Finite Group Databasebeta

← #22608909

Subgroups — #22608909

Order 9344.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 49 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#17989175C211yesmaximal, characteristic
2#17988743C211yesmaximal, characteristic, complemented
3#17988726C211yesmaximal, characteristic, complemented
4#17988323C211yesmaximal, characteristic, complemented
5#17988320C211yesmaximal, characteristic, complemented
6#17988311C211yesmaximal, characteristic, complemented
7#393×C73C211yesmaximal, characteristic, complemented
8C2×#11924018—21no—
9C2×#11924015—21no—
10#14556584—21no—
11#14556577—21no—
12#14556573—21no—
13#14556570C2211yescharacteristic
14#14556565C2211yescharacteristic
15#14556564—21no—
16#14556560—21no—
17C4×C22⋊D73—21no—
18#14556515—21no—
19#14556515—21no—
20C22⋊#10596831C2211yescharacteristic
21C22⋊#10596831C2211yescharacteristic
22C22×Q8×C73C2211yescharacteristic
23C2×C22⋊C4×C73—21no—
24C2×C22⋊C4×C73C2211yescharacteristic
25#95×C73—21no—
26#95×C73C2211yescharacteristic
27C2×Dic146D411yescharacteristic
28C2×D292D411yescharacteristic
29C2×C22⋊D73—21no—
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C2×C4×D73—21no—
33#11924018—42no—
34#11924015—42no—
35C2×#10596831—21no—
36C2×#10596831—21no—
37C4⋊Dic73D411yescharacteristic
38C4⋊Dic73D411yescharacteristic
39#11924007—21no—
40#11924007—21no—
41C22⋊Dic73—21no—
42C22⋊Dic73—21no—
43C22⋊Dic73—21no—
44#11924005—21no—
45#11924005—21no—
46C4×Dic73—21no—
47C24×C73D411yescharacteristic
48C2×Q8×C73—21no—
49C2×Q8×C73—21no—
50C2×Q8×C73—42no—
51C22×C4×C73—21no—
52C22×C4×C73—21no—
53C22×C4×C73D411yescharacteristic
54C22×C4×C73C2311yescharacteristic
55C22⋊C4×C73—21no—
56C22⋊C4×C73—21no—
57C22⋊C4×C73—42no—
58C23×C73—21no—
59C23×C73—21no—
60C23×C73—21no—
61C23×C73—41no—
62C23×C73—41no—
63C23×C73C2×D411yescharacteristic
64C22×D73—21no—
65Q8×C73—22no—
66Q8×C73—22no—
67Q8×C73—41no—
68Q8×C73—41no—
69C2×C4×C73—22no—
70C2×C4×C73—21no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73—41no—
74C2×C4×C73—41no—
75C2×C4×C73—41no—
76C2×C4×C73—41no—
77C2×C4×C73—41no—
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D411yescharacteristic
80C22⋊D73—41no—
81C22⋊D73—41no—
82C22⋊D73—81no—
83C22⋊D73—81no—
84C2×Dic73—21no—
85C2×Dic73—21no—
86C2×Dic73—21no—
87D292—41no—
88C4×D73—81no—
89Dic146—41no—
90#10596831—41no—
91#10596831—41no—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73—42no—
95C22×C73—41no—
96C22×C73—41no—
97C22×C73—41no—
98C22×C73—81no—
99C22×C73#12011yescharacteristic
100C22×C73#13511yescharacteristic
101C22×C73#13711yescharacteristic
102C2×D73—41no—
103C2×D73—41no—
104C2×D73—41no—
105C4×C73—21no—
106C4×C73—21no—
107C4×C73—41no—
108C4×C73—42no—
109C4×C73—81no—
110Dic73—41no—
111Dic73—41no—
112Dic73—41no—
113C2×C73—21no—
114C2×C73—21no—
115C2×C73—81no—
116C2×C73#45211yescharacteristic
117C2×C73#45511yescharacteristic
118C2×C73B(4,𝔽2)11yescharacteristic
119D73—81no—
120#1606—731nomaximal, Sylow
121C73#160611yescharacteristic, complemented, Sylow
122#538—731no—
123#451—731no—
124#448—731no—
125#393D7311yescharacteristic, complemented
126#328—731no—
127#327—731no—
128#323—731no—
129C22×Q8C2×D7311yescharacteristic
130C2×Q16—1461no—
131C2×SD16—1461no—
132#126—1461no—
133#124—1461no—
134#123—1461no—
135C22⋊Q8—731no—
136#121—731no—
137#121—1461no—
138#120—1461no—
139C4×D4—1461no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4C2×D7311yescharacteristic
142#103—1461no—
143#103—1461no—
144C22⋊C8—731no—
145C22⋊C8—731no—
146#95—21no—
147#95C2×D7311yescharacteristic
148C24C22⋊D7311yescharacteristic
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8—731no—
153C2×D4—731no—
154C2×D4—1461no—
155C2×D4—1461no—
156C2×D4—1461no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—1461no—
160C22×C4C22⋊D7311yescharacteristic
161C22×C4C22×D7311yescharacteristic
162Q16—2922no—
163SD16—2922no—
164C2×C8—1461no—
165C2×C8—1461no—
166C4⋊C4—731no—
167C4⋊C4—731no—
168C4⋊C4—1461no—
169C4⋊C4—1461no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—42no—
173C22⋊C4—1461no—
174C22⋊C4—1461no—
175C22⋊C4—1461no—
176C22⋊C4—1461no—
177C22⋊C4—1461no—
178C42—1461no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23—1461no—
185C23C2×C22⋊D7311yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—2921no—
191D4—2921no—
192D4—2921no—
193D4—2921no—
194D4—5841no—
195D4—5841no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—5841no—
206C2×C4—1461no—
207C2×C4—1461no—
208C2×C4—1461no—
209C2×C4D4×D7311yescharacteristic
210C2×C4D4×D7311yescharacteristic
211C8—2921no—
212C8—2921no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—2921no—
221C22—2921no—
222C22—2921no—
223C22#1455655911yescharacteristic
224C22#1455661111yescharacteristic
225C22#1455662211yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—81no—
231C4—2921no—
232C4—2921no—
233C4—2921no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—5841no—
238C2#1798874711yescharacteristic
239C2#1798876411yescharacteristic
240C2#1798877311yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#393×C73C2
socleC22×C73#120
hypercenter#393D73
hypocenterC73#1606
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #17988743C2semidirect
3. #17988726C2semidirect
4. #17988323C2semidirect
5. #17988320C2semidirect
6. #17988311C2semidirect
7. #393×C73C2semidirect
121. C73#1606semidirect
125. #393D73semidirect