Finite Group Databasebeta

← #21456742

Subgroups — #21456742

Order 7808.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840307C211yesmaximal, characteristic
2C2×#14519775C211yesmaximal, characteristic, complemented
3#16840133C212yesmaximal, complemented
4#16840111C212yesmaximal, complemented
5#16839966C212yesmaximal, complemented
6#16839965C212yesmaximal, complemented
7#16839903C211yesmaximal, characteristic, complemented
8#16839901C211yesmaximal, characteristic, complemented
9#16839900C211yesmaximal, characteristic, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#448C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C22×Dic122C2211yescharacteristic
14C2×#11758190C2212yes—
15C2×#11758200C2212yes—
16C2×#11758201C2212yes—
17#14519776C2211yescharacteristic
18#14519775—21no—
19#14519775—21no—
20#14519775C2212yes—
21#14519775C2212yes—
22#14519773C2211yescharacteristic
23#14519763—21no—
24#14519751C2211yescharacteristic
25#14519749—21no—
26D4×Dic61C2211yescharacteristic
27#14519739C2211yescharacteristic
28#14519737—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×C4×Dic61C2211yescharacteristic
32#14519706C2212yes—
33#14519702C2212yes—
34#14519701C2212yes—
35#14519700C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yes—
38C22×Q8×C61C2211yescharacteristic
39C2×SD16×C61C2212yes—
40#121×C61C2211yescharacteristic
41#103×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61—42no—
45C2×Q8×C61C2312yes—
46C2×D4×C61—21no—
47C2×D4×C61C2311yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—21no—
51C2×C22⋊D61—21no—
52C2×C22⋊D61—21no—
53C22×Dic61—21no—
54C22×Dic61—21no—
55C22×Dic61D411yescharacteristic
56C22×Dic61D411yescharacteristic
57#11758224—44no—
58C2×D244C2311yescharacteristic
59C2×C4×D61—21no—
60C2×Dic122—21no—
61C2×Dic122—21no—
62C2×Dic122—42no—
63C2×Dic122C2312yes—
64SD16×C61—42no—
65C2×C8×C61C2312yes—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C22⋊Dic61—21no—
69#11758201—42no—
70#11758200—42no—
71#11758198—21no—
72#11758198—21no—
73C4⋊Dic61C2311yescharacteristic
74#11758196—22no—
75#11758196—22no—
76#11758196—22no—
77#11758196—22no—
78#11758196—21no—
79C4×Dic61D411yescharacteristic
80C4×Dic61D411yescharacteristic
81C4×Dic61C2311yescharacteristic
82C4×Dic61C2311yescharacteristic
83C2×#92418C2312yes—
84#11758190—42no—
85C23×C61—21no—
86C23×C61C2×D411yescharacteristic
87C22×D61—21no—
88Q8×C61—22no—
89Q8×C61—22no—
90Q8×C61—42no—
91D4×C61—22no—
92D4×C61—42no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—42no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2411yescharacteristic
99C22⋊D61—42no—
100C22⋊D61—42no—
101C22⋊D61—42no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61SD1614yescomplemented
108C2×Dic61C2×D411yescharacteristic
109C2×Dic61C2×D411yescharacteristic
110C2×Dic61C2×D411yescharacteristic
111C2×Dic61C2×D411yescharacteristic
112D244—22no—
113C4×D61—42no—
114Dic122—22no—
115Dic122—22no—
116Dic122—42no—
117Dic122—42no—
118C8×C61—22no—
119#92418—22no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61C2×SD1612yes—
126C22×C61C22×D411yescharacteristic
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—41no—
130C4×C61—21no—
131C4×C61—42no—
132C4×C61—41no—
133C4×C61H(5,𝔽2)12yes—
134Dic61—21no—
135Dic61—42no—
136Dic61—41no—
137Dic61C2×SD1612yes—
138Dic61C2×SD1612yes—
139Dic61#13712yes—
140#3206—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61—81no—
143C2×C61#53511yescharacteristic
144C2×C61C22×SD1611yescharacteristic
145C2×C61C2×#13711yescharacteristic
146D61—81no—
147#532—611no—
148C2×C4⋊Q8—611no—
149#492—612no—
150#487—612no—
151#461—612no—
152#461—612no—
153#448—611no—
154#448—611no—
155#448—611no—
156#448D6111yescharacteristic, complemented
157#431—611no—
158C61#320611yescharacteristic, complemented, Sylow
159C2×#41—1221no—
160C22×Q8—611no—
161C22×Q8C2×D6111yescharacteristic
162C2×SD16—612no—
163C2×SD16—612no—
164C2×SD16—612no—
165C2×SD16C2×D6112yes—
166C4⋊Q8—611no—
167C4⋊Q8—612no—
168C4⋊Q8—612no—
169C4⋊Q8—1221no—
170C4⋊Q8—1221no—
171#127—611no—
172#124—1221no—
173#121—611no—
174#121—1221no—
175#121C2×D6111yescharacteristic
176C4×D4—611no—
177C4×D4—611no—
178C4×D4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1221no—
181C2×C42—611no—
182C4⋊C8—612no—
183#103—612no—
184#103—612no—
185#103—612no—
186#103C2×D6112yes—
187C22⋊C8—611no—
188C22⋊C8C2×D6111yescharacteristic
189C4×C8—612no—
190#41—2444no—
191C2×Q8—21no—
192C2×Q8—42no—
193C2×Q8—612no—
194C2×Q8—1221no—
195C2×Q8—1221no—
196C2×Q8—2442no—
197C2×Q8C22×D6112yes—
198C2×D4—21no—
199C2×D4—611no—
200C2×D4—1221no—
201C2×D4—1221no—
202C2×D4—1221no—
203C2×D4C22×D6111yescharacteristic
204C22×C4—21no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4C22×D6111yescharacteristic
211SD16—42no—
212SD16—2442no—
213SD16—2442no—
214SD16—2442no—
215C2×C8—612no—
216C2×C8C22×D6112yes—
217C4⋊C4—611no—
218C4⋊C4—1222no—
219C4⋊C4—1222no—
220C4⋊C4—1222no—
221C4⋊C4—1222no—
222C4⋊C4—1221no—
223C4⋊C4C22×D6111yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—1221no—
226C22⋊C4—1221no—
227C22⋊C4—1221no—
228C42—611no—
229C42—611no—
230C42—611no—
231C42—611no—
232C23—21no—
233C23—1221no—
234C23D4×D6111yescharacteristic
235Q8—22no—
236Q8—22no—
237Q8—42no—
238Q8—1222no—
239Q8—1222no—
240Q8—2442no—
241Q8—2442no—
242D4—22no—
243D4—42no—
244D4—1222no—
245D4—2442no—
246D4—2442no—
247D4—2442no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—611no—
253C2×C4—611no—
254C2×C4—611no—
255C2×C4—614no—
256C2×C4—611no—
257C2×C4—1222no—
258C2×C4—1221no—
259C2×C4—1222no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2442no—
263C2×C4D4×D6111yescharacteristic
264C2×C4C23×D6111yescharacteristic
265C8—22no—
266C8—1222no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—2441no—
273C22—2441no—
274C22—2441no—
275C22SD16×D6112yes—
276C22C2×D4×D6111yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—612no—
281C4—612no—
282C4—612no—
283C4—1221no—
284C4—2441no—
285C4—2442no—
286C4#1451982212yes—
287C2—22no—
288C2—81no—
289C2—4881no—
290C2#1684032711yescharacteristic
291C2C2×SD16×D6111yescharacteristic
292C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#448C2
socleC22×C61C22×D4
hypercenter#448D61
hypocenterC61#3206
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. C2×#14519775C2semidirect
3. #16840133C2semidirect
4. #16840111C2semidirect
5. #16839966C2semidirect
6. #16839965C2semidirect
7. #16839903C2semidirect
8. #16839901C2semidirect
9. #16839900C2semidirect
10. #16839812C2semidirect
11. C61×#448C2semidirect
107. C2×Dic61SD16semidirect
156. #448D61semidirect
158. C61#3206semidirect