Finite Group Databasebeta

← #22622208

Subgroups — #22622208

Order 9344.

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

normal subgroups only

This group has 374 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
1D4×Dic146C211yesmaximal, characteristic
2#17988939C211yesmaximal, characteristic, complemented
3#17988928C212yesmaximal, complemented
4#17988869C211yesmaximal, characteristic, complemented
5#17988843C212yesmaximal, complemented
6#17988797C211yesmaximal, characteristic, complemented
7#17988742C212yesmaximal, complemented
8C4×#11924018C211yesmaximal, characteristic, complemented
9#17988665C211yesmaximal, characteristic
10#17988595C212yesmaximal, complemented
11#556×C73C211yesmaximal, characteristic
12C22×Dic146C2212yes—
13C2×#11924018C2211yescharacteristic
14C2×#11924018C2212yes—
15C2×#11924012C2212yes—
16#14556591C2211yescharacteristic
17#14556590—21no—
18#14556570C2212yes—
19#14556568—22no—
20C4×Dic146C2211yescharacteristic
21D4×Dic73—21no—
22#14556524C2211yescharacteristic
23#14556522C2212yes—
24C4⋊#10596831C2211yescharacteristic
25#14556515C2211yescharacteristic
26#14556514C2212yes—
27#14556514C2212yes—
28#14556514C2212yes—
29#14556514C2211yescharacteristic
30#14556514C2212yes—
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—24no—
42C2×Dic146—22no—
43C2×Dic146—42no—
44C2×Dic146C2312yes—
45C2×Dic146C2311yescharacteristic
46C22×Dic73—22no—
47#11924018—22no—
48#11924018—42no—
49#11924012—42no—
50C2×#10596831C2311yescharacteristic
51C2×#10596831C2311yescharacteristic
52C2×#10596831C2312yes—
53C4⋊Dic73—21no—
54C4⋊Dic73—21no—
55C4⋊Dic73C2311yescharacteristic
56#11924007—21no—
57#11924007—22no—
58C22⋊Dic73—22no—
59C4×Dic73—21no—
60C2×Q8×C73—21no—
61C2×Q8×C73C2311yescharacteristic
62C2×D4×C73D411yescharacteristic
63C22×C4×C73C2312yes—
64C4⋊C4×C73—22no—
65C4⋊C4×C73—21no—
66C4⋊C4×C73—21no—
67C4⋊C4×C73D411yescharacteristic
68C4⋊C4×C73C2311yescharacteristic
69C4⋊C4×C73C2312yes—
70C22⋊C4×C73—22no—
71C22⋊C4×C73—22no—
72C22⋊C4×C73D412yes—
73C42×C73—22no—
74C42×C73—21no—
75C42×C73C2311yescharacteristic
76C23×C73C2×D412yes—
77Q8×C73—21no—
78Q8×C73—21no—
79Q8×C73—42no—
80D4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—22no—
86C2×C4×C73C2×D412yes—
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2411yescharacteristic
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—22no—
93C2×Dic73—44no—
94Dic146—21no—
95Dic146—22no—
96Dic146—22no—
97Dic146—44no—
98Dic146#4112yes—
99#10596831—21no—
100#10596831—21no—
101#10596831—22no—
102C22×C73—22no—
103C22×C73—22no—
104C22×C73—22no—
105C22×C73C22×D411yescharacteristic
106C4×C73—22no—
107C4×C73—21no—
108C4×C73—41no—
109C4×C73—42no—
110C4×C73—41no—
111C4×C73#13712yes—
112C4×C73C2×#4111yescharacteristic
113C4×C73H(5,𝔽2)11yescharacteristic
114Dic73—22no—
115Dic73—42no—
116Dic73—41no—
117C2×C73—42no—
118C2×C73#54611yescharacteristic
119C2×C73C2×#13711yescharacteristic
120C2×C73#57811yescharacteristic
121#3328—731nomaximal, Sylow
122C73#332811yescharacteristic, complemented, Sylow
123#556D7311yescharacteristic
124D4×Q8—731no—
125#487—731no—
126#485—732no—
127#475—731no—
128#470—732no—
129#462—731no—
130#451—732no—
131C4×Q16—731no—
132#436—731no—
133#419—732no—
134C22×Q8—732no—
135C2×Q16—732no—
136C2×Q16—731no—
137C2×M16—732no—
138C4⋊Q8—731no—
139C4⋊Q8—1461no—
140C4⋊Q8C2×D7311yescharacteristic
141#126—22no—
142#124—21no—
143C22⋊Q8—732no—
144C22⋊Q8—1462no—
145C22⋊Q8C2×D7312yes—
146C4×Q8—21no—
147C4×Q8—731no—
148C4×Q8C2×D7311yescharacteristic
149C4×D4—1461no—
150C4×D4C2×D7311yescharacteristic
151#117C2×D7312yes—
152#107—731no—
153#106—732no—
154C4⋊C8—731no—
155#103—731no—
156#103—731no—
157#103—732no—
158#103—732no—
159#103—732no—
160#103—732no—
161C22⋊C8—732no—
162C4×C8—731no—
163C2×Q8—21no—
164C2×Q8—2922no—
165C2×Q8—731no—
166C2×Q8—732no—
167C2×Q8—1464no—
168C2×Q8—1462no—
169C2×Q8C22×D7311yescharacteristic
170C2×D4C22⋊D7311yescharacteristic
171C22×C4—1462no—
172C22×C4C22×D7312yes—
173Q16—2922no—
174Q16—1462no—
175M16—2922no—
176C2×C8—731no—
177C2×C8—731no—
178C2×C8—732no—
179C4⋊C4—22no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—731no—
183C4⋊C4—1461no—
184C4⋊C4—1462no—
185C4⋊C4—1461no—
186C4⋊C4—1461no—
187C4⋊C4C22⋊D7311yescharacteristic
188C4⋊C4C22×D7312yes—
189C4⋊C4C22×D7311yescharacteristic
190C22⋊C4—22no—
191C22⋊C4—22no—
192C22⋊C4—1462no—
193C22⋊C4C22⋊D7312yes—
194C42—22no—
195C42—21no—
196C42—1461no—
197C42C22×D7311yescharacteristic
198C23C2×C22⋊D7312yes—
199Q8—21no—
200Q8—21no—
201Q8—42no—
202Q8—2924no—
203Q8—732no—
204Q8—1462no—
205Q8—1462no—
206Q8—1461no—
207D4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—2924no—
214C2×C4—1461no—
215C2×C4—1462no—
216C2×C4—1461no—
217C2×C4C2×C22⋊D7312yes—
218C2×C4C2×C22⋊D7311yescharacteristic
219C2×C4C2×C22⋊D7311yescharacteristic
220C2×C4C23×D7311yescharacteristic
221C8—1461no—
222C8—1461no—
223C8—1462no—
224C22—22no—
225C22—22no—
226C22—22no—
227C22C22×C22⋊D7311yescharacteristic
228C4—21no—
229C4—22no—
230C4—42no—
231C4—41no—
232C4—41no—
233C4—2921no—
234C4—2922no—
235C4—1462no—
236C4#1455662112yes—
237C4#41×D7311yescharacteristic
238C4#1455663711yescharacteristic
239C2—42no—
240C2#1798922511yescharacteristic
241C2C2×#1455662111yescharacteristic
242C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#556×C73C2
socleC22×C73C22×D4
hypercenter#556D73
hypocenterC73#3328
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. #17988939C2semidirect
3. #17988928C2semidirect
4. #17988869C2semidirect
5. #17988843C2semidirect
6. #17988797C2semidirect
7. #17988742C2semidirect
8. C4×#11924018C2semidirect
10. #17988595C2semidirect
122. C73#3328semidirect