Finite Group Databasebeta

← #22622540

Subgroups — #22622540

Order 9344.

342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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#17989294C211yesmaximal, characteristic
2#17988983C211yesmaximal, characteristic, complemented
3#17988928C212yesmaximal, complemented
4#17988915C212yesmaximal, complemented
5#17988882C211yesmaximal, characteristic, complemented
6#17988869C211yesmaximal, characteristic, complemented
7#17988843C212yesmaximal, complemented
8C4×#11924018C211yesmaximal, characteristic, complemented
9#17988665C211yesmaximal, characteristic
10#17988630C212yesmaximal, complemented
11#556×C73C211yesmaximal, characteristic
12C2×#11924018C2211yescharacteristic
13C2×#11924012C2212yes—
14#14556591C2211yescharacteristic
15#14556582—21no—
16#14556570C2212yes—
17#14556568—22no—
18C4×Dic146C2211yescharacteristic
19D4×Dic73—21no—
20C2×C4⋊Dic73C2212yes—
21#14556524C2212yes—
22#14556524C2211yescharacteristic
23#14556522C2212yes—
24#14556522C2212yes—
25#14556522C2212yes—
26C4⋊#10596831C2211yescharacteristic
27#14556515C2212yes—
28#14556515C2211yescharacteristic
29#14556514C2212yes—
30#14556514C2211yescharacteristic
31C22⋊#10596831C2212yes—
32C4×#10596831C2211yescharacteristic
33C4⋊Q8×C73C2211yescharacteristic
34#126×C73—22no—
35#124×C73—21no—
36C22⋊Q8×C73C2212yes—
37C4×Q8×C73—21no—
38C4×Q8×C73C2211yescharacteristic
39C4×D4×C73C2211yescharacteristic
40#117×C73C2212yes—
41C2×Dic146—21no—
42C2×Dic146C2311yescharacteristic
43C22×Dic73—22no—
44#11924018—22no—
45#11924012—24no—
46C2×#10596831C2311yescharacteristic
47C2×#10596831C2312yes—
48C2×#10596831C2311yescharacteristic
49C4⋊Dic73—22no—
50C4⋊Dic73—21no—
51C4⋊Dic73C2311yescharacteristic
52C4⋊Dic73C2312yes—
53#11924007—21no—
54#11924007—22no—
55C22⋊Dic73—22no—
56C4×Dic73—21no—
57C2×Q8×C73—21no—
58C2×Q8×C73C2311yescharacteristic
59C2×D4×C73D411yescharacteristic
60C22×C4×C73C2312yes—
61C4⋊C4×C73—22no—
62C4⋊C4×C73—21no—
63C4⋊C4×C73—21no—
64C4⋊C4×C73D411yescharacteristic
65C4⋊C4×C73C2311yescharacteristic
66C4⋊C4×C73C2312yes—
67C22⋊C4×C73—22no—
68C22⋊C4×C73—22no—
69C22⋊C4×C73D412yes—
70C42×C73—22no—
71C42×C73—21no—
72C42×C73C2311yescharacteristic
73C23×C73C2×D412yes—
74Q8×C73—21no—
75Q8×C73—21no—
76Q8×C73—42no—
77D4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D412yes—
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2411yescharacteristic
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—22no—
90C2×Dic73—82no—
91Dic146—21no—
92Dic146—21no—
93Dic146—81no—
94#10596831—22no—
95#10596831—21no—
96#10596831#4112yes—
97C22×C73—22no—
98C22×C73—22no—
99C22×C73—22no—
100C22×C73C22×D411yescharacteristic
101C4×C73—22no—
102C4×C73—21no—
103C4×C73—41no—
104C4×C73—42no—
105C4×C73—41no—
106C4×C73#13712yes—
107C4×C73C2×#4111yescharacteristic
108C4×C732−1+411yescharacteristic
109Dic73—41no—
110Dic73—42no—
111Dic73—41no—
112C2×C73—42no—
113C2×C73#54711yescharacteristic
114C2×C73C2×#13711yescharacteristic
115C2×C73#57711yescharacteristic
116#3356—731nomaximal, Sylow
117C73#335611yescharacteristic, complemented, Sylow
118#556D7311yescharacteristic
119#554—731no—
120#498—731no—
121#485—732no—
122#483—732no—
123#477—731no—
124#475—731no—
125#470—732no—
126C4×Q16—731no—
127#436—731no—
128#428—732no—
129C2×Q16—731no—
130C2×M16—732no—
131C4⋊Q8—731no—
132C4⋊Q8C2×D7311yescharacteristic
133#126—22no—
134#125—1461no—
135#124—21no—
136C22⋊Q8—732no—
137C22⋊Q8—1462no—
138C22⋊Q8C2×D7312yes—
139C4×Q8—21no—
140C4×Q8—731no—
141C4×Q8C2×D7311yescharacteristic
142C4×D4—1461no—
143C4×D4C2×D7311yescharacteristic
144#117C2×D7312yes—
145C2×C4⋊C4—732no—
146#107—731no—
147#107—732no—
148#106—732no—
149#106—732no—
150#106—732no—
151C4⋊C8—731no—
152#103—731no—
153#103—732no—
154#103—731no—
155#103—732no—
156C22⋊C8—732no—
157C4×C8—731no—
158C2×Q8—21no—
159C2×Q8—731no—
160C2×Q8—1461no—
161C2×Q8C22×D7311yescharacteristic
162C2×D4C22⋊D7311yescharacteristic
163C22×C4—1462no—
164C22×C4C22×D7312yes—
165Q16—1462no—
166M16—1464no—
167C2×C8—731no—
168C2×C8—731no—
169C2×C8—732no—
170C4⋊C4—22no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—731no—
174C4⋊C4—732no—
175C4⋊C4—1461no—
176C4⋊C4—1462no—
177C4⋊C4—1462no—
178C4⋊C4—1461no—
179C4⋊C4C22⋊D7311yescharacteristic
180C4⋊C4C22×D7312yes—
181C4⋊C4C22×D7311yescharacteristic
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—1462no—
185C22⋊C4C22⋊D7312yes—
186C42—22no—
187C42—21no—
188C42—1461no—
189C42C22×D7311yescharacteristic
190C23C2×C22⋊D7312yes—
191Q8—21no—
192Q8—21no—
193Q8—42no—
194Q8—5841no—
195Q8—1461no—
196Q8—1461no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—5842no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1462no—
207C2×C4C2×C22⋊D7312yes—
208C2×C4C2×C22⋊D7311yescharacteristic
209C2×C4C2×C22⋊D7311yescharacteristic
210C2×C4C23×D7311yescharacteristic
211C8—732no—
212C8—1462no—
213C8—1461no—
214C22—22no—
215C22—22no—
216C22—22no—
217C22C22×C22⋊D7311yescharacteristic
218C4—21no—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—2921no—
224C4—2922no—
225C4—2921no—
226C4#1455662112yes—
227C4#41×D7311yescharacteristic
228C4#1455663811yescharacteristic
229C2—42no—
230C2#1798923611yescharacteristic
231C2C2×#1455662111yescharacteristic
232C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#556×C73C2
socleC22×C73C22×D4
hypercenter#556D73
hypocenterC73#3356
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #17988983C2semidirect
3. #17988928C2semidirect
4. #17988915C2semidirect
5. #17988882C2semidirect
6. #17988869C2semidirect
7. #17988843C2semidirect
8. C4×#11924018C2semidirect
10. #17988630C2semidirect
117. C73#3356semidirect