Finite Group Databasebeta

← #22611106

Subgroups — #22611106

Order 9344.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#17989140C211yesmaximal, characteristic, complemented
2#17988603C211yesmaximal, characteristic
3C2×#14556517C211yesmaximal, characteristic
4#17988560C211yesmaximal, characteristic
5#17988348C211yesmaximal, characteristic, complemented
6#17988344C211yesmaximal, characteristic, complemented
7#344×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9#14556590—21no—
10#14556582—21no—
11#14556568—22no—
12C4×Dic146—22no—
13#14556550C2211yescharacteristic
14#14556550C2211yescharacteristic
15C2×C4×Dic73C2211yescharacteristic
16#14556517—21no—
17#14556517—21no—
18#14556517—22no—
19#14556505—22no—
20C2×M16×C73C2211yescharacteristic
21C2×M16×C73C2211yescharacteristic
22#117×C73C2211yescharacteristic
23#11924028—21no—
24#11924028—21no—
25#11924028—21no—
26#11924028—21no—
27C2×Dic146—22no—
28C2×Dic146Q811yescharacteristic, complemented
29C2×D292Q811yescharacteristic, complemented
30C2×C22⋊D73—21no—
31C22×Dic73—21no—
32C2×C4×D73—21no—
33C4⋊Dic73—22no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36#11924007—22no—
37#11924007—22no—
38C22⋊Dic73—21no—
39C22⋊Dic73—21no—
40C4×Dic73—21no—
41C4×Dic73—21no—
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73D412yes—
45C22×C4×C73C2311yescharacteristic
46M16×C73—21no—
47M16×C73—21no—
48M16×C73—21no—
49M16×C73—21no—
50C2×C8×C73—21no—
51C2×C8×C73—21no—
52C4⋊C4×C73—21no—
53C22⋊C4×C73D412yes—
54C42×C73—21no—
55C23×C73C2×D411yescharacteristic
56C22×D73—21no—
57C2×C4×C73—22no—
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×Q811yescharacteristic
61C2×C4×C73#4111yescharacteristic
62C2×C4×C73#4111yescharacteristic
63C2×C4×C73#4111yescharacteristic
64C22⋊D73—41no—
65C22⋊D73—41no—
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—22no—
69C2×Dic73—21no—
70C2×Dic73—42no—
71C2×Dic73—41no—
72D292—21no—
73D292—21no—
74C4×D73—41no—
75C4×D73—41no—
76Dic146—21no—
77Dic146—21no—
78Dic146—44no—
79C8×C73—41no—
80C8×C73—41no—
81C22×C73—41no—
82C22×C73#12011yescharacteristic
83C22×C73C22⋊Q811yescharacteristic
84C22×C73#12411yescharacteristic
85C2×D73—41no—
86C2×D73—81no—
87C4×C73—42no—
88C4×C73C22⋊Q811yescharacteristic
89C4×C73C22⋊Q811yescharacteristic
90C4×C73#12411yescharacteristic
91C4×C73#12411yescharacteristic
92Dic73—22no—
93Dic73—42no—
94Dic73—41no—
95Dic73—41no—
96Dic73—81no—
97C2×C73—21no—
98C2×C73—21no—
99C2×C73—21no—
100C2×C73#39311yescharacteristic
101D73—81no—
102#2031—731nomaximal, Sylow
103C73#203111yescharacteristic, complemented, Sylow
104#533—731no—
105#421—731no—
106C2×#104—731no—
107#410—731no—
108#344D7311yescharacteristic, complemented
109#339—731no—
110H(3,ℤ/4)—731no—
111C2×#41—731no—
112C2×M16C2×D7311yescharacteristic
113C2×M16C2×D7311yescharacteristic
114C4⋊Q8—1461no—
115#125—1461no—
116C22⋊Q8—1462no—
117C4×Q8—1462no—
118#117—731no—
119#117—731no—
120#117C2×D7311yescharacteristic
121C2×C42—731no—
122#104—1461no—
123#104—1461no—
124#104—1462no—
125#99—1462no—
126#41—1461no—
127#41—1461no—
128#41—1461no—
129#41—1461no—
130C2×Q8—731no—
131C2×Q8—1462no—
132C2×D4—731no—
133C2×D4—1461no—
134C22×C4—1461no—
135C22×C4—1461no—
136C22×C4C22×D7311yescharacteristic
137M16—21no—
138M16—21no—
139M16—21no—
140M16—21no—
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—1462no—
145C4⋊C4—1462no—
146C4⋊C4—1462no—
147C4⋊C4—1461no—
148C4⋊C4—1461no—
149C22⋊C4—1461no—
150C22⋊C4—1461no—
151C22⋊C4D29212yes—
152C42—21no—
153C42—731no—
154C42—731no—
155C42—732no—
156C42—1461no—
157C42—1461no—
158C23—1461no—
159C23C2×D29211yescharacteristic
160Q8—2924no—
161Q8—1461no—
162Q8—1461no—
163D4—2921no—
164D4—2921no—
165D4—1461no—
166D4—1461no—
167C2×C4—22no—
168C2×C4—2922no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—2921no—
172C2×C4—1461no—
173C2×C4—1462no—
174C2×C4—1461no—
175C2×C4—1461no—
176C2×C4D4×D7311yescharacteristic
177C2×C4D4×D7311yescharacteristic
178C2×C4Q8×D7311yescharacteristic
179C2×C4#1192402711yescharacteristic
180C2×C4#1192402811yescharacteristic
181C2×C4#1192402811yescharacteristic
182C8—41no—
183C8—41no—
184C22—41no—
185C22—2921no—
186C22—5841no—
187C22#1455656111yescharacteristic
188C22#1455657111yescharacteristic
189C22#1455657911yescharacteristic
190C4—42no—
191C4—2921no—
192C4—2922no—
193C4—2921no—
194C4—5841no—
195C4—1462no—
196C4#1455656911yescharacteristic
197C4#1455656911yescharacteristic
198C4#1455657711yescharacteristic
199C4#1455657711yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—5841no—
204C2#1798850011yescharacteristic
subgroupG/H
centerC4#14556577
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#344×C73C2
socleC2×C73#393
hypercenter#344D73
hypocenterC73#2031
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #17989140C2semidirect
5. #17988348C2semidirect
6. #17988344C2semidirect
7. #344×C73C2semidirect
28. C2×Dic146Q8semidirect
29. C2×D292Q8semidirect
103. C73#2031semidirect
108. #344D73semidirect