Finite Group Databasebeta

← #21461870

Subgroups — #21461870

Order 7808.

340 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840840C211yesmaximal, characteristic, complemented
2#16840749C211yesmaximal, characteristic, complemented
3C2×#14519837C212yesmaximal, complemented
4#16840643C212yesmaximal, complemented
5#16840327C211yesmaximal, characteristic
6#14519864—24no—
7D61⋊M16—21no—
8C2×#11758217—21no—
9C2×#11758217C2212yes—
10C2×#11758217C2212yes—
11#14519838—21no—
12#14519837—21no—
13#14519837—24no—
14C2×#11758224C2211yescharacteristic
15C22×C22⋊D61C2211yescharacteristic
16#14519773—21no—
17#14519763—21no—
18#14519750—21no—
19#14519749—21no—
20#14519747C411yescharacteristic
21#14519746C411yescharacteristic
22#14519745C411yescharacteristic
23#14519733C2211yescharacteristic
24#120×C61C411yescharacteristic
25C24×C61C2×C411yescharacteristic
26C23×D61C2×C411yescharacteristic
27C2×D4×C61—21no—
28C2×D4×C61C2×C411yescharacteristic
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C2×C22⋊D61—22no—
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—22no—
35C2×C22⋊D61C2×C411yescharacteristic
36C2×C22⋊D61D411yescharacteristic
37C22×Dic61D411yescharacteristic
38C22×Dic61C2311yescharacteristic
39#11758224—22no—
40#11758224—22no—
41C2×D244—21no—
42C2×C4×D61D411yescharacteristic
43C2×Dic122D411yescharacteristic
44#11758217—22no—
45#11758217—22no—
46#11758217—22no—
47#11758217—22no—
48#11758217D414yescomplemented
49C2×#92420—22no—
50C2×#92420—22no—
51C2×#92420—22no—
52#11758213—22no—
53D61⋊C8—22no—
54C22⋊C4×C61—21no—
55C22⋊C4×C61C2×C411yescharacteristic
56C22⋊Dic61—21no—
57C22⋊Dic61C2×C411yescharacteristic
58#11758198—21no—
59#11758198—21no—
60#11758196—21no—
61C4×Dic61—21no—
62C23×C61—21no—
63C23×C61—22no—
64C23×C61—81no—
65C23×C61C22⋊C411yescharacteristic
66C23×C61C22×C411yescharacteristic
67C22×D61—21no—
68C22×D61—22no—
69C22×D61—81no—
70C22×D61C22⋊C411yescharacteristic
71D4×C61—22no—
72D4×C61—81no—
73C2×C4×C61—21no—
74C2×C4×C61C22⋊C411yescharacteristic
75C22⋊D61—22no—
76C22⋊D61—22no—
77C22⋊D61—41no—
78C22⋊D61—42no—
79C22⋊D61—41no—
80C22⋊D61—81no—
81C22⋊D61—81no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61C22⋊C411yescharacteristic
86C2×Dic61C2×D412yes—
87C2×Dic61C2×D411yescharacteristic
88C2×Dic61C2×D411yescharacteristic
89C2×Dic61#4112yes—
90D244—81no—
91C4×D61—21no—
92C4×D61—21no—
93Dic122—22no—
94#92420—24no—
95#92420—42no—
96C22×C61—21no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—82no—
103C22×C61C2×C22⋊C411yescharacteristic
104C22×C61C4×D412yes—
105C2×D61—21no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—82no—
111C4×C61—21no—
112C4×C61—41no—
113Dic61—21no—
114Dic61—41no—
115Dic61#12011yescharacteristic
116Dic61#12112yes—
117Dic61#12311yescharacteristic
118#1914—611nomaximal, Sylow
119C2×C61—21no—
120C2×C61—22no—
121C2×C61—41no—
122C2×C61—81no—
123C2×C61#38611yescharacteristic
124D61—41no—
125D61—81no—
126#568—611no—
127#535—611no—
128#413—611no—
129C2×#100—612no—
130#344—612no—
131C61#191411yescharacteristic, complemented, Sylow
132C2×#41—611no—
133C22×D4—611no—
134#131—1224no—
135C2×M16—612no—
136C2×M16—612no—
137C2×M16—1221no—
138C2×M16—1221no—
139#127—1221no—
140#124—1221no—
141#121—1221no—
142#121—1221no—
143#120—611no—
144#120—611no—
145#120—611no—
146#120#692311yescharacteristic
147#117—611no—
148#101—1221no—
149#100—1224no—
150#100—1221no—
151C24—611no—
152C24C2×#692311yescharacteristic
153#41—1222no—
154#41—1222no—
155C2×Q8—611no—
156C2×D4—21no—
157C2×D4—611no—
158C2×D4—611no—
159C2×D4—1221no—
160C2×D4—1222no—
161C2×D4—1221no—
162C2×D4—1221no—
163C2×D4—1222no—
164C2×D4—1221no—
165C2×D4—1221no—
166C2×D4C2×#692311yescharacteristic
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170M16—614no—
171M16—1222no—
172M16—1222no—
173M16—1222no—
174M16—1222no—
175M16—1222no—
176C2×C8—1222no—
177C2×C8—1222no—
178C2×C8—1222no—
179C2×C8—1222no—
180C4⋊C4—1221no—
181C22⋊C4—21no—
182C22⋊C4—611no—
183C22⋊C4—1221no—
184C22⋊C4—1221no—
185C22⋊C4—1221no—
186C22⋊C4C2×#692311yescharacteristic
187C42—1221no—
188C23—21no—
189C23—22no—
190C23—81no—
191C23—611no—
192C23—1222no—
193C23—1221no—
194C23—4881no—
195C23C22⋊#692311yescharacteristic
196C23C22×#692311yescharacteristic
197Q8—1222no—
198D4—22no—
199D4—81no—
200D4—1222no—
201D4—1222no—
202D4—4881no—
203D4—4881no—
204D4—4881no—
205D4—2441no—
206D4—2442no—
207D4—2441no—
208C2×C4—21no—
209C2×C4—611no—
210C2×C4—611no—
211C2×C4—612no—
212C2×C4—612no—
213C2×C4—611no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4C22⋊#692311yescharacteristic
220C8—1224no—
221C8—2442no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—82no—
229C22—1221no—
230C22—4882no—
231C22—2441no—
232C22—2441no—
233C22—2441no—
234C22—2441no—
235C22C2×C22⋊#692311yescharacteristic
236C22D4×#692312yes—
237C4—21no—
238C4—41no—
239C4—611no—
240C4—612no—
241C4—611no—
242C4—1221no—
243C4—2441no—
244C2—21no—
245C2—22no—
246C2—41no—
247C2—81no—
248C2—4881no—
249C2—2441no—
250C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#120×C61C4
socleC2×C61#386
hypercenter#120#6923
hypocenterC61#1914
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #16840840C2semidirect
2. #16840749C2semidirect
3. C2×#14519837C2semidirect
4. #16840643C2semidirect
48. #11758217D4semidirect
131. C61#1914semidirect