Finite Group Databasebeta

← #22561200

Subgroups — #22561200

Order 8576.

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

normal subgroups only

This group has 228 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×#14524034C211yesmaximal, characteristic
2#16863419C211yesmaximal, characteristic
3M16×Dic67C211yesmaximal, characteristic
4#16863165C211yesmaximal, characteristic
5#16863164C211yesmaximal, characteristic
6#16863164C211yesmaximal, characteristic
7#343×C67C211yesmaximal, characteristic
8C2×#11761612C2211yescharacteristic
9C2×#11761612C2211yescharacteristic
10#14524034—21no—
11#14524034—21no—
12#14524034—21no—
13#14524034—21no—
14C2×C4⋊Dic67C412yes—
15C2×C4⋊Dic67C2211yescharacteristic
16C2×Dic67⋊C4C412yes—
17C2×C4×Dic67C2211yescharacteristic
18Dic67⋊C8—21no—
19Dic67⋊C8—21no—
20#14523953—21no—
21C8×Dic67—21no—
22C2×M16×C67C2211yescharacteristic
23C2×M16×C67C2211yescharacteristic
24C2×C4⋊C4×C67C2211yescharacteristic
25C22×Dic67C2×C412yes—
26C22×Dic67C2×C411yescharacteristic
27C22×Dic67C2×C411yescharacteristic
28#11761612—21no—
29#11761612—21no—
30#11761612—21no—
31#11761612Q812yes—
32C2×C67⋊C8—21no—
33C2×C67⋊C8—21no—
34C4⋊Dic67—21no—
35C4⋊Dic67—21no—
36C4⋊Dic67—22no—
37C4⋊Dic67—22no—
38Dic67⋊C4—22no—
39Dic67⋊C4—22no—
40C4×Dic67D411yescharacteristic
41C4×Dic67D411yescharacteristic
42C4×Dic67D411yescharacteristic
43C4×Dic67D411yescharacteristic
44C22×C4×C67C2×C412yes—
45C22×C4×C67C2311yescharacteristic
46M16×C67—21no—
47M16×C67—21no—
48M16×C67—21no—
49M16×C67Q812yes—
50C2×C8×C67—21no—
51C2×C8×C67—21no—
52C4⋊C4×C67—21no—
53C4⋊C4×C67—21no—
54C23×C67C22×C411yescharacteristic
55C2×C4×C67—22no—
56C2×C4×C67—42no—
57C2×C4×C67C2×D411yescharacteristic
58C2×C4×C67C2×D411yescharacteristic
59C2×C4×C67C2×Q811yescharacteristic
60C2×C4×C67C2×Q811yescharacteristic
61C2×C4×C67#4111yescharacteristic
62C2×C4×C67#4111yescharacteristic
63C2×Dic67—22no—
64C2×Dic67—41no—
65C2×Dic67—41no—
66C2×Dic67—42no—
67C2×Dic67C22⋊C411yescharacteristic
68C2×Dic67C22⋊C411yescharacteristic
69C2×Dic67C22⋊C411yescharacteristic
70C2×Dic67C22⋊C411yescharacteristic
71C8×C67—22no—
72C8×C67—41no—
73C67⋊C8—22no—
74C67⋊C8—41no—
75C22×C67—21no—
76C22×C67—21no—
77C22×C67C2×C22⋊C411yescharacteristic
78C22×C67C4×Q811yescharacteristic
79C22×C67C4×Q811yescharacteristic
80C4×C67—42no—
81C4×C67C22⋊Q811yescharacteristic
82C4×C67C22⋊Q811yescharacteristic
83C4×C67#12411yescharacteristic
84C4×C67C4⋊Q811yescharacteristic
85Dic67—21no—
86Dic67—21no—
87Dic67—21no—
88Dic67—21no—
89Dic67—42no—
90C2×C67—21no—
91C2×C67—21no—
92C2×C67#39111yescharacteristic
93C2×C67#41311yescharacteristic
94C2×C67#41311yescharacteristic
95#1998—671nomaximal, Sylow
96C67#199811yescharacteristic, complemented, Sylow
97C2×#125—671no—
98#423—671no—
99C4×M16—671no—
100#343—671no—
101#343—671no—
102#343—671no—
103#343D6711yescharacteristic
104C2×M16—671no—
105C2×M16—671no—
106C2×M16C2×D6711yescharacteristic
107C2×M16C2×D6711yescharacteristic
108#125—1341no—
109#125—1341no—
110#125—1341no—
111#125—1341no—
112C2×C4⋊C4—672no—
113C2×C4⋊C4—672no—
114C2×C4⋊C4—671no—
115C2×C4⋊C4C2×D6711yescharacteristic
116C2×C42—671no—
117C4⋊C8—1341no—
118C4⋊C8—1341no—
119#97—1341no—
120C4×C8—1341no—
121C22×C4—671no—
122C22×C4—671no—
123C22×C4—672no—
124C22×C4C4×D6712yes—
125C22×C4C22×D6711yescharacteristic
126M16—21no—
127M16—21no—
128M16—21no—
129M16—672no—
130M16—1341no—
131M16—1341no—
132M16—1341no—
133M16Dic13412yes—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1341no—
137C2×C8—1341no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1342no—
141C4⋊C4—1342no—
142C4⋊C4—1342no—
143C4⋊C4—1342no—
144C4⋊C4—1341no—
145C4⋊C4—1341no—
146C42—671no—
147C42—671no—
148C42—671no—
149C42—671no—
150C23C2×C4×D6711yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—2682no—
154C2×C4—2681no—
155C2×C4—2681no—
156C2×C4—671no—
157C2×C4—671no—
158C2×C4—671no—
159C2×C4—671no—
160C2×C4—1342no—
161C2×C4D4×D6711yescharacteristic
162C2×C4D4×D6711yescharacteristic
163C2×C4Q8×D6711yescharacteristic
164C2×C4C2×Dic13411yescharacteristic
165C2×C4#1176162711yescharacteristic
166C2×C4#1176162811yescharacteristic
167C8—22no—
168C8—41no—
169C8—2681no—
170C8—1342no—
171C22—21no—
172C22—21no—
173C22C22⋊C4×D6711yescharacteristic
174C22#1452400811yescharacteristic
175C22C4×Dic13411yescharacteristic
176C4—42no—
177C4—2682no—
178C4—1341no—
179C4—1341no—
180C4—1341no—
181C4—1341no—
182C4#1452402011yescharacteristic
183C4#1452402111yescharacteristic
184C4#1452402911yescharacteristic
185C4#1452404211yescharacteristic
186C2—21no—
187C2—21no—
188C2#1686330011yescharacteristic
189C2#1686337711yescharacteristic
190C2#1686337911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D67
commutatorC23×C67C22×C4
FrattiniC22×C4C22×D67
Fitting#343×C67C2
socleC22×C67C2×C22⋊C4
hypercenter#343D67
hypocenterC67#1998
LCSG ▷ C23×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
96. C67#1998semidirect