Finite Group Databasebeta

← #21458744

Subgroups — #21458744

Order 7808.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840487C211yesmaximal, characteristic, complemented
2D4×Dic122C211yesmaximal, characteristic
3#16840170C212yesmaximal, complemented
4#16840165C211yesmaximal, characteristic, complemented
5#16840064C212yesmaximal
6#16840056C212yesmaximal, complemented
7#16840048C211yesmaximal, characteristic, complemented
8#16839889C211yesmaximal, characteristic, complemented
9#16839859C212yesmaximal
10C4×#11758200C211yesmaximal, characteristic
11C61×#474C211yesmaximal, characteristic
12C22×Dic122—21no—
13C2×#11758200C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519776C2212yes—
16#14519775—21no—
17#14519768C2212yes—
18#14519767—22no—
19#14519756—21no—
20#14519754—22no—
21Q8×Dic61—21no—
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24#14519742C2212yes—
25D4×Dic61C2212yes—
26#14519710C2212yes—
27#14519710C2212yes—
28#14519709C2212yes—
29#14519708C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2212yes—
32#14519700C2211yescharacteristic
33#14519698C2211yescharacteristic
34#14519687C2212yes—
35C4×#92418C2211yescharacteristic
36C4⋊Q8×C61C2211yescharacteristic
37C4×D4×C61C2211yescharacteristic
38#107×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#102×C61C2212yes—
41C2×Q8×C61—21no—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C22×Dic61—22no—
45C2×Dic122—21no—
46C2×Dic122—22no—
47C2×Dic122—44no—
48C2×Dic122D411yescharacteristic
49C2×Dic122C2311yescharacteristic
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2312yes—
53C4⋊C4×C61C2311yescharacteristic
54C22⋊C4×C61—21no—
55C42×C61C2311yescharacteristic
56C22⋊Dic61—22no—
57#11758200Q814yescomplemented
58C4⋊Dic61—21no—
59C4⋊Dic61—22no—
60C4⋊Dic61D411yescharacteristic
61C4⋊Dic61C2311yescharacteristic
62C4⋊Dic61C2312yes—
63#11758196—21no—
64#11758196—22no—
65#11758196—22no—
66#11758196—22no—
67#11758196D412yes—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2311yescharacteristic
72C2×#92418C2311yescharacteristic
73C23×C61—21no—
74Q8×C61—42no—
75D4×C61—21no—
76D4×C61C2×Q812yes—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—42no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61—44no—
87C2×Dic61C2×D412yes—
88C2×Dic61C2×D412yes—
89Dic122—22no—
90Dic122—21no—
91Dic122—44no—
92Dic122—42no—
93Dic122C2×Q812yescomplemented
94C8×C61—22no—
95#92418—21no—
96#92418C2×Q812yescomplemented
97C22×C61—22no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61C22×D411yescharacteristic
101C4×C61—21no—
102C4×C61—41no—
103C4×C61—42no—
104C4×C61AGL(1,ℤ/8)12yes—
105C4×C61C22×Q811yescharacteristic
106C4×C612−1+411yescharacteristic
107Dic61—22no—
108Dic61—22no—
109Dic61—22no—
110Dic61—42no—
111Dic61—41no—
112#3386—611nomaximal, Sylow
113C2×C61—42no—
114C2×C61D4×Q811yescharacteristic
115C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
116C2×C61#57811yescharacteristic
117#557—611no—
118D4×Q8—611no—
119#501—612no—
120#500—611no—
121#478—612no—
122#477—612no—
123#475—611no—
124#474D6111yescharacteristic
125#446—611no—
126#440—612no—
127C4×SD16—611no—
128C61#338611yescharacteristic, complemented, Sylow
129C22×Q8—1221no—
130C2×SD16—611no—
131C4⋊Q8—612no—
132C4⋊Q8—611no—
133C4⋊Q8—1221no—
134C4⋊Q8C2×D6111yescharacteristic
135#125—612no—
136#125—1222no—
137C22⋊Q8—1222no—
138C22⋊Q8—1221no—
139C4×Q8—611no—
140C4×Q8—612no—
141C4×Q8—611no—
142C4×Q8—1221no—
143C4×D4—612no—
144C4×D4C2×D6111yescharacteristic
145#107—612no—
146#107—612no—
147#107C2×D6112yes—
148#106—612no—
149#106—611no—
150C4⋊C8—612no—
151C4⋊C8C2×D6111yescharacteristic
152#103—612no—
153#103—611no—
154#102—611no—
155#102C2×D6112yes—
156#97—612no—
157C4×C8—611no—
158C2×Q8—21no—
159C2×Q8—611no—
160C2×Q8—611no—
161C2×Q8—1222no—
162C2×Q8—1221no—
163C2×Q8—2444no—
164C2×D4C22×D6111yescharacteristic
165C22×C4—21no—
166C22×C4—1222no—
167SD16—614no—
168C2×C8—611no—
169C2×C8—611no—
170C2×C8C22×D6112yes—
171C4⋊C4—21no—
172C4⋊C4—612no—
173C4⋊C4—611no—
174C4⋊C4—611no—
175C4⋊C4—612no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1221no—
181C4⋊C4—1221no—
182C4⋊C4C22×D6112yes—
183C4⋊C4C22×D6111yescharacteristic
184C22⋊C4—21no—
185C22⋊C4—1222no—
186C42—612no—
187C42—1222no—
188C42—1221no—
189C42C22×D6111yescharacteristic
190C23—21no—
191Q8—42no—
192Q8—612no—
193Q8—1221no—
194Q8—1222no—
195Q8—2444no—
196Q8—2442no—
197D4—21no—
198D4Q8×D6112yes—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—612no—
203C2×C4—612no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1222no—
207C2×C4—2444no—
208C2×C4D4×D6111yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—612no—
213C8—1221no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22C2×D4×D6111yescharacteristic
218C4—21no—
219C4—41no—
220C4—42no—
221C4—1222no—
222C4—1222no—
223C4—1222no—
224C4—2442no—
225C4—2441no—
226C4#1451980112yes—
227C4C2×Q8×D6111yescharacteristic
228C4#1451982411yescharacteristic
229C2—42no—
230C2#1684042511yescharacteristic
231C2C2×#1451980111yescharacteristic
232C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#474C2
socleC22×C61C22×D4
hypercenter#474D61
hypocenterC61#3386
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16840487C2semidirect
3. #16840170C2semidirect
4. #16840165C2semidirect
6. #16840056C2semidirect
7. #16840048C2semidirect
8. #16839889C2semidirect
57. #11758200Q8semidirect
93. Dic122C2×Q8semidirect
96. #92418C2×Q8semidirect
128. C61#3386semidirect