Finite Group Databasebeta

← #21458731

Subgroups — #21458731

Order 7808.

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

normal subgroups only

This group has 340 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, complemented
2#16840472C211yesmaximal, characteristic
3#16840171C212yesmaximal, complemented
4#16840167C211yesmaximal, characteristic, complemented
5#16840070C212yesmaximal, complemented
6#16840058C211yesmaximal, characteristic, complemented
7#16840053C211yesmaximal, characteristic
8#16840043C212yesmaximal
9#16839864C212yesmaximal
10C4×#11758190C211yesmaximal, characteristic
11C61×#446C211yesmaximal, characteristic, complemented
12C2×#11758190C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519777C2212yes—
15#14519777C2211yescharacteristic
16#14519776—21no—
17#14519776—22no—
18#14519769C2212yes—
19#14519755—22no—
20#14519753—21no—
21Q8×Dic61—21no—
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2212yes—
24C4×D244C2212yes—
25C4×D244C2211yescharacteristic
26C4⋊C4×D61—21no—
27#14519711C2212yes—
28#14519711C2212yes—
29#14519711C2212yes—
30#14519709C2212yes—
31#14519709C2211yescharacteristic
32#14519702C2212yes—
33#14519702C2211yescharacteristic
34#14519699C2211yescharacteristic
35#14519699C2212yes—
36C4×Q8×C61C2211yescharacteristic
37C4⋊C8×C61C2212yes—
38C4⋊C8×C61C2211yescharacteristic
39#97×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61D411yescharacteristic
42C2×D244C2311yescharacteristic
43C2×C4×D61—21no—
44C2×C4×D61—22no—
45C2×Dic122—21no—
46C2×Dic122—22no—
47C2×Dic122—21no—
48C2×Dic122C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C2×C8×C61C2312yes—
51C2×C8×C61C2311yescharacteristic
52C4⋊C4×C61D411yescharacteristic
53C4⋊C4×C61D412yes—
54C42×C61C2311yescharacteristic
55C42×C61C2312yes—
56#11758198—22no—
57#11758198—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61—22no—
60C4⋊Dic61—21no—
61C4⋊Dic61C2311yescharacteristic
62C4⋊Dic61C2312yes—
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2312yes—
65#11758196—22no—
66#11758196—22no—
67#11758196—21no—
68#11758196—22no—
69C4×Dic61—22no—
70C4×Dic61—21no—
71#11758190Q814yescomplemented
72C22×D61—21no—
73Q8×C61—22no—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2411yescharacteristic
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—22no—
84D244—21no—
85D244C2×Q812yes—
86C4×D61—42no—
87C4×D61—82no—
88Dic122—21no—
89Dic122—81no—
90Dic122—82no—
91Dic122—81no—
92Dic122C2×Q812yes—
93C8×C61—21no—
94C8×C61—22no—
95C8×C61C2×Q812yes—
96C22×C61C22×D411yescharacteristic
97C2×D61—22no—
98C2×D61—41no—
99C2×D61—41no—
100C4×C61—22no—
101C4×C61—21no—
102C4×C61—22no—
103C4×C61#13712yes—
104C4×C61C22×Q811yescharacteristic
105C4×C612−1+411yescharacteristic
106Dic61—22no—
107Dic61—41no—
108Dic61—42no—
109Dic61—41no—
110Dic61—42no—
111#3385—611nomaximal, Sylow
112C2×C61D4×Q811yescharacteristic
113C2×C61C2×#13711yescharacteristic
114C2×C61#57611yescharacteristic
115D61—42no—
116Q82—611no—
117#554—611no—
118#501—612no—
119#500—611no—
120#479—612no—
121#477—611no—
122#476—611no—
123#474—612no—
124#446D6111yescharacteristic, complemented
125#440—612no—
126C4×SD16—611no—
127C61#338511yescharacteristic, complemented, Sylow
128C2×SD16—611no—
129C4⋊Q8—611no—
130C4⋊Q8—612no—
131C4⋊Q8—611no—
132C4⋊Q8—1221no—
133C4⋊Q8—1222no—
134#125—612no—
135C22⋊Q8—1221no—
136C22⋊Q8—1222no—
137C4×Q8—611no—
138C4×Q8—612no—
139C4×Q8—1221no—
140C4×Q8C2×D6111yescharacteristic
141C4×D4—611no—
142C4×D4—612no—
143C2×C4⋊C4—1221no—
144#107—612no—
145#107—612no—
146#107—612no—
147#106—611no—
148#106—612no—
149C4⋊C8C2×D6112yes—
150C4⋊C8C2×D6111yescharacteristic
151#103—611no—
152#103—612no—
153#102—611no—
154#102—612no—
155#97C2×D6112yes—
156C4×C8C2×D6111yescharacteristic
157C2×Q8—611no—
158C2×Q8—1221no—
159C2×Q8—1221no—
160C2×Q8—1222no—
161C2×Q8D24411yescharacteristic
162C2×D4—611no—
163C22×C4—1222no—
164C22×C4—1221no—
165SD16—614no—
166C2×C8C22×D6111yescharacteristic
167C2×C8C22×D6112yes—
168C2×C8C22×D6111yescharacteristic
169C4⋊C4—611no—
170C4⋊C4—612no—
171C4⋊C4—611no—
172C4⋊C4—612no—
173C4⋊C4—1222no—
174C4⋊C4—1221no—
175C4⋊C4—1221no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1221no—
180C4⋊C4D24411yescharacteristic
181C4⋊C4D24412yes—
182C22⋊C4—1221no—
183C22⋊C4—1222no—
184C42—1222no—
185C42—1221no—
186C42C22×D6111yescharacteristic
187C42C22×D6112yes—
188C23—1221no—
189Q8—22no—
190Q8—612no—
191Q8—1221no—
192Q8—4882no—
193Q8—4881no—
194Q8—4881no—
195D4—612no—
196D4—1221no—
197C2×C4—1221no—
198C2×C4—1222no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1222no—
202C2×C4—4882no—
203C2×C4—2442no—
204C2×C4C2×D24412yes—
205C2×C4C2×D24411yescharacteristic
206C2×C4C2×D24412yes—
207C2×C4C2×D24411yescharacteristic
208C2×C4C23×D6111yescharacteristic
209C8—21no—
210C8—22no—
211C8Q8×D6112yes—
212C22—1222no—
213C22—2441no—
214C22—2441no—
215C22C22×D24411yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—1222no—
220C4—2441no—
221C4—2442no—
222C4—2441no—
223C4—2442no—
224C4#1451981012yes—
225C4C2×Q8×D6111yescharacteristic
226C4#1451982411yescharacteristic
227C2—2442no—
228C2Q8×D24411yescharacteristic
229C2C2×#1451981011yescharacteristic
230C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3385
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
1. Q8×Dic122C2semidirect
3. #16840171C2semidirect
4. #16840167C2semidirect
5. #16840070C2semidirect
6. #16840058C2semidirect
11. C61×#446C2semidirect
71. #11758190Q8semidirect
124. #446D61semidirect
127. C61#3385semidirect