Finite Group Databasebeta

← #22611571

Subgroups — #22611571

Order 9344.

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

normal subgroups only

This group has 264 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#17989095C211yesmaximal, characteristic
2#17988568C211yesmaximal, characteristic, complemented
3#17988559C211yesmaximal, characteristic, complemented
4#17988377C211yesmaximal, characteristic, complemented
5#17988375C211yesmaximal, characteristic, complemented
6#17988373C211yesmaximal, characteristic, complemented
7#352×C73C211yesmaximal, characteristic, complemented
8C2×#11924027C2211yescharacteristic
9C22×C4×D73C411yescharacteristic, complemented
10M16×D73—21no—
11#14556574C411yescharacteristic, complemented
12#14556569—21no—
13#14556564—21no—
14#14556561C411yescharacteristic, complemented
15#14556559C2211yescharacteristic
16#14556553—21no—
17#14556551—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
27C23×D73C2×C411yescharacteristic
28#11924027—41no—
29#11924027—41no—
30C2×Dic146D411yescharacteristic
31C2×D292—21no—
32C2×C22⋊D73—21no—
33C2×C22⋊D73C2×C411yescharacteristic
34C2×C22⋊D73D411yescharacteristic
35C22×Dic73C2×C411yescharacteristic
36C22×Dic73D411yescharacteristic
37C2×C4×D73—21no—
38C2×C4×D73—21no—
39C2×C4×D73—41no—
40C2×C4×D73—41no—
41C2×C4×D73D411yescharacteristic
42#11924012—21no—
43#11924011—41no—
44C8×D73—41no—
45#11924007—21no—
46#11924007—21no—
47#11924007—41no—
48C22⋊Dic73—21no—
49C22⋊Dic73C2×C411yescharacteristic
50#11924005—21no—
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×D73—21no—
65C22×D73—42no—
66C22×D73—41no—
67C22×D73C22⋊C411yescharacteristic
68D4×C73—41no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73C2×D411yescharacteristic
74C22⋊D73—41no—
75C22⋊D73—41no—
76C22⋊D73—42no—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—41no—
83C2×Dic73C22⋊C411yescharacteristic
84C2×Dic73C22⋊C411yescharacteristic
85C2×Dic73C22⋊C411yescharacteristic
86D292—42no—
87C4×D73—21no—
88C4×D73—21no—
89C4×D73—42no—
90C4×D73—41no—
91C4×D73—41no—
92Dic146—41no—
93C8×C73—41no—
94#10596831—41no—
95C22×C73—21no—
96C22×C73—21no—
97C22×C73—41no—
98C22×C73—41no—
99C22×C73C2×C22⋊C411yescharacteristic
100C2×D73—22no—
101C2×D73—21no—
102C2×D73—41no—
103C2×D73—42no—
104C2×D73—41no—
105C2×D73—41no—
106C2×D73—42no—
107C4×C73—21no—
108C4×C73—41no—
109C4×C73—41no—
110C4×C73—81no—
111Dic73—21no—
112Dic73—21no—
113Dic73—41no—
114Dic73—81no—
115Dic73#9911yescharacteristic
116Dic73#9911yescharacteristic
117C2×C73—21no—
118C2×C73—41no—
119C2×C73—41no—
120C2×C73C2×#9911yescharacteristic
121D73—41no—
122D73—42no—
123#2120—731nomaximal, Sylow
124C73#212011yescharacteristic, complemented, Sylow
125#525—731no—
126#413—731no—
127#410—731no—
128#352—731no—
129#352D7311yescharacteristic, complemented
130AΣL(1,𝔽16)—731no—
131AΣL(1,𝔽16)—731no—
132C2×#41—731no—
133C23×C4—731no—
134C2×M16—1461no—
135#123—731no—
136#123C2×D7311yescharacteristic
137C22⋊Q8—1461no—
138#121—1461no—
139#120—731no—
140#120—731no—
141C4×D4—1461no—
142C4×D4—1461no—
143#117—731no—
144#117—1461no—
145#101—1461no—
146#100—731no—
147#100C2×D7311yescharacteristic
148#99—731no—
149#99—1461no—
150#99C2×D7311yescharacteristic
151C24—731no—
152#41—2921no—
153#41—2921no—
154C2×Q8—731no—
155C2×D4—731no—
156C2×D4—731no—
157C2×D4—1461no—
158C2×D4—1461no—
159C2×D4C22×D7311yescharacteristic
160C22×C4—2921no—
161C22×C4—2921no—
162C22×C4—731no—
163C22×C4—731no—
164C22×C4—731no—
165C22×C4—1461no—
166C22×C4—1461no—
167C22×C4C4×D7311yescharacteristic
168M16—21no—
169M16—2921no—
170M16—1461no—
171C2×C8—2921no—
172C4⋊C4—21no—
173C4⋊C4—2921no—
174C4⋊C4—1461no—
175C4⋊C4—1461no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—731no—
179C22⋊C4—1461no—
180C22⋊C4—1461no—
181C22⋊C4—1461no—
182C22⋊C4—1461no—
183C22⋊C4C4×D7311yescharacteristic
184C42—2921no—
185C42—1461no—
186C23—2921no—
187C23—2922no—
188C23—731no—
189C23—1461no—
190C23C2×C4×D7311yescharacteristic
191C23D4×D7311yescharacteristic
192Q8—2921no—
193D4—41no—
194D4—2922no—
195D4—2922no—
196D4—2921no—
197D4—2921no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—2921no—
203C2×C4—2921no—
204C2×C4—2922no—
205C2×C4—2921no—
206C2×C4—731no—
207C2×C4—731no—
208C2×C4—731no—
209C2×C4—1461no—
210C2×C4—1461no—
211C2×C4—1461no—
212C2×C4—1461no—
213C2×C4—1461no—
214C2×C4—1461no—
215C2×C4—1461no—
216C2×C4D4×D7311yescharacteristic
217C8—41no—
218C8—2921no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—2921no—
224C22—2921no—
225C22—2922no—
226C22—2922no—
227C22—2921no—
228C22—1462no—
229C22—1461no—
230C22C22⋊C4×D7311yescharacteristic
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—2921no—
236C4—5841no—
237C4—731no—
238C4—731no—
239C4—1461no—
240C4—1461no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—2922no—
245C2—2921no—
246C2#99×D7311yescharacteristic
subgroupG/H
centerC2#99×D73
commutatorC23×C73C22×C4
FrattiniC2×D4C22×D73
Fitting#352×C73C2
socleC2×C73C2×#99
hypercenter#352D73
hypocenterC73#2120
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
2. #17988568C2semidirect
3. #17988559C2semidirect
4. #17988377C2semidirect
5. #17988375C2semidirect
6. #17988373C2semidirect
7. #352×C73C2semidirect
9. C22×C4×D73C4semidirect
11. #14556574C4semidirect
14. #14556561C4semidirect
19. #14556547C4semidirect
124. C73#2120semidirect
129. #352D73semidirect