescharacteristic
35#14519702—22no—
36#14519700—22no—
37#14519698—22no—
38#14519688C2×C411yescharacteristic
39#14519687—21no—
40#127×C61C2×C411yescharacteristic
41#125×C61C2×C411yescharacteristic
42#102×C61—22no—
43#97×C61C2×C411yescharacteristic
44C2×D4×C61—41no—
45C2×D4×C61C22⋊C412yes—
46C2×C22⋊D61—22no—
47C22×Dic61—22no—
48#11758224—42no—
49#11758224—42no—
50C2×C4×D61—21no—
51C2×C4×D61C22⋊C411yescharacteristic
52C2×Dic122—41no—
53C2×Dic122C2×D412yes—
54#11758217—42no—
55#11758217—42no—
56#11758217—82no—
57C2×#92420—82no—
58C2×C8×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61—41no—
61C42×C61C22×C411yescharacteristic
62C22⋊Dic61—42no—
63#11758198—41no—
64C4⋊Dic61—21no—
65C4⋊Dic61—41no—
66#11758196—41no—
67#11758196—41no—
68C4×Dic61—21no—
69C4×Dic61—41no—
70C4×Dic61C22⋊C411yescharacteristic
71C2×#92418—21no—
72C8×D61—41no—
73C8×D61—41no—
74C23×C61—22no—
75C22×D61#9911yescharacteristic
76D4×C61—42no—
77D4×C61—82no—
78C2×C4×C61—21no—
79C2×C4×C61—41no—
80C2×C4×C61C2×C22⋊C411yescharacteristic
81C22⋊D61—82no—
82C2×Dic61—21no—
83C2×Dic61—22no—
84C2×Dic61—42no—
85C2×Dic61—42no—
86C2×Dic61—41no—
87C2×Dic61#9911yescharacteristic
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—81no—
91Dic122—42no—
92Dic122—82no—
93#92420—82no—
94#92420—82no—
95C8×C61—41no—
96#92418—41no—
97#13598—611nomaximal, Sylow
98C22×C61—42no—
99C22×C61—82no—
100C22×C61C2×#9911yescharacteristic
101C2×D61—21no—
102C2×D61—41no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61—81no—
106Dic61—41no—
107Dic61—42no—
108Dic61—81no—
109Dic61#35411yescharacteristic
110Dic61#35411yescharacteristic
111#3135—611no—
112#2132—612no—
113#1413—611no—
114#1413—611no—
115#1413—612no—
116C2×C61—21no—
117C2×C61—82no—
118C2×C61C2×#35411yescharacteristic
119D61—41no—
120#533—611no—
121#532—611no—
122#491—611no—
123#491—611no—
124#490—611no—
125#490#692311yescharacteristic
126#489—1222no—
127#416—1222no—
128#413—1222no—
129C2×#97—611no—
130#356—612no—
131#356—612no—
132#355—1222no—
133C61#1359811yescharacteristic, complemented, Sylow
134C2×#41—612no—
135C2×M16—2442no—
136C22×C8—1221no—
137C4⋊Q8—611no—
138C4⋊Q8—1221no—
139#127C2×#692311yescharacteristic
140#125—611no—
141#125C2×#692311yescharacteristic
142#124—612no—
143C22⋊Q8—2441no—
144#121—2441no—
145C4×Q8—2441no—
146C4×D4—2441no—
147#117—1221no—
148C2×C42—611no—
149#103—1222no—
150#103—1222no—
151#102—22no—
152#102—1222no—
153#101—1222no—
154#101—1222no—
155#100—2442no—
156#97—611no—
157#97—1221no—
158#97C2×#692311yescharacteristic
159#41—2442no—
160#41—2442no—
161C2×Q8—612no—
162C2×Q8—2441no—
163C2×D4—41no—
164C2×D4—1222no—
165C2×D4C22⋊#692312yes—
166C22×C4—611no—
167C22×C4—1221no—
168C22×C4—1222no—
169M16—4882no—
170M16—2442no—
171M16—2442no—
172C2×C8—21no—
173C2×C8—1221no—
174C2×C8—4882no—
175C2×C8—2441no—
176C2×C8—2441no—
177C4⋊C4—21no—
178C4⋊C4—41no—
179C4⋊C4—1221no—
180C4⋊C4—2441no—
181C4⋊C4—2441no—
182C4⋊C4—2441no—
183C22⋊C4—2441no—
184C22⋊C4—2442no—
185C42—611no—
186C42—1221no—
187C42—2441no—
188C42C22×#692311yescharacteristic
189C23—22no—
190C23—611no—
191Q8—4882no—
192Q8—2442no—
193D4—42no—
194D4—82no—
195D4—4882no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—611no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1222no—
203C2×C4—4881no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4—2441no—
207C2×C4C2×C22⋊#692311yescharacteristic
208C8—41no—
209C8—4882no—
210C8—4882no—
211C8—2441no—
212C22—42no—
213C22—82no—
214C22—1221no—
215C22—2441no—
216C22D61⋊#9911yescharacteristic
217C4—21no—
218C4—41no—
219C4—81no—
220C4—611no—
221C4—611no—
222C4—4881no—
223C4—2441no—
224C4—2442no—
225C2—21no—
226C2—82no—
227C2—2441no—
228C2D61⋊#35411yescharacteristic
subgroupG/H
centerC2D61⋊#354
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#490C4
socleC2×C61C2×#354
prime radical#16840310C22
cosocle#14519777C23
hypercenter#490#6923
hypocenterC61#13598
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #21460963C2semidirect
3. #21460962C2semidirect
4. #21460961C2semidirect
133. C61#13598semidirect

Maximal subgroups

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

subgroupindex
#214621112
#214609632
#214609622
#214609612
#214561632
#1359861