Finite Group Databasebeta

← #22615142

Subgroups — #22615142

Order 9344.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14556556C211yesmaximal, characteristic
3#17988527C211yesmaximal, characteristic
4#17988526C211yesmaximal, characteristic
5#17988525C211yesmaximal, characteristic
6#17988491C212yesmaximal
7#17988491C212yesmaximal
8#17988491C212yesmaximal
9#17988451C212yesmaximal
10#17988438C211yesmaximal, characteristic
11#400×C73C211yesmaximal, characteristic
12C22×Dic146C2212yes—
13C22×Dic146C2211yescharacteristic
14#14556590—24no—
15#14556556—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×C4×Dic73C2212yes—
22C2×C4×Dic73C2211yescharacteristic
23C2×C4×Dic73C2211yescharacteristic
24C2×C4×Dic73C2211yescharacteristic
25#14556498C2211yescharacteristic
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34#95×C73C2211yescharacteristic
35#95×C73C2212yes—
36#95×C73C2212yes—
37C2×Dic146—22no—
38C2×Dic146—22no—
39C2×Dic146—24no—
40C2×Dic146—28no—
41C2×Dic146Q814yescomplemented
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C4⋊Dic73—22no—
49#11924007—22no—
50#11924007—22no—
51#11924007—24no—
52#11924007—24no—
53C4×Dic73—22no—
54C4×Dic73—22no—
55C4×Dic73—24no—
56C4×Dic73D414yes—
57C22×C4×C73C2312yes—
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2312yes—
60C22×C4×C73C2311yescharacteristic
61C22×C4×C73C2311yescharacteristic
62C4⋊C4×C73—22no—
63C4⋊C4×C73—22no—
64C23×C73C2411yescharacteristic
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—22no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—24no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73C2×D412yes—
76C2×C4×C73C2×Q812yes—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—24no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73C2×D412yes—
87C2×Dic73C2×D412yes—
88C2×Dic73C2×Q812yes—
89C2×Dic73C2×Q812yes—
90C2×Dic73#4112yes—
91C2×Dic73#4114yes—
92Dic146—28no—
93Dic146—48no—
94C22×C73C22×D411yescharacteristic
95C22×C73C22×Q811yescharacteristic
96C22×C73C2×#4111yescharacteristic
97C22×C73C2×#4112yes—
98C22×C732−1+412yes—
99C4×C73—22no—
100C4×C73—22no—
101C4×C73—42no—
102C4×C73—41no—
103C4×C73—42no—
104Dic73—22no—
105Dic73—42no—
106Dic73—41no—
107Dic73—42no—
108Dic73C22⋊Q814yes—
109Dic73#12414yes—
110C2×C73C2×C22⋊Q811yescharacteristic
111C2×C73C2×#12411yescharacteristic
112C2×C73#53611yescharacteristic
113C2×C73#55612yes—
114C2×C73#55712yes—
115#2568—731nomaximal, Sylow
116C73#256811yescharacteristic, complemented, Sylow
117C2×C4⋊Q8—731no—
118C2×C4×Q8—731no—
119#400—731no—
120#400—731no—
121#400—731no—
122#400D7311yescharacteristic
123#391—732no—
124#391—732no—
125#391—732no—
126#382—732no—
127C4×C4⋊C4—731no—
128C22×Q8—731no—
129C22×Q8—732no—
130C4⋊Q8—1464no—
131C4×Q8—1464no—
132C2×C4⋊C4—731no—
133C2×C4⋊C4—731no—
134C2×C4⋊C4—732no—
135C2×C4⋊C4—731no—
136C2×C4⋊C4—732no—
137C2×C4⋊C4C2×D7311yescharacteristic
138C2×C4⋊C4C2×D7311yescharacteristic
139C2×C42—731no—
140C2×C42—731no—
141C2×C42—731no—
142C2×C42—732no—
143#95—731no—
144#95—732no—
145#95—732no—
146#95—732no—
147#95—732no—
148#95—732no—
149#95—732no—
150#95C2×D7311yescharacteristic
151#95C2×D7312yes—
152#95C2×D7312yes—
153C2×Q8—734no—
154C2×Q8—1464no—
155C2×Q8—1468no—
156C2×Q8—1462no—
157C2×Q8—1462no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—732no—
162C22×C4—731no—
163C22×C4—732no—
164C22×C4C22×D7312yes—
165C22×C4C22×D7311yescharacteristic
166C22×C4C22×D7312yes—
167C22×C4C22×D7311yescharacteristic
168C22×C4C22×D7311yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—1464no—
172C4⋊C4—1462no—
173C4⋊C4—1464no—
174C4⋊C4—1462no—
175C4⋊C4—1462no—
176C42—734no—
177C42—1464no—
178C42—1462no—
179C42—1462no—
180C23C23×D7311yescharacteristic
181Q8—2928no—
182Q8—1468no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—732no—
194C2×C4—732no—
195C2×C4—732no—
196C2×C4—732no—
197C2×C4—734no—
198C2×C4—732no—
199C2×C4—1461no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4—1462no—
203C2×C4—1464no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4—1461no—
207C2×C4—1461no—
208C2×C4D4×D7312yes—
209C2×C4Q8×D7312yes—
210C22C2×D4×D7311yescharacteristic
211C22C2×Q8×D7311yescharacteristic
212C22#41×D7311yescharacteristic
213C22#41×D7312yes—
214C22#1455663812yes—
215C4—22no—
216C4—22no—
217C4—41no—
218C4—42no—
219C4—42no—
220C4—2921no—
221C4—2922no—
222C4—2922no—
223C4—734no—
224C4—734no—
225C4—1462no—
226C2C22⋊Q8×D7311yescharacteristic
227C2#124×D7311yescharacteristic
228C2#1798915911yescharacteristic
229C2#1798930412yes—
230C2#1798931412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2568
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
41. C2×Dic146Q8semidirect
116. C73#2568semidirect