Finite Group Databasebeta

← #22608476

Subgroups — #22608476

Order 9344.

252 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 61 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#17989132C211yesmaximal, characteristic
2#17988641C211yesmaximal, characteristic, complemented
3#17988454C211yesmaximal, characteristic, complemented
4#17988322C211yesmaximal, characteristic, complemented
5#17988321C211yesmaximal, characteristic, complemented
6#17988320C211yesmaximal, characteristic, complemented
7#327×C73C211yesmaximal, characteristic, complemented
8C2×#11924027—21no—
9#14556590C411yescharacteristic, complemented
10#14556587C411yescharacteristic, complemented
11#14556577—21no—
12#14556565C2211yescharacteristic
13#14556563—21no—
14D4×Dic73C411yescharacteristic, complemented
15#14556553C411yescharacteristic, complemented
16#14556551—21no—
17C2×C4×Dic73C2211yescharacteristic
18#14556520—21no—
19C22⋊#10596831C2211yescharacteristic
20#14556501—21no—
21#14556498—21no—
22#14556498—21no—
23#14556498C2211yescharacteristic
24#121×C73C2211yescharacteristic
25C22⋊C8×C73C2211yescharacteristic
26#95×C73C2211yescharacteristic
27#11924027—42no—
28#11924027—42no—
29C2×Dic146—21no—
30C2×D292C2×C411yescharacteristic
31C2×C22⋊D73—21no—
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34C22×Dic73—21no—
35C22×Dic73—21no—
36C22×Dic73D411yescharacteristic
37C22×Dic73D411yescharacteristic
38C2×C4×D73—21no—
39C2×#10596831—21no—
40C4⋊Dic73C2×C411yescharacteristic
41#11924007—21no—
42C22⋊Dic73—21no—
43#11924005—21no—
44#11924005—21no—
45C4×Dic73C2×C411yescharacteristic
46C4×Dic73C2×C411yescharacteristic
47C4×Dic73D411yescharacteristic
48C4×Dic73D411yescharacteristic
49C2×D4×C73—21no—
50C2×D4×C73C2×C411yescharacteristic
51C22×C4×C73—21no—
52C22×C4×C73C2311yescharacteristic
53C2×C8×C73—21no—
54C4⋊C4×C73C2×C411yescharacteristic
55C22⋊C4×C73—21no—
56C23×C73—21no—
57C23×C73C2×D411yescharacteristic
58C22×D73—21no—
59D4×C73—41no—
60D4×C73—41no—
61D4×C73—41no—
62C2×C4×C73—21no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73C22×C411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C22⋊D73—42no—
70C22⋊D73—42no—
71C22⋊D73—41no—
72C22⋊D73—41no—
73C2×Dic73—21no—
74C2×Dic73—21no—
75C2×Dic73—21no—
76C2×Dic73—41no—
77C2×Dic73—42no—
78C2×Dic73—41no—
79C2×Dic73—41no—
80C2×Dic73—41no—
81C2×Dic73C22⋊C411yescharacteristic
82C2×Dic73C22⋊C411yescharacteristic
83C2×Dic73C22⋊C411yescharacteristic
84C2×Dic73C22⋊C411yescharacteristic
85D292—41no—
86C4×D73—42no—
87Dic146—42no—
88C8×C73—41no—
89#10596831—41no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73—41no—
93C22×C73—41no—
94C22×C73—41no—
95C22×C73C2×C22⋊C411yescharacteristic
96C22×C73AGL(1,ℤ/8)11yescharacteristic
97C22×C73AGL(1,ℤ/8)11yescharacteristic
98C2×D73—41no—
99C2×D73—41no—
100C2×D73—41no—
101C4×C73—21no—
102C4×C73—21no—
103C4×C73—41no—
104C4×C73—81no—
105Dic73—21no—
106Dic73—21no—
107Dic73—21no—
108Dic73—21no—
109Dic73—41no—
110Dic73—81no—
111C2×C73—21no—
112C2×C73—21no—
113C2×C73—81no—
114C2×C73#41011yescharacteristic
115C2×C73#41811yescharacteristic
116C2×C73#42111yescharacteristic
117D73—81no—
118#1514—731nomaximal, Sylow
119C73#151411yescharacteristic, complemented, Sylow
120#532—731no—
121#432—731no—
122#383—731no—
123#327—731no—
124#327—731no—
125#327—731no—
126#327D7311yescharacteristic, complemented
127C2×#41—1461no—
128C4⋊Q8—731no—
129#127—731no—
130#124—1461no—
131#121—731no—
132#121—1461no—
133#121C2×D7311yescharacteristic
134C4×D4—731no—
135C4×D4—731no—
136C4×D4—1461no—
137C2×C42—731no—
138C4⋊C8—1461no—
139C22⋊C8—731no—
140C22⋊C8C2×D7311yescharacteristic
141#97—1461no—
142#95—731no—
143#95—1461no—
144#95—1461no—
145#95C2×D7311yescharacteristic
146#41—2922no—
147#41—2922no—
148C2×Q8—1461no—
149C2×D4—21no—
150C2×D4—731no—
151C2×D4—1461no—
152C2×D4—1461no—
153C2×D4—1461no—
154C2×D4C4×D7311yescharacteristic
155C22×C4—21no—
156C22×C4—731no—
157C22×C4—731no—
158C22×C4—1461no—
159C22×C4—1461no—
160C22×C4—1461no—
161C22×C4C22×D7311yescharacteristic
162C2×C8—21no—
163C2×C8—1461no—
164C4⋊C4—731no—
165C4⋊C4—1461no—
166C4⋊C4C4×D7311yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—1461no—
169C22⋊C4—1461no—
170C22⋊C4—1461no—
171C42—731no—
172C42—731no—
173C42—731no—
174C42—731no—
175C23—21no—
176C23—1461no—
177C23D4×D7311yescharacteristic
178Q8—2922no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—2921no—
183D4—2921no—
184D4—2921no—
185D4—2922no—
186D4—2922no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—2922no—
193C2×C4—2922no—
194C2×C4—2921no—
195C2×C4—2921no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—731no—
199C2×C4—731no—
200C2×C4—731no—
201C2×C4—731no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4C2×C4×D7311yescharacteristic
206C2×C4D4×D7311yescharacteristic
207C8—41no—
208C8—2921no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—2921no—
215C22—2921no—
216C22—2921no—
217C22C22⋊C4×D7311yescharacteristic
218C22#1455661511yescharacteristic
219C22#1455661811yescharacteristic
220C4—21no—
221C4—21no—
222C4—41no—
223C4—81no—
224C4—2921no—
225C4—5841no—
226C4—1461no—
227C4—1461no—
228C4—1461no—
229C4—1461no—
230C2—21no—
231C2—21no—
232C2—81no—
233C2—5841no—
234C2#1798855911yescharacteristic
235C2#1798859011yescharacteristic
236C2#1798860211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#327×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#327D73
hypocenterC73#1514
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #17988641C2semidirect
3. #17988454C2semidirect
4. #17988322C2semidirect
5. #17988321C2semidirect
6. #17988320C2semidirect
7. #327×C73C2semidirect
9. #14556590C4semidirect
10. #14556587C4semidirect
14. D4×Dic73C4semidirect
15. #14556553C4semidirect
119. C73#1514semidirect
126. #327D73semidirect