Finite Group Databasebeta

← #30605740

Subgroups — #30605740

Order 15616.

258 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 64 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#21462188C211yesmaximal, characteristic
2#21462188C211yesmaximal, characteristic
3#21460840C212yesmaximal, complemented
4#21460839C212yesmaximal, complemented
5#21456372C211yesmaximal, characteristic
6#16840685C2212yes—
7#16840685C2212yes—
8#16840658—21no—
9#16840658—21no—
10#16840654—21no—
11#16840654—21no—
12C2×#14519769C411yescharacteristic
13#16840168—21no—
14#16840168—21no—
15#16840161C411yescharacteristic
16#16840161C411yescharacteristic
17#16840161C2211yescharacteristic
18#16840161C2211yescharacteristic
19#16839805—21no—
20#16839805—21no—
21C4×#11758194C2211yescharacteristic
22C61×#533C411yescharacteristic
23#14519851—22no—
24#14519851—22no—
25C2×#11758194D411yescharacteristic
26C2×#11758194D411yescharacteristic
27#14519769—21no—
28#14519769—41no—
29#14519769C2×C411yescharacteristic
30#14519769C2×C411yescharacteristic
31C2×C4⋊Dic61—21no—
32C2×#11758196—41no—
33#14519710—21no—
34#14519710—21no—
35#14519710—21no—
36#14519710—21no—
37#14519708—21no—
38#14519708—21no—
39#14519708—21no—
40#14519708—21no—
41#14519688D411yescharacteristic
42#14519688D411yescharacteristic
43C4×#92418C2×C411yescharacteristic
44C4×#92418C2311yescharacteristic
45C4⋊Q8×C61—21no—
46#125×C61C2×C411yescharacteristic
47#125×C61C2×C411yescharacteristic
48C22⋊Q8×C61—41no—
49C4×Q8×C61—41no—
50#117×C61—21no—
51C2×C42×C61C2×C411yescharacteristic
52C2×Q8×C61—41no—
53C22×C4×C61—21no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×Dic61—41no—
56C4⋊C4×C61—21no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—41no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C22⋊C4×C61—41no—
62C42×C61—21no—
63C42×C61—41no—
64C42×C61C22⋊C411yescharacteristic
65C42×C61C22×C411yescharacteristic
66C4⋊Dic61—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—41no—
69#11758196—42no—
70#11758196—41no—
71#11758196—41no—
72#11758194—22no—
73#11758194—22no—
74C2×#92418C22⋊C411yescharacteristic
75C2×#92418C22⋊C411yescharacteristic
76C2×#92418C2×D411yescharacteristic
77C2×#92418C2×D411yescharacteristic
78#11758187—42no—
79#11758187—42no—
80C23×C61#10011yescharacteristic
81Q8×C61—82no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—81no—
89C2×C4×C61#10011yescharacteristic
90C2×C4×C61C2×C22⋊C411yescharacteristic
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—82no—
94#92418—21no—
95#92418—21no—
96#92418#13712yes—
97#92418#13712yes—
98#11994—611nomaximal, Sylow
99C22×C61—21no—
100C22×C61—41no—
101C22×C61C2×#10011yescharacteristic
102C4×C61—21no—
103C4×C61—41no—
104C4×C61—41no—
105C4×C61—81no—
106C4×C61—81no—
107C4×C61#41911yescharacteristic
108C4×C61#41911yescharacteristic
109Dic61—81no—
110Dic61—81no—
111#3166—611no—
112#2165—611no—
113#2165—611no—
114#1366—612no—
115#1366—612no—
116C2×C61—21no—
117C2×C61—41no—
118C2×C61#155811yescharacteristic
119#533#692311yescharacteristic
120C2×#125—611no—
121#501—1221no—
122#501—1221no—
123#499—611no—
124#499—611no—
125#499—611no—
126#499—611no—
127#428—1221no—
128#428—1221no—
129C4×M16—611no—
130#364—612no—
131#364—612no—
132#349—1221no—
133#349—1221no—
134#347—1221no—
135#347—1221no—
136C61#1199411yescharacteristic, complemented, Sylow
137C2×M16—611no—
138C2×M16—611no—
139C4⋊Q8—21no—
140#125—611no—
141#125—611no—
142#125—1221no—
143#125—2441no—
144#125C2×#692311yescharacteristic
145#125C2×#692311yescharacteristic
146C22⋊Q8—41no—
147C4×Q8—41no—
148#117—21no—
149C2×C4⋊C4—1221no—
150C2×C4⋊C4—2441no—
151C2×C42C2×#692311yescharacteristic
152M32—1222no—
153M32—1222no—
154#107—1221no—
155#107—1221no—
156#107—1221no—
157#107—1221no—
158#106—1221no—
159#106—1221no—
160#106—1221no—
161#106—1221no—
162#97—611no—
163#97—611no—
164C4×C8—611no—
165C4×C8—611no—
166C2×Q8—41no—
167C22×C4—21no—
168C22×C4—2441no—
169C22×C4C22⋊#692311yescharacteristic
170M16—1222no—
171M16—1222no—
172C2×C8—611no—
173C2×C8—611no—
174C2×C8—611no—
175C2×C8—611no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—1221no—
182C4⋊C4—1221no—
183C4⋊C4—2441no—
184C4⋊C4—2441no—
185C4⋊C4—2442no—
186C4⋊C4—2441no—
187C22⋊C4—41no—
188C42—21no—
189C42—41no—
190C42C22⋊#692311yescharacteristic
191C42C22×#692311yescharacteristic
192C16—2442no—
193C16—2442no—
194C23#1451983711yescharacteristic
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—81no—
203C2×C4—4882no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4#1451983711yescharacteristic
207C2×C4C2×C22⋊#692311yescharacteristic
208C8—612no—
209C8—612no—
210C8—1221no—
211C8—1221no—
212C22—21no—
213C22—41no—
214C22C2×#1451983711yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—81no—
220C4—4881no—
221C4—4881no—
222C4#1684075511yescharacteristic
223C4#1684075511yescharacteristic
224C2—21no—
225C2—41no—
226C2#2146135211yescharacteristic
subgroupG/H
centerC2#21461352
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#533C4
socleC2×C61#1558
prime radicalC23×C61#100
cosocleC4×#92418C23
hypercenter#533#6923
hypocenterC61#11994
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #21460840C2semidirect
4. #21460839C2semidirect
136. C61#11994semidirect

Maximal subgroups

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

subgroupindex
#214621882
#214608402
#214608392
#214563722
#1199461