Finite Group Databasebeta

← #29596293

Subgroups — #29596293

Order 15616.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#21454459C211yesmaximal, characteristic
2#21445924C212yesmaximal
3#21443949C212yesmaximal
4#21443940C211yesmaximal, characteristic
5C61×#1392C211yesmaximal, characteristic
6#41×Dic61C2211yescharacteristic
7#16839820—22no—
8#16839812—22no—
9#16839790C411yescharacteristic, complemented
10#16839788C411yescharacteristic, complemented
11#16839736C2212yes—
12#16839729C2211yescharacteristic
13M16×Dic61C411yescharacteristic, complemented
14C2×C8×Dic61C411yescharacteristic, complemented
15#16839523—22no—
16#16839519—22no—
17C61×#413C2212yes—
18C61×#408C2211yescharacteristic
19C2×#11758194C2×C411yescharacteristic
20C22×#92418C2×C411yescharacteristic
21Q8×Dic61—21no—
22D4×Dic61—21no—
23D4×Dic61—22no—
24#14519736—22no—
25#14519736C2×C411yescharacteristic
26#14519736D412yes—
27C2×C4×Dic61C2×C411yescharacteristic
28C2×C4×Dic61D412yes—
29#14519706—22no—
30#14519706—22no—
31#14519692—22no—
32#14519692—22no—
33C22⋊#92418—22no—
34#14519687—21no—
35C8×Dic61—21no—
36C8×Dic61—21no—
37C8×Dic61—21no—
38C2×#41×C61C2311yescharacteristic
39C2×M16×C61—22no—
40C2×M16×C61C2×C411yescharacteristic
41C22×C8×C61C2×C411yescharacteristic
42#101×C61—22no—
43#100×C61—22no—
44C22⋊C8×C61—22no—
45#41×C61—41no—
46#41×C61—41no—
47C2×Q8×C61#4111yescharacteristic
48C2×D4×C61#4111yescharacteristic
49C2×D4×C61#4112yes—
50C22×C4×C61C22×C411yescharacteristic
51C22×C4×C61C2×D412yes—
52C22×Dic61—21no—
53C22×Dic61—22no—
54M16×C61—41no—
55M16×C61—42no—
56M16×C61—42no—
57C2×C8×C61—21no—
58C2×C8×C61—21no—
59C2×C8×C61—41no—
60C2×C8×C61—42no—
61C22⋊Dic61—21no—
62C22⋊Dic61—22no—
63C22⋊Dic61—42no—
64C4⋊Dic61—21no—
65C4⋊Dic61—22no—
66C4⋊Dic61—42no—
67C4×Dic61—21no—
68C4×Dic61—22no—
69C4×Dic61—42no—
70C4×Dic61C22⋊C411yescharacteristic
71C4×Dic61C22⋊C411yescharacteristic
72C4×Dic61C22⋊C412yes—
73#11758194—41no—
74C2×#92418—21no—
75C2×#92418—21no—
76C2×#92418—41no—
77C23×C61#11711yescharacteristic
78C23×C61#12312yes—
79Q8×C61—41no—
80D4×C61—42no—
81D4×C61—41no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61C2×C22⋊C411yescharacteristic
87C2×C4×C61#11711yescharacteristic
88C2×C4×C61#12312yes—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—42no—
93C2×Dic61—44no—
94C2×Dic61—82no—
95C8×C61—41no—
96C8×C61—41no—
97C8×C61—82no—
98#92418—41no—
99#92418—41no—
100#12864—611nomaximal, Sylow
101C22×C61—22no—
102C22×C61—21no—
103C22×C61—41no—
104C22×C61—42no—
105C22×C61#38111yescharacteristic
106C4×C61—22no—
107C4×C61—21no—
108C4×C61#41011yescharacteristic
109C4×C61#41011yescharacteristic
110Dic61—22no—
111Dic61—41no—
112Dic61—42no—
113Dic61—162no—
114#2922—611no—
115#1827—612no—
116#1395—612no—
117#1392D6111yescharacteristic
118#1391—611no—
119C2×C61—21no—
120C2×C61—42no—
121C2×C61—41no—
122C2×C61#182011yescharacteristic
123C4×#41—611no—
124#433—1222no—
125#431—1222no—
126#424—611no—
127#424—611no—
128#413C2×D6112yes—
129#410—612no—
130#408—611no—
131#408C2×D6111yescharacteristic
132C4×M16—611no—
133C2×C4×C8—611no—
134#339—1222no—
135H(3,ℤ/4)—1222no—
136C61#1286411yescharacteristic, complemented, Sylow
137C2×#41C22×D6111yescharacteristic
138C2×M16—22no—
139C2×M16—611no—
140C2×M16C4×D6111yescharacteristic
141C22×C8—611no—
142C22×C8C4×D6111yescharacteristic
143C4×Q8—1221no—
144C4×D4—1222no—
145C4×D4—1221no—
146#117—611no—
147#117—612no—
148#117—1222no—
149C2×C42—611no—
150C2×C42—612no—
151C4⋊C8—1222no—
152C4⋊C8—1222no—
153#101—22no—
154#100—22no—
155#99—1222no—
156#99—1222no—
157C22⋊C8—22no—
158C22⋊C8—1222no—
159#97—1221no—
160C4×C8—1221no—
161C4×C8—1221no—
162C4×C8—1221no—
163#41—41no—
164#41—41no—
165C2×Q8#1175822411yescharacteristic
166C2×D4#1175822212yes—
167C2×D4#1175822611yescharacteristic
168C22×C4—1221no—
169C22×C4—1222no—
170C22×C4C2×C4×D6111yescharacteristic
171C22×C4D4×D6112yes—
172M16—41no—
173M16—42no—
174M16—42no—
175M16—2441no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—1221no—
181C2×C8—1221no—
182C2×C8—2441no—
183C4⋊C4—1221no—
184C4⋊C4—1222no—
185C4⋊C4—2442no—
186C22⋊C4—1221no—
187C22⋊C4—1222no—
188C22⋊C4—2442no—
189C42—611no—
190C42—611no—
191C42—612no—
192C42—1221no—
193C42—1222no—
194C42—2442no—
195C23#1451973411yescharacteristic
196C23#1451976212yes—
197Q8—41no—
198D4—42no—
199D4—41no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1222no—
207C2×C4—4882no—
208C2×C4—2442no—
209C2×C4—2444no—
210C2×C4C22⋊C4×D6111yescharacteristic
211C2×C4#1451973511yescharacteristic
212C2×C4#1451975912yes—
213C8—41no—
214C8—41no—
215C8—82no—
216C8—2441no—
217C8—2441no—
218C22—22no—
219C22—21no—
220C22—41no—
221C22—42no—
222C22#1683962411yescharacteristic
223C4—22no—
224C4—21no—
225C4—1222no—
226C4—9762no—
227C4—2441no—
228C4—2442no—
229C4#1683973411yescharacteristic
230C4#1683973411yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#2144589511yescharacteristic
subgroupG/H
centerC4#16839734
commutatorC22×C4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#1392C2
socleC2×C61#1820
prime radical, cosocleC2×#41×C61C23
hypercenter#1392D61
hypocenterC61#12864
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

Complements

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

NH ≅ G/Ntype
9. #16839790C4semidirect
10. #16839788C4semidirect
13. M16×Dic61C4semidirect
14. C2×C8×Dic61C4semidirect
136. C61#12864semidirect

Maximal subgroups

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

subgroupindex
#214544592
#214459242
#214439492
#214439402
C61×#13922
#1286461