Finite Group Databasebeta

← #21458753

Subgroups — #21458753

Order 7808.

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

normal subgroups only

This group has 326 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
1Q8×Dic122C211yesmaximal, characteristic
2#16840490C211yesmaximal, characteristic
3#16840171C212yesmaximal
4#16840160C211yesmaximal, characteristic
5#16840070C212yesmaximal
6#16840058C211yesmaximal, characteristic
7#16840048C211yesmaximal, characteristic
8#16840048C212yesmaximal
9#16839870C212yesmaximal
10C4×Dic244C211yesmaximal, characteristic
11C61×#446C211yesmaximal, characteristic
12C2×Dic244C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519777C2212yes—
15#14519777C2211yescharacteristic
16#14519776—21no—
17#14519776—22no—
18#14519775—21no—
19#14519769C2212yes—
20#14519767—22no—
21Q8×Dic61—21no—
22C4×Dic122C2212yes—
23C4×Dic122C2211yescharacteristic
24C4×Dic122C2211yescharacteristic
25C4×Dic122C2212yes—
26#14519742—21no—
27#14519711C2212yes—
28#14519711C2211yescharacteristic
29#14519709C2212yes—
30#14519709C2212yes—
31#14519709C2212yes—
32#14519702C2211yescharacteristic
33#14519702C2212yes—
34#14519702C2212yes—
35#14519702C2211yescharacteristic
36C4×Q8×C61C2211yescharacteristic
37C4⋊C8×C61C2211yescharacteristic
38C4⋊C8×C61C2212yes—
39#97×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61D411yescharacteristic
42C2×Dic122—21no—
43C2×Dic122—22no—
44C2×Dic122—21no—
45C2×Dic122C2311yescharacteristic
46C2×Dic122C2311yescharacteristic
47C2×C8×C61C2311yescharacteristic
48C2×C8×C61C2312yes—
49C2×C8×C61C2311yescharacteristic
50C4⋊C4×C61D411yescharacteristic
51C4⋊C4×C61D412yes—
52C42×C61C2311yescharacteristic
53C42×C61C2312yes—
54C4⋊Dic61—22no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61C2312yes—
58C4⋊Dic61C2311yescharacteristic
59C4⋊Dic61C2312yes—
60C4⋊Dic61C2311yescharacteristic
61#11758196—22no—
62#11758196—21no—
63#11758196—22no—
64#11758196—22no—
65#11758196—21no—
66#11758196—22no—
67C4×Dic61—22no—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C4×Dic61—21no—
71Dic244Q814yescomplemented
72Q8×C61—22no—
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2411yescharacteristic
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—21no—
84Dic122—21no—
85Dic122—21no—
86Dic122—42no—
87Dic122—82no—
88Dic122—81no—
89Dic122C2×Q812yes—
90Dic122C2×Q812yes—
91C8×C61—21no—
92C8×C61—22no—
93C8×C61C2×Q812yes—
94C22×C61C22×D411yescharacteristic
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—21no—
98C4×C61#13712yes—
99C4×C61C22×Q811yescharacteristic
100C4×C612−1+411yescharacteristic
101Dic61—22no—
102Dic61—22no—
103Dic61—42no—
104Dic61—41no—
105Dic61—42no—
106Dic61—41no—
107#3387—611nomaximal, Sylow
108C2×C61D4×Q811yescharacteristic
109C2×C61C2×#13711yescharacteristic
110C2×C61#57711yescharacteristic
111Q82—611no—
112#557—611no—
113#501—612no—
114#498—611no—
115#479—612no—
116#477—611no—
117#475—612no—
118#475—611no—
119#446D6111yescharacteristic
120#441—612no—
121C4×Q16—611no—
122C61#338711yescharacteristic, complemented, Sylow
123C2×Q16—611no—
124C4⋊Q8—611no—
125C4⋊Q8—612no—
126C4⋊Q8—611no—
127C4⋊Q8—1221no—
128C4⋊Q8—1221no—
129C4⋊Q8—1222no—
130#125—612no—
131#125—1222no—
132C4×Q8—611no—
133C4×Q8—612no—
134C4×Q8—611no—
135C4×Q8—612no—
136C4×Q8—1221no—
137C4×Q8—1221no—
138C4×Q8C2×D6111yescharacteristic
139#107—611no—
140#107—612no—
141#106—612no—
142#106—612no—
143#106—612no—
144C4⋊C8C2×D6111yescharacteristic
145C4⋊C8C2×D6112yes—
146#103—611no—
147#103—611no—
148#103—612no—
149#103—612no—
150#97C2×D6112yes—
151C4×C8C2×D6111yescharacteristic
152C2×Q8—611no—
153C2×Q8—611no—
154C2×Q8—1222no—
155C2×Q8—1221no—
156C2×Q8—1221no—
157C2×Q8D24411yescharacteristic
158Q16—614no—
159C2×C8C22×D6111yescharacteristic
160C2×C8C22×D6112yes—
161C2×C8C22×D6111yescharacteristic
162C4⋊C4—612no—
163C4⋊C4—611no—
164C4⋊C4—612no—
165C4⋊C4—611no—
166C4⋊C4—1221no—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C4⋊C4—1221no—
170C4⋊C4—1222no—
171C4⋊C4—1222no—
172C4⋊C4—1222no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C4⋊C4D24411yescharacteristic
176C4⋊C4D24412yes—
177C42—1222no—
178C42—1221no—
179C42—1222no—
180C42—1221no—
181C42C22×D6111yescharacteristic
182C42C22×D6112yes—
183Q8—22no—
184Q8—612no—
185Q8—612no—
186Q8—1221no—
187Q8—1221no—
188Q8—4882no—
189Q8—4881no—
190Q8—2442no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1221no—
197C2×C4C2×D24412yes—
198C2×C4C2×D24412yes—
199C2×C4C2×D24411yescharacteristic
200C2×C4C2×D24411yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—21no—
203C8—22no—
204C8Q8×D6112yes—
205C22C22×D24411yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—1222no—
210C4—1222no—
211C4—2442no—
212C4—2441no—
213C4—2442no—
214C4—2441no—
215C4#1451981012yes—
216C4C2×Q8×D6111yescharacteristic
217C4#1451982411yescharacteristic
218C2Q8×D24411yescharacteristic
219C2C2×#1451981011yescharacteristic
220C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3387
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
71. Dic244Q8semidirect
122. C61#3387semidirect