Finite Group Databasebeta

← #22620583

Subgroups — #22620583

Order 9344.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#17989197C212yesmaximal
2#17988988C211yesmaximal, characteristic, complemented
3#17988965C211yesmaximal, characteristic, complemented
4#17988954C212yesmaximal, complemented
5#17988843C212yesmaximal
6#17988828C211yesmaximal, characteristic
7#17988691C212yesmaximal, complemented
8Q16×Dic73C211yesmaximal, characteristic, complemented
9#17988681C211yesmaximal, characteristic, complemented
10#17988542C211yesmaximal, characteristic
11#467×C73C211yesmaximal, characteristic
12C2×Dic292C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924012C2211yescharacteristic
15#14556589C2212yes—
16#14556584—22no—
17#14556584—22no—
18#14556582—22no—
19#14556582C2212yes—
20#14556581—22no—
21#14556570C2212yes—
22Q8×Dic73C2212yes—
23#14556556C2212yes—
24#14556550C2211yescharacteristic
25#14556525C2211yescharacteristic
26#14556522C2212yes—
27#14556516C2212yes—
28#14556515C2212yes—
29#14556514C2212yes—
30#14556501C2211yescharacteristic
31#14556501C2211yescharacteristic
32C8×Dic73C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34C2×Q16×C73C2211yescharacteristic
35C22×C8×C73C2211yescharacteristic
36C22⋊Q8×C73C2212yes—
37#107×C73C2211yescharacteristic
38#103×C73C2212yes—
39C2×Dic146C2312yes—
40Dic292—22no—
41#11924018—24no—
42#11924012—22no—
43C2×#10596831C2311yescharacteristic
44C2×#10596831C2311yescharacteristic
45C4⋊Dic73—22no—
46C4⋊Dic73—22no—
47C4⋊Dic73D411yescharacteristic
48C4⋊Dic73D411yescharacteristic
49C4⋊Dic73C2312yes—
50#11924007—22no—
51#11924007—22no—
52#11924007—22no—
53#11924007—22no—
54#11924007—22no—
55C22⋊Dic73—22no—
56C22⋊Dic73D411yescharacteristic
57C22⋊Dic73D411yescharacteristic
58C4×Dic73—22no—
59C4×Dic73—22no—
60C4×Dic73C2311yescharacteristic
61C4×Dic73C2311yescharacteristic
62C2×Q8×C73C2312yes—
63C22×C4×C73C2311yescharacteristic
64Q16×C73—22no—
65C2×C8×C73—22no—
66C2×C8×C73C2311yescharacteristic
67C2×C8×C73C2311yescharacteristic
68C4⋊C4×C73—22no—
69C4⋊C4×C73C2312yes—
70C22⋊C4×C73—22no—
71C23×C73C2×D411yescharacteristic
72Q8×C73—22no—
73Q8×C73—22no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2411yescharacteristic
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73C2×D411yescharacteristic
83C2×Dic73C2×D411yescharacteristic
84C2×Dic73C2×D411yescharacteristic
85C2×Dic73C2×D411yescharacteristic
86Dic146—22no—
87Dic146—22no—
88C8×C73—21no—
89C8×C73#4112yes—
90#10596831—21no—
91#10596831#4112yes—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73C22×D411yescharacteristic
96C4×C73—21no—
97C4×C73—42no—
98C4×C73—42no—
99C4×C73C2×#4111yescharacteristic
100C4×C73C2×#4111yescharacteristic
101Dic73—21no—
102Dic73—21no—
103Dic73—21no—
104Dic73—21no—
105Dic73—42no—
106Dic73—42no—
107C2×C73—41no—
108C2×C73#53211yescharacteristic
109C2×C73#57811yescharacteristic
110C2×C73#57811yescharacteristic
111#3177—731nomaximal, Sylow
112C73#317711yescharacteristic, complemented, Sylow
113#541—732no—
114#499—731no—
115#494—731no—
116#491—732no—
117#470—732no—
118#467—731no—
119#467D7311yescharacteristic
120#441—732no—
121C4×Q16—731no—
122C4×Q16—731no—
123#405—731no—
124C2×Q16—732no—
125C2×Q16—731no—
126C2×Q16C2×D7311yescharacteristic
127C2×M16—731no—
128C22×C8C2×D7311yescharacteristic
129C4⋊Q8—732no—
130#126—1462no—
131#126—1462no—
132#125—732no—
133#125—1462no—
134#125—1462no—
135C22⋊Q8—732no—
136C22⋊Q8C2×D7312yes—
137C4×Q8—732no—
138C4×Q8—732no—
139#117—731no—
140#107—731no—
141#107C2×D7311yescharacteristic
142#106—732no—
143#103—732no—
144#103—732no—
145#103—732no—
146#103C2×D7312yes—
147#97—731no—
148#97—731no—
149C4×C8—731no—
150C4×C8—731no—
151C2×Q8—732no—
152C2×Q8C22×D7312yes—
153C22×C4C22×D7311yescharacteristic
154Q16—22no—
155Q16—1464no—
156Q16—1462no—
157M16—1462no—
158C2×C8—22no—
159C2×C8—731no—
160C2×C8—731no—
161C2×C8C22×D7311yescharacteristic
162C2×C8C22×D7311yescharacteristic
163C4⋊C4—22no—
164C4⋊C4—731no—
165C4⋊C4—731no—
166C4⋊C4—732no—
167C4⋊C4—1462no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1462no—
172C4⋊C4—1462no—
173C4⋊C4—1462no—
174C4⋊C4C22×D7312yes—
175C22⋊C4—22no—
176C22⋊C4—731no—
177C22⋊C4—731no—
178C22⋊C4—1462no—
179C42—731no—
180C42—731no—
181C42—1462no—
182C42—1462no—
183C23D4×D7311yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—1462no—
187Q8—1462no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—731no—
193C2×C4—731no—
194C2×C4—731no—
195C2×C4—731no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4D4×D7311yescharacteristic
199C2×C4C23×D7311yescharacteristic
200C8—21no—
201C8—732no—
202C8—1461no—
203C8#1192402712yes—
204C22—21no—
205C22—21no—
206C22—21no—
207C22C2×D4×D7311yescharacteristic
208C4—21no—
209C4—42no—
210C4—42no—
211C4—2922no—
212C4—2922no—
213C4—1461no—
214C4—1461no—
215C4—1461no—
216C4—1461no—
217C4#41×D7311yescharacteristic
218C4C2×#1192402711yescharacteristic
219C2—41no—
220C2#1798913211yescharacteristic
221C2#1798940011yescharacteristic
222C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#467×C73C2
socleC22×C73C22×D4
hypercenter#467D73
hypocenterC73#3177
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #17988988C2semidirect
3. #17988965C2semidirect
4. #17988954C2semidirect
7. #17988691C2semidirect
8. Q16×Dic73C2semidirect
9. #17988681C2semidirect
112. C73#3177semidirect