Finite Group Databasebeta

← #22610201

Subgroups — #22610201

Order 9344.

298 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 115 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×Q8×Dic73C211yesmaximal, characteristic
2C2×#14556523C211yesmaximal, characteristic
3C2×#14556515C211yesmaximal, characteristic
4#17988486C211yesmaximal, characteristic
5#17988349C211yesmaximal, characteristic
6#17988341C211yesmaximal, characteristic
7C2×#103×C73C211yesmaximal, characteristic
8C22×#10596831C2211yescharacteristic
9Q8×Dic73—22no—
10Q8×Dic73—22no—
11C2×C4⋊Dic73—21no—
12C2×C4⋊Dic73—21no—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×C4×Dic73—21no—
16C2×C4×Dic73C2211yescharacteristic
17#14556523—22no—
18#14556515—22no—
19#14556498—21no—
20C22×Q8×C73C2211yescharacteristic
21C22×C8×C73C2211yescharacteristic
22C2×C4⋊C4×C73C2211yescharacteristic
23#103×C73C414yescomplemented
24C22×Dic73—21no—
25C22×Dic73—21no—
26C22×Dic73D411yescharacteristic
27C22×Dic73D411yescharacteristic
28C2×#10596831—21no—
29C2×#10596831—21no—
30C2×#10596831—21no—
31C4⋊Dic73—24no—
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—42no—
36C4⋊Dic73D412yes—
37C4×Dic73—24no—
38C4×Dic73—21no—
39C4×Dic73—21no—
40C2×Q8×C73—21no—
41C2×Q8×C73—21no—
42C2×Q8×C73—21no—
43C2×Q8×C73C2×C412yes—
44C2×Q8×C73D412yes—
45C2×Q8×C73Q812yes—
46C22×C4×C73—21no—
47C22×C4×C73—21no—
48C22×C4×C73C2311yescharacteristic
49C2×C8×C73—21no—
50C2×C8×C73—21no—
51C2×C8×C73C2×C412yes—
52C4⋊C4×C73—21no—
53C4⋊C4×C73C2×C412yes—
54C23×C73C2×D411yescharacteristic
55Q8×C73—22no—
56Q8×C73—22no—
57Q8×C73—22no—
58Q8×C73C4⋊C414yescomplemented
59C2×C4×C73—22no—
60C2×C4×C73—22no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73C22×C411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×Q811yescharacteristic
69C2×C4×C73#4111yescharacteristic
70C2×C4×C73#4111yescharacteristic
71C2×Dic73—21no—
72C2×Dic73—21no—
73C2×Dic73—21no—
74C2×Dic73—22no—
75C2×Dic73—21no—
76C2×Dic73—21no—
77C2×Dic73—41no—
78C2×Dic73—41no—
79C2×Dic73—41no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73SD1612yes—
83C8×C73—22no—
84#10596831—41no—
85C22×C73C4×D411yescharacteristic
86C22×C73#12011yescharacteristic
87C22×C73C22⋊Q811yescharacteristic
88C22×C73C2×SD1611yescharacteristic
89C22×C73#13511yescharacteristic
90C22×C73#13711yescharacteristic
91C22×C73#13711yescharacteristic
92C4×C73—24no—
93C4×C73—42no—
94C4×C73C2×C4⋊C411yescharacteristic
95C4×C73C4×D411yescharacteristic
96C4×C73C22⋊Q811yescharacteristic
97C4×C73#12311yescharacteristic
98Dic73—22no—
99Dic73—41no—
100Dic73—42no—
101Dic73—81no—
102C2×C73#38511yescharacteristic
103C2×C73C4×SD1611yescharacteristic
104C2×C73#44111yescharacteristic
105C2×C73#44811yescharacteristic
106C2×C73#45211yescharacteristic
107C2×C73#47511yescharacteristic
108C2×C73#47911yescharacteristic
109#1865—731nomaximal, Sylow
110C73#186511yescharacteristic, complemented, Sylow
111C2×C4×Q8—731no—
112C2×#106—731no—
113C2×#103—731no—
114C2×#103D7311yescharacteristic
115#389—731no—
116#340—731no—
117#336—731no—
118C22×Q8C2×D7311yescharacteristic
119C22×C8—731no—
120C22×C8C2×D7311yescharacteristic
121C4×Q8—1462no—
122C4×Q8—1462no—
123C2×C4⋊C4—731no—
124C2×C4⋊C4—731no—
125C2×C4⋊C4—1461no—
126C2×C4⋊C4—1461no—
127C2×C4⋊C4C2×D7311yescharacteristic
128C2×C42—731no—
129C2×C42—1461no—
130#106—1462no—
131#103—1462no—
132#103Dic7314yescomplemented
133#95—1461no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8Dic14612yes—
138C2×Q8D29212yes—
139C2×Q8C2×Dic7312yes—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—1461no—
145C22×C4—1461no—
146C22×C4C22×D7311yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—1461no—
150C2×C8—1461no—
151C2×C8—1461no—
152C2×C8C2×Dic7312yes—
153C4⋊C4—21no—
154C4⋊C4—2922no—
155C4⋊C4—732no—
156C4⋊C4—1464no—
157C4⋊C4—1461no—
158C4⋊C4—1461no—
159C4⋊C4—1461no—
160C4⋊C4C2×Dic7312yes—
161C42—1464no—
162C42—1461no—
163C42—1461no—
164C23D4×D7311yescharacteristic
165Q8—22no—
166Q8—22no—
167Q8—22no—
168Q8C4⋊Dic7314yescomplemented
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—2921no—
176C2×C4—2921no—
177C2×C4—2921no—
178C2×C4—2921no—
179C2×C4—2921no—
180C2×C4—732no—
181C2×C4—1462no—
182C2×C4—1461no—
183C2×C4—1461no—
184C2×C4—1461no—
185C2×C4—1461no—
186C2×C4—1461no—
187C2×C4C22×Dic7311yescharacteristic
188C2×C4D4×D7311yescharacteristic
189C2×C4C2×D29211yescharacteristic
190C2×C4C2×Dic14611yescharacteristic
191C2×C4#1192402711yescharacteristic
192C2×C4#1192402711yescharacteristic
193C8—22no—
194C8—2921no—
195C22D4×Dic7311yescharacteristic
196C22#1455656111yescharacteristic
197C22#1455656811yescharacteristic
198C22SD16×D7311yescharacteristic
199C22#1455661211yescharacteristic
200C22#1455662311yescharacteristic
201C22#1455662311yescharacteristic
202C4—24no—
203C4—42no—
204C4—2922no—
205C4—2921no—
206C4—5841no—
207C4—1462no—
208C4C2×C4⋊Dic7311yescharacteristic
209C4D4×Dic7311yescharacteristic
210C4#1455656811yescharacteristic
211C4#1455657511yescharacteristic
212C2#1798846211yescharacteristic
213C2SD16×Dic7311yescharacteristic
214C2#1798869411yescharacteristic
215C2#1798872711yescharacteristic
216C2#1798875211yescharacteristic
217C2#1798887011yescharacteristic
218C2#1798889211yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#103×C73C2
socleC23×C73C2×D4
hypercenterC2×#103D73
hypocenterC73#1865
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
23. #103×C73C4semidirect
58. Q8×C73C4⋊C4semidirect
110. C73#1865semidirect
132. #103Dic73semidirect
168. Q8C4⋊Dic73semidirect