Finite Group Databasebeta

← #21446301

Subgroups — #21446301

Order 7808.

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

normal subgroups only

This group has 324 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#16840529C211yesmaximal, characteristic, complemented
2#16839779C211yesmaximal, characteristic, complemented
3#16839767C211yesmaximal, characteristic, complemented
4C2×#14519694C211yesmaximal, characteristic, complemented
5#16839533C211yesmaximal, characteristic, complemented
6#16839520C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic
8#14519784—22no—
9#14519784—22no—
10C2×#11758194—22no—
11C2×#11758194C2211yescharacteristic
12C2×#11758194C2211yescharacteristic
13C2×#11758194C2211yescharacteristic
14#14519736C2211yescharacteristic
15#14519704—22no—
16#14519698—22no—
17#14519694—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×C61D412yes—
29#41×C61D412yes—
30C2×Q8×C61C2×C411yescharacteristic
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61C2×C412yes—
38C2×D4×C61C2×C411yescharacteristic
39C22×C4×C61—21no—
40C22×C4×C61C2311yescharacteristic
41SD16×C61—24no—
42D8×C61—24no—
43M16×C61—21no—
44M16×C61—21no—
45C2×C8×C61C2×C412yes—
46C22⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4×Dic61—21no—
49#11758194—24no—
50#11758194—21no—
51#11758194—21no—
52#11758194—21no—
53#11758194—21no—
54#11758194—21no—
55#11758194D412yes—
56C2×#92418—24no—
57C2×#92418—21no—
58C2×#92418—21no—
59C2×#92418D412yes—
60C23×C61—21no—
61C23×C61—22no—
62C23×C61—41no—
63C23×C61—41no—
64C23×C61—82no—
65C23×C61#4111yescharacteristic
66Q8×C61—21no—
67Q8×C61C22⋊C412yes—
68D4×C61—22no—
69D4×C61—22no—
70D4×C61—22no—
71D4×C61—21no—
72D4×C61—22no—
73D4×C61—41no—
74D4×C61—41no—
75D4×C61C22⋊C412yes—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61C22×C411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C2×Dic61—41no—
86C8×C61—22no—
87#92418—22no—
88#92418—22no—
89#92418—41no—
90C22×C61—22no—
91C22×C61—41no—
92C22×C61—42no—
93C22×C61—81no—
94C22×C61—82no—
95C22×C61—82no—
96C22×C61—82no—
97C22×C61C4×D411yescharacteristic
98C22×C61#12111yescharacteristic
99C22×C61#12311yescharacteristic
100C4×C61—22no—
101C4×C61C2×C22⋊C411yescharacteristic
102C4×C61C4×D411yescharacteristic
103C4×C61#12011yescharacteristic
104C4×C61#12111yescharacteristic
105Dic61—81no—
106#1903—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—21no—
110C2×C61—42no—
111C2×C61—82no—
112C2×C61#38611yescharacteristic
113C2×AGL(1,ℤ/8)D6111yescharacteristic
114#568—611no—
115#421—611no—
116#418—611no—
117C2×#100—611no—
118#344—611no—
119#338—611no—
120C61#190311yescharacteristic, complemented, Sylow
121C2×#41C2×D6111yescharacteristic
122C22×D4C2×D6111yescharacteristic
123AGL(1,ℤ/8)—22no—
124AGL(1,ℤ/8)—22no—
125C2×SD16Dic6112yescomplemented
126C2×D8Dic6112yescomplemented
127#131—1222no—
128#131—1222no—
129C2×M16—611no—
130C2×M16—611no—
131C2×M16—611no—
132C2×M16—1222no—
133C2×M16C2×D6111yescharacteristic
134#117—611no—
135#104—1222no—
136#102—1222no—
137#100—1222no—
138C24—21no—
139#41—21no—
140#41—21no—
141#41C22⋊D6112yes—
142#41C22⋊D6112yes—
143C2×Q8C2×Dic6111yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4C2×Dic6112yes—
151C2×D4C2×Dic6111yescharacteristic
152C22×C4—21no—
153C22×C4C22×D6111yescharacteristic
154SD16—24no—
155D8—24no—
156M16—21no—
157M16—21no—
158M16—612no—
159M16—1224no—
160M16—1221no—
161M16—1221no—
162M16—1221no—
163M16—1221no—
164M16—1221no—
165C2×C8—612no—
166C2×C8—1224no—
167C2×C8—1221no—
168C2×C8—1221no—
169C2×C8C2×Dic6112yes—
170C4⋊C4—1221no—
171C22⋊C4—1221no—
172C42—1221no—
173C23—21no—
174C23—22no—
175C23—41no—
176C23—41no—
177C23—82no—
178C23#1175822411yescharacteristic
179Q8—21no—
180Q8C22⋊Dic6112yes—
181D4—22no—
182D4—22no—
183D4—22no—
184D4—21no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4C22⋊Dic6112yes—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—2441no—
193C2×C4D4×D6111yescharacteristic
194C2×C4D4×D6111yescharacteristic
195C2×C4#1175822411yescharacteristic
196C2×C4C22×Dic6111yescharacteristic
197C2×C4C2×C22⋊D6111yescharacteristic
198C2×C4C2×C22⋊D6111yescharacteristic
199C8—22no—
200C8—1222no—
201C8—1222no—
202C8—2441no—
203C22—22no—
204C22—41no—
205C22—42no—
206C22—81no—
207C22—82no—
208C22—82no—
209C22—82no—
210C22D4×Dic6111yescharacteristic
211C22#1451974911yescharacteristic
212C22#1451975811yescharacteristic
213C4—22no—
214C4—4881no—
215C4C2×C22⋊Dic6111yescharacteristic
216C4D4×Dic6111yescharacteristic
217C4#1451974511yescharacteristic
218C4#1451974911yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—42no—
223C2—82no—
224C2#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#1903
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. #16840529C2semidirect
2. #16839779C2semidirect
3. #16839767C2semidirect
4. C2×#14519694C2semidirect
5. #16839533C2semidirect
6. #16839520C2semidirect
22. C2×SD16×C61C4semidirect
23. C2×D8×C61C4semidirect
120. C61#1903semidirect
125. C2×SD16Dic61semidirect
126. C2×D8Dic61semidirect