Finite Group Databasebeta

← #21446308

Subgroups — #21446308

Order 7808.

346 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 93 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#16840237C211yesmaximal, characteristic, complemented
2#16839779C211yesmaximal, characteristic, complemented
3#16839767C211yesmaximal, characteristic, complemented
4#16839736C211yesmaximal, characteristic, complemented
5#16839533C211yesmaximal, characteristic, complemented
6#16839519C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9D4×Dic61—22no—
10D4×Dic61—22no—
11#14519736C2211yescharacteristic
12#14519736C2211yescharacteristic
13#14519736C2211yescharacteristic
14C2×C22⋊Dic61—22no—
15#14519704—22no—
16#14519698—22no—
17#14519692—22no—
18C2×#41×C61C2211yescharacteristic
19C22×D4×C61C2211yescharacteristic
20AGL(1,ℤ/8)×C61—22no—
21AGL(1,ℤ/8)×C61—22no—
22C2×SD16×C61C412yescomplemented
23C2×D8×C61C412yescomplemented
24C2×M16×C61C2211yescharacteristic
25C24×C61—21no—
26#41×C61—21no—
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30C2×Q8×C61C2×C411yescharacteristic, complemented
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61C2×C412yes—
36C2×D4×C61C2×C411yescharacteristic, complemented
37C2×D4×C61D412yes—
38C2×D4×C61D412yes—
39C22×C4×C61—21no—
40C22×C4×C61C2311yescharacteristic
41C22×Dic61—24no—
42SD16×C61—24no—
43D8×C61—24no—
44M16×C61—21no—
45M16×C61—21no—
46C2×C8×C61C2×C412yescomplemented
47C22⋊Dic61—24no—
48C22⋊Dic61—21no—
49C22⋊Dic61—21no—
50C22⋊Dic61D412yes—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53C4⋊Dic61—21no—
54C4×Dic61—21no—
55C4×Dic61—21no—
56C4×Dic61D412yes—
57#11758194—21no—
58#11758194—21no—
59C2×#92418—21no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—21no—
64C23×C61—82no—
65C23×C61C2×D411yescharacteristic
66Q8×C61—21no—
67Q8×C61—21no—
68D4×C61—21no—
69D4×C61—22no—
70D4×C61—21no—
71D4×C61—22no—
72D4×C61—22no—
73D4×C61—41no—
74D4×C61—41no—
75D4×C61C22⋊C414yes—
76C2×C4×C61—21no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C22×C411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—41no—
88C2×Dic61—84no—
89C8×C61—22no—
90#92418—41no—
91C22×C61—24no—
92C22×C61—41no—
93C22×C61—44no—
94C22×C61—41no—
95C22×C61—82no—
96C22×C61—82no—
97C22×C61—81no—
98C22×C61C4×D411yescharacteristic
99C22×C61#12011yescharacteristic
100C22×C61#12111yescharacteristic
101C4×C61—41no—
102C4×C61C2×C22⋊C411yescharacteristic
103C4×C61C4×D411yescharacteristic
104C4×C61#12111yescharacteristic
105C4×C61#12311yescharacteristic
106Dic61—42no—
107Dic61—42no—
108Dic61—81no—
109#1904—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—21no—
112C2×C61—21no—
113C2×C61—44no—
114C2×C61—81no—
115C2×C61#38611yescharacteristic
116C2×AGL(1,ℤ/8)D6111yescharacteristic
117#518—611no—
118#421—611no—
119#418—611no—
120#410—611no—
121#344—611no—
122H(3,ℤ/4)—611no—
123C61#190411yescharacteristic, complemented, Sylow
124C2×#41C2×D6111yescharacteristic
125C22×D4C2×D6111yescharacteristic
126AGL(1,ℤ/8)—22no—
127AGL(1,ℤ/8)—22no—
128C2×SD16Dic6112yescomplemented
129C2×D8Dic6112yescomplemented
130C2×M16—611no—
131C2×M16C2×D6111yescharacteristic
132C4×D4—1222no—
133C4×D4—1222no—
134#117—611no—
135#117—611no—
136#117—611no—
137C2×C22⋊C4—1222no—
138#104—1222no—
139#102—1222no—
140#99—1222no—
141C24—21no—
142#41—21no—
143#41—21no—
144#41—21no—
145#41—21no—
146C2×Q8C2×Dic6111yescharacteristic, complemented
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4C2×Dic6112yes—
152C2×D4C2×Dic6111yescharacteristic, complemented
153C2×D4C22⋊D6112yes—
154C2×D4C22⋊D6112yes—
155C22×C4—21no—
156C22×C4—1224no—
157C22×C4C22×D6111yescharacteristic
158SD16—24no—
159D8—24no—
160M16—21no—
161M16—21no—
162M16—1221no—
163M16—1221no—
164C2×C8—1221no—
165C2×C8C2×Dic6112yescomplemented
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C22⋊C4—612no—
170C22⋊C4—1224no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C42—612no—
174C42—1221no—
175C42—1221no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—21no—
180C23—82no—
181C23D4×D6111yescharacteristic
182Q8—21no—
183Q8—21no—
184D4—21no—
185D4—22no—
186D4—21no—
187D4—22no—
188D4—22no—
189D4—41no—
190D4—41no—
191D4C22⋊Dic6114yes—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—4884no—
198C2×C4—2441no—
199C2×C4D4×D6111yescharacteristic
200C2×C4#1175822411yescharacteristic
201C2×C4#1175822411yescharacteristic
202C2×C4C22×Dic6111yescharacteristic
203C2×C4C2×C22⋊D6111yescharacteristic
204C2×C4C2×C22⋊D6111yescharacteristic
205C8—22no—
206C8—2441no—
207C22—24no—
208C22—41no—
209C22—44no—
210C22—41no—
211C22—82no—
212C22—82no—
213C22—81no—
214C22D4×Dic6111yescharacteristic
215C22#1451974511yescharacteristic
216C22#1451974911yescharacteristic
217C4—41no—
218C4—4881no—
219C4—2442no—
220C4—2442no—
221C4C2×C22⋊Dic6111yescharacteristic
222C4D4×Dic6111yescharacteristic
223C4#1451974911yescharacteristic
224C4#1451975811yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—44no—
229C2—81no—
230C2#1683964211yescharacteristic
subgroupG/H
centerC2#16839642
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×AGL(1,ℤ/8)×C61C2
socleC2×C61#386
hypercenterC2×AGL(1,ℤ/8)D61
hypocenterC61#1904
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #16840237C2semidirect
2. #16839779C2semidirect
3. #16839767C2semidirect
4. #16839736C2semidirect
5. #16839533C2semidirect
6. #16839519C2semidirect
22. C2×SD16×C61C4semidirect
23. C2×D8×C61C4semidirect
30. C2×Q8×C61C2×C4semidirect
36. C2×D4×C61C2×C4semidirect
46. C2×C8×C61C2×C4semidirect
123. C61#1904semidirect
128. C2×SD16Dic61semidirect
129. C2×D8Dic61semidirect
146. C2×Q8C2×Dic61semidirect
152. C2×D4C2×Dic61semidirect
165. C2×C8C2×Dic61semidirect