Finite Group Databasebeta

← #22561575

Subgroups — #22561575

Order 8576.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14523979C211yesmaximal, characteristic
2#16863439C211yesmaximal, characteristic
3#16863404C211yesmaximal, characteristic
4C2×#14523968C211yesmaximal, characteristic
5C2×#14523961C211yesmaximal, characteristic
6#16863164C211yesmaximal, characteristic
7#424×C67C211yesmaximal, characteristic
8C22×Dic134C2211yescharacteristic
9C2×#11761612C2211yescharacteristic
10C2×#11761612C2211yescharacteristic
11C2×C4⋊Dic67C2211yescharacteristic
12#14523979—22no—
13#14523976—21no—
14#14523974—21no—
15#14523968—22no—
16#14523966—21no—
17#14523966—21no—
18#14523961—22no—
19C2×M16×C67C2211yescharacteristic
20C22×C8×C67C2211yescharacteristic
21#117×C67C2211yescharacteristic
22C4⋊C8×C67—22no—
23C2×Dic134—21no—
24C2×Dic134—21no—
25C2×Dic134—21no—
26C2×Dic134—21no—
27C2×Dic134—21no—
28C2×Dic134Q812yes—
29C22×Dic67—21no—
30C22×Dic67—21no—
31#11761612—21no—
32#11761612—21no—
33#11761612—21no—
34#11761612D412yes—
35C2×C67⋊C8—21no—
36C2×C67⋊C8—21no—
37C4⋊Dic67—21no—
38C4⋊Dic67—21no—
39C22×C4×C67C2311yescharacteristic
40M16×C67—21no—
41M16×C67—21no—
42C2×C8×C67—21no—
43C2×C8×C67—21no—
44C2×C8×C67—21no—
45C2×C8×C67D412yes—
46C4⋊C4×C67D411yescharacteristic
47C4⋊C4×C67D411yescharacteristic
48C22⋊C4×C67—21no—
49C42×C67—21no—
50C23×C67#4111yescharacteristic
51C2×C4×C67—21no—
52C2×C4×C67—21no—
53C2×C4×C67C2×D411yescharacteristic
54C2×C4×C67C2×D411yescharacteristic
55C2×C4×C67C2×D411yescharacteristic
56C2×C4×C67C2×Q811yescharacteristic
57C2×C4×C67#4111yescharacteristic
58C2×C4×C67#4111yescharacteristic
59C2×Dic67—22no—
60C2×Dic67—41no—
61C2×Dic67—41no—
62C2×Dic67—41no—
63C2×Dic67—81no—
64Dic134—22no—
65Dic134—22no—
66Dic134—41no—
67Dic134—41no—
68C8×C67—22no—
69C8×C67—41no—
70C67⋊C8—22no—
71C67⋊C8—41no—
72C22×C67—21no—
73C22×C67—21no—
74C22×C67#12111yescharacteristic
75C22×C67C22⋊Q811yescharacteristic
76C22×C67#12611yescharacteristic
77C4×C67—41no—
78C4×C67—41no—
79C4×C67#12111yescharacteristic
80C4×C67#12111yescharacteristic
81C4×C67C22⋊Q811yescharacteristic
82C4×C67C22⋊Q811yescharacteristic
83Dic67—42no—
84Dic67—81no—
85C2×C67—21no—
86C2×C67—21no—
87C2×C67#39611yescharacteristic
88C2×C67#47111yescharacteristic
89C2×C67#47311yescharacteristic
90#2064—671nomaximal, Sylow
91C67#206411yescharacteristic, complemented, Sylow
92C2×#108—671no—
93#428—671no—
94#424D6711yescharacteristic
95#419—671no—
96C2×#103—671no—
97C2×#101—671no—
98#343—671no—
99C22×Q8—671no—
100C2×M16—671no—
101C2×M16—671no—
102C2×M16C2×D6711yescharacteristic
103C22×C8C2×D6711yescharacteristic
104#117C2×D6711yescharacteristic
105C2×C4⋊C4—671no—
106#108—1342no—
107#107—1341no—
108#106—1341no—
109C4⋊C8—22no—
110#103—1342no—
111#103—1341no—
112#103—1341no—
113#101—1342no—
114C2×Q8—672no—
115C2×Q8—1341no—
116C2×Q8—1341no—
117C2×Q8—1341no—
118C2×Q8—1341no—
119C2×Q8—1341no—
120C22×C4—1341no—
121C22×C4—1341no—
122C22×C4C22×D6711yescharacteristic
123M16—21no—
124M16—21no—
125M16—672no—
126M16—1341no—
127M16—1341no—
128M16—1341no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—1341no—
133C2×C8—1341no—
134C2×C8C22⋊D6712yes—
135C4⋊C4—1341no—
136C4⋊C4—1341no—
137C4⋊C4D26811yescharacteristic
138C4⋊C4D26811yescharacteristic
139C22⋊C4—21no—
140C42—21no—
141C23#1176162811yescharacteristic
142Q8—2681no—
143Q8—2681no—
144Q8—1342no—
145Q8—1342no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—2681no—
149C2×C4—2681no—
150C2×C4—2681no—
151C2×C4—5361no—
152C2×C4—1342no—
153C2×C4D4×D6711yescharacteristic
154C2×C4C2×C22⋊D6711yescharacteristic
155C2×C4C2×D26811yescharacteristic
156C2×C4Q8×D6711yescharacteristic
157C2×C4#1176162711yescharacteristic
158C2×C4#1176162911yescharacteristic
159C8—22no—
160C8—41no—
161C8—2681no—
162C8—1342no—
163C22—21no—
164C22—21no—
165C22#1452401711yescharacteristic
166C22#1452402111yescharacteristic
167C22#1452403811yescharacteristic
168C4—41no—
169C4—41no—
170C4—2682no—
171C4—5361no—
172C4#1452401511yescharacteristic
173C4#1452401811yescharacteristic
174C4#1452401911yescharacteristic
175C4#1452402311yescharacteristic
176C2—21no—
177C2—21no—
178C2#1686331811yescharacteristic
179C2#1686365911yescharacteristic
180C2#1686367111yescharacteristic
subgroupG/H
centerC22#14524017
commutatorC22×C4×C67C23
FrattiniC22×C4C22×D67
Fitting#424×C67C2
socleC22×C67#121
hypercenter#424D67
hypocenterC67#2064
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
91. C67#2064semidirect