Finite Group Databasebeta

← #22620671

Subgroups — #22620671

Order 9344.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#17989139C212yesmaximal
2#17988984C211yesmaximal, characteristic, complemented
3#17988965C211yesmaximal, characteristic, complemented
4#17988936C212yesmaximal, complemented
5#17988845C211yesmaximal, characteristic
6#17988843C212yesmaximal
7#17988694C211yesmaximal, characteristic, complemented
8#17988693C211yesmaximal, characteristic, complemented
9#17988691C212yesmaximal, complemented
10M16×Dic73C211yesmaximal, characteristic
11#470×C73C211yesmaximal, characteristic
12C2×Dic292C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924012C2211yescharacteristic
15#14556590C2212yes—
16#14556589C2212yes—
17#14556581—22no—
18#14556570C2212yes—
19#14556568—22no—
20Q8×Dic73C2212yes—
21#14556556—22no—
22#14556556C2212yes—
23#14556547—22no—
24C2×C4×Dic73C2211yescharacteristic
25#14556523C2211yescharacteristic
26#14556522C2212yes—
27#14556516C2212yes—
28#14556515C2212yes—
29#14556514C2212yes—
30#14556501C2211yescharacteristic
31#14556501C2211yescharacteristic
32C8×Dic73C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34C2×Q16×C73C2211yescharacteristic
35C2×M16×C73C2211yescharacteristic
36C22⋊Q8×C73C2212yes—
37#106×C73C2211yescharacteristic
38#103×C73C2212yes—
39C2×Dic146—22no—
40C2×Dic146C2312yes—
41C22×Dic73D412yes—
42Dic292—22no—
43#11924018—24no—
44#11924012—22no—
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2311yescharacteristic
47C4⋊Dic73—22no—
48C4⋊Dic73C2312yes—
49#11924007—22no—
50#11924007—22no—
51#11924007—22no—
52#11924007—22no—
53#11924007—22no—
54C22⋊Dic73—22no—
55C4×Dic73—22no—
56C4×Dic73—22no—
57C4×Dic73D412yes—
58C4×Dic73C2311yescharacteristic
59C4×Dic73C2311yescharacteristic
60C2×Q8×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62Q16×C73—22no—
63M16×C73—22no—
64C2×C8×C73C2311yescharacteristic
65C2×C8×C73C2311yescharacteristic
66C4⋊C4×C73—22no—
67C4⋊C4×C73C2312yes—
68C22⋊C4×C73—22no—
69C23×C73C2×D411yescharacteristic
70Q8×C73—22no—
71Q8×C73—22no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2411yescharacteristic
78C2×Dic73—24no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73C2×D412yes—
82C2×Dic73C2×D412yes—
83Dic146—22no—
84Dic146—22no—
85Dic146—44no—
86C8×C73—21no—
87C8×C73#4112yes—
88#10596831—21no—
89#10596831#4112yes—
90C22×C73—21no—
91C22×C73—22no—
92C22×C73C22×D411yescharacteristic
93C4×C73—21no—
94C4×C73—42no—
95C4×C73—42no—
96C4×C73C2×#4111yescharacteristic
97C4×C73C2×#4111yescharacteristic
98Dic73—22no—
99Dic73—42no—
100Dic73—42no—
101Dic73#13714yes—
102C2×C73—41no—
103C2×C73#53211yescharacteristic
104C2×C73C2×#13712yes—
105#3185—731nomaximal, Sylow
106C73#318511yescharacteristic, complemented, Sylow
107#533—732no—
108#498—731no—
109#494—731no—
110#487—732no—
111#470—731no—
112#470—732no—
113#470D7311yescharacteristic
114#441—731no—
115#441—731no—
116#441—732no—
117C4×M16—731no—
118C2×Q16—732no—
119C2×Q16—731no—
120C2×Q16C2×D7311yescharacteristic
121C2×M16—731no—
122C2×M16C2×D7311yescharacteristic
123C4⋊Q8—732no—
124C4⋊Q8—732no—
125#125—1462no—
126C22⋊Q8—732no—
127C22⋊Q8—1462no—
128C22⋊Q8C2×D7312yes—
129C4×Q8—732no—
130C4×Q8—732no—
131C4×Q8—1462no—
132#117—1462no—
133C2×C42—731no—
134#106—731no—
135#106—732no—
136#106C2×D7311yescharacteristic
137#103—732no—
138#103—732no—
139#103—732no—
140#103C2×D7312yes—
141#97—731no—
142#97—731no—
143C4×C8—731no—
144C4×C8—731no—
145C2×Q8—732no—
146C2×Q8—1462no—
147C2×Q8C22×D7312yes—
148C22×C4—732no—
149C22×C4C22×D7311yescharacteristic
150Q16—22no—
151Q16—1464no—
152Q16—1462no—
153M16—22no—
154M16—1462no—
155C2×C8—731no—
156C2×C8—731no—
157C2×C8C22×D7311yescharacteristic
158C2×C8C22×D7311yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—732no—
161C4⋊C4—1462no—
162C4⋊C4—1462no—
163C4⋊C4—1462no—
164C4⋊C4—1462no—
165C4⋊C4—1462no—
166C4⋊C4—1462no—
167C4⋊C4C22×D7312yes—
168C22⋊C4—22no—
169C22⋊C4—1462no—
170C42—732no—
171C42—731no—
172C42—731no—
173C42—1462no—
174C42—1462no—
175C23D4×D7311yescharacteristic
176Q8—22no—
177Q8—22no—
178Q8—2924no—
179Q8—1462no—
180Q8—1462no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—732no—
186C2×C4—732no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4—1464no—
190C2×C4D4×D7311yescharacteristic
191C2×C4C23×D7311yescharacteristic
192C8—21no—
193C8—732no—
194C8—1461no—
195C8#1192402712yes—
196C22—22no—
197C22—21no—
198C22C2×D4×D7311yescharacteristic
199C4—21no—
200C4—42no—
201C4—42no—
202C4—2922no—
203C4—2922no—
204C4—734no—
205C4—1462no—
206C4#41×D7311yescharacteristic
207C4C2×#1192402711yescharacteristic
208C2—41no—
209C2#1798913211yescharacteristic
210C2#137×D7312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#470×C73C2
socleC22×C73C22×D4
hypercenter#470D73
hypocenterC73#3185
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #17988984C2semidirect
3. #17988965C2semidirect
4. #17988936C2semidirect
7. #17988694C2semidirect
8. #17988693C2semidirect
9. #17988691C2semidirect
106. C73#3185semidirect