Finite Group Databasebeta

← #21461971

Subgroups — #21461971

Order 7808.

300 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 70 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×#14519847C211yesmaximal, characteristic, complemented
2C2×#14519842C211yesmaximal, characteristic, complemented
3C2×#14519841C211yesmaximal, characteristic, complemented
4#16840737C211yesmaximal, characteristic, complemented
5#16840736C211yesmaximal, characteristic, complemented
6C2×C8×#6923C211yesmaximal, characteristic, complemented
7C2×#14519798C211yesmaximal, characteristic
8C2×#11758213C2211yescharacteristic
9C2×#11758213C2211yescharacteristic
10C2×D61⋊C8C2211yescharacteristic
11C2×C4×#6923C2211yescharacteristic
12#14519847—22no—
13#14519842—22no—
14#14519841—22no—
15#14519834—22no—
16C22⋊#92420—22no—
17C8×#6923—22no—
18C2×#11758226C2211yescharacteristic
19C2×#11758224C2211yescharacteristic
20#14519798—22no—
21#14519798—22no—
22C2×#11758202C411yescharacteristic, complemented
23C2×#11758190C411yescharacteristic, complemented
24C2×#11758199C411yescharacteristic, complemented
25C2×C8×D61C2211yescharacteristic
26C2×SD16×C61C411yescharacteristic, complemented
27C22×#6923—21no—
28C2×Q8×C61C2×C411yescharacteristic
29C2×D4×C61C2×C411yescharacteristic
30C2×C22⋊D61—21no—
31C22×Dic61—21no—
32#11758226—21no—
33#11758226—21no—
34#11758226—21no—
35#11758226—21no—
36#11758224—21no—
37#11758224—21no—
38#11758224—21no—
39#11758224—21no—
40C2×D244—21no—
41C2×D244C2×C411yescharacteristic
42C2×C4×D61—21no—
43C2×C4×D61C2311yescharacteristic
44C2×Dic122C2×C411yescharacteristic
45C2×#92420—21no—
46C2×#92420—21no—
47C2×#92420D412yes—
48C4×#6923—21no—
49C4×#6923D412yes—
50#11758213—21no—
51#11758213—21no—
52#11758213—21no—
53#11758213—21no—
54D61⋊C8—21no—
55D61⋊C8—21no—
56SD16×C61—22no—
57C2×C8×C61C2×C411yescharacteristic
58#11758202—22no—
59#11758199—22no—
60C2×#92418C2×C411yescharacteristic
61#11758190—22no—
62C8×D61D412yes—
63C8×D61D412yes—
64C23×C61—21no—
65C22×D61—21no—
66C22×D61#4111yescharacteristic
67C2×#6923—24no—
68C2×#6923—22no—
69Q8×C61—21no—
70Q8×C61—21no—
71D4×C61—21no—
72D4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61C22×C411yescharacteristic
75C22⋊D61—41no—
76C22⋊D61—41no—
77C2×Dic61—21no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61C2×D411yescharacteristic
81D244—21no—
82D244—21no—
83D244—41no—
84D244—41no—
85C4×D61—41no—
86C4×D61—41no—
87C4×D61C2×D411yescharacteristic
88C4×D61C2×D411yescharacteristic
89C4×D61C2×D411yescharacteristic
90C4×D61#4111yescharacteristic
91Dic122—21no—
92Dic122—21no—
93#92420—22no—
94#92420—41no—
95#92420—41no—
96C8×C61C22⋊C412yes—
97#92418C22⋊C412yes—
98C22×C61—41no—
99C22×C61—42no—
100C22×C61C4×D411yescharacteristic
101C2×D61—22no—
102C2×D61—41no—
103C2×D61—42no—
104C2×D61#12111yescharacteristic
105C2×D61#12411yescharacteristic
106#6923—24no—
107C4×C61—41no—
108C4×C61C2×C22⋊C411yescharacteristic
109C4×C61C4×D411yescharacteristic
110Dic61—41no—
111Dic61#12111yescharacteristic
112Dic61#12711yescharacteristic
113#1974—611nomaximal, Sylow
114C2×C61—81no—
115C2×C61#39011yescharacteristic
116C2×C61#44312yes—
117D61—21no—
118D61—21no—
119D61—81no—
120C2×#135—611no—
121C2×#108—611no—
122C2×#104—611no—
123C2×#104—611no—
124#408—611no—
125#408—611no—
126C2×C4×C8—611no—
127C61#197411yescharacteristic, complemented, Sylow
128C2×#41—611no—
129C2×#41—611no—
130#135—1222no—
131#135—1222no—
132C2×Q16—611no—
133C2×SD16—611no—
134C2×SD16#692311yescharacteristic, complemented
135C2×D8—611no—
136C2×M16—611no—
137C2×M16—611no—
138C22×C8—611no—
139C22×C8—611no—
140C2×C42—611no—
141#108—1222no—
142#104—1222no—
143#104—1222no—
144C22⋊C8—1222no—
145C22⋊C8—1222no—
146C4×C8—1222no—
147#41—1221no—
148#41—1221no—
149#41—1221no—
150#41—1221no—
151#41—1221no—
152#41—1221no—
153#41—1221no—
154#41—1221no—
155C2×Q8—611no—
156C2×Q8C2×#692311yescharacteristic
157C2×D4—611no—
158C2×D4—1221no—
159C2×D4—1221no—
160C2×D4C2×#692311yescharacteristic
161C22×C4—611no—
162C22×C4—1221no—
163C22×C4—1221no—
164C22×C4—1221no—
165Q16—1222no—
166SD16—22no—
167SD16—1222no—
168D8—1222no—
169M16—1221no—
170M16—1221no—
171M16—1221no—
172M16—1221no—
173C2×C8—611no—
174C2×C8—612no—
175C2×C8—612no—
176C2×C8—612no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—1221no—
180C2×C8—1221no—
181C2×C8C2×#692311yescharacteristic
182C42—612no—
183C42—1221no—
184C23—21no—
185C23—611no—
186C23—1221no—
187Q8—21no—
188Q8—21no—
189Q8—1221no—
190Q8—1221no—
191D4—21no—
192D4—21no—
193D4—1221no—
194D4—1221no—
195D4—2441no—
196D4—2441no—
197D4—2441no—
198D4—2441no—
199C2×C4—21no—
200C2×C4—611no—
201C2×C4—611no—
202C2×C4—611no—
203C2×C4—611no—
204C2×C4—611no—
205C2×C4—1222no—
206C2×C4—1224no—
207C2×C4—1221no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4C22×#692311yescharacteristic
213C8—612no—
214C8—1222no—
215C8—2441no—
216C8—2441no—
217C8C22⋊#692312yes—
218C22—41no—
219C22—42no—
220C22—611no—
221C22—611no—
222C22—1222no—
223C22—2441no—
224C22—2442no—
225C22D4×#692311yescharacteristic
226C4—41no—
227C4—611no—
228C4—611no—
229C4—1224no—
230C4—2441no—
231C4C2×C22⋊#692311yescharacteristic
232C4D4×#692311yescharacteristic
233C2—81no—
234C2—1221no—
235C2—1221no—
236C2—4881no—
237C2#1684071411yescharacteristic
238C2#1684080512yes—
subgroupG/H
centerC22D4×#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×SD16×C61C4
socleC22×C61C4×D4
hypercenterC2×SD16#6923
hypocenterC61#1974
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14519847C2semidirect
2. C2×#14519842C2semidirect
3. C2×#14519841C2semidirect
4. #16840737C2semidirect
5. #16840736C2semidirect
6. C2×C8×#6923C2semidirect
22. C2×#11758202C4semidirect
23. C2×#11758190C4semidirect
24. C2×#11758199C4semidirect
26. C2×SD16×C61C4semidirect
127. C61#1974semidirect
134. C2×SD16#6923semidirect