Finite Group Databasebeta

← #21446331

Subgroups — #21446331

Order 7808.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14519808C211yesmaximal, characteristic
2C2×#14519785C211yesmaximal, characteristic
3#16839764C211yesmaximal, characteristic
4C2×#14519701C211yesmaximal, characteristic, complemented
5#16839530C211yesmaximal, characteristic, complemented
6#16839526C211yesmaximal, characteristic, complemented
7C2×#101×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—22no—
10#14519808C414yescomplemented
11C2×#11758202—21no—
12C2×#11758201—21no—
13#14519785—22no—
14#14519785—22no—
15C2×#11758194C2211yescharacteristic
16C2×#11758189—21no—
17C22×#92418C2211yescharacteristic
18C2×C8×D61—21no—
19C2×C4⋊Dic61C2211yescharacteristic
20#14519702—21no—
21#14519701—21no—
22#14519701—21no—
23#14519699—21no—
24C22×Q8×C61C2211yescharacteristic
25C2×M16×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27#101×C61—22no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61C2×C412yes—
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—21no—
37C22×Dic61—21no—
38#11758222—21no—
39#11758222—21no—
40#11758222C2×C412yes—
41#11758222D412yes—
42C2×D244D411yescharacteristic
43C2×C4×D61—21no—
44C2×Dic122D411yescharacteristic
45M16×C61—21no—
46M16×C61—21no—
47M16×C61—21no—
48M16×C61D412yes—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51#11758202—24no—
52#11758201—24no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55#11758194—21no—
56#11758194C2×C412yes—
57C2×#92418—21no—
58C2×#92418—21no—
59C2×#92418—21no—
60C2×#92418D411yescharacteristic
61C2×#92418D411yescharacteristic
62#11758189—24no—
63C8×D61—24no—
64C23×C61#4111yescharacteristic
65C22×D61—21no—
66Q8×C61—22no—
67Q8×C61—22no—
68Q8×C61—41no—
69Q8×C61—41no—
70C2×C4×C61—22no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61C22×C411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C22⋊D61—22no—
80C22⋊D61—22no—
81C2×Dic61—21no—
82C2×Dic61—41no—
83C2×Dic61—81no—
84D244—21no—
85D244C22⋊C412yes—
86C4×D61—22no—
87C4×D61—22no—
88Dic122—21no—
89Dic122C22⋊C412yes—
90C8×C61—22no—
91C8×C61—41no—
92#92418—22no—
93#92418—21no—
94#92418—21no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61C4×D411yescharacteristic
98C22×C61#12111yescharacteristic
99C22×C61#12311yescharacteristic
100C2×D61—22no—
101C2×D61—41no—
102C2×D61—41no—
103C4×C61—42no—
104C4×C61C2×C22⋊C411yescharacteristic
105C4×C61C4×D411yescharacteristic
106C4×C61#12011yescharacteristic
107C4×C61#12111yescharacteristic
108Dic61—22no—
109Dic61—81no—
110#1908—611nomaximal, Sylow
111C2×C61—21no—
112C2×C61—21no—
113C2×C61#38611yescharacteristic
114C2×C61#47111yescharacteristic
115C2×C61#47311yescharacteristic
116D61—42no—
117C2×#137—611no—
118C2×#131—611no—
119#417—611no—
120C2×#103—611no—
121C2×#101D6111yescharacteristic, complemented
122#343—611no—
123#341—611no—
124C61#190811yescharacteristic, complemented, Sylow
125C2×#41—611no—
126C22×Q8C2×D6111yescharacteristic
127#137—614no—
128#137—1222no—
129C2×Q16—1221no—
130C2×SD16—1221no—
131#131—1222no—
132#131—1222no—
133C2×M16—611no—
134C2×M16—1221no—
135C2×M16C2×D6111yescharacteristic
136C2×M16C2×D6111yescharacteristic
137C22×C8—611no—
138C22×C8—1221no—
139C2×C4⋊C4—611no—
140#103—1221no—
141#103—1221no—
142#103—1221no—
143#102—1221no—
144#101—22no—
145#41—612no—
146#41—612no—
147#41—1221no—
148#41—1221no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—611no—
155C2×Q8C4×D6112yes—
156C2×D4—611no—
157C2×D4—1221no—
158C22×C4—21no—
159C22×C4—1221no—
160C22×C4—1221no—
161C22×C4C22×D6111yescharacteristic
162Q16—1224no—
163SD16—1224no—
164M16—21no—
165M16—21no—
166M16—21no—
167M16—612no—
168M16—1224no—
169M16—1221no—
170M16C22⋊D6112yes—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—611no—
174C2×C8—611no—
175C2×C8—1224no—
176C2×C8—1221no—
177C2×C8—1221no—
178C2×C8—1221no—
179C4⋊C4—1221no—
180C4⋊C4—1221no—
181C23—1221no—
182C23#1175822211yescharacteristic
183Q8—22no—
184Q8—22no—
185Q8—41no—
186Q8—41no—
187Q8—612no—
188Q8—1221no—
189D4—612no—
190D4—1222no—
191D4—1222no—
192D4—1221no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—1221no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—4881no—
200C2×C4—2441no—
201C2×C4C2×C4×D6111yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C2×C4D4×D6111yescharacteristic
204C2×C4D4×D6111yescharacteristic
205C2×C4#1175822411yescharacteristic
206C2×C4C2×C22⋊D6111yescharacteristic
207C8—22no—
208C8—41no—
209C8—1222no—
210C8—1221no—
211C8—1221no—
212C22—21no—
213C22—21no—
214C22—1222no—
215C22—2441no—
216C22—2441no—
217C22C4×C22⋊D6111yescharacteristic
218C22#1451975011yescharacteristic
219C22#1451975911yescharacteristic
220C4—42no—
221C4—1222no—
222C4—4881no—
223C4C22⋊C4×D6111yescharacteristic
224C4#1451973711yescharacteristic
225C4#1451974511yescharacteristic
226C4#1451974811yescharacteristic
227C2—21no—
228C2—21no—
229C2—2442no—
230C2#1683963811yescharacteristic
231C2#1684002811yescharacteristic
232C2#1684003611yescharacteristic
subgroupG/H
centerC22#14519750
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61#121
hypercenterC2×#101D61
hypocenterC61#1908
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
4. C2×#14519701C2semidirect
5. #16839530C2semidirect
6. #16839526C2semidirect
7. C2×#101×C61C2semidirect
10. #14519808C4semidirect
121. C2×#101D61semidirect
124. C61#1908semidirect