Finite Group Databasebeta

← #30601718

Subgroups — #30601718

Order 15616.

434 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 102 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#21461368C211yesmaximal, characteristic
2#21461121C212yesmaximal
3#21461062C212yesmaximal
4#21461032C211yesmaximal, characteristic
5C2×Q16×Dic61C211yesmaximal, characteristic
6#16840778C2212yes—
7#16840778C2211yescharacteristic
8#16840778C2211yescharacteristic
9#16840626—21no—
10#16840624—21no—
11Q8⋊#92420—24no—
12#16840607—24no—
13#92420⋊C8—21no—
14#92420⋊C8—21no—
15C2×Q8×Dic61C2212yes—
16Q16×Dic61—21no—
17Q16×Dic61—21no—
18Q16×Dic61—21no—
19Q16×Dic61—21no—
20C2×#14519711C411yescharacteristic
21C2×#14519701C412yes—
22C2×C8×Dic61C2211yescharacteristic
23C22×Q16×C61C411yescharacteristic
24C4⋊#92420—22no—
25C4⋊#92420—21no—
26C4⋊#92420D412yes—
27C22⋊#92420—21no—
28C22⋊#92420—22no—
29C22⋊#92420D412yes—
30C4×#92420—21no—
31C4×#92420—21no—
32C4×#92420—22no—
33C22×#92418C2×C411yescharacteristic
34Q8×Dic61—22no—
35Q8×Dic61—22no—
36Q8×Dic61—22no—
37Q8×Dic61—22no—
38C2×C4⋊Dic61—22no—
39C2×C4⋊Dic61C2×C412yes—
40C2×C4×Dic61—22no—
41C2×C4×Dic61C2311yescharacteristic
42#14519711—21no—
43#14519711—21no—
44#14519701—22no—
45#14519701—22no—
46C8×Dic61D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C22×Q8×C61C2×C412yes—
51C2×Q16×C61—24no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C22×C8×C61C2×C411yescharacteristic
55C2×Q8×C61—22no—
56C2×Q8×C61—22no—
57C2×Q8×C61—22no—
58C2×Q8×C61—22no—
59C2×Q8×C61—22no—
60C2×Q8×C61M1614yes—
61C22×C4×C61—22no—
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—22no—
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61#4111yescharacteristic
66C2×#92420—22no—
67C2×#92420—22no—
68C2×#92420—42no—
69Q16×C61—24no—
70Q16×C61—24no—
71C2×C8×C61—22no—
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22⋊C411yescharacteristic
74C4⋊Dic61—22no—
75C4⋊Dic61—22no—
76C4⋊Dic61—42no—
77C4⋊Dic61—42no—
78C4×Dic61—42no—
79C4×Dic61—42no—
80C4×Dic61C2×D411yescharacteristic
81C4×Dic61C2×D411yescharacteristic
82C4×Dic61C2×D411yescharacteristic
83C4×Dic61#4111yescharacteristic
84C2×#92418—22no—
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C22⋊C411yescharacteristic
87C23×C61C4×D411yescharacteristic
88Q8×C61—24no—
89Q8×C61—24no—
90Q8×C61—42no—
91Q8×C61—42no—
92C2×C4×C61—24no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C4×D411yescharacteristic
97C2×C4×C61C2×M1612yes—
98C2×C4×C61#13112yes—
99C2×Dic61—22no—
100C2×Dic61—41no—
101C2×Dic61—42no—
102C2×Dic61—82no—
103C2×Dic61#12111yescharacteristic
104C2×Dic61#12111yescharacteristic
105C2×Dic61#12411yescharacteristic
106C2×Dic61#12711yescharacteristic
107#92420—42no—
108#92420—42no—
109#92420—82no—
110C8×C61—21no—
111C8×C61—21no—
112#92418—21no—
113#92418—21no—
114#9671—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61#39011yescharacteristic
118C22×C61#43512yes—
119C4×C61—44no—
120C4×C61#40711yescharacteristic
121C4×C61#40811yescharacteristic
122C4×C61#43512yes—
123Dic61—21no—
124Dic61—21no—
125Dic61—21no—
126Dic61—82no—
127Dic61#47312yes—
128C2×C4×Q16—611no—
129#1564—611no—
130#1479—612no—
131#1461—612no—
132#1452—611no—
133C2×C61—22no—
134C2×C61#195511yescharacteristic
135C2×C61#197611yescharacteristic
136C2×C61#197911yescharacteristic
137C22×Q16#692311yescharacteristic
138C2×C4×Q8—612no—
139C4×Q16—1221no—
140C4×Q16—1221no—
141C4×Q16—1221no—
142C4×Q16—1221no—
143#431—611no—
144#431—611no—
145#431—612no—
146C2×#107—611no—
147C2×#103—612no—
148C2×C4×C8—611no—
149#335—1221no—
150#334—1221no—
151Q8⋊C8—1224no—
152#324—1224no—
153#322—1221no—
154#322—1221no—
155C61#967111yescharacteristic, complemented, Sylow
156C22×Q8C2×#692312yes—
157C2×Q16—24no—
158C2×Q16—21no—
159C2×Q16—21no—
160C22×C8—611no—
161C22×C8C2×#692311yescharacteristic
162C4×Q8—1222no—
163C4×Q8—1222no—
164C4×Q8—1222no—
165C4×Q8—1222no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—1222no—
168C2×C42—611no—
169C2×C42—1222no—
170#107—1221no—
171#107—1221no—
172C4⋊C8—612no—
173C4⋊C8—1221no—
174C4⋊C8—1222no—
175#103—1222no—
176#103—1222no—
177C22⋊C8—612no—
178C22⋊C8—1221no—
179C22⋊C8—1222no—
180C4×C8—611no—
181C4×C8—611no—
182C4×C8—611no—
183C4×C8—611no—
184C4×C8—1221no—
185C4×C8—1221no—
186C4×C8—1222no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8#1175821714yes—
193C22×C4—22no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—1222no—
197C22×C4C22×#692311yescharacteristic
198Q16—24no—
199Q16—24no—
200C2×C8—22no—
201C2×C8—611no—
202C2×C8—611no—
203C2×C8—1222no—
204C2×C8—1222no—
205C2×C8—1222no—
206C2×C8—2442no—
207C2×C8C22⋊#692311yescharacteristic
208C2×C8C22⋊#692311yescharacteristic
209C4⋊C4—1222no—
210C4⋊C4—1222no—
211C4⋊C4—2442no—
212C4⋊C4—2442no—
213C42—611no—
214C42—611no—
215C42—611no—
216C42—611no—
217C42—2442no—
218C42—2442no—
219C23D4×#692311yescharacteristic
220Q8—24no—
221Q8—24no—
222Q8—42no—
223Q8—42no—
224C2×C4—24no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—611no—
228C2×C4—611no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—1222no—
232C2×C4—4882no—
233C2×C4—2441no—
234C2×C4—2442no—
235C2×C4C2×C22⋊#692311yescharacteristic
236C2×C4D4×#692311yescharacteristic
237C2×C4C2×#1175821712yes—
238C2×C4#1451986412yes—
239C8—21no—
240C8—21no—
241C8—1221no—
242C8—1221no—
243C8—4882no—
244C8—2442no—
245C8—2442no—
246C22—21no—
247C22—21no—
248C22#1684071411yescharacteristic
249C22#1684079312yes—
250C4—44no—
251C4—612no—
252C4—1221no—
253C4—1221no—
254C4—1221no—
255C4—4882no—
256C4#1684073211yescharacteristic
257C4#1684073611yescharacteristic
258C4#1684079312yes—
259C2—22no—
260C2#2146194311yescharacteristic
261C2#2146197811yescharacteristic
262C2#2146198111yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×Q16×C61C4
socleC22×C61#390
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenterC22×Q16#6923
hypocenterC61#9671
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
155. C61#9671semidirect

Maximal subgroups

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

subgroupindex
#214613682
#214611212
#214610622
#214610322
C2×Q16×Dic612
#967161