Finite Group Databasebeta

← #22608342

Subgroups — #22608342

Order 9344.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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#17989121C211yesmaximal, characteristic
2C4×#11924012C211yesmaximal, characteristic, complemented
3#17988317C212yesmaximal, complemented
4#17988314C212yesmaximal, complemented
5C2×C4⋊C8×C73C211yesmaximal, characteristic, complemented
6C2×#11924012—21no—
7#14556585—21no—
8#14556583C411yescharacteristic
9#14556579C411yescharacteristic
10#14556574—21no—
11#14556570C411yescharacteristic
12#14556565C411yescharacteristic
13C4×Dic146C2211yescharacteristic
14C4×D292C2211yescharacteristic
15C4×C22⋊D73—21no—
16#14556548—21no—
17#14556502—21no—
18C4×#10596831C2212yes—
19C22×C8×C73—21no—
20C2×C42×C73C2211yescharacteristic
21C4⋊C8×C73—21no—
22C4⋊C8×C73C2212yes—
23C2×Dic146C2×C411yescharacteristic
24C2×D292C2×C411yescharacteristic
25C2×C22⋊D73—21no—
26C2×C4×D73—21no—
27#11924012—24no—
28C2×#10596831—22no—
29C4⋊Dic73C2×C411yescharacteristic
30C4⋊Dic73C2×C411yescharacteristic
31#11924007—21no—
32#11924007—21no—
33#11924007—21no—
34#11924007—21no—
35C22⋊Dic73—21no—
36#11924005—21no—
37#11924005—21no—
38#11924005—21no—
39#11924005—21no—
40C4×Dic73—21no—
41C22×C4×C73C2×C411yescharacteristic
42C22×C4×C73D411yescharacteristic
43C22×C4×C73D411yescharacteristic
44C2×C8×C73—22no—
45C2×C8×C73—42no—
46C42×C73C2×C411yescharacteristic
47C42×C73D411yescharacteristic
48C42×C73D411yescharacteristic
49C42×C73C2311yescharacteristic
50C23×C73C22⋊C411yescharacteristic
51C22×D73—21no—
52C2×C4×C73—22no—
53C2×C4×C73—22no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C22⋊D73—42no—
63C2×Dic73—21no—
64C2×Dic73—21no—
65C2×Dic73—21no—
66D292—22no—
67C4×D73—41no—
68C4×D73—41no—
69Dic146—22no—
70C8×C73—42no—
71#10596831—24no—
72C22×C73—21no—
73C22×C73—21no—
74C22×C73#10412yes—
75C22×C73C2×C22⋊C411yescharacteristic
76C2×D73—41no—
77C2×D73—41no—
78C2×D73—41no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—21no—
82C4×C73—21no—
83C4×C73#13112yes—
84C4×C73AGL(1,ℤ/8)11yescharacteristic
85C4×C73#13711yescharacteristic
86Dic73—41no—
87Dic73—41no—
88Dic73—41no—
89C2×C73—22no—
90C2×C73#40811yescharacteristic
91C2×C73#41711yescharacteristic
92C2×C73C2×#10411yescharacteristic
93D73—81no—
94#1483—731nomaximal, Sylow
95C73#148311yescharacteristic, complemented, Sylow
96#529—731no—
97C2×C4⋊C8D7311yescharacteristic, complemented
98C4×M16—731no—
99Q8⋊C8—732no—
100D4⋊C8—732no—
101C2×M16—1461no—
102C22×C8—21no—
103#126—1461no—
104#125—731no—
105#124—731no—
106#123—1461no—
107C22⋊Q8—731no—
108#121—731no—
109C4×Q8—731no—
110C4×D4—731no—
111C4×D4—1461no—
112#117—1461no—
113C2×C42C2×D7311yescharacteristic
114C4⋊C8—21no—
115C4⋊C8C2×D7312yes—
116#97—1461no—
117C4×C8—732no—
118C2×Q8—731no—
119C2×D4—731no—
120C2×D4—1461no—
121C22×C4—1461no—
122C22×C4C4×D7311yescharacteristic
123C22×C4D29211yescharacteristic
124C22×C4C22⋊D7311yescharacteristic
125M16—1464no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—1462no—
129C4⋊C4—731no—
130C4⋊C4—731no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C4⋊C4—1461no—
134C4⋊C4—1461no—
135C22⋊C4—1461no—
136C22⋊C4—1461no—
137C22⋊C4—1461no—
138C22⋊C4—1461no—
139C22⋊C4—1461no—
140C42—1461no—
141C42C4×D7311yescharacteristic
142C42D29211yescharacteristic
143C42C22⋊D7311yescharacteristic
144C42C22×D7311yescharacteristic
145C23—1461no—
146C23#1192400511yescharacteristic
147Q8—1462no—
148D4—2922no—
149D4—1462no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—2921no—
155C2×C4—2921no—
156C2×C4—1461no—
157C2×C4—1461no—
158C2×C4—1461no—
159C2×C4#1192400511yescharacteristic
160C2×C4#1192400511yescharacteristic
161C2×C4#1192400511yescharacteristic
162C2×C4C2×C4×D7311yescharacteristic
163C2×C4C2×C22⋊D7311yescharacteristic
164C2×C4C2×D29211yescharacteristic
165C8—42no—
166C8—1464no—
167C22—21no—
168C22—21no—
169C22—2921no—
170C22—2921no—
171C22—2921no—
172C22#1455651712yes—
173C22C2×#1192400511yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—2921no—
179C4—2921no—
180C4—2921no—
181C4#1455659712yes—
182C4#1455661711yescharacteristic
183C4#1455662211yescharacteristic
184C2—22no—
185C2—5841no—
186C2#1798855311yescharacteristic
187C2#1798858611yescharacteristic
188C2C2×#1455651711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
FittingC2×C4⋊C8×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C8D73
hypocenterC73#1483
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#11924012C2semidirect
3. #17988317C2semidirect
4. #17988314C2semidirect
5. C2×C4⋊C8×C73C2semidirect
95. C73#1483semidirect
97. C2×C4⋊C8D73semidirect