Finite Group Databasebeta

← #21455304

Subgroups — #21455304

Order 7808.

480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14519807C211yesmaximal, characteristic
2C2×#14519775C211yesmaximal, characteristic, complemented
3#41×Dic61C211yesmaximal, characteristic
4#16839970C214yesmaximal, complemented
5#16839965C214yesmaximal, complemented
6#16839785C211yesmaximal, characteristic, complemented
7#16839772C211yesmaximal, characteristic, complemented
8#16839771C211yesmaximal, characteristic, complemented
9C2×#137×C61C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11#14519807—24no—
12C2×#11758202C2212yes—
13C2×#11758200C2212yes—
14C2×#11758194C2211yescharacteristic
15#14519775—21no—
16#14519775—21no—
17#14519775C2214yes—
18Q8×Dic61C2212yes—
19D4×Dic61—22no—
20D4×Dic61C2212yes—
21#14519736—21no—
22#14519736C2211yescharacteristic
23C2×#11758196—22no—
24C2×C4×Dic61—21no—
25C2×C4×Dic61C2211yescharacteristic
26#14519706C2214yes—
27#14519702C2214yes—
28#14519701C2214yes—
29C2×#41×C61C2211yescharacteristic
30C22×Q8×C61C2211yescharacteristic
31#137×C61—24no—
32C2×Q16×C61C2212yes—
33C2×SD16×C61C2212yes—
34C2×M16×C61C2211yescharacteristic
35#41×C61—22no—
36#41×C61D414yes—
37C2×Q8×C61—21no—
38C2×Q8×C61—22no—
39C2×Q8×C61—22no—
40C2×Q8×C61C2312yes—
41C2×Q8×C61C2311yescharacteristic
42C2×D4×C61—21no—
43C2×D4×C61C2311yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C22×Dic61—21no—
48C22×Dic61—22no—
49C22×Dic61D412yes—
50C2×Dic122—22no—
51C2×Dic122—22no—
52C2×Dic122—21no—
53C2×Dic122C2312yes—
54Q16×C61—24no—
55SD16×C61—24no—
56M16×C61—22no—
57C2×C8×C61C2312yes—
58C22⋊Dic61—21no—
59C22⋊Dic61—22no—
60#11758202—24no—
61#11758200—24no—
62C4⋊Dic61—22no—
63C4⋊Dic61C2312yes—
64#11758196—24no—
65#11758196—24no—
66C4×Dic61—21no—
67C4×Dic61—22no—
68C4×Dic61D411yescharacteristic
69C4×Dic61D411yescharacteristic
70C4×Dic61C2312yes—
71#11758194—22no—
72C2×#92418C2312yes—
73C23×C61—21no—
74C23×C61C2×D411yescharacteristic
75Q8×C61—21no—
76Q8×C61—22no—
77Q8×C61—22no—
78Q8×C61—42no—
79Q8×C61C2×D412yes—
80D4×C61—24no—
81D4×C61—21no—
82D4×C61C2×D412yes—
83C2×C4×C61—21no—
84C2×C4×C61—24no—
85C2×C4×C61—22no—
86C2×C4×C61—42no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D412yes—
89C2×C4×C61#4112yes—
90C2×C4×C61C2411yescharacteristic
91C2×Dic61—24no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—42no—
95C2×Dic61—44no—
96C2×Dic61C2×D412yes—
97C2×Dic61C2×D412yes—
98Dic122—22no—
99Dic122—22no—
100Dic122—42no—
101C8×C61—22no—
102#92418—22no—
103C22×C61—22no—
104C22×C61—22no—
105C22×C61—42no—
106C22×C61#12112yes—
107C22×C61C22×D411yescharacteristic
108C4×C61—22no—
109C4×C61—42no—
110C4×C61#12112yes—
111C4×C61C22×D411yescharacteristic
112C4×C61C2×#4111yescharacteristic
113Dic61—22no—
114Dic61—42no—
115Dic61—42no—
116Dic61#13714yescomplemented
117#3039—611nomaximal, Sylow
118C2×C61—22no—
119C2×C61—42no—
120C2×C61C2×#12111yescharacteristic
121C2×C61C2×#13712yes—
122C2×#137—611no—
123C2×#137D6111yescharacteristic
124C2×C4⋊Q8—611no—
125C4×#41—611no—
126#462—614no—
127#461—614no—
128#423—611no—
129#419—611no—
130#419—611no—
131C61#303911yescharacteristic, complemented, Sylow
132C2×#41C2×D6111yescharacteristic
133C22×Q8—611no—
134C22×Q8C2×D6111yescharacteristic
135#137—24no—
136#137—1224no—
137C2×Q16—612no—
138C2×Q16C2×D6112yes—
139C2×SD16—612no—
140C2×SD16C2×D6112yes—
141C2×M16—611no—
142C2×M16C2×D6111yescharacteristic
143C4⋊Q8—614no—
144C4⋊Q8—1221no—
145C4⋊Q8—1221no—
146C4×Q8—612no—
147C4×D4—612no—
148C4×D4—1222no—
149#117—611no—
150#117—1221no—
151C2×C4⋊C4—1222no—
152C2×C42—611no—
153C2×C42—1221no—
154C4⋊C8—614no—
155#103—614no—
156#103—614no—
157#41—22no—
158#41C22⋊D6114yes—
159C2×Q8—21no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—612no—
163C2×Q8—1221no—
164C2×Q8—1222no—
165C2×Q8—1222no—
166C2×Q8C22×D6112yes—
167C2×Q8C22×D6111yescharacteristic
168C2×D4—21no—
169C2×D4C22×D6111yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—612no—
173C22×C4—1222no—
174C22×C4—1221no—
175C22×C4C22×D6111yescharacteristic
176Q16—24no—
177Q16—1224no—
178SD16—24no—
179SD16—1224no—
180M16—22no—
181M16—1222no—
182C2×C8—612no—
183C2×C8C22×D6112yes—
184C4⋊C4—612no—
185C4⋊C4—1224no—
186C4⋊C4—1224no—
187C4⋊C4—1222no—
188C22⋊C4—1222no—
189C22⋊C4—1221no—
190C42—611no—
191C42—611no—
192C42—612no—
193C42—1222no—
194C42—1221no—
195C23—21no—
196C23D4×D6111yescharacteristic
197Q8—21no—
198Q8—22no—
199Q8—22no—
200Q8—42no—
201Q8—1222no—
202Q8—1222no—
203Q8—2442no—
204Q8C2×C22⋊D6112yes—
205D4—24no—
206D4—21no—
207D4C2×C22⋊D6112yes—
208C2×C4—21no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—612no—
213C2×C4—612no—
214C2×C4—1224no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—2444no—
218C2×C4—2442no—
219C2×C4D4×D6111yescharacteristic
220C2×C4#1175822412yes—
221C2×C4C2×C22⋊D6112yes—
222C2×C4C23×D6111yescharacteristic
223C8—22no—
224C8—1222no—
225C22—22no—
226C22—22no—
227C22—42no—
228C22#1451974912yes—
229C22C2×D4×D6111yescharacteristic
230C4—22no—
231C4—42no—
232C4—614no—
233C4—1222no—
234C4—2442no—
235C4—2442no—
236C4#1451974912yes—
237C4C22×C22⋊D6111yescharacteristic
238C4C2×#1175822411yescharacteristic
239C2—22no—
240C2—42no—
241C2C2×#1451974911yescharacteristic
242C2#137×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3039
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#14519775C2semidirect
4. #16839970C2semidirect
5. #16839965C2semidirect
6. #16839785C2semidirect
7. #16839772C2semidirect
8. #16839771C2semidirect
116. Dic61#137semidirect
131. C61#3039semidirect