Finite Group Databasebeta

← #22560863

Subgroups — #22560863

Order 8576.

212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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#16863404C211yesmaximal, characteristic
2C2×#14523966C211yesmaximal, characteristic
3C2×#14523961C211yesmaximal, characteristic
4#16863352C211yesmaximal, characteristic
5#16863165C211yesmaximal, characteristic
6#16863160C211yesmaximal, characteristic
7#428×C67C211yesmaximal, characteristic
8C22×Dic134C2211yescharacteristic
9C2×#11761612C2211yescharacteristic
10C2×#11761612C2211yescharacteristic
11C22×C67⋊C8C2211yescharacteristic
12#14523966—21no—
13#14523966—21no—
14#14523966—21no—
15#14523966—21no—
16#14523961C414yescomplemented
17#14523954—21no—
18C4×C67⋊C8—21no—
19C2×M16×C67C2211yescharacteristic
20#117×C67C2211yescharacteristic
21C2×C4⋊C4×C67C2211yescharacteristic
22#107×C67—21no—
23#106×C67—21no—
24C2×Dic134—21no—
25C2×Dic134—21no—
26C2×Dic134—21no—
27C2×Dic134—21no—
28C2×Dic134—21no—
29C2×Dic134C2×C412yes—
30C22×Dic67—21no—
31#11761612—21no—
32#11761612—21no—
33#11761612—21no—
34#11761612C2×C412yes—
35C2×C67⋊C8—21no—
36C2×C67⋊C8—21no—
37C2×C67⋊C8—21no—
38C2×C67⋊C8—21no—
39C2×C67⋊C8D411yescharacteristic
40C2×C67⋊C8D411yescharacteristic
41C22×C4×C67—21no—
42C22×C4×C67C2311yescharacteristic
43M16×C67—21no—
44M16×C67C2×C412yes—
45C2×C8×C67—21no—
46C4⋊C4×C67—21no—
47C4⋊C4×C67—21no—
48C4⋊C4×C67D411yescharacteristic
49C4⋊C4×C67D411yescharacteristic
50C22⋊C4×C67—21no—
51C42×C67—21no—
52C23×C67#4111yescharacteristic
53C2×C4×C67—21no—
54C2×C4×C67—21no—
55C2×C4×C67—41no—
56C2×C4×C67—81no—
57C2×C4×C67C22×C411yescharacteristic
58C2×C4×C67C2×D411yescharacteristic
59C2×C4×C67C2×D411yescharacteristic
60C2×C4×C67#4111yescharacteristic
61C2×C4×C67#4111yescharacteristic
62C2×C4×C67#4111yescharacteristic
63C2×Dic67—22no—
64C2×Dic67—41no—
65C2×Dic67—41no—
66Dic134—22no—
67Dic134—22no—
68Dic134—41no—
69Dic134—41no—
70C8×C67—22no—
71C67⋊C8—22no—
72C67⋊C8—21no—
73C67⋊C8—21no—
74C67⋊C8—41no—
75C22×C67—21no—
76C22×C67—21no—
77C22×C67#11711yescharacteristic
78C22×C67#12111yescharacteristic
79C22×C67#12611yescharacteristic
80C4×C67—41no—
81C4×C67—41no—
82C4×C67—81no—
83C4×C67C4×D411yescharacteristic
84C4×C67C4×D411yescharacteristic
85C4×C67#12311yescharacteristic
86C4×C67#12411yescharacteristic
87Dic67—42no—
88C2×C67—21no—
89C2×C67—21no—
90C2×C67#38811yescharacteristic
91C2×C67#47111yescharacteristic
92C2×C67#47311yescharacteristic
93#1930—671nomaximal, Sylow
94C67#193011yescharacteristic, complemented, Sylow
95#428D6711yescharacteristic
96#419—671no—
97C2×#103—671no—
98C2×#101—671no—
99#405—671no—
100#343—671no—
101#341—671no—
102C22×Q8—671no—
103C2×M16—671no—
104C2×M16—671no—
105C2×M16C2×D6711yescharacteristic
106C22×C8—671no—
107#117C2×D6711yescharacteristic
108C2×C4⋊C4C2×D6711yescharacteristic
109#107—21no—
110#106—21no—
111#103—1341no—
112#103—1341no—
113#103—1341no—
114#103—1341no—
115#101—674no—
116#97—1341no—
117C4×C8—1341no—
118C2×Q8—672no—
119C2×Q8—1341no—
120C2×Q8—1341no—
121C2×Q8—1341no—
122C2×Q8—1341no—
123C2×Q8—1341no—
124C22×C4—21no—
125C22×C4—1341no—
126C22×C4C22×D6711yescharacteristic
127M16—21no—
128M16—672no—
129M16—1341no—
130M16—1341no—
131M16—1341no—
132M16C4×D6712yes—
133C2×C8—21no—
134C2×C8—671no—
135C2×C8—671no—
136C2×C8—1341no—
137C2×C8—1341no—
138C2×C8—1341no—
139C2×C8—1341no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4C22⋊D6711yescharacteristic
143C4⋊C4C22⋊D6711yescharacteristic
144C22⋊C4—21no—
145C42—21no—
146C23#1176162711yescharacteristic
147Q8—2681no—
148Q8—2681no—
149Q8—1342no—
150Q8—1342no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—81no—
155C2×C4—2681no—
156C2×C4—2681no—
157C2×C4—1342no—
158C2×C4C2×C4×D6711yescharacteristic
159C2×C4D4×D6711yescharacteristic
160C2×C4C2×C22⋊D6711yescharacteristic
161C2×C4#1176162811yescharacteristic
162C2×C4#1176162911yescharacteristic
163C2×C4#1176162911yescharacteristic
164C8—22no—
165C8—2681no—
166C8—1342no—
167C8—1341no—
168C8—1341no—
169C22—21no—
170C22—21no—
171C22#1452400111yescharacteristic
172C22#1452401511yescharacteristic
173C22#1452403811yescharacteristic
174C4—41no—
175C4—41no—
176C4—81no—
177C4—2682no—
178C4C4×C22⋊D6711yescharacteristic
179C4#1452400511yescharacteristic
180C4#1452402811yescharacteristic
181C4#1452403211yescharacteristic
182C2—21no—
183C2—21no—
184C2#1686328611yescharacteristic
185C2#1686365711yescharacteristic
186C2#1686366911yescharacteristic
subgroupG/H
centerC22#14524015
commutatorC2×C4×C67C22×C4
FrattiniC22×C4C22×D67
Fitting#428×C67C2
socleC22×C67#121
hypercenter#428D67
hypocenterC67#1930
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
16. #14523961C4semidirect
94. C67#1930semidirect