Finite Group Databasebeta

← #21445752

Subgroups — #21445752

Order 7808.

592 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C22×Q8×D61C211yesmaximal, characteristic
2C2×#14519702C211yesmaximal, characteristic, complemented
3C2×#14519701C211yesmaximal, characteristic, complemented
4C2×#14519700C211yesmaximal, characteristic, complemented
5C2×#14519689C211yesmaximal, characteristic
6#16839619C211yesmaximal, characteristic
7C2×#103×C61C211yesmaximal, characteristic, complemented
8C22×Dic122—21no—
9C22×Dic122C2211yescharacteristic
10C2×Q8×D61—22no—
11C2×Q8×D61—22no—
12C2×Q8×D61—22no—
13C2×Q8×D61—22no—
14C2×Q8×D61—22no—
15C2×Q8×D61C414yescomplemented
16C22×C4×D61—21no—
17C22×C4×D61C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×#11758198—21no—
21#14519702—22no—
22#14519701—22no—
23#14519700—22no—
24#14519689—22no—
25#14519684—21no—
26C22×Q8×C61C2211yescharacteristic
27C22×C8×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29#103×C61—22no—
30C23×D61D411yescharacteristic
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61C2×C412yes—
35C2×Q8×C61D412yes—
36C2×Q8×C61D412yes—
37C22×C4×C61—21no—
38C22×C4×C61—21no—
39C22×C4×C61C2311yescharacteristic
40C22×Dic61—21no—
41C22×Dic61—21no—
42C22×Dic61D411yescharacteristic
43Q8×D61—28no—
44Q8×D61—28no—
45Q8×D61—28no—
46Q8×D61—28no—
47C2×C4×D61—24no—
48C2×C4×D61—24no—
49C2×C4×D61—24no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61C2×C412yes—
55C2×C4×D61D412yes—
56C2×Dic122—24no—
57C2×Dic122—24no—
58C2×Dic122—21no—
59C2×Dic122—21no—
60C2×Dic122—21no—
61C2×Dic122—24no—
62C2×Dic122C2×C412yes—
63C2×Dic122D412yes—
64C2×Dic122D412yes—
65C2×C8×C61—21no—
66C2×C8×C61—21no—
67C2×C8×C61—21no—
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70#11758198—42no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C2×#92418—21no—
74C2×#92418—21no—
75C2×#92418—21no—
76C23×C61C2×D411yescharacteristic
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—21no—
81C22×D61C22⋊C412yes—
82C22×D61SD1612yes—
83C22×D61Q1612yes—
84Q8×C61—22no—
85Q8×C61—22no—
86Q8×C61—22no—
87Q8×C61C22⋊C414yescomplemented
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61C22×C411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×Dic61—22no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61C22⋊C412yes—
109C4×D61—216no—
110C4×D61—22no—
111C4×D61—22no—
112C4×D61—22no—
113C4×D61—22no—
114Dic122—216no—
115Dic122—22no—
116Dic122—22no—
117Dic122—22no—
118Dic122C22⋊C414yescomplemented
119C8×C61—41no—
120#92418—41no—
121C22×C61C2×C22⋊C411yescharacteristic
122C22×C61#12011yescharacteristic
123C22×C61#12011yescharacteristic
124C22×C61C2×SD1611yescharacteristic
125C22×C61C2×Q1611yescharacteristic
126C22×C61#13711yescharacteristic
127C22×C61#13711yescharacteristic
128C2×D61—22no—
129C2×D61—22no—
130C2×D61—22no—
131C2×D61—22no—
132C2×D61—22no—
133C2×D61—22no—
134C2×D61#10314yescomplemented
135C4×C61—24no—
136C4×C61—81no—
137C4×C61C2×C22⋊C411yescharacteristic
138C4×C61C2×C22⋊C411yescharacteristic
139C4×C61#12011yescharacteristic
140C4×C61#12011yescharacteristic
141Dic61—22no—
142Dic61—24no—
143Dic61—81no—
144#1787—611nomaximal, Sylow
145C2×C61#37911yescharacteristic
146C2×C61C2×#10311yescharacteristic
147C2×C61#41911yescharacteristic
148C2×C61#44811yescharacteristic
149C2×C61#44811yescharacteristic
150C2×C61#45111yescharacteristic
151C2×C61#45111yescharacteristic
152D61—24no—
153C23×Q8—611no—
154C2×#103—611no—
155C2×#103—611no—
156C2×#103—611no—
157C2×#103D6111yescharacteristic, complemented
158C2×C22⋊C8—611no—
159#380—611no—
160C61#178711yescharacteristic, complemented, Sylow
161C22×Q8—614no—
162C22×Q8—611no—
163C22×Q8—1221no—
164C22×Q8—1222no—
165C22×Q8—1222no—
166C22×Q8—1222no—
167C22×Q8—1222no—
168C22×Q8—1222no—
169C22×Q8C2×D6111yescharacteristic
170C23×C4—611no—
171C23×C4—1221no—
172C22×C8—611no—
173C22×C8C2×D6111yescharacteristic
174C2×C4⋊C4—611no—
175C2×C4⋊C4C2×D6111yescharacteristic
176C2×C22⋊C4—1221no—
177#103—22no—
178#103—1222no—
179#103—1222no—
180#103—1222no—
181C22⋊C8—1222no—
182#95—1221no—
183C24—611no—
184C2×Q8—21no—
185C2×Q8—21no—
186C2×Q8—21no—
187C2×Q8—612no—
188C2×Q8—612no—
189C2×Q8—612no—
190C2×Q8—1224no—
191C2×Q8—1224no—
192C2×Q8—1224no—
193C2×Q8—1228no—
194C2×Q8—1228no—
195C2×Q8—1228no—
196C2×Q8—1228no—
197C2×Q8—1221no—
198C2×Q8—1221no—
199C2×Q8—1221no—
200C2×Q8C4×D6112yes—
201C2×Q8D24412yes—
202C2×Q8C22⋊D6112yes—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—611no—
206C22×C4—612no—
207C22×C4—612no—
208C22×C4—1224no—
209C22×C4—1224no—
210C22×C4—1224no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4C22×D6111yescharacteristic
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—1221no—
222C2×C8—1221no—
223C2×C8—1221no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—1221no—
227C4⋊C4—1221no—
228C22⋊C4—2442no—
229C23—612no—
230C23—612no—
231C23—612no—
232C23—1221no—
233C23—1221no—
234C23—1221no—
235C23—1221no—
236C23D4×D6111yescharacteristic
237Q8—22no—
238Q8—22no—
239Q8—22no—
240Q8—614no—
241Q8—12216no—
242Q8—1222no—
243Q8—1222no—
244Q8—1222no—
245Q8#1175819814yescomplemented
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—612no—
253C2×C4—12216no—
254C2×C4—1222no—
255C2×C4—1221no—
256C2×C4—1222no—
257C2×C4—1221no—
258C2×C4—1222no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4C2×C4×D6111yescharacteristic
267C2×C4C2×D24411yescharacteristic
268C2×C4D4×D6111yescharacteristic
269C2×C4D4×D6111yescharacteristic
270C2×C4D4×D6111yescharacteristic
271C2×C4C2×C22⋊D6111yescharacteristic
272C8—41no—
273C8—2441no—
274C22—614no—
275C22—1222no—
276C22—1222no—
277C22—1222no—
278C22—1222no—
279C22—1222no—
280C22—1222no—
281C22C22⋊C4×D6111yescharacteristic
282C22#1451974511yescharacteristic
283C22#1451974711yescharacteristic
284C22SD16×D6111yescharacteristic
285C22Q16×D6111yescharacteristic
286C22#1451980611yescharacteristic
287C22#1451980911yescharacteristic
288C4—24no—
289C4—81no—
290C4—1222no—
291C4—1224no—
292C4—4881no—
293C4C22⋊C4×D6111yescharacteristic
294C4C2×#1175819811yescharacteristic
295C4#1451974511yescharacteristic
296C4#1451974711yescharacteristic
297C2—1224no—
298C2#1683961711yescharacteristic
299C2#103×D6111yescharacteristic
300C2#1683976911yescharacteristic
301C2#1683989911yescharacteristic
302C2#1683990211yescharacteristic
303C2#1683991611yescharacteristic
304C2#1683991911yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#1787
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#14519702C2semidirect
3. C2×#14519701C2semidirect
4. C2×#14519700C2semidirect
7. C2×#103×C61C2semidirect
15. C2×Q8×D61C4semidirect
87. Q8×C61C22⋊C4semidirect
118. Dic122C22⋊C4semidirect
134. C2×D61#103semidirect
157. C2×#103D61semidirect
160. C61#1787semidirect
245. Q8#11758198semidirect