Finite Group Databasebeta

← #30597607

Subgroups — #30597607

Order 15616.

428 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 118 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#21461110C212yesmaximal
2#21461032C211yesmaximal, characteristic, complemented
3C2×C8×#92420C211yesmaximal, characteristic, complemented
4#21460652C212yesmaximal, complemented
5#21454459C211yesmaximal, characteristic
6#16840778C2212yes—
7C2×C4×#92420C2212yes—
8Q8⋊#92420C414yes—
9D4⋊#92420C414yes—
10#92420⋊C8—22no—
11C8×#92420—22no—
12#41×Dic61C2211yescharacteristic
13#16839820—22no—
14#16839812—22no—
15#16839790C411yescharacteristic
16#16839788C411yescharacteristic
17#16839729C411yescharacteristic
18M16×Dic61C2211yescharacteristic
19C2×C8×Dic61C2211yescharacteristic
20C61×#408C411yescharacteristic
21C22×#92420—22no—
22C4⋊#92420C2×C414yes—
23C22⋊#92420—22no—
24C4×#92420—22no—
25C4×#92420—22no—
26C4×#92420C2×C414yes—
27C2×#11758194C2×C411yescharacteristic
28C22×#92418C2×C411yescharacteristic
29Q8×Dic61C2×C412yes—
30D4×Dic61—22no—
31D4×Dic61C2×C412yes—
32#14519736—21no—
33#14519736C2×C411yescharacteristic
34C2×C4×Dic61—21no—
35C2×C4×Dic61C2311yescharacteristic
36#14519706—22no—
37#14519706—22no—
38C22⋊#92418—22no—
39#14519687—21no—
40C8×Dic61—21no—
41C8×Dic61D412yes—
42C8×Dic61D412yes—
43C2×#41×C61C2×C411yescharacteristic
44C2×M16×C61C2×C411yescharacteristic
45C22×C8×C61C2×C411yescharacteristic
46C22⋊C8×C61—22no—
47#41×C61—22no—
48#41×C61—22no—
49C2×Q8×C61C4211yescharacteristic
50C2×D4×C61—21no—
51C2×D4×C61C4211yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61C22×C411yescharacteristic
54C22×Dic61—22no—
55C22×Dic61#4112yes—
56C2×#92420—28no—
57C2×#92420—24no—
58C2×#92420—24no—
59M16×C61—22no—
60C2×C8×C61—22no—
61C2×C8×C61—21no—
62C2×C8×C61C22⋊C412yes—
63C22⋊Dic61—21no—
64C22⋊Dic61—22no—
65C4⋊Dic61—22no—
66C4⋊Dic61C4212yes—
67C4×Dic61—21no—
68C4×Dic61—22no—
69C4×Dic61C22×C412yes—
70C4×Dic61C2×D411yescharacteristic
71C4×Dic61C2×D411yescharacteristic
72#11758194—22no—
73C2×#92418—22no—
74C2×#92418—21no—
75C2×#92418C22⋊C412yes—
76C23×C61—21no—
77C23×C61#11711yescharacteristic
78Q8×C61—22no—
79D4×C61—22no—
80D4×C61—42no—
81C2×C4×C61—21no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61C2×C4211yescharacteristic
85C2×C4×C61C2×C22⋊C411yescharacteristic
86C2×C4×C61#13112yes—
87C2×C4×C61#13112yes—
88C2×Dic61—24no—
89C2×Dic61—22no—
90C2×Dic61—44no—
91C2×Dic61C4×D412yes—
92C2×Dic61C4×D412yes—
93#92420—28no—
94#92420—44no—
95C8×C61—22no—
96C8×C61—41no—
97#92418—22no—
98#92418—41no—
99#8187—611nomaximal, Sylow
100C22×C61—22no—
101C22×C61—41no—
102C22×C61—42no—
103C22×C61C4×C22⋊C411yescharacteristic
104C22×C61#43312yes—
105C4×C61—41no—
106C4×C61#40512yes—
107C4×C61#40811yescharacteristic
108C4×C61#40811yescharacteristic
109Dic61—22no—
110Dic61—42no—
111Dic61#44314yes—
112#2922—611no—
113#1476—612no—
114#1452—611no—
115C2×C82—611no—
116#1278—612no—
117C2×C61—22no—
118C2×C61—81no—
119C2×C61#175011yescharacteristic
120C2×C61#176412yes—
121C4×#41—611no—
122#433—1222no—
123#431—612no—
124#431—1222no—
125#424—611no—
126#424—611no—
127#408—611no—
128#408#692311yescharacteristic
129C4×M16—611no—
130C2×C4×C8—611no—
131C2×C4×C8—612no—
132Q8⋊C8—614no—
133D4⋊C8—614no—
134#322—1222no—
135C82—1222no—
136C61#818711yescharacteristic, complemented, Sylow
137C2×#41C2×#692311yescharacteristic
138C2×M16—611no—
139C2×M16C2×#692311yescharacteristic
140C22×C8—611no—
141C22×C8—1222no—
142C22×C8C2×#692311yescharacteristic
143C4×Q8—612no—
144C4×D4—612no—
145C4×D4—1222no—
146#117—611no—
147#117—1221no—
148C2×C42—611no—
149C2×C42—1221no—
150C4⋊C8—614no—
151C4⋊C8—1222no—
152C4⋊C8—1222no—
153C22⋊C8—22no—
154C22⋊C8—1222no—
155C22⋊C8—1222no—
156#97—1221no—
157C4×C8—612no—
158C4×C8—612no—
159C4×C8—614no—
160C4×C8—1221no—
161C4×C8—1222no—
162C4×C8—1222no—
163#41—22no—
164#41—22no—
165C2×Q8C4×#692311yescharacteristic
166C2×D4—21no—
167C2×D4C4×#692311yescharacteristic
168C22×C4—21no—
169C22×C4—612no—
170C22×C4—1222no—
171C22×C4C22×#692311yescharacteristic
172M16—22no—
173M16—1222no—
174C2×C8—22no—
175C2×C8—21no—
176C2×C8—612no—
177C2×C8—1224no—
178C2×C8—1228no—
179C2×C8—1222no—
180C2×C8—1224no—
181C2×C8—1221no—
182C2×C8C22⋊#692312yes—
183C4⋊C4—612no—
184C4⋊C4—1222no—
185C22⋊C4—1222no—
186C22⋊C4—1221no—
187C42—612no—
188C42—611no—
189C42—611no—
190C42—1222no—
191C42—1221no—
192C23—21no—
193C23#1451985611yescharacteristic
194Q8—22no—
195D4—22no—
196D4—42no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—612no—
201C2×C4—612no—
202C2×C4—1224no—
203C2×C4—1222no—
204C2×C4—2444no—
205C2×C4C2×C4×#692311yescharacteristic
206C2×C4C2×C22⋊#692311yescharacteristic
207C2×C4#1451986412yes—
208C2×C4#1451986412yes—
209C8—22no—
210C8—41no—
211C8—1228no—
212C8—1222no—
213C8—2444no—
214C8—2441no—
215C22—22no—
216C22—41no—
217C22—42no—
218C22C4×C22⋊#692311yescharacteristic
219C22#1684078612yes—
220C4—41no—
221C4—614no—
222C4—1222no—
223C4—2442no—
224C4#1684072612yes—
225C4#1684073511yescharacteristic
226C4#1684073611yescharacteristic
227C2—22no—
228C2—81no—
229C2#2146154911yescharacteristic
230C2#2146159312yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC22×C61C4×C22⋊C4
prime radicalC2×#41×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenter#408#6923
hypocenterC61#8187
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #21461032C2semidirect
3. C2×C8×#92420C2semidirect
4. #21460652C2semidirect
136. C61#8187semidirect

Maximal subgroups

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

subgroupindex
#214611102
#214610322
C2×C8×#924202
#214606522
#214544592
#818761