Finite Group Databasebeta

← #22561758

Subgroups — #22561758

Order 8576.

238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14523976C211yesmaximal, characteristic
2C2×#14523968C211yesmaximal, characteristic
3C2×#14523966C211yesmaximal, characteristic
4#16863301C211yesmaximal, characteristic
5#16863261C211yesmaximal, characteristic
6#16863150C211yesmaximal, characteristic
7C2×#106×C67C211yesmaximal, characteristic
8C22×Dic134C2211yescharacteristic
9C22×C67⋊C8C2211yescharacteristic
10C2×C4⋊Dic67C2211yescharacteristic
11C2×C4×Dic67C2211yescharacteristic
12#14523976—22no—
13#14523968—22no—
14#14523966—22no—
15C67⋊#95—22no—
16C67⋊#95—22no—
17C22×C8×C67C2211yescharacteristic
18C2×C4⋊C4×C67C2211yescharacteristic
19C2×C4⋊C4×C67C2211yescharacteristic
20#106×C67—22no—
21C2×Dic134—21no—
22C2×Dic134—21no—
23C2×Dic134—21no—
24C2×Dic134—21no—
25C2×Dic134—21no—
26C2×Dic134Q812yes—
27C22×Dic67—21no—
28C22×Dic67—21no—
29C22×Dic67D412yes—
30C2×C67⋊C8—21no—
31C2×C67⋊C8—21no—
32C2×C67⋊C8D412yes—
33C4⋊Dic67—21no—
34C4⋊Dic67—21no—
35C4×Dic67—21no—
36C4×Dic67—21no—
37C22×C4×C67—21no—
38C22×C4×C67—21no—
39C22×C4×C67C2311yescharacteristic
40C2×C8×C67—21no—
41C2×C8×C67—21no—
42C2×C8×C67D412yes—
43C4⋊C4×C67—21no—
44C4⋊C4×C67—21no—
45C4⋊C4×C67—21no—
46C4⋊C4×C67—21no—
47C23×C67C2×D411yescharacteristic
48C2×C4×C67—41no—
49C2×C4×C67—41no—
50C2×C4×C67—42no—
51C2×C4×C67—42no—
52C2×C4×C67C2×D411yescharacteristic
53C2×C4×C67C2×D411yescharacteristic
54C2×C4×C67C2×Q811yescharacteristic
55C2×C4×C67#4111yescharacteristic
56C2×C4×C67#4111yescharacteristic
57C2×C4×C67#4111yescharacteristic
58C2×Dic67—22no—
59C2×Dic67—22no—
60C2×Dic67—22no—
61C2×Dic67—22no—
62C2×Dic67—41no—
63C2×Dic67—41no—
64C2×Dic67—41no—
65C2×Dic67—42no—
66Dic134—22no—
67Dic134—22no—
68Dic134—41no—
69Dic134—41no—
70C8×C67—22no—
71C67⋊C8—22no—
72C22×C67C22⋊Q811yescharacteristic
73C22×C67#12311yescharacteristic
74C22×C67#12711yescharacteristic
75C22×C67#13512yes—
76C22×C67#13712yes—
77C4×C67—81no—
78C4×C67—81no—
79C4×C67C22⋊Q811yescharacteristic
80C4×C67C22⋊Q811yescharacteristic
81C4×C67#12311yescharacteristic
82C4×C67#12311yescharacteristic
83Dic67—42no—
84Dic67—42no—
85Dic67—81no—
86C2×C67#39911yescharacteristic
87C2×C67#47912yes—
88C2×C67#48512yes—
89C2×C67#49511yescharacteristic
90C2×C67#49711yescharacteristic
91#2097—671nomaximal, Sylow
92C67#209711yescharacteristic, complemented, Sylow
93C2×#107—671no—
94C2×#106D6711yescharacteristic
95C2×#103—671no—
96C2×#103—671no—
97#391—671no—
98#382—671no—
99#336—671no—
100C22×Q8—671no—
101C22×C8—671no—
102C22×C8C2×D6711yescharacteristic
103C2×C4⋊C4—671no—
104C2×C4⋊C4C2×D6711yescharacteristic
105C2×C4⋊C4C2×D6711yescharacteristic
106C2×C42—671no—
107#107—1342no—
108#106—22no—
109#103—1342no—
110#103—1342no—
111#95—1342no—
112#95—1342no—
113C2×Q8—672no—
114C2×Q8—1341no—
115C2×Q8—1341no—
116C2×Q8—1341no—
117C2×Q8—1341no—
118C2×Q8—1341no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—672no—
122C22×C4—1341no—
123C22×C4—1341no—
124C22×C4C22×D6711yescharacteristic
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—672no—
128C2×C8—1341no—
129C2×C8—1341no—
130C2×C8C22⋊D6712yes—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—1341no—
136C4⋊C4—1341no—
137C42—1341no—
138C42—1341no—
139C23D4×D6711yescharacteristic
140Q8—2681no—
141Q8—2681no—
142Q8—1342no—
143Q8—1342no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—2681no—
149C2×C4—2681no—
150C2×C4—2681no—
151C2×C4—2682no—
152C2×C4—1342no—
153C2×C4—1342no—
154C2×C4—1342no—
155C2×C4—1342no—
156C2×C4D4×D6711yescharacteristic
157C2×C4C2×C22⋊D6711yescharacteristic
158C2×C4Q8×D6711yescharacteristic
159C2×C4#1176162811yescharacteristic
160C2×C4#1176162811yescharacteristic
161C2×C4#1176162911yescharacteristic
162C8—22no—
163C8—1342no—
164C22#1452402111yescharacteristic
165C22#1452402811yescharacteristic
166C22#1452403911yescharacteristic
167C22#1452406412yes—
168C22#1452407212yes—
169C4—81no—
170C4—81no—
171C4—2682no—
172C4—2682no—
173C4—5361no—
174C4#1452401911yescharacteristic
175C4#1452402111yescharacteristic
176C4#1452402611yescharacteristic
177C4#1452402811yescharacteristic
178C2#1686333111yescharacteristic
179C2#1686370612yes—
180C2#1686374012yes—
181C2#1686377711yescharacteristic
182C2#1686378711yescharacteristic
subgroupG/H
centerC23D4×D67
commutatorC22×C4×C67C23
FrattiniC22×C4C22×D67
FittingC2×#106×C67C2
socleC23×C67C2×D4
hypercenterC2×#106D67
hypocenterC67#2097
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
92. C67#2097semidirect