Finite Group Databasebeta

← #21451766

Subgroups — #21451766

Order 7808.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14519776C211yesmaximal, characteristic
2C2×#14519767C211yesmaximal, characteristic
3#16839704C212yesmaximal
4#16839703C212yesmaximal
5#16839702C211yesmaximal, characteristic
6#16839701C211yesmaximal, characteristic
7#16839700C211yesmaximal, characteristic
8#16839666C212yesmaximal
9#16839666C212yesmaximal
10#16839607C211yesmaximal, characteristic
11C61×#400C211yesmaximal, characteristic
12C22×Dic122C2212yes—
13#14519776—24no—
14#14519767—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×C4×Dic61C2212yes—
23C2×C4×Dic61C2211yescharacteristic
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34#95×C61C2211yescharacteristic
35#95×C61C2212yes—
36#95×C61C2212yes—
37C22×C4×C61C2312yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×Dic122—24no—
49C2×Dic122—28no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54#11758196—22no—
55#11758196—22no—
56#11758196—22no—
57#11758196—22no—
58#11758196—24no—
59C4×Dic61—24no—
60C4×Dic61D414yes—
61C23×C61C2411yescharacteristic
62C2×C4×C61—22no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—24no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61C2×D412yes—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—24no—
81C2×Dic61—22no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61C2×D412yes—
87C2×Dic61C2×D412yes—
88C2×Dic61#4114yes—
89Dic122—48no—
90C22×C61C22×D411yescharacteristic
91C22×C61C2×#4112yes—
92C22×C612−1+412yes—
93C22×C612−1+411yescharacteristic
94C22×C612−1+411yescharacteristic
95C4×C61—22no—
96C4×C61—42no—
97C4×C61—41no—
98C4×C61—41no—
99C4×C61—42no—
100Dic61—22no—
101Dic61—42no—
102Dic61—41no—
103Dic61—41no—
104Dic61—42no—
105Dic61#12414yes—
106#2642—611nomaximal, Sylow
107C2×C61C2×#12411yescharacteristic
108C2×C61#53611yescharacteristic
109C2×C61#53611yescharacteristic
110C2×C61#54112yes—
111C2×C61#54112yes—
112C2×C4⋊Q8—611no—
113C2×#125—611no—
114#400—611no—
115#400—611no—
116#400—611no—
117#400—612no—
118#400—612no—
119#400D6111yescharacteristic
120#391—612no—
121#391—612no—
122#376—611no—
123C61#264211yescharacteristic, complemented, Sylow
124C22×Q8—612no—
125C4⋊Q8—1224no—
126#125—1224no—
127C2×C4⋊C4—611no—
128C2×C4⋊C4—611no—
129C2×C4⋊C4—611no—
130C2×C4⋊C4—611no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4C2×D6111yescharacteristic
135C2×C4⋊C4C2×D6111yescharacteristic
136C2×C42—611no—
137C2×C42—612no—
138#95—612no—
139#95—611no—
140#95—612no—
141#95—612no—
142#95—612no—
143#95—612no—
144#95—612no—
145#95—612no—
146#95C2×D6111yescharacteristic
147#95C2×D6112yes—
148#95C2×D6112yes—
149C2×Q8—1224no—
150C2×Q8—1228no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—612no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—612no—
157C22×C4C22×D6112yes—
158C22×C4C22×D6111yescharacteristic
159C22×C4C22×D6111yescharacteristic
160C22×C4C22×D6112yes—
161C22×C4C22×D6111yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—1222no—
165C4⋊C4—1222no—
166C4⋊C4—1222no—
167C4⋊C4—1224no—
168C4⋊C4—1222no—
169C4⋊C4—1222no—
170C4⋊C4—1222no—
171C42—614no—
172C42—1224no—
173C23C23×D6111yescharacteristic
174Q8—2448no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—612no—
187C2×C4—614no—
188C2×C4—612no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1224no—
196C2×C4—1222no—
197C2×C4—1221no—
198C2×C4—1222no—
199C2×C4—1221no—
200C2×C4—1222no—
201C2×C4D4×D6112yes—
202C22C2×D4×D6111yescharacteristic
203C22#41×D6112yes—
204C22#1451982412yes—
205C22#1451982411yescharacteristic
206C22#1451982511yescharacteristic
207C4—22no—
208C4—42no—
209C4—41no—
210C4—41no—
211C4—42no—
212C4—614no—
213C4—1222no—
214C4—2442no—
215C4—2441no—
216C4—2441no—
217C4—2442no—
218C2#124×D6111yescharacteristic
219C2#1684033411yescharacteristic
220C2#1684033511yescharacteristic
221C2#1684036912yes—
222C2#1684037112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2642
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
123. C61#2642semidirect