Finite Group Databasebeta

← #22611569

Subgroups — #22611569

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#17989093C211yesmaximal, characteristic
2#17988568C211yesmaximal, characteristic, complemented
3#17988559C211yesmaximal, characteristic, complemented
4#17988378C211yesmaximal, characteristic, complemented
5#17988376C211yesmaximal, characteristic, complemented
6#17988374C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C73C211yesmaximal, characteristic, complemented
8C2×#11924027C2211yescharacteristic
9C23×Dic73C411yescharacteristic, complemented
10M16×D73—21no—
11#14556575C411yescharacteristic, complemented
12#14556572C2211yescharacteristic
13#14556568—21no—
14#14556563—21no—
15#14556560C411yescharacteristic, complemented
16D4×Dic73—21no—
17#14556551—21no—
18#14556547—21no—
19#14556547C411yescharacteristic, complemented
20#14556509—21no—
21#14556508C2211yescharacteristic
22#14556506C2211yescharacteristic
23#14556505—21no—
24#120×C73C2211yescharacteristic
25#100×C73C2211yescharacteristic
26#99×C73C2211yescharacteristic
27#11924027—41no—
28#11924027—41no—
29C2×Dic146D411yescharacteristic
30C2×C22⋊D73—21no—
31C2×C22⋊D73C2×C411yescharacteristic
32C2×C22⋊D73D411yescharacteristic
33C22×Dic73—21no—
34C22×Dic73—21no—
35C22×Dic73—41no—
36C22×Dic73—41no—
37C22×Dic73C2×C411yescharacteristic
38C22×Dic73C2×C411yescharacteristic
39C22×Dic73D411yescharacteristic
40C2×C4×D73D411yescharacteristic
41#11924012—21no—
42#11924011—41no—
43C8×D73—41no—
44C4⋊Dic73—21no—
45#11924007—21no—
46#11924007—21no—
47#11924007—41no—
48C22⋊Dic73—21no—
49C22⋊Dic73—21no—
50C22⋊Dic73—21no—
51C22⋊Dic73C2×C411yescharacteristic
52#11924005—21no—
53C4×Dic73—21no—
54C4×Dic73—41no—
55C24×C73C2×C411yescharacteristic
56C2×D4×C73—21no—
57C2×D4×C73C2311yescharacteristic
58M16×C73—21no—
59C22⋊C4×C73—21no—
60C22⋊C4×C73—21no—
61C22⋊C4×C73C2×C411yescharacteristic
62C23×C73—21no—
63C23×C73—42no—
64C23×C73—41no—
65C23×C73C22×C411yescharacteristic
66C23×C73C2×D411yescharacteristic
67C22×D73C22⋊C411yescharacteristic
68D4×C73—41no—
69D4×C73—42no—
70C2×C4×C73—21no—
71C2×C4×C73—41no—
72C2×C4×C73C2×D411yescharacteristic
73C22⋊D73—41no—
74C22⋊D73—41no—
75C22⋊D73—42no—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—42no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85C2×Dic73—41no—
86C2×Dic73—41no—
87C2×Dic73C22⋊C411yescharacteristic
88C2×Dic73C22⋊C411yescharacteristic
89C2×Dic73C22⋊C411yescharacteristic
90C4×D73—21no—
91C4×D73—21no—
92Dic146—41no—
93C8×C73—41no—
94#10596831—41no—
95C22×C73—22no—
96C22×C73—21no—
97C22×C73—21no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73—41no—
101C22×C73—42no—
102C22×C73—42no—
103C22×C73—41no—
104C22×C73C2×C22⋊C411yescharacteristic
105C2×D73—21no—
106C2×D73—41no—
107C4×C73—21no—
108C4×C73—41no—
109C4×C73—81no—
110Dic73—21no—
111Dic73—21no—
112Dic73—41no—
113Dic73—41no—
114Dic73—81no—
115Dic73#9911yescharacteristic
116Dic73#9911yescharacteristic
117C2×C73—21no—
118C2×C73—41no—
119C2×C73—42no—
120C2×C73—41no—
121C2×C73C2×#9911yescharacteristic
122D73—41no—
123#2120—731nomaximal, Sylow
124C73#212011yescharacteristic, complemented, Sylow
125#525—731no—
126#413—731no—
127#410—731no—
128#352—731no—
129#352—731no—
130AΣL(1,𝔽16)—731no—
131AΣL(1,𝔽16)D7311yescharacteristic, complemented
132C2×#41—731no—
133C23×C4—731no—
134C2×M16—1461no—
135#123—731no—
136#123—731no—
137C22⋊Q8—1461no—
138#121—1461no—
139#120—731no—
140#120C2×D7311yescharacteristic
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
151C24C4×D7311yescharacteristic
152#41—2921no—
153#41—2921no—
154C2×Q8—731no—
155C2×D4—21no—
156C2×D4—731no—
157C2×D4—731no—
158C2×D4—1461no—
159C2×D4C22×D7311yescharacteristic
160C22×C4—2921no—
161C22×C4—2921no—
162C22×C4—731no—
163C22×C4—731no—
164C22×C4—731no—
165C22×C4—731no—
166C22×C4—1461no—
167C22×C4—1461no—
168M16—21no—
169M16—2921no—
170M16—1461no—
171C2×C8—2921no—
172C4⋊C4—2921no—
173C4⋊C4—1461no—
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—21no—
187C23—41no—
188C23—42no—
189C23—731no—
190C23C2×C4×D7311yescharacteristic
191C23D4×D7311yescharacteristic
192Q8—2921no—
193D4—41no—
194D4—42no—
195D4—2922no—
196D4—2921no—
197D4—2921no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—2921no—
201C2×C4—2921no—
202C2×C4—2922no—
203C2×C4—2921no—
204C2×C4—2921no—
205C2×C4—731no—
206C2×C4—731no—
207C2×C4—731no—
208C2×C4—1461no—
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—22no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—2921no—
229C22—1461no—
230C22C22⋊C4×D7311yescharacteristic
231C4—21no—
232C4—41no—
233C4—81no—
234C4—2921no—
235C4—2921no—
236C4—5841no—
237C4—731no—
238C4—731no—
239C4—1461no—
240C4—1461no—
241C2—21no—
242C2—41no—
243C2—42no—
244C2—41no—
245C2—2921no—
246C2#99×D7311yescharacteristic
subgroupG/H
centerC2#99×D73
commutatorC23×C73C22×C4
FrattiniC2×D4C22×D73
FittingAΣL(1,𝔽16)×C73C2
socleC2×C73C2×#99
hypercenterAΣL(1,𝔽16)D73
hypocenterC73#2120
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #17988568C2semidirect
3. #17988559C2semidirect
4. #17988378C2semidirect
5. #17988376C2semidirect
6. #17988374C2semidirect
7. AΣL(1,𝔽16)×C73C2semidirect
9. C23×Dic73C4semidirect
11. #14556575C4semidirect
15. #14556560C4semidirect
19. #14556547C4semidirect
124. C73#2120semidirect
131. AΣL(1,𝔽16)D73semidirect