Finite Group Databasebeta

← #21455094

Subgroups — #21455094

Order 7808.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#14519823C211yesmaximal, characteristic
2C2×#14519808C211yesmaximal, characteristic, complemented
3C22×#11758201C211yesmaximal, characteristic, complemented
4#16839922C214yesmaximal, complemented
5#16839912C214yesmaximal, complemented
6#16839766C211yesmaximal, characteristic, complemented
7#16839756C211yesmaximal, characteristic, complemented
8#16839729C211yesmaximal, characteristic, complemented
9C61×#536C211yesmaximal, characteristic, complemented
10#14519823—24no—
11#14519823—24no—
12C2×#11758226—21no—
13C2×#11758222C2212yes—
14C2×#11758222C2211yescharacteristic
15C22×D244C2212yes—
16C22×D244C2211yescharacteristic
17C2×D4×D61—22no—
18C2×D4×D61—21no—
19#14519808—24no—
20C2×#11758202C2212yescomplemented
21C2×#11758201—24no—
22C2×#11758201C2214yescomplemented
23C2×#11758201C2212yescomplemented
24C2×#11758194C2211yescharacteristic, complemented
25C22×#92418C2211yescharacteristic, complemented
26#14519700C2212yescomplemented
27#14519697C2212yescomplemented
28#14519697C2214yescomplemented
29C22⋊#92418C2214yescomplemented
30C2×#41×C61C2211yescharacteristic
31C22×Q8×C61C2211yescharacteristic, complemented
32C4⋊Q8×C61—21no—
33#124×C61—21no—
34#123×C61—22no—
35C22⋊Q8×C61C2214yescomplemented
36#117×C61C2211yescharacteristic, complemented
37C23×D61—22no—
38C23×D61—21no—
39#41×C61—22no—
40#41×C61—22no—
41C2×Q8×C61—21no—
42C2×Q8×C61—22no—
43C2×Q8×C61—22no—
44C2×Q8×C61D411yescharacteristic
45C2×Q8×C61C2312yes—
46C2×D4×C61D412yes—
47C2×D4×C61D411yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61C2312yes—
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61—22no—
52C2×C22⋊D61—21no—
53#11758226—28no—
54D4×D61—216no—
55D4×D61—28no—
56#11758222—22no—
57#11758222—24no—
58#11758222—24no—
59#11758222D414yes—
60C2×D244—22no—
61C2×D244—21no—
62C2×D244—22no—
63C2×D244—24no—
64C2×D244—24no—
65C2×D244D414yes—
66C2×D244C2311yescharacteristic
67C2×D244C2312yes—
68C2×C4×D61—22no—
69C2×C4×D61—21no—
70C2×Dic122C2311yescharacteristic
71C4⋊C4×C61—24no—
72C4⋊C4×C61C2312yes—
73C22⋊C4×C61—21no—
74C22⋊C4×C61—24no—
75C42×C61—21no—
76#11758202—24no—
77#11758201—24no—
78#11758201—28no—
79#11758194—22no—
80C2×#92418—22no—
81C2×#92418C2312yes—
82C2×#92418C2312yes—
83C23×C61C2×D412yes—
84C23×C61C2×D411yescharacteristic
85C22×D61—22no—
86C22×D61—21no—
87C22×D61—28no—
88C22×D61—24no—
89C22×D61—82no—
90C22×D61—84no—
91Q8×C61—22no—
92Q8×C61—22no—
93Q8×C61—22no—
94Q8×C61—42no—
95D4×C61—24no—
96D4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—42no—
102C2×C4×C61C2×D412yes—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D412yes—
105C2×C4×C61C2×D412yes—
106C2×C4×C61C2411yescharacteristic
107C22⋊D61—28no—
108C22⋊D61—24no—
109C2×Dic61—21no—
110D244—28no—
111D244—24no—
112D244—21no—
113D244—22no—
114D244C2×D412yes—
115D244C2×D414yes—
116C4×D61—28no—
117C4×D61—24no—
118Dic122—21no—
119Dic122C2×D412yes—
120#92418—22no—
121#92418—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—24no—
125C22×C61#12012yes—
126C22×C61C22×D411yescharacteristic
127C2×D61—24no—
128C2×D61—22no—
129C2×D61—44no—
130C2×D61—42no—
131C2×D61—84no—
132C2×D61—88no—
133C4×C61—22no—
134C4×C61—42no—
135C4×C61—42no—
136C4×C61#12012yes—
137C4×C61C22×D411yescharacteristic
138C4×C61C22×D411yescharacteristic
139Dic61—22no—
140#3009—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61—42no—
143C2×C61C2×#12011yescharacteristic
144C2×C61#57712yes—
145D61—44no—
146D61—42no—
147C2×H(5,𝔽2)—611no—
148C2×#137—611no—
149C22×SD16—611no—
150#536D6111yescharacteristic, complemented
151#452—614no—
152#450—614no—
153#418—611no—
154#416—611no—
155#408—611no—
156C61#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—1224no—
158H(5,𝔽2)—1224no—
159C2×#41—611no—
160C2×#41—612no—
161C2×#41—1221no—
162C2×#41C2×D6111yescharacteristic
163C22×Q8C2×D6111yescharacteristic, complemented
164C22×D4—611no—
165C22×D4—612no—
166C22×D4—1222no—
167C22×D4—1221no—
168#137—1224no—
169C2×Q16—612no—
170C2×SD16—614no—
171C2×SD16—612no—
172C2×SD16—1224no—
173C2×M16—611no—
174C22×C8—611no—
175C4⋊Q8—21no—
176#124—21no—
177#123—22no—
178C22⋊Q8C2×D6114yescomplemented
179#117C2×D6111yescharacteristic, complemented
180#103—612no—
181#102—612no—
182#102—614no—
183C22⋊C8—614no—
184C24—1222no—
185C24—1221no—
186#41—22no—
187#41—22no—
188#41—614no—
189#41—1224no—
190#41—1224no—
191#41—1228no—
192#41—1222no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—611no—
197C2×Q8C22⋊D6111yescharacteristic
198C2×Q8C22×D6112yes—
199C2×D4—614no—
200C2×D4—612no—
201C2×D4—611no—
202C2×D4—1224no—
203C2×D4—1224no—
204C2×D4—12216no—
205C2×D4—1228no—
206C2×D4—1222no—
207C2×D4—1221no—
208C2×D4—1222no—
209C2×D4—1222no—
210C2×D4—1221no—
211C2×D4C22⋊D6112yes—
212C2×D4C22⋊D6111yescharacteristic
213C22×C4—21no—
214C22×C4—1222no—
215C22×C4—1221no—
216C22×C4C22×D6112yes—
217C22×C4C22×D6111yescharacteristic
218Q16—1224no—
219SD16—1228no—
220SD16—1224no—
221M16—1222no—
222C2×C8—612no—
223C2×C8—612no—
224C2×C8—1222no—
225C4⋊C4—24no—
226C4⋊C4C22×D6112yes—
227C22⋊C4—21no—
228C22⋊C4—24no—
229C42—21no—
230C23—1228no—
231C23—1224no—
232C23—1222no—
233C23—1221no—
234C23—4882no—
235C23—4884no—
236C23C2×C22⋊D6112yes—
237C23C2×C22⋊D6111yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—612no—
243Q8—1221no—
244D4—24no—
245D4—22no—
246D4—614no—
247D4—612no—
248D4—1228no—
249D4—1228no—
250D4—1224no—
251D4—1221no—
252D4—1222no—
253D4—1224no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—1228no—
260C2×C4—1221no—
261C2×C4—1224no—
262C2×C4D4×D6112yes—
263C2×C4D4×D6112yes—
264C2×C4C2×C22⋊D6112yes—
265C2×C4C2×C22⋊D6111yescharacteristic
266C2×C4C23×D6111yescharacteristic
267C8—1222no—
268C8—1222no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—1224no—
273C22—1222no—
274C22—4884no—
275C22—4888no—
276C22—2444no—
277C22—2442no—
278C22#1451974512yes—
279C22C22×C22⋊D6111yescharacteristic
280C4—22no—
281C4—42no—
282C4—42no—
283C4—1222no—
284C4#1451974512yes—
285C4C2×D4×D6111yescharacteristic
286C4C2×D4×D6111yescharacteristic
287C2—22no—
288C2—42no—
289C2—2444no—
290C2—2442no—
291C2C2×#1451974511yescharacteristic
292C2#1684057012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#536C2
socleC22×C61C22×D4
hypercenter#536D61
hypocenterC61#3009
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#14519808C2semidirect
3. C22×#11758201C2semidirect
4. #16839922C2semidirect
5. #16839912C2semidirect
6. #16839766C2semidirect
7. #16839756C2semidirect
8. #16839729C2semidirect
9. C61×#536C2semidirect
20. C2×#11758202C22semidirect
22. C2×#11758201C22semidirect
23. C2×#11758201C22semidirect
24. C2×#11758194C22semidirect
25. C22×#92418C22semidirect
26. #14519700C22semidirect
27. #14519697C22semidirect
28. #14519697C22semidirect
29. C22⋊#92418C22semidirect
31. C22×Q8×C61C22semidirect
35. C22⋊Q8×C61C22semidirect
36. #117×C61C22semidirect
150. #536D61semidirect
156. C61#3009semidirect
163. C22×Q8C2×D61semidirect
178. C22⋊Q8C2×D61semidirect
179. #117C2×D61semidirect