Finite Group Databasebeta

← #21447207

Subgroups — #21447207

Order 7808.

284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14519710C211yesmaximal, characteristic, complemented
2C2×C4⋊#92418C211yesmaximal, characteristic, complemented
3C2×#14519698C211yesmaximal, characteristic
4C2×#14519698C211yesmaximal, characteristic
5#16839660C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C61×#390C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13#14519710—22no—
14C4⋊#92418—22no—
15#14519698—22no—
16#14519698—22no—
17#14519684—21no—
18C22×D4×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C22⋊C4×C61—21no—
21C2×C22⋊C4×C61—21no—
22C2×C42×C61C2211yescharacteristic
23C24×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61Q812yes—
30C22×C4×C61—21no—
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C22×Dic61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C22⋊C4×C61—42no—
39C22⋊C4×C61—42no—
40C42×C61—21no—
41C42×C61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61D412yes—
46#11758196—42no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C2×#92418—21no—
51C2×#92418—21no—
52C2×#92418D412yes—
53C23×C61—22no—
54C23×C61—41no—
55C23×C61—41no—
56C23×C61—41no—
57C23×C61—41no—
58C23×C61—41no—
59C23×C61—41no—
60C23×C61C2×D411yescharacteristic
61D4×C61—22no—
62D4×C61—22no—
63D4×C61—41no—
64D4×C61—41no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61D812yes—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×Q811yescharacteristic
77C2×C4×C61#4111yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×Dic61—22no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86#92418—22no—
87#92418—41no—
88C22×C61—42no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—81no—
92C22×C61—81no—
93C22×C61—81no—
94C22×C61—81no—
95C22×C61#12111yescharacteristic
96C22×C61#12111yescharacteristic
97C22×C61C22⋊Q811yescharacteristic
98C22×C61C2×D811yescharacteristic
99C22×C61#13511yescharacteristic
100C22×C61AGL(1,ℤ/8)11yescharacteristic
101C22×C61#13711yescharacteristic
102C4×C61—22no—
103C4×C61—41no—
104C4×C61—81no—
105C4×C61#12111yescharacteristic
106C4×C61C22⋊Q811yescharacteristic
107C4×C61C22⋊Q811yescharacteristic
108C4×C61#12611yescharacteristic
109Dic61—42no—
110Dic61—81no—
111#2067—611nomaximal, Sylow
112C2×C61—82no—
113C2×C61#39611yescharacteristic
114C2×C61#45911yescharacteristic
115C2×C61#46411yescharacteristic
116C2×C61#46611yescharacteristic
117C2×C61#46811yescharacteristic
118C2×C61#47411yescharacteristic
119C2×C61#47811yescharacteristic
120C2×#107—611no—
121C2×C4⋊C8—611no—
122C2×#102—611no—
123C2×#102—611no—
124#390D6111yescharacteristic
125#389—611no—
126#340—611no—
127C61#206711yescharacteristic, complemented, Sylow
128C22×D4C2×D6111yescharacteristic
129C22×C8—611no—
130C22×C8—611no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4—1221no—
134C2×C4⋊C4C2×D6111yescharacteristic
135C2×C22⋊C4—21no—
136C2×C22⋊C4—21no—
137C2×C42C2×D6111yescharacteristic
138#107—1222no—
139C4⋊C8—1222no—
140#102—1222no—
141#102—1222no—
142#95—1221no—
143C24—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4Dic12212yes—
150C22×C4—21no—
151C22×C4—1221no—
152C22×C4—1221no—
153C22×C4C22⋊D6111yescharacteristic
154C22×C4C22⋊D6111yescharacteristic
155C22×C4C22×D6111yescharacteristic
156C2×C8—612no—
157C2×C8—1221no—
158C2×C8—1221no—
159C2×C8—1221no—
160C2×C8—1221no—
161C2×C8—1221no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—612no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4—2442no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C42—21no—
172C42—21no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23C2×C22⋊D6111yescharacteristic
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—1222no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4#1175819912yes—
200C2×C4C2×Dic12211yescharacteristic
201C2×C4#1175822211yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C2×C4D4×D6111yescharacteristic
204C2×C4#1175822411yescharacteristic
205C2×C4#1175822411yescharacteristic
206C8—1222no—
207C8—2441no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—81no—
215C22#1451974811yescharacteristic
216C22#1451974911yescharacteristic
217C22#1451975611yescharacteristic
218C22C2×#1175819911yescharacteristic
219C22#1451979711yescharacteristic
220C22#1451980311yescharacteristic
221C22#1451980711yescharacteristic
222C4—22no—
223C4—41no—
224C4—81no—
225C4—4881no—
226C4—2442no—
227C4#1451975011yescharacteristic
228C4#1451975411yescharacteristic
229C4#1451975411yescharacteristic
230C4#1451977011yescharacteristic
231C2—82no—
232C2#1683968511yescharacteristic
233C2#1683995411yescharacteristic
234C2#1683998111yescharacteristic
235C2#1683999611yescharacteristic
236C2#1684000611yescharacteristic
237C2#1684004211yescharacteristic
238C2#1684006211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#390C2
socleC23×C61C2×D4
hypercenter#390D61
hypocenterC61#2067
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14519710C2semidirect
2. C2×C4⋊#92418C2semidirect
5. #16839660C2semidirect
6. #16839524C2semidirect
127. C61#2067semidirect