Finite Group Databasebeta

← #22619776

Subgroups — #22619776

Order 9344.

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

normal subgroups only

This group has 362 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
1#17989215C211yesmaximal, characteristic
2#17989064C211yesmaximal, characteristic
3#17988897C212yesmaximal, complemented
4#17988893C212yesmaximal, complemented
5#17988881C212yesmaximal, complemented
6#17988871C212yesmaximal, complemented
7#17988630C211yesmaximal, characteristic
8#17988613C211yesmaximal, characteristic
9#17988595C211yesmaximal, characteristic
10C2×#14556516C211yesmaximal, characteristic
11#427×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C2×#11924012C2211yescharacteristic
14#14556591—21no—
15#14556590C2212yes—
16#14556583—21no—
17#14556582C2212yes—
18#14556568—22no—
19C4×Dic146—21no—
20C4×Dic146—21no—
21#14556556C2212yes—
22#14556556C2212yes—
23#14556550C2211yescharacteristic
24#14556547—22no—
25C2×C4⋊Dic73C2211yescharacteristic
26#14556524C2212yes—
27#14556522C2212yes—
28#14556520C2212yes—
29#14556520C2212yes—
30#14556516C2212yes—
31#14556516C2212yes—
32#14556514C2212yes—
33#14556514C2212yes—
34C22×C8×C73C2211yescharacteristic
35#117×C73C2211yescharacteristic
36#117×C73C2211yescharacteristic
37#107×C73C2211yescharacteristic
38#107×C73C2211yescharacteristic
39#106×C73C2211yescharacteristic
40#106×C73C2211yescharacteristic
41C2×Dic146—21no—
42C2×Dic146—22no—
43C2×Dic146—22no—
44C2×Dic146Q814yescomplemented
45C2×Dic146C2312yes—
46C22×Dic73—21no—
47C22×Dic73—21no—
48#11924012—22no—
49C2×#10596831C2312yes—
50C4⋊Dic73—21no—
51C4⋊Dic73—22no—
52C4⋊Dic73D411yescharacteristic
53C4⋊Dic73D411yescharacteristic
54C4⋊Dic73C2312yes—
55#11924007—22no—
56#11924007—22no—
57#11924007—22no—
58#11924007—22no—
59C22⋊Dic73D412yes—
60C4×Dic73—22no—
61C4×Dic73—22no—
62C4×Dic73C2312yes—
63C22×C4×C73C2311yescharacteristic
64C2×C8×C73—22no—
65C2×C8×C73C2311yescharacteristic
66C2×C8×C73C2311yescharacteristic
67C4⋊C4×C73C2311yescharacteristic
68C4⋊C4×C73C2311yescharacteristic
69C4⋊C4×C73C2311yescharacteristic
70C4⋊C4×C73C2311yescharacteristic
71C22⋊C4×C73—21no—
72C22⋊C4×C73—21no—
73C42×C73—21no—
74C42×C73—21no—
75C23×C73C2×D411yescharacteristic
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×Q812yes—
82C2×C4×C73#4112yes—
83C2×C4×C73C2411yescharacteristic
84C2×Dic73—24no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—81no—
88C2×Dic73C2×D412yes—
89C2×Dic73C2×D412yes—
90Dic146—24no—
91Dic146—22no—
92Dic146—82no—
93Dic146C2×Q814yes—
94C8×C73—21no—
95C8×C73—21no—
96#10596831—22no—
97C22×C73—21no—
98C22×C73—21no—
99C22×C73C22⋊Q812yes—
100C22×C73C22×D411yescharacteristic
101C4×C73—41no—
102C4×C73—41no—
103C4×C73—41no—
104C4×C73—41no—
105C4×C73C22⋊Q812yes—
106C4×C73C22×Q811yescharacteristic
107C4×C73C2×#4111yescharacteristic
108Dic73—24no—
109Dic73—22no—
110Dic73—22no—
111Dic73—42no—
112C2×C73—22no—
113C2×C73C2×C22⋊Q811yescharacteristic
114C2×C73#57711yescharacteristic
115C2×C73#57811yescharacteristic
116#3082—731nomaximal, Sylow
117C73#308211yescharacteristic, complemented, Sylow
118#544—731no—
119#519—731no—
120#479—732no—
121#479—732no—
122#477—732no—
123#475—732no—
124#428—731no—
125#427D7311yescharacteristic
126#424—731no—
127#419—731no—
128C2×#103—731no—
129C22×Q8—731no—
130C2×M16—731no—
131C22×C8C2×D7311yescharacteristic
132C4⋊Q8—732no—
133C4⋊Q8—1461no—
134#125—732no—
135#125—1461no—
136C22⋊Q8—1462no—
137C4×Q8—732no—
138C4×Q8—732no—
139C4×Q8—1461no—
140C4×Q8—1461no—
141#117—731no—
142#117—1462no—
143#117C2×D7311yescharacteristic
144#117C2×D7311yescharacteristic
145C2×C4⋊C4—731no—
146#107—732no—
147#107C2×D7311yescharacteristic
148#107C2×D7311yescharacteristic
149#106—732no—
150#106C2×D7311yescharacteristic
151#106C2×D7311yescharacteristic
152C4⋊C8—732no—
153C4⋊C8—732no—
154#103—732no—
155#103—732no—
156#103—732no—
157#103—732no—
158C2×Q8—734no—
159C2×Q8—732no—
160C2×Q8—1462no—
161C2×Q8—1461no—
162C2×Q8—1462no—
163C22×C4—1461no—
164C22×C4—1461no—
165C22×C4C22×D7311yescharacteristic
166M16—1462no—
167C2×C8—22no—
168C2×C8—732no—
169C2×C8C22×D7311yescharacteristic
170C2×C8C22×D7311yescharacteristic
171C4⋊C4—731no—
172C4⋊C4—731no—
173C4⋊C4—732no—
174C4⋊C4—1462no—
175C4⋊C4—1462no—
176C4⋊C4—1462no—
177C4⋊C4—1462no—
178C4⋊C4—1462no—
179C4⋊C4—1461no—
180C4⋊C4C22×D7311yescharacteristic
181C4⋊C4C22×D7311yescharacteristic
182C4⋊C4C22×D7311yescharacteristic
183C4⋊C4C22×D7311yescharacteristic
184C22⋊C4—21no—
185C22⋊C4—21no—
186C22⋊C4—732no—
187C42—21no—
188C42—21no—
189C42—732no—
190C42—1462no—
191C42—1462no—
192C23D4×D7311yescharacteristic
193Q8—5842no—
194Q8—734no—
195Q8—1464no—
196Q8—1462no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—5841no—
202C2×C4—732no—
203C2×C4—732no—
204C2×C4—1462no—
205C2×C4—1464no—
206C2×C4—1462no—
207C2×C4D4×D7311yescharacteristic
208C2×C4Q8×D7312yes—
209C2×C4#1192402812yes—
210C2×C4C23×D7311yescharacteristic
211C8—21no—
212C8—21no—
213C8—1462no—
214C22—21no—
215C22—21no—
216C22#1455656912yes—
217C22C2×D4×D7311yescharacteristic
218C4—41no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—2922no—
223C4—1462no—
224C4—1462no—
225C4—1464no—
226C4#1455656912yes—
227C4C2×Q8×D7311yescharacteristic
228C4C2×#1192402811yescharacteristic
229C2—22no—
230C2C2×#1455656911yescharacteristic
231C2#1798939411yescharacteristic
232C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#427×C73C2
socleC22×C73C22×D4
hypercenter#427D73
hypocenterC73#3082
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
3. #17988897C2semidirect
4. #17988893C2semidirect
5. #17988881C2semidirect
6. #17988871C2semidirect
44. C2×Dic146Q8semidirect
117. C73#3082semidirect