Finite Group Databasebeta

← #22611311

Subgroups — #22611311

Order 9344.

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

normal subgroups only

This group has 248 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×#14556523C211yesmaximal, characteristic
2C2×#14556516C211yesmaximal, characteristic
3C2×#14556516C211yesmaximal, characteristic
4#17988493C211yesmaximal, characteristic
5#17988485C211yesmaximal, characteristic
6#17988350C211yesmaximal, characteristic
7C2×C4⋊C8×C73C211yesmaximal, characteristic
8C22×Dic146C2211yescharacteristic
9C2×C4⋊Dic73C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007—21no—
13#14556523—22no—
14#14556516—22no—
15#14556516—22no—
16#14556498—21no—
17#14556498—21no—
18#14556498—21no—
19C22×C8×C73C2211yescharacteristic
20C22×C8×C73C2211yescharacteristic
21C2×C42×C73C2211yescharacteristic
22C4⋊C8×C73—22no—
23C2×Dic146—21no—
24C2×Dic146—21no—
25C2×Dic146—21no—
26C2×Dic146—21no—
27C2×Dic146—21no—
28C2×Dic146Q812yes—
29C22×Dic73—21no—
30C22×Dic73—21no—
31C22×Dic73—21no—
32C22×Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C4⋊Dic73—21no—
38C4⋊Dic73D412yes—
39#11924007—42no—
40C22×C4×C73D411yescharacteristic
41C22×C4×C73D411yescharacteristic
42C22×C4×C73C2311yescharacteristic
43C2×C8×C73—21no—
44C2×C8×C73—21no—
45C2×C8×C73—21no—
46C2×C8×C73—21no—
47C2×C8×C73—21no—
48C2×C8×C73D412yes—
49C42×C73—21no—
50C42×C73—21no—
51C23×C73C2×D411yescharacteristic
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73SD1612yes—
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×Q811yescharacteristic
61C2×C4×C73#4111yescharacteristic
62C2×C4×C73#4111yescharacteristic
63C2×C4×C73#4111yescharacteristic
64C2×Dic73—22no—
65C2×Dic73—22no—
66C2×Dic73—41no—
67C2×Dic73—41no—
68C2×Dic73—41no—
69C2×Dic73—41no—
70C2×Dic73—41no—
71C2×Dic73—41no—
72C2×Dic73—41no—
73C2×Dic73—41no—
74C2×Dic73—41no—
75C2×Dic73—41no—
76Dic146—22no—
77Dic146—22no—
78Dic146—41no—
79Dic146—41no—
80C8×C73—22no—
81C8×C73—41no—
82C22×C73#12111yescharacteristic
83C22×C73#12111yescharacteristic
84C22×C73C22⋊Q811yescharacteristic
85C22×C73C2×SD1611yescharacteristic
86C22×C73#13511yescharacteristic
87C22×C73#13711yescharacteristic
88C22×C73#13711yescharacteristic
89C4×C73—22no—
90C4×C73—41no—
91C4×C73#12111yescharacteristic
92C4×C73C22⋊Q811yescharacteristic
93C4×C73C22⋊Q811yescharacteristic
94C4×C73#12611yescharacteristic
95Dic73—42no—
96Dic73—42no—
97Dic73—81no—
98Dic73—81no—
99C2×C73#39611yescharacteristic
100C2×C73#46111yescharacteristic
101C2×C73#46411yescharacteristic
102C2×C73#46511yescharacteristic
103C2×C73#47011yescharacteristic
104C2×C73#47511yescharacteristic
105C2×C73#47911yescharacteristic
106#2066—731nomaximal, Sylow
107C73#206611yescharacteristic, complemented, Sylow
108C2×#106—731no—
109C2×C4⋊C8D7311yescharacteristic
110C2×#103—731no—
111C2×#103—731no—
112#391—731no—
113#389—731no—
114#340—731no—
115C22×Q8—731no—
116C22×C8C2×D7311yescharacteristic
117C22×C8C2×D7311yescharacteristic
118C2×C4⋊C4—731no—
119C2×C4⋊C4—731no—
120C2×C4⋊C4—731no—
121C2×C4⋊C4—1461no—
122C2×C42C2×D7311yescharacteristic
123#106—1462no—
124C4⋊C8—22no—
125#103—1462no—
126#103—1462no—
127#95—1461no—
128#95—1461no—
129#95—1461no—
130C2×Q8—732no—
131C2×Q8—1461no—
132C2×Q8—1461no—
133C2×Q8—1461no—
134C2×Q8—1461no—
135C2×Q8—1461no—
136C22×C4—1461no—
137C22×C4—1461no—
138C22×C4—1461no—
139C22×C4—1461no—
140C22×C4D29211yescharacteristic
141C22×C4D29211yescharacteristic
142C22×C4C22×D7311yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8C22⋊D7312yes—
149C4⋊C4—2922no—
150C4⋊C4—732no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C4⋊C4—1461no—
155C4⋊C4—1461no—
156C42—21no—
157C42—21no—
158C23C2×D29211yescharacteristic
159Q8—2921no—
160Q8—2921no—
161Q8—1462no—
162Q8—1462no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—2921no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—2921no—
172C2×C4—2921no—
173C2×C4—2921no—
174C2×C4—2921no—
175C2×C4—2921no—
176C2×C4—2921no—
177C2×C4—2921no—
178C2×C4—1462no—
179C2×C4—1462no—
180C2×C4#1192401712yes—
181C2×C4D4×D7311yescharacteristic
182C2×C4C2×C22⋊D7311yescharacteristic
183C2×C4Q8×D7311yescharacteristic
184C2×C4#1192402711yescharacteristic
185C2×C4#1192402811yescharacteristic
186C2×C4#1192402911yescharacteristic
187C8—22no—
188C8—41no—
189C22#1455656511yescharacteristic
190C22#1455656611yescharacteristic
191C22#1455657111yescharacteristic
192C22C2×#1192401711yescharacteristic
193C22#1455661311yescharacteristic
194C22#1455662411yescharacteristic
195C22#1455662411yescharacteristic
196C4—22no—
197C4—41no—
198C4—2922no—
199C4—2922no—
200C4—5841no—
201C4—5841no—
202C4#1455656311yescharacteristic
203C4#1455656711yescharacteristic
204C4#1455656911yescharacteristic
205C4#1455658611yescharacteristic
206C2#1798850911yescharacteristic
207C2#1798879311yescharacteristic
208C2#1798881011yescharacteristic
209C2#1798881611yescharacteristic
210C2#1798884511yescharacteristic
211C2#1798887311yescharacteristic
212C2#1798889511yescharacteristic
subgroupG/H
centerC23C2×D292
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×C4⋊C8×C73C2
socleC23×C73C2×D4
hypercenterC2×C4⋊C8D73
hypocenterC73#2066
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
107. C73#2066semidirect