Finite Group Databasebeta

← #22611583

Subgroups — #22611583

Order 9344.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#17989159C211yesmaximal, characteristic
2#17988568C211yesmaximal, characteristic
3#17988559C211yesmaximal, characteristic
4#17988378C211yesmaximal, characteristic, complemented
5#17988377C211yesmaximal, characteristic, complemented
6#17988376C211yesmaximal, characteristic, complemented
7#352×C73C211yesmaximal, characteristic, complemented
8C2×#11924027C2211yescharacteristic
9C22×Dic146C411yescharacteristic, complemented
10M16×D73—21no—
11#14556590—21no—
12#14556577—21no—
13#14556575C411yescharacteristic, complemented
14#14556574C411yescharacteristic, complemented
15#14556572C2211yescharacteristic
16#14556569—21no—
17#14556568—21no—
18#14556547—21no—
19#14556547C411yescharacteristic, complemented
20#14556509—21no—
21#14556508C2211yescharacteristic
22#14556506C2211yescharacteristic
23#14556505—21no—
24#123×C73C2211yescharacteristic
25#100×C73C2211yescharacteristic
26#99×C73C2211yescharacteristic
27#11924027—41no—
28#11924027—41no—
29C2×Dic146—21no—
30C2×Dic146—21no—
31C2×Dic146—41no—
32C2×Dic146—41no—
33C2×Dic146D411yescharacteristic
34C2×C22⋊D73C2×C411yescharacteristic
35C2×C22⋊D73D411yescharacteristic
36C22×Dic73C2×C411yescharacteristic
37C22×Dic73C2×C411yescharacteristic
38C22×Dic73D411yescharacteristic
39C2×C4×D73D411yescharacteristic
40#11924012—21no—
41#11924011—41no—
42C8×D73—41no—
43C4⋊Dic73—21no—
44#11924007—21no—
45#11924007—21no—
46#11924007—21no—
47#11924007—41no—
48C22⋊Dic73—21no—
49C22⋊Dic73—21no—
50C22⋊Dic73C2×C411yescharacteristic
51#11924005—21no—
52#11924005—21no—
53C4×Dic73—21no—
54C4×Dic73—41no—
55C2×D4×C73C2311yescharacteristic
56C22×C4×C73C2×C411yescharacteristic
57M16×C73—21no—
58C4⋊C4×C73—21no—
59C22⋊C4×C73—21no—
60C22⋊C4×C73—21no—
61C22⋊C4×C73C2×C411yescharacteristic
62C23×C73C22×C411yescharacteristic
63C23×C73C2×D411yescharacteristic
64C22×D73C22⋊C411yescharacteristic
65D4×C73—41no—
66C2×C4×C73—21no—
67C2×C4×C73—21no—
68C2×C4×C73—41no—
69C2×C4×C73—41no—
70C2×C4×C73C2×D411yescharacteristic
71C22⋊D73—41no—
72C22⋊D73—41no—
73C2×Dic73—21no—
74C2×Dic73—21no—
75C2×Dic73—21no—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—41no—
80C2×Dic73—41no—
81C2×Dic73C22⋊C411yescharacteristic
82C2×Dic73C22⋊C411yescharacteristic
83C2×Dic73C22⋊C411yescharacteristic
84C4×D73—21no—
85C4×D73—21no—
86Dic146—41no—
87Dic146—42no—
88Dic146—41no—
89Dic146—41no—
90C8×C73—41no—
91#10596831—41no—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73—41no—
95C22×C73—41no—
96C22×C73C2×C22⋊C411yescharacteristic
97C2×D73—21no—
98C2×D73—41no—
99C4×C73—21no—
100C4×C73—41no—
101C4×C73—41no—
102C4×C73—81no—
103Dic73—21no—
104Dic73—21no—
105Dic73—41no—
106Dic73—41no—
107Dic73—81no—
108Dic73#9911yescharacteristic
109Dic73#9911yescharacteristic
110C2×C73—21no—
111C2×C73—41no—
112C2×C73—41no—
113C2×C73C2×#9911yescharacteristic
114D73—41no—
115#2123—731nomaximal, Sylow
116C73#212311yescharacteristic, complemented, Sylow
117#536—731no—
118#413—731no—
119#410—731no—
120#352—731no—
121#352—731no—
122#352—731no—
123#352D7311yescharacteristic, complemented
124C2×#41—731no—
125C22×Q8—731no—
126C2×M16—1461no—
127C4⋊Q8—1461no—
128#124—1461no—
129#123—731no—
130#123—731no—
131#123—731no—
132#123C2×D7311yescharacteristic
133C22⋊Q8—1461no—
134C22⋊Q8—1461no—
135#117—731no—
136#117—1461no—
137#101—1461no—
138#100—731no—
139#100C2×D7311yescharacteristic
140#99—731no—
141#99—1461no—
142#99C2×D7311yescharacteristic
143#41—2921no—
144#41—2921no—
145C2×Q8—2921no—
146C2×Q8—2921no—
147C2×Q8—731no—
148C2×Q8—1461no—
149C2×Q8—1461no—
150C2×D4—731no—
151C2×D4—731no—
152C2×D4C22×D7311yescharacteristic
153C22×C4—731no—
154C22×C4—731no—
155C22×C4—731no—
156C22×C4—731no—
157C22×C4C4×D7311yescharacteristic
158M16—21no—
159M16—2921no—
160M16—1461no—
161C2×C8—2921no—
162C4⋊C4—21no—
163C4⋊C4—2921no—
164C4⋊C4—1461no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—731no—
171C22⋊C4—1461no—
172C22⋊C4—1461no—
173C22⋊C4—1461no—
174C22⋊C4—1461no—
175C22⋊C4C4×D7311yescharacteristic
176C42—2921no—
177C42—1461no—
178C23—731no—
179C23C2×C4×D7311yescharacteristic
180C23D4×D7311yescharacteristic
181Q8—2921no—
182Q8—2921no—
183Q8—2921no—
184Q8—2922no—
185D4—41no—
186D4—2921no—
187D4—2921no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—731no—
195C2×C4—731no—
196C2×C4—731no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4—1461no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4D4×D7311yescharacteristic
206C8—41no—
207C8—2921no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—2921no—
213C22—1461no—
214C22C22⋊C4×D7311yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—2921no—
220C4—2921no—
221C4—5841no—
222C4—731no—
223C4—731no—
224C4—1461no—
225C4—1461no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—2921no—
230C2#99×D7311yescharacteristic
subgroupG/H
centerC2#99×D73
commutatorC23×C73C22×C4
FrattiniC2×D4C22×D73
Fitting#352×C73C2
socleC2×C73C2×#99
hypercenter#352D73
hypocenterC73#2123
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #17988378C2semidirect
5. #17988377C2semidirect
6. #17988376C2semidirect
7. #352×C73C2semidirect
9. C22×Dic146C4semidirect
13. #14556575C4semidirect
14. #14556574C4semidirect
19. #14556547C4semidirect
116. C73#2123semidirect
123. #352D73semidirect