Finite Group Databasebeta

← #22620673

Subgroups — #22620673

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#17989141C212yesmaximal
2#17988984C211yesmaximal, characteristic, complemented
3#17988965C211yesmaximal, characteristic, complemented
4#17988936C212yesmaximal, complemented
5#17988846C211yesmaximal, characteristic
6#17988844C212yesmaximal
7#17988842C211yesmaximal, characteristic
8#17988695C211yesmaximal, characteristic, complemented
9#17988692C212yesmaximal, complemented
10#17988539C211yesmaximal, characteristic
11#441×C73C211yesmaximal, characteristic, complemented
12C2×Dic292C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924011C2211yescharacteristic
15C2×#11924011C2211yescharacteristic
16#14556590C2212yes—
17#14556589C2212yes—
18#14556581—22no—
19#14556571C2212yes—
20#14556569—22no—
21#14556567C2212yes—
22C4×Dic146—22no—
23C4×Dic146C2212yes—
24#14556548—22no—
25C42×D73C2211yescharacteristic
26#14556523C2211yescharacteristic
27#14556522C2212yes—
28#14556516C2212yes—
29#14556515C2212yes—
30#14556514C2212yes—
31#14556502C2211yescharacteristic
32C8×Dic73C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34C2×Q16×C73C2211yescharacteristic
35C4×Q8×C73C2212yes—
36#106×C73C2211yescharacteristic
37#103×C73C2212yes—
38#97×C73C2211yescharacteristic
39C2×Dic146—22no—
40C2×Dic146C2312yes—
41C2×C4×D73D412yes—
42C2×C4×D73C2311yescharacteristic
43Dic292—22no—
44#11924018—24no—
45#11924011—22no—
46#11924011—22no—
47C2×#10596831C2311yescharacteristic
48C2×#10596831C2311yescharacteristic
49C4⋊Dic73—22no—
50C4⋊Dic73C2312yes—
51#11924007—22no—
52#11924007—22no—
53#11924007—22no—
54#11924007—22no—
55#11924007—22no—
56#11924005—22no—
57#11924005—22no—
58C4×Dic73—22no—
59C4×Dic73D412yes—
60C4×Dic73C2311yescharacteristic
61C2×Q8×C73C2312yes—
62Q16×C73—22no—
63C2×C8×C73C2311yescharacteristic
64C2×C8×C73C2311yescharacteristic
65C4⋊C4×C73—22no—
66C4⋊C4×C73C2312yes—
67C42×C73—22no—
68C42×C73C2311yescharacteristic
69C22×D73C2×D411yescharacteristic
70Q8×C73—22no—
71Q8×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73C2×D412yes—
75C2×C4×C73C2411yescharacteristic
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73C2×D411yescharacteristic
79C2×Dic73C2×D412yes—
80C4×D73—21no—
81C4×D73—21no—
82C4×D73—24no—
83Dic146—22no—
84Dic146—22no—
85Dic146—44no—
86C8×C73—21no—
87C8×C73#4112yes—
88#10596831—21no—
89#10596831#4112yes—
90C22×C73C22×D411yescharacteristic
91C2×D73—21no—
92C2×D73—22no—
93C4×C73—22no—
94C4×C73—42no—
95C4×C73—42no—
96C4×C73C2×#4111yescharacteristic
97C4×C73C2×#4111yescharacteristic
98Dic73—21no—
99Dic73—42no—
100Dic73—42no—
101Dic73#13714yes—
102C2×C73#53211yescharacteristic
103C2×C73C2×#13712yes—
104D73—41no—
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—731no—
113#470—732no—
114#441—732no—
115#441—731no—
116#441D7311yescharacteristic, complemented
117C4×M16—731no—
118C2×Q16—732no—
119C2×Q16—731no—
120C2×Q16C2×D7311yescharacteristic
121C2×M16—731no—
122C2×M16—731no—
123C4⋊Q8—732no—
124C4⋊Q8—732no—
125#125—1462no—
126C22⋊Q8—732no—
127C22⋊Q8—732no—
128C22⋊Q8—1462no—
129C4×Q8—732no—
130C4×Q8—1462no—
131C4×Q8C2×D7312yes—
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#97C2×D7311yescharacteristic
143C4×C8—731no—
144C4×C8—731no—
145C2×Q8—732no—
146C2×Q8—1462no—
147C2×Q8C22×D7312yes—
148C22×C4—732no—
149C22×C4—731no—
150Q16—22no—
151Q16—1464no—
152Q16—1462no—
153M16—1462no—
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—1462no—
169C22⋊C4—1462no—
170C42—22no—
171C42—732no—
172C42—731no—
173C42—1462no—
174C42C22×D7311yescharacteristic
175C23—731no—
176Q8—22no—
177Q8—22no—
178Q8—2924no—
179Q8—1462no—
180Q8—1462no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—732no—
184C2×C4—731no—
185C2×C4—1464no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4—1461no—
189C2×C4—1461no—
190C2×C4D4×D7312yes—
191C2×C4C23×D7311yescharacteristic
192C8—21no—
193C8—732no—
194C8—1461no—
195C8#1192402812yes—
196C22—1462no—
197C22—1461no—
198C22C2×D4×D7311yescharacteristic
199C4—22no—
200C4—42no—
201C4—42no—
202C4—2922no—
203C4—2922no—
204C4—734no—
205C4—1461no—
206C4#41×D7311yescharacteristic
207C4C2×#1192402811yescharacteristic
208C2—2921no—
209C2#1798913411yescharacteristic
210C2#137×D7312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#441×C73C2
socleC22×C73C22×D4
hypercenter#441D73
hypocenterC73#3185
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #17988984C2semidirect
3. #17988965C2semidirect
4. #17988936C2semidirect
8. #17988695C2semidirect
9. #17988692C2semidirect
11. #441×C73C2semidirect
106. C73#3185semidirect
116. #441D73semidirect