Finite Group Databasebeta

← #21446487

Subgroups — #21446487

Order 7808.

216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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#16839778C211yesmaximal, characteristic
2C2×#14519703C211yesmaximal, characteristic
3#16839744C211yesmaximal, characteristic
4M16×Dic61C211yesmaximal, characteristic, complemented
5#16839533C211yesmaximal, characteristic, complemented
6#16839523C211yesmaximal, characteristic, complemented
7C61×#430C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519736C2211yescharacteristic
11C2×C4×Dic61C2211yescharacteristic
12#14519703—22no—
13#14519703—21no—
14#14519703—21no—
15#14519695C412yescomplemented
16#14519693C412yescomplemented
17#14519687—21no—
18C8×Dic61—21no—
19C2×M16×C61C2211yescharacteristic
20C2×M16×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22#108×C61—22no—
23C22×C4×C61C2311yescharacteristic
24C2×C22⋊D61—21no—
25C22×Dic61—21no—
26#11758222—21no—
27#11758222—21no—
28#11758222—21no—
29#11758222—21no—
30C2×D244C2×C411yescharacteristic
31C2×C4×D61—21no—
32C2×Dic122C2×C411yescharacteristic
33M16×C61—21no—
34M16×C61—21no—
35M16×C61—21no—
36M16×C61—21no—
37M16×C61C2×C412yes—
38M16×C61D412yes—
39C2×C8×C61—21no—
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C22⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4×Dic61—21no—
45C4×Dic61—21no—
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48#11758194—21no—
49#11758194C2×C412yes—
50C2×#92418—21no—
51C23×C61#4111yescharacteristic
52C22×D61—21no—
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C2×C4×C61#4111yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C22⋊D61—41no—
60C22⋊D61—41no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—42no—
65C2×Dic61—41no—
66D244—21no—
67D244—21no—
68C4×D61—41no—
69C4×D61—41no—
70Dic122—21no—
71Dic122—21no—
72C8×C61—22no—
73C8×C61—22no—
74C8×C61—41no—
75#92418—22no—
76C22×C61—41no—
77C22×C61#11711yescharacteristic
78C22×C61#12311yescharacteristic
79C22×C61#12411yescharacteristic
80C2×D61—41no—
81C2×D61—81no—
82C4×C61C4×D411yescharacteristic
83C4×C61C4×D411yescharacteristic
84C4×C61#12111yescharacteristic
85C4×C61#12611yescharacteristic
86Dic61—22no—
87Dic61—41no—
88Dic61—41no—
89Dic61—81no—
90#1932—611nomaximal, Sylow
91C2×C61—21no—
92C2×C61—21no—
93C2×C61—21no—
94C2×C61#38811yescharacteristic
95D61—81no—
96#430D6111yescharacteristic, complemented
97#421—611no—
98C2×#104—611no—
99#413—611no—
100C4×M16—611no—
101#344—611no—
102#339—611no—
103C61#193211yescharacteristic, complemented, Sylow
104C2×#41—611no—
105C2×M16—611no—
106C2×M16C2×D6111yescharacteristic
107C2×M16C2×D6111yescharacteristic
108C2×M16C2×D6111yescharacteristic
109#117—611no—
110C2×C42—611no—
111#108—22no—
112#104—1221no—
113#104—1221no—
114#104—1222no—
115#101—612no—
116#100—612no—
117#97—1221no—
118C4×C8—1221no—
119#41—1221no—
120#41—1221no—
121#41—1221no—
122#41—1221no—
123C2×Q8—611no—
124C2×D4—611no—
125C2×D4—1221no—
126C22×C4—1221no—
127C22×C4—1221no—
128C22×C4C22×D6111yescharacteristic
129M16—21no—
130M16—21no—
131M16—21no—
132M16—21no—
133M16—612no—
134M16—1221no—
135M16C4×D6112yes—
136M16C22⋊D6112yes—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—1221no—
141C4⋊C4—1221no—
142C22⋊C4—1221no—
143C42—611no—
144C42—611no—
145C42—1221no—
146C42—1221no—
147C23—1221no—
148C23#1175822611yescharacteristic
149Q8—1221no—
150Q8—1221no—
151D4—1221no—
152D4—1221no—
153D4—2441no—
154D4—2441no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—1221no—
158C2×C4—2442no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4C2×C4×D6111yescharacteristic
163C2×C4#1175822211yescharacteristic
164C2×C4D4×D6111yescharacteristic
165C2×C4#1175822411yescharacteristic
166C2×C4#1175822611yescharacteristic
167C2×C4C2×C22⋊D6111yescharacteristic
168C8—22no—
169C8—22no—
170C8—41no—
171C8—1222no—
172C22—41no—
173C22—4881no—
174C22—2441no—
175C22#1451973511yescharacteristic
176C22#1451976211yescharacteristic
177C22#1451976611yescharacteristic
178C4—1222no—
179C4—4881no—
180C4—2441no—
181C4—2441no—
182C4C4×C22⋊D6111yescharacteristic
183C4#1451973911yescharacteristic
184C4#1451974911yescharacteristic
185C4#1451977211yescharacteristic
186C2—21no—
187C2—21no—
188C2—21no—
189C2—4881no—
190C2#1683965211yescharacteristic
subgroupG/H
centerC4#14519749
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#430C2
socleC2×C61#388
hypercenter#430D61
hypocenterC61#1932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
4. M16×Dic61C2semidirect
5. #16839533C2semidirect
6. #16839523C2semidirect
7. C61×#430C2semidirect
15. #14519695C4semidirect
16. #14519693C4semidirect
96. #430D61semidirect
103. C61#1932semidirect