Finite Group Databasebeta

← #22622357

Subgroups — #22622357

Order 9344.

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

normal subgroups only

This group has 340 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#17989307C211yesmaximal, characteristic
2#17988990C211yesmaximal, characteristic, complemented
3#17988928C212yesmaximal, complemented
4#17988925C212yesmaximal, complemented
5#17988872C211yesmaximal, characteristic, complemented
6#17988869C211yesmaximal, characteristic, complemented
7#17988826C212yesmaximal, complemented
8C4×#11924018C211yesmaximal, characteristic, complemented
9D4×#10596831C211yesmaximal, characteristic
10#17988623C212yesmaximal, complemented
11#556×C73C211yesmaximal, characteristic
12C2×#11924018C2211yescharacteristic
13C22×#10596831C2212yes—
14#14556591C2211yescharacteristic
15#14556584—22no—
16#14556578—21no—
17#14556570C2212yes—
18C4×Dic146C2211yescharacteristic
19#14556556—21no—
20#14556550C2212yes—
21#14556524C2211yescharacteristic
22#14556524C2212yes—
23#14556524C2212yes—
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
43#11924018—22no—
44C2×#10596831—24no—
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2312yes—
47C2×#10596831C2311yescharacteristic
48C4⋊Dic73—21no—
49C4⋊Dic73C2311yescharacteristic
50C4⋊Dic73C2312yes—
51#11924007—22no—
52#11924007—21no—
53C22⋊Dic73—22no—
54C22⋊Dic73—22no—
55C4×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—
90Dic146—21no—
91Dic146—21no—
92Dic146—42no—
93#10596831—22no—
94#10596831—21no—
95#10596831#4112yes—
96C22×C73—22no—
97C22×C73—22no—
98C22×C73—22no—
99C22×C73C22×D411yescharacteristic
100C4×C73—22no—
101C4×C73—21no—
102C4×C73—41no—
103C4×C73—42no—
104C4×C73—41no—
105C4×C73#13512yes—
106C4×C73C2×#4111yescharacteristic
107C4×C732−1+411yescharacteristic
108Dic73—41no—
109Dic73—42no—
110Dic73—41no—
111C2×C73—42no—
112C2×C73#54711yescharacteristic
113C2×C73C2×#13511yescharacteristic
114C2×C73#57811yescharacteristic
115#3342—731nomaximal, Sylow
116C73#334211yescharacteristic, complemented, Sylow
117#556—731no—
118#556D7311yescharacteristic
119#500—731no—
120#485—732no—
121#485—732no—
122#475—731no—
123#475—731no—
124#467—732no—
125C4×Q16—731no—
126C8×D4—731no—
127#427—732no—
128C2×Q16—731no—
129C22×C8—732no—
130C4⋊Q8—731no—
131C4⋊Q8C2×D7311yescharacteristic
132#126—22no—
133#126—1462no—
134#124—21no—
135#124—1461no—
136C22⋊Q8—732no—
137C22⋊Q8C2×D7312yes—
138C4×Q8—21no—
139C4×Q8—731no—
140C4×Q8—1461no—
141C4×Q8C2×D7311yescharacteristic
142C4×D4C2×D7311yescharacteristic
143#117—732no—
144#117C2×D7312yes—
145#107—731no—
146#107—732no—
147#107—732no—
148#106—732no—
149#106—732no—
150C4⋊C8—731no—
151#103—731no—
152#103—732no—
153#103—731no—
154#103—732no—
155C22⋊C8—732no—
156C4×C8—731no—
157C2×Q8—21no—
158C2×Q8—731no—
159C2×Q8—1461no—
160C2×Q8C22×D7311yescharacteristic
161C2×D4C22⋊D7311yescharacteristic
162C22×C4C22×D7312yes—
163Q16—1462no—
164C2×C8—731no—
165C2×C8—731no—
166C2×C8—732no—
167C2×C8—1464no—
168C4⋊C4—22no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—731no—
172C4⋊C4—732no—
173C4⋊C4—1461no—
174C4⋊C4—1462no—
175C4⋊C4—1461no—
176C4⋊C4C22⋊D7311yescharacteristic
177C4⋊C4C22×D7311yescharacteristic
178C4⋊C4C22×D7312yes—
179C22⋊C4—22no—
180C22⋊C4—22no—
181C22⋊C4—1462no—
182C22⋊C4—1462no—
183C22⋊C4C22⋊D7312yes—
184C42—22no—
185C42—21no—
186C42—1462no—
187C42—1461no—
188C42C22×D7311yescharacteristic
189C23C2×C22⋊D7312yes—
190Q8—21no—
191Q8—21no—
192Q8—42no—
193Q8—2922no—
194Q8—1461no—
195Q8—1461no—
196D4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—1461no—
203C2×C4—1462no—
204C2×C4—1461no—
205C2×C4C2×C22⋊D7312yes—
206C2×C4C2×C22⋊D7311yescharacteristic
207C2×C4C2×C22⋊D7311yescharacteristic
208C2×C4C23×D7311yescharacteristic
209C8—732no—
210C8—1462no—
211C8—1461no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22C22×C22⋊D7311yescharacteristic
216C4—21no—
217C4—22no—
218C4—41no—
219C4—41no—
220C4—42no—
221C4—2921no—
222C4—2921no—
223C4—2922no—
224C4#1455661112yes—
225C4#41×D7311yescharacteristic
226C4#1455663811yescharacteristic
227C2—42no—
228C2#1798923611yescharacteristic
229C2C2×#1455661111yescharacteristic
230C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#556×C73C2
socleC22×C73C22×D4
hypercenter#556D73
hypocenterC73#3342
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. #17988990C2semidirect
3. #17988928C2semidirect
4. #17988925C2semidirect
5. #17988872C2semidirect
6. #17988869C2semidirect
7. #17988826C2semidirect
8. C4×#11924018C2semidirect
10. #17988623C2semidirect
116. C73#3342semidirect