Finite Group Databasebeta

← #21458132

Subgroups — #21458132

Order 7808.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840473C211yesmaximal, characteristic, complemented
2#16840416C211yesmaximal, characteristic
3#16840114C211yesmaximal, characteristic, complemented
4#16840094C212yesmaximal, complemented
5#16840021C212yesmaximal, complemented
6#16839973C211yesmaximal, characteristic, complemented
7#16839925C212yesmaximal, complemented
8C4×#11758200C211yesmaximal, characteristic, complemented
9#16839839C211yesmaximal, characteristic, complemented
10#16839760C212yesmaximal, complemented
11C61×#476C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yes—
13C2×Dic244C2212yes—
14C2×#11758200C2211yescharacteristic
15C2×#11758189C2212yes—
16#14519777C2211yescharacteristic
17#14519768—21no—
18#14519761—22no—
19#14519757C2212yes—
20#14519757C2212yes—
21#14519753—22no—
22#14519751—21no—
23C4×Dic122C2211yescharacteristic
24C4×D244C2211yescharacteristic
25#14519739—21no—
26C2×C4⋊Dic61—21no—
27C4⋊C4×D61C2212yes—
28#14519708C2211yescharacteristic
29#14519702C2212yes—
30#14519700C2212yes—
31#14519700C2211yescharacteristic
32#14519700C2212yes—
33#14519698C2211yescharacteristic
34#14519689C2212yes—
35C4×#92418C2211yescharacteristic
36C4⋊Q8×C61C2211yescharacteristic
37C4×D4×C61C2211yescharacteristic
38#106×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#102×C61C2212yes—
41C2×Q8×C61—21no—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C2×C22⋊D61—22no—
45C22×Dic61—22no—
46#11758224—24no—
47#11758224—42no—
48C2×D244D411yescharacteristic
49C2×C4×D61—22no—
50C2×C4×D61C2312yes—
51C2×Dic122C2312yes—
52C2×Dic122C2311yescharacteristic
53C2×C8×C61C2312yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61C2312yes—
56C4⋊C4×C61C2311yescharacteristic
57C22⋊C4×C61—21no—
58C42×C61C2311yescharacteristic
59#11758200—22no—
60#11758198—22no—
61#11758198—22no—
62#11758198D412yes—
63C4⋊Dic61—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61—22no—
66C4⋊Dic61—22no—
67C4⋊Dic61D411yescharacteristic
68C4⋊Dic61C2311yescharacteristic
69#11758196—21no—
70#11758196—22no—
71C4×Dic61—21no—
72C2×#92418C2311yescharacteristic
73C2×#92418C2311yescharacteristic
74Dic244—42no—
75#11758189—42no—
76C23×C61—21no—
77C22×D61C2×D412yes—
78Q8×C61—81no—
79D4×C61—21no—
80D4×C61#4112yes—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—42no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C22⋊D61—44no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—44no—
92C2×Dic61C2×D412yes—
93D244—22no—
94C4×D61—22no—
95C4×D61—22no—
96C4×D61—82no—
97Dic122—21no—
98Dic122—22no—
99Dic122—21no—
100Dic122—22no—
101C8×C61—22no—
102#92418—21no—
103#92418—21no—
104C22×C61—22no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61C22×D411yescharacteristic
108C2×D61—22no—
109C2×D61—22no—
110C2×D61—22no—
111C4×C61—21no—
112C4×C61—41no—
113C4×C61—42no—
114C4×C61#13712yes—
115C4×C61C2×#4111yescharacteristic
116C4×C61H(5,𝔽2)11yescharacteristic
117Dic61—22no—
118Dic61—41no—
119Dic61—42no—
120Dic61—41no—
121#3331—611nomaximal, Sylow
122C2×C61—42no—
123C2×C61#54611yescharacteristic
124C2×C61C2×#13711yescharacteristic
125C2×C61#57711yescharacteristic
126D61—42no—
127#554—611no—
128#547—611no—
129#487—611no—
130#483—612no—
131#476D6111yescharacteristic, complemented
132#470—612no—
133#462—611no—
134#452—612no—
135C4×SD16—611no—
136#436—611no—
137#417—612no—
138C61#333111yescharacteristic, complemented, Sylow
139C2×#41—612no—
140C2×Q16—612no—
141C2×SD16—611no—
142C2×M16—612no—
143C4⋊Q8—611no—
144C4⋊Q8C2×D6111yescharacteristic
145#125—1221no—
146#123—1222no—
147C22⋊Q8—612no—
148C22⋊Q8—612no—
149C22⋊Q8—1222no—
150#121—1221no—
151C4×Q8—611no—
152C4×D4—611no—
153C4×D4—1221no—
154C4×D4C2×D6111yescharacteristic
155C2×C4⋊C4—612no—
156C2×C4⋊C4—1221no—
157#106—611no—
158#106C2×D6112yes—
159C4⋊C8C2×D6111yescharacteristic
160#103—612no—
161#103—612no—
162#103—611no—
163#103—612no—
164#102—611no—
165#102C2×D6112yes—
166C22⋊C8—612no—
167C4×C8—611no—
168#41—1224no—
169#41—2442no—
170C2×Q8—21no—
171C2×Q8—612no—
172C2×Q8—611no—
173C2×D4—611no—
174C2×D4—1222no—
175C2×D4C22×D6111yescharacteristic
176C22×C4—21no—
177C22×C4—612no—
178C22×C4—1222no—
179C22×C4—1222no—
180Q16—2442no—
181SD16—1222no—
182M16—2442no—
183C2×C8—611no—
184C2×C8—611no—
185C2×C8C22×D6112yes—
186C4⋊C4—21no—
187C4⋊C4—611no—
188C4⋊C4—611no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C4⋊C4C22×D6112yes—
196C4⋊C4C22×D6111yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—612no—
199C22⋊C4—1222no—
200C22⋊C4—1222no—
201C42—1221no—
202C42C22×D6111yescharacteristic
203C23—21no—
204C23—612no—
205Q8—81no—
206Q8—1221no—
207Q8—1222no—
208Q8—1221no—
209Q8—1222no—
210D4—21no—
211D4—1222no—
212D4—2444no—
213D4#1175822612yes—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—612no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—4882no—
224C2×C4—2444no—
225C2×C4D4×D6111yescharacteristic
226C2×C4D4×D6111yescharacteristic
227C2×C4C23×D6111yescharacteristic
228C8—22no—
229C8—1221no—
230C8—1221no—
231C22—22no—
232C22—41no—
233C22—41no—
234C22—1222no—
235C22—1222no—
236C22—1222no—
237C22C2×D4×D6111yescharacteristic
238C4—21no—
239C4—41no—
240C4—42no—
241C4—1222no—
242C4—2441no—
243C4—2442no—
244C4—2441no—
245C4#1451980612yes—
246C4C2×#1175822611yescharacteristic
247C4#1451982311yescharacteristic
248C2—42no—
249C2—2442no—
250C2#1684040311yescharacteristic
251C2C2×#1451980611yescharacteristic
252C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#476C2
socleC22×C61C22×D4
hypercenter#476D61
hypocenterC61#3331
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16840473C2semidirect
3. #16840114C2semidirect
4. #16840094C2semidirect
5. #16840021C2semidirect
6. #16839973C2semidirect
7. #16839925C2semidirect
8. C4×#11758200C2semidirect
9. #16839839C2semidirect
10. #16839760C2semidirect
11. C61×#476C2semidirect
131. #476D61semidirect
138. C61#3331semidirect