Finite Group Databasebeta

← #22609986

Subgroups — #22609986

Order 9344.

256 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556597C211yesmaximal, characteristic
2#17988625C211yesmaximal, characteristic, complemented
3#17988603C212yesmaximal
4#17988358C212yesmaximal, complemented
5C2×#108×C73C211yesmaximal, characteristic, complemented
6C2×#11924028C2211yescharacteristic
7#14556597—21no—
8#14556597—21no—
9#14556597C412yescomplemented
10#14556597C412yescomplemented
11C2×#11924012C2211yescharacteristic
12C2×#11924011—21no—
13C2×C8×D73—21no—
14#14556550C2212yes—
15#14556525—21no—
16#14556523—21no—
17#14556517—24no—
18C2×M16×C73C2212yes—
19C22×C8×C73C2211yescharacteristic
20#108×C73—21no—
21#108×C73—21no—
22#11924028—21no—
23#11924028—21no—
24#11924028C2×C412yes—
25#11924028D412yes—
26C2×Dic146Q811yescharacteristic
27C2×D292Q811yescharacteristic
28C2×C22⋊D73—21no—
29C2×C4×D73—21no—
30#11924012—21no—
31#11924012C2×C412yes—
32#11924011—22no—
33#11924011—22no—
34C2×#10596831—21no—
35C8×D73—22no—
36C8×D73—22no—
37C4⋊Dic73—22no—
38C22⋊Dic73—22no—
39C4×Dic73—22no—
40C22×C4×C73C2311yescharacteristic
41M16×C73—22no—
42M16×C73—22no—
43C2×C8×C73—22no—
44C2×C8×C73C2×C411yescharacteristic
45C2×C8×C73C2×C411yescharacteristic
46C2×C8×C73D411yescharacteristic
47C2×C8×C73D411yescharacteristic
48C2×C8×C73D411yescharacteristic
49C2×C8×C73D411yescharacteristic
50C23×C73#4111yescharacteristic
51C22×D73—21no—
52C2×C4×C73C22×C411yescharacteristic
53C2×C4×C73C2×D411yescharacteristic
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×Q811yescharacteristic
57C2×C4×C73#4111yescharacteristic
58C22⋊D73—22no—
59C22⋊D73—22no—
60C2×Dic73—21no—
61C2×Dic73—42no—
62D292—21no—
63D292C4⋊C412yes—
64C4×D73—22no—
65C4×D73—22no—
66Dic146—21no—
67Dic146C4⋊C412yes—
68C8×C73—42no—
69C8×C73C22⋊C411yescharacteristic
70C8×C73C22⋊C411yescharacteristic
71C8×C73C22⋊C411yescharacteristic
72C8×C73C22⋊C411yescharacteristic
73#10596831—22no—
74C22×C73—41no—
75C22×C73#11711yescharacteristic
76C22×C73#12111yescharacteristic
77C22×C73C22⋊Q811yescharacteristic
78C2×D73—22no—
79C2×D73—42no—
80C4×C73C2×C22⋊C411yescharacteristic
81C4×C73C2×C4⋊C411yescharacteristic
82C4×C73#12111yescharacteristic
83C4×C73C22⋊Q811yescharacteristic
84Dic73—22no—
85Dic73—82no—
86C2×C73—21no—
87C2×C73—21no—
88C2×C73—21no—
89C2×C73#38011yescharacteristic
90D73—42no—
91#1814—731nomaximal, Sylow
92C73#181411yescharacteristic, complemented, Sylow
93C2×#131—731no—
94C2×#108D7311yescharacteristic, complemented
95#427—731no—
96#421—732no—
97#344—732no—
98C2×#41—731no—
99#131—732no—
100#131—732no—
101#131—1461no—
102#131—1461no—
103C2×M16—731no—
104C2×M16—1461no—
105C2×M16C2×D7312yes—
106C22×C8—1461no—
107C22×C8C2×D7311yescharacteristic
108#117—732no—
109#108—21no—
110#108—21no—
111#107—1461no—
112#106—1461no—
113#104—1464no—
114#41—732no—
115#41—732no—
116#41—1461no—
117#41—1461no—
118C2×Q8—731no—
119C2×D4—731no—
120C2×D4—1461no—
121C22×C4—1461no—
122C22×C4C22×D7311yescharacteristic
123M16—22no—
124M16—22no—
125M16—732no—
126M16—1461no—
127M16—1462no—
128M16—1462no—
129C2×C8—22no—
130C2×C8—1461no—
131C2×C8—1462no—
132C2×C8—1462no—
133C2×C8C4×D7311yescharacteristic
134C2×C8C4×D7311yescharacteristic
135C2×C8D29211yescharacteristic
136C2×C8D29211yescharacteristic
137C2×C8C22⋊D7311yescharacteristic
138C2×C8C22⋊D7311yescharacteristic
139C4⋊C4—1462no—
140C22⋊C4—1462no—
141C42—1462no—
142C23—1461no—
143C23#1192402911yescharacteristic
144Q8—732no—
145Q8—1461no—
146D4—732no—
147D4—1462no—
148D4—1462no—
149D4—1461no—
150C2×C4—2922no—
151C2×C4—1461no—
152C2×C4—1462no—
153C2×C4—1462no—
154C2×C4C2×C4×D7311yescharacteristic
155C2×C4D4×D7311yescharacteristic
156C2×C4C2×C22⋊D7311yescharacteristic
157C2×C4C2×D29211yescharacteristic
158C2×C4Q8×D7311yescharacteristic
159C2×C4#1192402711yescharacteristic
160C8—42no—
161C8—1462no—
162C8#1192400511yescharacteristic
163C8#1192400511yescharacteristic
164C8#1192400511yescharacteristic
165C8#1192400511yescharacteristic
166C22—41no—
167C22—2922no—
168C22—1462no—
169C22#1455654911yescharacteristic
170C22#1455656611yescharacteristic
171C22#1455656711yescharacteristic
172C4—5842no—
173C4—1462no—
174C4C2×#1192400511yescharacteristic
175C4C4⋊C4×D7311yescharacteristic
176C4#1455656211yescharacteristic
177C4#1455657111yescharacteristic
178C2—21no—
179C2—21no—
180C2—21no—
181C2—2922no—
182C2#1798844411yescharacteristic
subgroupG/H
centerC4#14556562
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#108×C73C2
socleC2×C73#380
hypercenterC2×#108D73
hypocenterC73#1814
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. #17988625C2semidirect
4. #17988358C2semidirect
5. C2×#108×C73C2semidirect
9. #14556597C4semidirect
10. #14556597C4semidirect
92. C73#1814semidirect
94. C2×#108D73semidirect