Finite Group Databasebeta

← #22611071

Subgroups — #22611071

Order 9344.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14556590C211yesmaximal, characteristic
2C2×#14556516C211yesmaximal, characteristic
3C2×#14556514C211yesmaximal, characteristic
4#17988492C211yesmaximal, characteristic
5#17988349C211yesmaximal, characteristic
6#17988341C211yesmaximal, characteristic
7#340×C73C211yesmaximal, characteristic
8C22×Dic146—21no—
9C22×Dic146C2211yescharacteristic
10C22×#10596831C2211yescharacteristic
11#14556590—22no—
12#14556590—22no—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924007—21no—
15C2×C4×Dic73C2211yescharacteristic
16#14556516—22no—
17#14556514—22no—
18#14556498—21no—
19#14556498—21no—
20C22×C8×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×C4⋊C4×C73C2211yescharacteristic
23C2×Dic146—21no—
24C2×Dic146—21no—
25C2×Dic146—21no—
26C2×Dic146—21no—
27C2×Dic146—24no—
28C2×Dic146—21no—
29C2×Dic146—42no—
30C2×Dic146—42no—
31C2×Dic146Q812yescomplemented
32C22×Dic73—21no—
33C22×Dic73—21no—
34C22×Dic73D411yescharacteristic
35C22×Dic73D411yescharacteristic
36C2×#10596831—21no—
37C2×#10596831—21no—
38C2×#10596831—21no—
39C4⋊Dic73—21no—
40C4⋊Dic73D412yes—
41#11924007—24no—
42C4×Dic73—21no—
43C4×Dic73—21no—
44C22×C4×C73—21no—
45C22×C4×C73—21no—
46C22×C4×C73C2311yescharacteristic
47C2×C8×C73—21no—
48C2×C8×C73—21no—
49C2×C8×C73—21no—
50C4⋊C4×C73—21no—
51C4⋊C4×C73—21no—
52C4⋊C4×C73—21no—
53C4⋊C4×C73D412yes—
54C23×C73C2×D411yescharacteristic
55C2×C4×C73—22no—
56C2×C4×C73—41no—
57C2×C4×C73—41no—
58C2×C4×C73—41no—
59C2×C4×C73—41no—
60C2×C4×C73—41no—
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73C2×Q811yescharacteristic
64C2×C4×C73#4111yescharacteristic
65C2×C4×C73#4111yescharacteristic
66C2×C4×C73#4111yescharacteristic
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—21no—
71C2×Dic73—22no—
72C2×Dic73—22no—
73C2×Dic73—41no—
74C2×Dic73—41no—
75C2×Dic73—41no—
76C2×Dic73—41no—
77C2×Dic73SD1612yes—
78C2×Dic73Q1612yes—
79Dic146—22no—
80Dic146—22no—
81Dic146—48no—
82Dic146—41no—
83Dic146—41no—
84C8×C73—41no—
85#10596831—41no—
86C22×C73#12011yescharacteristic
87C22×C73C22⋊Q811yescharacteristic
88C22×C73#12411yescharacteristic
89C22×C73C2×SD1611yescharacteristic
90C22×C73C2×Q1611yescharacteristic
91C22×C73AGL(1,ℤ/8)11yescharacteristic
92C22×C73#13711yescharacteristic
93C4×C73—42no—
94C4×C73—81no—
95C4×C73C22⋊Q811yescharacteristic
96C4×C73C22⋊Q811yescharacteristic
97C4×C73#12411yescharacteristic
98C4×C73#12411yescharacteristic
99Dic73—22no—
100Dic73—22no—
101Dic73—42no—
102Dic73—42no—
103C2×C73#39311yescharacteristic
104C2×C73#45011yescharacteristic
105C2×C73#45111yescharacteristic
106C2×C73#47511yescharacteristic
107C2×C73#47711yescharacteristic
108C2×C73#48711yescharacteristic
109C2×C73#48911yescharacteristic
110#2024—731nomaximal, Sylow
111C73#202411yescharacteristic, complemented, Sylow
112C2×C4⋊Q8—731no—
113C2×#103—731no—
114C2×#103—731no—
115#391—731no—
116#340—731no—
117#340D7311yescharacteristic
118#336—731no—
119C22×Q8—731no—
120C22×Q8—1461no—
121C22×C8—731no—
122C22×C8C2×D7311yescharacteristic
123C4⋊Q8—1462no—
124C4⋊Q8—1462no—
125C2×C4⋊C4—731no—
126C2×C4⋊C4—1461no—
127C2×C4⋊C4C2×D7311yescharacteristic
128C2×C4⋊C4C2×D7311yescharacteristic
129C2×C42—731no—
130#103—1462no—
131#103—1462no—
132#95—1461no—
133#95—1461no—
134C2×Q8—2922no—
135C2×Q8—2922no—
136C2×Q8—732no—
137C2×Q8—1464no—
138C2×Q8—1461no—
139C2×Q8—1461no—
140C2×Q8—1461no—
141C2×Q8—1461no—
142C2×Q8—1461no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—731no—
146C22×C4—731no—
147C22×C4—1461no—
148C22×C4—1461no—
149C22×C4C22×D7311yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—1461no—
154C2×C8—1461no—
155C2×C8—1461no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—732no—
160C4⋊C4—1464no—
161C4⋊C4—1461no—
162C4⋊C4D29212yes—
163C42—1461no—
164C42—1461no—
165C23D4×D7311yescharacteristic
166Q8—2928no—
167Q8—2921no—
168Q8—2921no—
169Q8—1462no—
170Q8—1462no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—2921no—
178C2×C4—2921no—
179C2×C4—2921no—
180C2×C4—2921no—
181C2×C4—732no—
182C2×C4—732no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4—1461no—
186C2×C4—1461no—
187C2×C4—1461no—
188C2×C4—1461no—
189C2×C4D4×D7311yescharacteristic
190C2×C4C2×D29211yescharacteristic
191C2×C4Q8×D7311yescharacteristic
192C2×C4#1192402711yescharacteristic
193C2×C4#1192402811yescharacteristic
194C2×C4#1192402811yescharacteristic
195C8—41no—
196C8—2921no—
197C22#1455656111yescharacteristic
198C22#1455656911yescharacteristic
199C22#1455657711yescharacteristic
200C22SD16×D7311yescharacteristic
201C22Q16×D7311yescharacteristic
202C22#1455661511yescharacteristic
203C22#1455662011yescharacteristic
204C4—42no—
205C4—81no—
206C4—2922no—
207C4—2922no—
208C4—1462no—
209C4—1462no—
210C4#1455656911yescharacteristic
211C4#1455657111yescharacteristic
212C4#1455657711yescharacteristic
213C4#1455657911yescharacteristic
214C2#1798850011yescharacteristic
215C2#1798873911yescharacteristic
216C2#1798874411yescharacteristic
217C2#1798887111yescharacteristic
218C2#1798888111yescharacteristic
219C2#1798893611yescharacteristic
220C2#1798894511yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#340×C73C2
socleC23×C73C2×D4
hypercenter#340D73
hypocenterC73#2024
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic146Q8semidirect
111. C73#2024semidirect