Finite Group Databasebeta

← #22608346

Subgroups — #22608346

Order 9344.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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#17989134C211yesmaximal, characteristic
2#17988639C211yesmaximal, characteristic, complemented
3C4×#11924011C211yesmaximal, characteristic, complemented
4#17988316C211yesmaximal, characteristic, complemented
5D4⋊#10596831C211yesmaximal, characteristic, complemented
6#17988314C211yesmaximal, characteristic, complemented
7D4⋊C8×C73C211yesmaximal, characteristic, complemented
8C2×#11924028—21no—
9C2×#11924011—21no—
10#14556590C411yescharacteristic
11#14556587C411yescharacteristic
12#14556577—21no—
13#14556566C411yescharacteristic
14#14556564—21no—
15#14556562C411yescharacteristic
16C4×D292C2211yescharacteristic
17C4×C22⋊D73—21no—
18C42×D73C2211yescharacteristic
19C4⋊#10596831C2211yescharacteristic
20#14556503—21no—
21#14556501—21no—
22C4×#10596831C2211yescharacteristic
23C8×Dic73—21no—
24C4×D4×C73C2211yescharacteristic
25C4⋊C8×C73C2211yescharacteristic
26C4×C8×C73C2211yescharacteristic
27#11924028—42no—
28#11924028—42no—
29C2×Dic146—21no—
30C2×D292—21no—
31C2×D292C2×C411yescharacteristic
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34C2×C22⋊D73—21no—
35C2×C4×D73—21no—
36C2×C4×D73C2×C411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39#11924011—24no—
40C2×#10596831—21no—
41C2×#10596831—21no—
42C4⋊Dic73C2×C411yescharacteristic
43#11924007—21no—
44C22⋊Dic73—21no—
45#11924005—21no—
46#11924005—21no—
47C4×Dic73C2×C411yescharacteristic
48C4×Dic73D411yescharacteristic
49C4×Dic73D411yescharacteristic
50C2×D4×C73C2×C411yescharacteristic
51C22×C4×C73—21no—
52C2×C8×C73—21no—
53C2×C8×C73—21no—
54C4⋊C4×C73C2×C411yescharacteristic
55C22⋊C4×C73—21no—
56C42×C73C2311yescharacteristic
57C23×C73—21no—
58C22×D73—21no—
59C22×D73C22⋊C411yescharacteristic
60D4×C73—21no—
61D4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73C22×C411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C22⋊D73—42no—
69C22⋊D73—42no—
70C22⋊D73—42no—
71C2×Dic73—21no—
72C2×Dic73C22⋊C411yescharacteristic
73C2×Dic73C22⋊C411yescharacteristic
74C2×Dic73C22⋊C411yescharacteristic
75D292—21no—
76D292—21no—
77D292—42no—
78C4×D73—21no—
79C4×D73—21no—
80C4×D73—21no—
81C4×D73—21no—
82C4×D73—22no—
83C4×D73—41no—
84C4×D73—41no—
85Dic146—42no—
86C8×C73—22no—
87C8×C73—41no—
88#10596831—22no—
89#10596831—41no—
90C22×C73—41no—
91C22×C73—41no—
92C22×C73—41no—
93C22×C73C2×C22⋊C411yescharacteristic
94C2×D73—21no—
95C2×D73—21no—
96C2×D73—21no—
97C2×D73—41no—
98C2×D73—41no—
99C2×D73—41no—
100C4×C73—21no—
101C4×C73—41no—
102C4×C73#13111yescharacteristic
103C4×C73#13111yescharacteristic
104C4×C73AGL(1,ℤ/8)11yescharacteristic
105C4×C73AGL(1,ℤ/8)11yescharacteristic
106Dic73—21no—
107Dic73—21no—
108Dic73—41no—
109Dic73#10412yes—
110C2×C73—81no—
111C2×C73#40811yescharacteristic
112C2×C73#41811yescharacteristic
113C2×C73C2×#10411yescharacteristic
114D73—41no—
115D73—81no—
116#1484—731nomaximal, Sylow
117C73#148411yescharacteristic, complemented, Sylow
118#532—731no—
119#431—731no—
120C4×M16—731no—
121D4⋊C8—731no—
122D4⋊C8—731no—
123D4⋊C8—731no—
124D4⋊C8D7311yescharacteristic, complemented
125C2×#41—1461no—
126C2×M16—1461no—
127C4⋊Q8—731no—
128#127—731no—
129#124—1461no—
130#121—731no—
131#121—731no—
132#121—1461no—
133C4×D4—731no—
134C4×D4—1461no—
135C4×D4C2×D7311yescharacteristic
136C2×C42—731no—
137C4⋊C8—731no—
138C4⋊C8C2×D7311yescharacteristic
139C22⋊C8—1461no—
140#97—1461no—
141C4×C8—731no—
142C4×C8—1461no—
143C4×C8C2×D7311yescharacteristic
144#41—2922no—
145#41—2922no—
146C2×Q8—1461no—
147C2×D4—731no—
148C2×D4—1461no—
149C2×D4—1461no—
150C2×D4—1461no—
151C2×D4—1461no—
152C2×D4C4×D7311yescharacteristic
153C22×C4—21no—
154C22×C4—731no—
155C22×C4—731no—
156C22×C4—731no—
157C22×C4—1461no—
158M16—1464no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—1461no—
162C2×C8—1461no—
163C4⋊C4—731no—
164C4⋊C4—1461no—
165C4⋊C4C4×D7311yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—1461no—
168C22⋊C4—1461no—
169C22⋊C4—1461no—
170C42—731no—
171C42—731no—
172C42—731no—
173C42C22×D7311yescharacteristic
174C23—21no—
175C23—731no—
176C23—1461no—
177Q8—2922no—
178D4—21no—
179D4—21no—
180D4—2922no—
181D4—2922no—
182D4—2922no—
183D4—2922no—
184D4—1461no—
185D4—1461no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—731no—
192C2×C4—731no—
193C2×C4—731no—
194C2×C4—1462no—
195C2×C4—1461no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4C2×C4×D7311yescharacteristic
201C2×C4D4×D7311yescharacteristic
202C2×C4D4×D7311yescharacteristic
203C8—22no—
204C8—41no—
205C8—2921no—
206C8—1462no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—2921no—
211C22—2921no—
212C22—2921no—
213C22—1461no—
214C22—1461no—
215C22—1461no—
216C22C22⋊C4×D7311yescharacteristic
217C4—21no—
218C4—41no—
219C4—2921no—
220C4—732no—
221C4—1461no—
222C4—1461no—
223C4#1455659711yescharacteristic
224C4#1455659911yescharacteristic
225C4#1455661511yescharacteristic
226C4#1455661811yescharacteristic
227C2—81no—
228C2—2921no—
229C2—5841no—
230C2#1798855211yescharacteristic
231C2#1798859011yescharacteristic
232C2#104×D7311yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
FittingD4⋊C8×C73C2
socleC22×C73C2×C22⋊C4
hypercenterD4⋊C8D73
hypocenterC73#1484
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #17988639C2semidirect
3. C4×#11924011C2semidirect
4. #17988316C2semidirect
5. D4⋊#10596831C2semidirect
6. #17988314C2semidirect
7. D4⋊C8×C73C2semidirect
117. C73#1484semidirect
124. D4⋊C8D73semidirect