Finite Group Databasebeta

← #21446321

Subgroups — #21446321

Order 7808.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840562C211yesmaximal, characteristic
2#16840230C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic, complemented
4C2×#14519703C211yesmaximal, characteristic, complemented
5#16839735C211yesmaximal, characteristic, complemented
6#16839523C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758222C2211yescharacteristic
10#14519810—21no—
11#14519810C412yescomplemented
12#14519805—21no—
13#14519805C412yescomplemented
14#14519799—22no—
15#14519742—21no—
16#14519739—21no—
17#14519737—22no—
18#14519736C2211yescharacteristic
19#14519734—21no—
20C2×C4×Dic61C2211yescharacteristic
21C42×D61—21no—
22#14519703—22no—
23#14519703—21no—
24#14519703—21no—
25#14519691—22no—
26C2×M16×C61C2211yescharacteristic
27C2×M16×C61C2211yescharacteristic
28#117×C61C2211yescharacteristic
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C22×Dic61—21no—
33#11758222—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38#11758222—21no—
39#11758222C2×C412yes—
40#11758222D412yes—
41C2×D244C2×C411yescharacteristic, complemented
42C2×D244D411yescharacteristic
43C2×C4×D61—21no—
44C2×C4×D61—22no—
45C2×C4×D61—21no—
46C2×Dic122C2×C411yescharacteristic, complemented
47C2×Dic122D411yescharacteristic
48M16×C61—21no—
49M16×C61—21no—
50M16×C61—21no—
51M16×C61C2×C412yescomplemented
52C2×C8×C61—21no—
53C2×C8×C61—21no—
54C4⋊C4×C61—21no—
55C22⋊C4×C61D412yes—
56C42×C61—21no—
57C22⋊Dic61—21no—
58#11758198—22no—
59C4⋊Dic61—21no—
60#11758196—22no—
61C4×Dic61—22no—
62C4×Dic61—21no—
63C4×Dic61—21no—
64C4×Dic61D411yescharacteristic
65C4×Dic61D411yescharacteristic
66Dic244—22no—
67D488—22no—
68#11758190—22no—
69#11758190—22no—
70C23×C61C2×D411yescharacteristic
71C22×D61—21no—
72C22×D61—21no—
73C2×C4×C61—22no—
74C2×C4×C61C22×C411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C22⋊D61—22no—
81C22⋊D61—22no—
82C22⋊D61—41no—
83C22⋊D61—41no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—42no—
89C2×Dic61—41no—
90D244—21no—
91D244—21no—
92D244—21no—
93D244C22⋊C412yes—
94C4×D61—22no—
95C4×D61—22no—
96C4×D61—44no—
97C4×D61—41no—
98C4×D61—41no—
99Dic122—21no—
100Dic122—21no—
101Dic122—21no—
102Dic122C22⋊C412yes—
103C8×C61—22no—
104C8×C61—41no—
105C22×C61—41no—
106C22×C61C4×D411yescharacteristic
107C22×C61#12011yescharacteristic
108C22×C61#12111yescharacteristic
109C2×D61—22no—
110C2×D61—42no—
111C2×D61—41no—
112C2×D61—81no—
113C4×C61—42no—
114C4×C61C2×C22⋊C411yescharacteristic
115C4×C61C4×D411yescharacteristic
116C4×C61#12111yescharacteristic
117C4×C61#12311yescharacteristic
118Dic61—22no—
119Dic61—22no—
120Dic61—41no—
121Dic61—41no—
122Dic61—81no—
123#1906—611nomaximal, Sylow
124C2×C61—21no—
125C2×C61—21no—
126C2×C61—21no—
127C2×C61#38611yescharacteristic
128D61—42no—
129D61—81no—
130#575—611no—
131C4×#41—611no—
132#421—611no—
133C2×#104—611no—
134#410—611no—
135#344D6111yescharacteristic, complemented
136#339—611no—
137C61#190611yescharacteristic, complemented, Sylow
138C2×#41—611no—
139C2×#41—611no—
140#137—612no—
141#137—1221no—
142AGL(1,ℤ/8)—612no—
143AGL(1,ℤ/8)—1221no—
144#135—1222no—
145C2×M16C2×D6111yescharacteristic
146C2×M16C2×D6111yescharacteristic
147C4×Q8—1221no—
148C4×D4—1221no—
149C4×D4—1222no—
150#117—611no—
151#117—1221no—
152#117C2×D6111yescharacteristic
153C2×C42—611no—
154C2×C42—1221no—
155#104—1221no—
156#104—1221no—
157#104—1222no—
158#99—1222no—
159#41—612no—
160#41—612no—
161#41—1221no—
162#41—1221no—
163#41—1221no—
164#41—1221no—
165#41—1221no—
166#41—1221no—
167C2×Q8—611no—
168C2×Q8—611no—
169C2×D4—611no—
170C2×D4—611no—
171C2×D4—1221no—
172C2×D4—1221no—
173C22×C4—1222no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178Q16—1222no—
179SD16—1222no—
180SD16—1222no—
181D8—1222no—
182M16—21no—
183M16—21no—
184M16—21no—
185M16C4×D6112yescomplemented
186C2×C8—21no—
187C2×C8—21no—
188C4⋊C4—21no—
189C4⋊C4—1222no—
190C4⋊C4—1221no—
191C22⋊C4—1222no—
192C22⋊C4—1221no—
193C22⋊C4D24412yes—
194C42—21no—
195C42—611no—
196C42—611no—
197C42—1222no—
198C42—1221no—
199C42—1221no—
200C23—1221no—
201C23—1221no—
202C23C2×D24411yescharacteristic
203Q8—612no—
204Q8—1221no—
205Q8—1221no—
206Q8—1221no—
207D4—612no—
208D4—1222no—
209D4—1222no—
210D4—1221no—
211D4—1221no—
212D4—1221no—
213D4—2441no—
214D4—2441no—
215C2×C4—22no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—2444no—
223C2×C4—2442no—
224C2×C4—2441no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4C2×C4×D6111yescharacteristic
228C2×C4#1175822211yescharacteristic
229C2×C4D4×D6111yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4#1175822611yescharacteristic
233C8—22no—
234C8—41no—
235C22—41no—
236C22—1222no—
237C22—4881no—
238C22—2442no—
239C22—2441no—
240C22C4×D24411yescharacteristic
241C22#1451974711yescharacteristic
242C22#1451975211yescharacteristic
243C4—42no—
244C4—1222no—
245C4—1222no—
246C4—4881no—
247C4—2441no—
248C4—2441no—
249C4C22⋊C4×D6111yescharacteristic
250C4#1451973911yescharacteristic
251C4#1451975011yescharacteristic
252C4#1451976211yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—4881no—
257C2—2442no—
258C2#1683964011yescharacteristic
subgroupG/H
centerC4#14519750
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61#386
hypercenter#344D61
hypocenterC61#1906
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #16840230C2semidirect
3. #16839778C2semidirect
4. C2×#14519703C2semidirect
5. #16839735C2semidirect
6. #16839523C2semidirect
7. C61×#344C2semidirect
11. #14519810C4semidirect
13. #14519805C4semidirect
41. C2×D244C2×C4semidirect
46. C2×Dic122C2×C4semidirect
51. M16×C61C2×C4semidirect
135. #344D61semidirect
137. C61#1906semidirect
185. M16C4×D61semidirect