Finite Group Databasebeta

← #22615878

Subgroups — #22615878

Order 9344.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556581C211yesmaximal, characteristic
3#17988529C212yesmaximal
4#17988528C212yesmaximal
5#17988527C211yesmaximal, characteristic
6#17988526C211yesmaximal, characteristic
7#17988525C211yesmaximal, characteristic
8#17988491C212yesmaximal
9#17988491C212yesmaximal
10#17988432C211yesmaximal, characteristic
11#400×C73C211yesmaximal, characteristic
12C22×Dic146C2212yes—
13#14556590—24no—
14#14556581—24no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2212yes—
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×C4×Dic73C2212yes—
23C2×C4×Dic73C2211yescharacteristic
24#14556498C2211yescharacteristic
25#14556498C2212yes—
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—24no—
38C2×Dic146—28no—
39C22×Dic73C2312yes—
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2311yescharacteristic
45C4⋊Dic73—22no—
46C4⋊Dic73—22no—
47#11924007—22no—
48#11924007—22no—
49#11924007—22no—
50#11924007—22no—
51#11924007—24no—
52C4×Dic73—24no—
53C4×Dic73D414yes—
54C22×C4×C73C2312yes—
55C22×C4×C73C2311yescharacteristic
56C22×C4×C73C2311yescharacteristic
57C22×C4×C73C2312yes—
58C22×C4×C73C2311yescharacteristic
59C4⋊C4×C73—22no—
60C4⋊C4×C73—22no—
61C23×C73C2411yescharacteristic
62C2×C4×C73—22no—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—24no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—21no—
73C2×C4×C73C2×D412yes—
74C2×Dic73—21no—
75C2×Dic73—21no—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—24no—
81C2×Dic73—22no—
82C2×Dic73—21no—
83C2×Dic73—22no—
84C2×Dic73—21no—
85C2×Dic73—22no—
86C2×Dic73C2×D412yes—
87C2×Dic73C2×D412yes—
88C2×Dic73#4114yes—
89Dic146—48no—
90C22×C73C22×D411yescharacteristic
91C22×C73C2×#4112yes—
92C22×C732−1+412yes—
93C22×C732−1+411yescharacteristic
94C22×C732−1+411yescharacteristic
95C4×C73—22no—
96C4×C73—42no—
97C4×C73—41no—
98C4×C73—41no—
99C4×C73—42no—
100Dic73—22no—
101Dic73—42no—
102Dic73—41no—
103Dic73—41no—
104Dic73—42no—
105Dic73#12414yes—
106C2×C73C2×#12411yescharacteristic
107C2×C73#53611yescharacteristic
108C2×C73#53611yescharacteristic
109C2×C73#54112yes—
110C2×C73#54112yes—
111#2642—731nomaximal, Sylow
112C73#264211yescharacteristic, complemented, Sylow
113C2×C4⋊Q8—731no—
114C2×#125—731no—
115#400—731no—
116#400—731no—
117#400—731no—
118#400—732no—
119#400—732no—
120#400D7311yescharacteristic
121#391—732no—
122#391—732no—
123#376—731no—
124C22×Q8—732no—
125C4⋊Q8—1464no—
126#125—1464no—
127C2×C4⋊C4—731no—
128C2×C4⋊C4—731no—
129C2×C4⋊C4—731no—
130C2×C4⋊C4—731no—
131C2×C4⋊C4—731no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—731no—
134C2×C4⋊C4C2×D7311yescharacteristic
135C2×C4⋊C4C2×D7311yescharacteristic
136C2×C42—731no—
137C2×C42—732no—
138#95—732no—
139#95—731no—
140#95—732no—
141#95—732no—
142#95—732no—
143#95—732no—
144#95—732no—
145#95—732no—
146#95C2×D7311yescharacteristic
147#95C2×D7312yes—
148#95C2×D7312yes—
149C2×Q8—1464no—
150C2×Q8—1468no—
151C22×C4—731no—
152C22×C4—731no—
153C22×C4—732no—
154C22×C4—731no—
155C22×C4—731no—
156C22×C4—732no—
157C22×C4C22×D7312yes—
158C22×C4C22×D7311yescharacteristic
159C22×C4C22×D7311yescharacteristic
160C22×C4C22×D7312yes—
161C22×C4C22×D7311yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—1462no—
165C4⋊C4—1462no—
166C4⋊C4—1462no—
167C4⋊C4—1464no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C42—734no—
172C42—1464no—
173C23C23×D7311yescharacteristic
174Q8—2928no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—732no—
187C2×C4—734no—
188C2×C4—732no—
189C2×C4—1461no—
190C2×C4—1461no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1464no—
194C2×C4—1462no—
195C2×C4—1461no—
196C2×C4—1462no—
197C2×C4—1461no—
198C2×C4—1462no—
199C2×C4—1461no—
200C2×C4—1461no—
201C2×C4D4×D7312yes—
202C22C2×D4×D7311yescharacteristic
203C22#41×D7312yes—
204C22#1455663812yes—
205C22#1455663811yescharacteristic
206C22#1455663911yescharacteristic
207C4—22no—
208C4—41no—
209C4—41no—
210C4—42no—
211C4—42no—
212C4—2921no—
213C4—2921no—
214C4—2922no—
215C4—2922no—
216C4—734no—
217C4—1462no—
218C2#124×D7311yescharacteristic
219C2#1798915911yescharacteristic
220C2#1798916011yescharacteristic
221C2#1798919412yes—
222C2#1798919612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2642
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
112. C73#2642semidirect