Finite Group Databasebeta

← #22608489

Subgroups — #22608489

Order 9344.

264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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#17988637C211yesmaximal, characteristic, complemented
3#17988451C211yesmaximal, 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×#11924007—21no—
18C2×C4×Dic73C2211yescharacteristic
19#14556520—21no—
20C22⋊#10596831C2211yescharacteristic
21C8×Dic73—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—
42#11924007—42no—
43C22⋊Dic73—21no—
44#11924005—21no—
45#11924005—21no—
46C4×Dic73C2×C411yescharacteristic
47C4×Dic73C2×C411yescharacteristic
48C4×Dic73D411yescharacteristic
49C4×Dic73D411yescharacteristic
50C2×D4×C73—21no—
51C2×D4×C73C2×C411yescharacteristic
52C22×C4×C73—21no—
53C22×C4×C73C2311yescharacteristic
54C2×C8×C73—21no—
55C4⋊C4×C73C2×C411yescharacteristic
56C22⋊C4×C73—21no—
57C23×C73—21no—
58C23×C73C2×D411yescharacteristic
59C22×D73—21no—
60D4×C73—41no—
61D4×C73—41no—
62D4×C73—41no—
63C2×C4×C73—21no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73C22×C411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C22⋊D73—42no—
71C22⋊D73—41no—
72C22⋊D73—41no—
73C22⋊D73—42no—
74C2×Dic73—21no—
75C2×Dic73—41no—
76C2×Dic73—42no—
77C2×Dic73—41no—
78C2×Dic73—41no—
79C2×Dic73—41no—
80C2×Dic73C22⋊C411yescharacteristic
81C2×Dic73C22⋊C411yescharacteristic
82C2×Dic73C22⋊C411yescharacteristic
83C2×Dic73C22⋊C411yescharacteristic
84C2×Dic73D812yes—
85C2×Dic73SD1612yes—
86D292—41no—
87C4×D73—42no—
88Dic146—42no—
89C8×C73—41no—
90#10596831—41no—
91C22×C73—21no—
92C22×C73—21no—
93C22×C73—41no—
94C22×C73—41no—
95C22×C73—41no—
96C22×C73C2×C22⋊C411yescharacteristic
97C22×C73C2×D811yescharacteristic
98C22×C73C2×SD1611yescharacteristic
99C2×D73—41no—
100C2×D73—41no—
101C2×D73—41no—
102C4×C73—21no—
103C4×C73—21no—
104C4×C73—41no—
105C4×C73—81no—
106Dic73—21no—
107Dic73—21no—
108Dic73—41no—
109Dic73—81no—
110Dic73#10212yes—
111Dic73#10212yes—
112C2×C73—21no—
113C2×C73—21no—
114C2×C73—81no—
115C2×C73#41011yescharacteristic
116C2×C73C2×#10211yescharacteristic
117C2×C73#42111yescharacteristic
118D73—81no—
119#1517—731nomaximal, Sylow
120C73#151711yescharacteristic, complemented, Sylow
121#532—731no—
122#431—731no—
123#382—731no—
124#327—731no—
125#327—731no—
126#327—731no—
127#327D7311yescharacteristic, complemented
128C2×#41—1461no—
129C4⋊Q8—731no—
130#127—731no—
131#124—1461no—
132#121—731no—
133#121—1461no—
134#121C2×D7311yescharacteristic
135C4×D4—731no—
136C4×D4—731no—
137C4×D4—1461no—
138C2×C4⋊C4—1461no—
139C2×C42—731no—
140C4⋊C8—1461no—
141C22⋊C8—731no—
142C22⋊C8C2×D7311yescharacteristic
143C4×C8—1461no—
144#95—731no—
145#95—1461no—
146#95C2×D7311yescharacteristic
147#41—2922no—
148#41—2922no—
149C2×Q8—1461no—
150C2×D4—21no—
151C2×D4—731no—
152C2×D4—1461no—
153C2×D4—1461no—
154C2×D4—1461no—
155C2×D4C4×D7311yescharacteristic
156C22×C4—21no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—1461no—
160C22×C4—1461no—
161C22×C4—1461no—
162C22×C4C22×D7311yescharacteristic
163C2×C8—21no—
164C2×C8—1461no—
165C4⋊C4—2922no—
166C4⋊C4—731no—
167C4⋊C4—1461no—
168C4⋊C4C4×D7311yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—1461no—
171C22⋊C4—1461no—
172C22⋊C4—1461no—
173C42—731no—
174C42—731no—
175C42—731no—
176C42—731no—
177C23—21no—
178C23—1461no—
179C23D4×D7311yescharacteristic
180Q8—2922no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—2921no—
185D4—2921no—
186D4—2921no—
187D4—2922no—
188D4—2922no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—2922no—
195C2×C4—2922no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—2921no—
199C2×C4—2921no—
200C2×C4—731no—
201C2×C4—731no—
202C2×C4—732no—
203C2×C4—732no—
204C2×C4—731no—
205C2×C4—731no—
206C2×C4—1461no—
207C2×C4C2×C4×D7311yescharacteristic
208C2×C4D4×D7311yescharacteristic
209C8—41no—
210C8—2921no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—2921no—
217C22—2921no—
218C22—2921no—
219C22C22⋊C4×D7311yescharacteristic
220C22D8×D7311yescharacteristic
221C22SD16×D7311yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—2921no—
227C4—5841no—
228C4—732no—
229C4—732no—
230C4—1461no—
231C4—1461no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—5841no—
236C2#1798855911yescharacteristic
237C2#102×D7311yescharacteristic
238C2#1798860211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#327×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#327D73
hypocenterC73#1517
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. #17988637C2semidirect
3. #17988451C2semidirect
4. #17988322C2semidirect
5. #17988321C2semidirect
6. #17988320C2semidirect
7. #327×C73C2semidirect
9. #14556590C4semidirect
10. #14556587C4semidirect
14. D4×Dic73C4semidirect
15. #14556553C4semidirect
120. C73#1517semidirect
127. #327D73semidirect