Finite Group Databasebeta

← #21445789

Subgroups — #21445789

Order 7808.

588 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 121 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#16839779C212yesmaximal, complemented
2#16839767C212yesmaximal, complemented
3#16839746C211yesmaximal, characteristic, complemented
4#16839736C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C61C211yesmaximal, characteristic
6C2×#11758194C2212yescomplemented
7#14519736C2212yescomplemented
8#14519704—24no—
9#14519698—24no—
10#14519696—21no—
11#14519694—21no—
12#14519692—22no—
13H(5,𝔽2)×C61—24no—
14H(5,𝔽2)×C61—24no—
15C2×#41×C61—21no—
16C2×#41×C61C412yescomplemented
17C2×#41×C61C2211yescharacteristic
18C2×#41×C61C2211yescharacteristic
19C22×D4×C61—22no—
20C22×D4×C61—21no—
21C22×D4×C61C412yescomplemented
22C22×D4×C61C2211yescharacteristic
23C24×C61—22no—
24C24×C61—21no—
25#41×C61—28no—
26#41×C61—24no—
27#41×C61—24no—
28#41×C61—22no—
29#41×C61—22no—
30#41×C61—22no—
31#41×C61D414yes—
32C2×Q8×C61C2×C411yescharacteristic
33C2×Q8×C61D411yescharacteristic
34C2×D4×C61—216no—
35C2×D4×C61—28no—
36C2×D4×C61—22no—
37C2×D4×C61—21no—
38C2×D4×C61—24no—
39C2×D4×C61—24no—
40C2×D4×C61—22no—
41C2×D4×C61—21no—
42C2×D4×C61—22no—
43C2×D4×C61C2×C411yescharacteristic
44C2×D4×C61C2×C412yes—
45C2×D4×C61D412yes—
46C2×D4×C61D411yescharacteristic
47C2×D4×C61D414yes—
48C22×C4×C61—22no—
49C22×C4×C61—21no—
50C22×C4×C61C2×C412yes—
51C22×C4×C61C2311yescharacteristic
52C22⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4×Dic61—22no—
55#11758194—22no—
56#11758194—22no—
57C2×#92418—22no—
58C23×C61—28no—
59C23×C61—22no—
60C23×C61—21no—
61C23×C61—24no—
62C23×C61—82no—
63C23×C61—84no—
64C23×C61C22⋊C412yes—
65C23×C61C2×D411yescharacteristic
66Q8×C61—21no—
67Q8×C61—22no—
68Q8×C61C22⋊C412yes—
69D4×C61—28no—
70D4×C61—28no—
71D4×C61—24no—
72D4×C61—24no—
73D4×C61—22no—
74D4×C61—21no—
75D4×C61—22no—
76D4×C61—24no—
77D4×C61C22⋊C412yes—
78D4×C61C22⋊C414yes—
79C2×C4×C61—28no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—24no—
84C2×C4×C61C22⋊C412yes—
85C2×C4×C61C22×C411yescharacteristic
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×D412yes—
88C2×C4×C61C2×D411yescharacteristic
89C2×Dic61—42no—
90#92418—42no—
91C22×C61—22no—
92C22×C61—24no—
93C22×C61—22no—
94C22×C61—41no—
95C22×C61—42no—
96C22×C61—44no—
97C22×C61—42no—
98C22×C61—84no—
99C22×C61—88no—
100C22×C61C2×C22⋊C411yescharacteristic
101C22×C61#12012yes—
102C4×C61—22no—
103C4×C61—22no—
104C4×C61C2×C22⋊C411yescharacteristic
105C4×C61C2×C22⋊C411yescharacteristic
106C4×C61#12012yes—
107Dic61—82no—
108#1795—611nomaximal, Sylow
109C2×C61—22no—
110C2×C61—21no—
111C2×C61—44no—
112C2×C61—42no—
113C2×C61—42no—
114C2×C61#37911yescharacteristic
115C2×H(5,𝔽2)D6111yescharacteristic
116#421—612no—
117#418—612no—
118#413—611no—
119#410—611no—
120C61#179511yescharacteristic, complemented, Sylow
121H(5,𝔽2)—24no—
122H(5,𝔽2)—24no—
123C2×#41—21no—
124C2×#41Dic6112yescomplemented
125C2×#41C2×D6111yescharacteristic
126C2×#41C2×D6111yescharacteristic
127C22×D4—22no—
128C22×D4—21no—
129C22×D4Dic6112yescomplemented
130C22×D4C2×D6111yescharacteristic
131C2×M16—612no—
132#117—612no—
133#104—1224no—
134#102—1224no—
135#101—1221no—
136#100—1221no—
137#99—1222no—
138C24—22no—
139C24—21no—
140#41—28no—
141#41—24no—
142#41—24no—
143#41—22no—
144#41—22no—
145#41—22no—
146#41C22⋊D6114yes—
147C2×Q8C2×Dic6111yescharacteristic
148C2×Q8C22⋊D6111yescharacteristic
149C2×D4—216no—
150C2×D4—28no—
151C2×D4—22no—
152C2×D4—21no—
153C2×D4—24no—
154C2×D4—24no—
155C2×D4—22no—
156C2×D4—21no—
157C2×D4—22no—
158C2×D4C2×Dic6111yescharacteristic
159C2×D4C2×Dic6112yes—
160C2×D4C22⋊D6112yes—
161C2×D4C22⋊D6111yescharacteristic
162C2×D4C22⋊D6114yes—
163C22×C4—22no—
164C22×C4—21no—
165C22×C4C2×Dic6112yes—
166C22×C4C22×D6111yescharacteristic
167M16—1222no—
168M16—1222no—
169C2×C8—1222no—
170C4⋊C4—1222no—
171C22⋊C4—1222no—
172C42—1222no—
173C23—28no—
174C23—22no—
175C23—21no—
176C23—24no—
177C23—82no—
178C23—84no—
179C23C22⋊Dic6112yes—
180C23C2×C22⋊D6111yescharacteristic
181Q8—21no—
182Q8—22no—
183Q8C22⋊Dic6112yes—
184D4—28no—
185D4—28no—
186D4—24no—
187D4—24no—
188D4—22no—
189D4—21no—
190D4—22no—
191D4—24no—
192D4C22⋊Dic6112yes—
193D4C22⋊Dic6114yes—
194C2×C4—28no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—2442no—
200C2×C4C22⋊Dic6112yes—
201C2×C4C22×Dic6111yescharacteristic
202C2×C4C2×C22⋊D6112yes—
203C2×C4C2×C22⋊D6112yes—
204C2×C4C2×C22⋊D6111yescharacteristic
205C8—2442no—
206C22—22no—
207C22—24no—
208C22—22no—
209C22—41no—
210C22—42no—
211C22—44no—
212C22—42no—
213C22—84no—
214C22—88no—
215C22C2×C22⋊Dic6111yescharacteristic
216C22#1451974612yes—
217C4—22no—
218C4—22no—
219C4—4882no—
220C4C2×C22⋊Dic6111yescharacteristic
221C4C2×C22⋊Dic6111yescharacteristic
222C4#1451974612yes—
223C2—22no—
224C2—21no—
225C2—44no—
226C2—42no—
227C2—42no—
228C2#1683961811yescharacteristic
subgroupG/H
centerC2#16839618
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×H(5,𝔽2)×C61C2
socleC2×C61#379
hypercenterC2×H(5,𝔽2)D61
hypocenterC61#1795
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #16839779C2semidirect
2. #16839767C2semidirect
3. #16839746C2semidirect
4. #16839736C2semidirect
6. C2×#11758194C22semidirect
7. #14519736C22semidirect
16. C2×#41×C61C4semidirect
21. C22×D4×C61C4semidirect
120. C61#1795semidirect
124. C2×#41Dic61semidirect
129. C22×D4Dic61semidirect