Finite Group Databasebeta

← #21455512

Subgroups — #21455512

Order 7808.

472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519807C211yesmaximal, characteristic, complemented
2C2×#14519784C211yesmaximal, characteristic, complemented
3#16840333C211yesmaximal, characteristic, complemented
4#16840018C212yesmaximal, complemented
5#16840006C212yesmaximal, complemented
6#16840001C212yesmaximal, complemented
7#16839989C212yesmaximal, complemented
8#16839802C211yesmaximal, characteristic, complemented
9#16839758C211yesmaximal, characteristic, complemented
10C2×#14519700C211yesmaximal, characteristic, complemented
11C61×#537C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13#14519807—24no—
14C2×#11758202C2212yes—
15C2×#11758200C2212yes—
16#14519784—24no—
17C2×#11758194C2212yes—
18C2×#11758194C2211yescharacteristic
19C22×#92418C2212yes—
20C22×#92418C2211yescharacteristic
21#14519775—21no—
22#14519764—21no—
23#14519758—22no—
24#14519756C2212yes—
25#14519756C2212yes—
26#14519736C2211yescharacteristic
27#14519710C2212yes—
28#14519708C2212yes—
29#14519701C2211yescharacteristic
30#14519701C2211yescharacteristic
31#14519700C2212yes—
32#14519700C2212yes—
33#14519698C2211yescharacteristic
34#14519698C2211yescharacteristic
35C2×#41×C61C2211yescharacteristic
36C2×#41×C61C2211yescharacteristic
37C22⋊Q8×C61—21no—
38C22⋊Q8×C61C2212yes—
39#121×C61—21no—
40#121×C61—22no—
41#121×C61C2212yes—
42C2×C4⋊C4×C61C2211yescharacteristic
43#41×C61—22no—
44#41×C61—22no—
45#41×C61—22no—
46#41×C61—22no—
47C2×Q8×C61D411yescharacteristic
48C2×Q8×C61C2311yescharacteristic
49C2×D4×C61—21no—
50C2×D4×C61—22no—
51C2×D4×C61D412yes—
52C2×D4×C61D411yescharacteristic
53C2×D4×C61C2311yescharacteristic
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C2312yes—
57C22×C4×C61C2311yescharacteristic
58C22×Dic61—21no—
59C2×Dic122—22no—
60C2×Dic122—22no—
61C2×Dic122—21no—
62C2×Dic122C2312yes—
63C4⋊C4×C61—21no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61C2312yes—
66C22⋊C4×C61—22no—
67C22⋊C4×C61—22no—
68C22⋊Dic61—21no—
69C22⋊Dic61—22no—
70C22⋊Dic61—22no—
71#11758202—24no—
72#11758200—24no—
73C4⋊Dic61C2311yescharacteristic
74C4⋊Dic61C2311yescharacteristic
75#11758196—22no—
76#11758196—22no—
77C4×Dic61—21no—
78#11758194—24no—
79#11758194D414yescomplemented
80C2×#92418—22no—
81C2×#92418—24no—
82C2×#92418C2311yescharacteristic
83C2×#92418C2311yescharacteristic
84C2×#92418C2312yes—
85C23×C61—21no—
86C23×C61C2×D412yes—
87C23×C61C2×D411yescharacteristic
88Q8×C61—22no—
89Q8×C61—21no—
90Q8×C61—21no—
91D4×C61—24no—
92D4×C61—22no—
93D4×C61—21no—
94D4×C61—21no—
95D4×C61—42no—
96D4×C61—82no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—42no—
102C2×C4×C61—81no—
103C2×C4×C61C2×D412yes—
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2×D412yes—
106C2×C4×C61#4112yes—
107C2×C4×C61C2411yescharacteristic
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61—42no—
112Dic122—22no—
113Dic122—22no—
114Dic122—42no—
115#92418—21no—
116#92418—21no—
117#92418C2×D414yes—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61#12112yes—
127C22×C61C22×D411yescharacteristic
128C4×C61—22no—
129C4×C61—41no—
130C4×C61—42no—
131C4×C61#12112yes—
132C4×C61C22×D411yescharacteristic
133C4×C61C2×#4111yescharacteristic
134Dic61—42no—
135Dic61—41no—
136Dic61—41no—
137#3063—611nomaximal, Sylow
138C2×C61—22no—
139C2×C61—42no—
140C2×C61—81no—
141C2×C61C2×#12111yescharacteristic
142C2×C61#57711yescharacteristic
143C2×C61#57811yescharacteristic
144C2×#137—611no—
145C2×#131—611no—
146#537D6111yescharacteristic
147#536—611no—
148#470—612no—
149#468—612no—
150#467—612no—
151#465—612no—
152#428—611no—
153#416—611no—
154C2×#103—611no—
155C61#306311yescharacteristic, complemented, Sylow
156C2×#41C2×D6111yescharacteristic
157C2×#41C2×D6111yescharacteristic
158C22×Q8—611no—
159#137—1224no—
160C2×Q16—612no—
161C2×SD16—612no—
162#131—1224no—
163C2×M16—611no—
164C2×M16—612no—
165C22×C8—611no—
166C22×C8—612no—
167C4⋊Q8—1221no—
168#124—1221no—
169#123—1222no—
170C22⋊Q8—21no—
171C22⋊Q8—612no—
172C22⋊Q8—612no—
173C22⋊Q8C2×D6112yes—
174#121—21no—
175#121—22no—
176#121C2×D6112yes—
177#117—611no—
178C2×C4⋊C4C2×D6111yescharacteristic
179#107—612no—
180#106—612no—
181#103—611no—
182#103—611no—
183#103—612no—
184#103—612no—
185#102—611no—
186#102—611no—
187#41—22no—
188#41—22no—
189#41—22no—
190#41—22no—
191C2×Q8—612no—
192C2×Q8—1221no—
193C2×Q8—1222no—
194C2×Q8—1222no—
195C2×Q8C22⋊D6111yescharacteristic
196C2×Q8C22×D6111yescharacteristic
197C2×D4—21no—
198C2×D4—22no—
199C2×D4C22⋊D6112yes—
200C2×D4C22⋊D6111yescharacteristic
201C2×D4C22×D6111yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—1221no—
205C22×C4C22×D6112yes—
206C22×C4C22×D6111yescharacteristic
207Q16—1224no—
208SD16—1224no—
209M16—614no—
210M16—1224no—
211C2×C8—612no—
212C2×C8—611no—
213C2×C8—611no—
214C2×C8—1224no—
215C2×C8—1222no—
216C4⋊C4—21no—
217C4⋊C4—22no—
218C4⋊C4—611no—
219C4⋊C4—611no—
220C4⋊C4—1222no—
221C4⋊C4—1222no—
222C4⋊C4C22×D6112yes—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—1221no—
226C22⋊C4—1222no—
227C22⋊C4—1222no—
228C42—1221no—
229C23—21no—
230C23C2×C22⋊D6112yes—
231C23C2×C22⋊D6111yescharacteristic
232Q8—22no—
233Q8—21no—
234Q8—21no—
235Q8—1222no—
236Q8—1222no—
237Q8—2442no—
238D4—24no—
239D4—21no—
240D4—21no—
241D4—22no—
242D4—42no—
243D4—82no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—1222no—
253C2×C4—2442no—
254C2×C4D4×D6112yes—
255C2×C4#1175822412yes—
256C2×C4C2×C22⋊D6112yes—
257C2×C4C2×C22⋊D6111yescharacteristic
258C2×C4C23×D6111yescharacteristic
259C8—614no—
260C8—1221no—
261C8—1221no—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22#1451974912yes—
271C22C22×C22⋊D6111yescharacteristic
272C4—22no—
273C4—41no—
274C4—42no—
275C4—2442no—
276C4—2441no—
277C4—2441no—
278C4#1451974912yes—
279C4C2×D4×D6111yescharacteristic
280C4C2×#1175822411yescharacteristic
281C2—22no—
282C2—42no—
283C2—81no—
284C2C2×#1451974911yescharacteristic
285C2#1684057311yescharacteristic
286C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#537C2
socleC22×C61C22×D4
hypercenter#537D61
hypocenterC61#3063
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
2. C2×#14519784C2semidirect
3. #16840333C2semidirect
4. #16840018C2semidirect
5. #16840006C2semidirect
6. #16840001C2semidirect
7. #16839989C2semidirect
8. #16839802C2semidirect
9. #16839758C2semidirect
10. C2×#14519700C2semidirect
79. #11758194D4semidirect
155. C61#3063semidirect