Finite Group Databasebeta

← #21458460

Subgroups — #21458460

Order 7808.

370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840490C211yesmaximal, characteristic, complemented
2#16840427C211yesmaximal, characteristic
3#16840114C211yesmaximal, characteristic, complemented
4#16840111C212yesmaximal, complemented
5#16840046C212yesmaximal, complemented
6#16839968C211yesmaximal, characteristic
7#16839966C212yesmaximal
8#16839886C211yesmaximal, characteristic, complemented
9C4×#11758201C211yesmaximal, characteristic
10#16839849C212yesmaximal
11C61×#475C211yesmaximal, characteristic, complemented
12C2×Q8×D61—21no—
13C2×#11758190C2212yes—
14C2×#11758201C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519776C2212yes—
17#14519775C2212yes—
18#14519769—21no—
19#14519767—22no—
20#14519755—22no—
21#14519753—21no—
22C4×Dic122—21no—
23C4×Dic122C2211yescharacteristic
24#14519742C2212yes—
25C4×D244C2211yescharacteristic
26#14519739C2212yes—
27#14519708C2211yescharacteristic
28#14519706C2212yes—
29#14519702C2212yes—
30#14519701C2211yescharacteristic
31#14519700C2212yes—
32#14519700C2212yes—
33#14519697C2211yescharacteristic
34C4×#92418C2211yescharacteristic
35C8×Dic61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37C4×Q8×C61C2211yescharacteristic
38#106×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61—21no—
42C2×Q8×C61C2311yescharacteristic
43Q8×D61—44no—
44C2×D244C2311yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61—22no—
47C2×Dic122—22no—
48C2×Dic122D411yescharacteristic
49C2×Dic122C2312yes—
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2312yes—
54C4⋊C4×C61C2311yescharacteristic
55C42×C61—21no—
56C42×C61C2311yescharacteristic
57#11758201—22no—
58#11758198—21no—
59#11758198—22no—
60C4⋊Dic61—21no—
61C4⋊Dic61—21no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2311yescharacteristic
64#11758196—22no—
65#11758196—22no—
66#11758196—22no—
67#11758196—22no—
68#11758196D412yes—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2311yescharacteristic
72C2×#92418C2311yescharacteristic
73#11758190—24no—
74C22×D61—21no—
75Q8×C61—21no—
76Q8×C61—21no—
77Q8×C61—42no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2411yescharacteristic
84C2×Dic61—22no—
85C2×Dic61—21no—
86C2×Dic61C2×D412yes—
87C2×Dic61C2×D412yes—
88D244—21no—
89D244#4112yes—
90C4×D61—42no—
91C4×D61—44no—
92Dic122—22no—
93Dic122—22no—
94Dic122—44no—
95Dic122SD1614yescomplemented
96C8×C61—22no—
97#92418—21no—
98#92418—21no—
99C22×C61C22×D411yescharacteristic
100C2×D61—22no—
101C2×D61—41no—
102C2×D61—41no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61—42no—
106C4×C61—41no—
107C4×C61C2×SD1612yes—
108C4×C61C2×#4111yescharacteristic
109C4×C612−1+411yescharacteristic
110Dic61—22no—
111Dic61—42no—
112Dic61—41no—
113Dic61C2×SD1614yes—
114#3359—611nomaximal, Sylow
115C2×C61#54811yescharacteristic
116C2×C61C22×SD1611yescharacteristic
117C2×C61#57811yescharacteristic
118D61—42no—
119#557—611no—
120D4×Q8—611no—
121#487—611no—
122#487—612no—
123#475—612no—
124#475D6111yescharacteristic, complemented
125#461—611no—
126#461—612no—
127C8×Q8—611no—
128C4×SD16—611no—
129C4×SD16—612no—
130C61#335911yescharacteristic, complemented, Sylow
131C22×Q8—1221no—
132C2×SD16—611no—
133C2×SD16—612no—
134C4⋊Q8—612no—
135C4⋊Q8—612no—
136C4⋊Q8—611no—
137C4⋊Q8C2×D6111yescharacteristic
138#125—1221no—
139#125—1222no—
140C22⋊Q8—1222no—
141C22⋊Q8—1221no—
142C4×Q8—611no—
143C4×Q8—612no—
144C4×Q8—1221no—
145C4×Q8C2×D6111yescharacteristic
146C4×D4—612no—
147C4×D4—611no—
148#106—611no—
149#106C2×D6112yes—
150C4⋊C8—612no—
151C4⋊C8C2×D6111yescharacteristic
152#103—611no—
153#103—612no—
154#103—612no—
155#103—612no—
156#103C2×D6112yes—
157#102—611no—
158C4×C8—612no—
159C4×C8—611no—
160C2×Q8—21no—
161C2×Q8—611no—
162C2×Q8—612no—
163C2×Q8—1222no—
164C2×Q8—2444no—
165C2×Q8C22×D6111yescharacteristic
166C2×D4—611no—
167C22×C4—1222no—
168C22×C4—1221no—
169SD16—1224no—
170SD16—1222no—
171C2×C8—611no—
172C2×C8—611no—
173C2×C8C22×D6112yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—612no—
177C4⋊C4—611no—
178C4⋊C4—611no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C4⋊C4C22×D6111yescharacteristic
186C4⋊C4C22×D6112yes—
187C22⋊C4—1222no—
188C22⋊C4—1221no—
189C42—21no—
190C42—612no—
191C42—1222no—
192C42C22×D6111yescharacteristic
193C23—1221no—
194Q8—21no—
195Q8—21no—
196Q8—42no—
197Q8—614no—
198Q8—1222no—
199Q8—1222no—
200Q8—2444no—
201D4—612no—
202D4—1221no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—612no—
207C2×C4—612no—
208C2×C4—1222no—
209C2×C4—1221no—
210C2×C4—2444no—
211C2×C4—2442no—
212C2×C4D4×D6111yescharacteristic
213C2×C4D4×D6111yescharacteristic
214C2×C4C23×D6111yescharacteristic
215C8—22no—
216C8—1221no—
217C8—1221no—
218C22—1222no—
219C22—2441no—
220C22—2441no—
221C22C2×D4×D6111yescharacteristic
222C4—21no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—614no—
227C4—1222no—
228C4—2441no—
229C4—2442no—
230C4SD16×D6112yes—
231C4#41×D6111yescharacteristic
232C4#1451982511yescharacteristic
233C2—2442no—
234C2#1684042211yescharacteristic
235C2C2×SD16×D6111yescharacteristic
236C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#475C2
socleC22×C61C22×D4
hypercenter#475D61
hypocenterC61#3359
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #16840490C2semidirect
3. #16840114C2semidirect
4. #16840111C2semidirect
5. #16840046C2semidirect
8. #16839886C2semidirect
11. C61×#475C2semidirect
95. Dic122SD16semidirect
124. #475D61semidirect
130. C61#3359semidirect