Finite Group Databasebeta

← #21446825

Subgroups — #21446825

Order 7808.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11758190C211yesmaximal, characteristic, complemented
2C2×#14519757C211yesmaximal, characteristic, complemented
3C2×#14519752C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic, complemented
5C2×#14519697C211yesmaximal, characteristic, complemented
6C2×#14519689C211yesmaximal, characteristic, complemented
7C61×#340C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×D244—21no—
10C22×D244C2211yescharacteristic
11C22×C4×D61C2211yescharacteristic
12C2×#11758190—22no—
13C2×#11758190—22no—
14C2×#11758190—22no—
15C22×#92418C2211yescharacteristic
16#14519757—22no—
17#14519757—22no—
18#14519752—22no—
19#14519752—22no—
20C2×C4⋊Dic61—21no—
21C2×#11758198—21no—
22C2×#11758198—21no—
23#14519700—22no—
24#14519697—22no—
25#14519689—22no—
26C22×C8×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C23×D61—21no—
30C23×D61D411yescharacteristic
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C22×Dic61D411yescharacteristic
36C2×D244—21no—
37C2×D244—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—24no—
41C2×D244—21no—
42C2×D244—42no—
43C2×D244—42no—
44C2×D244D412yes—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×Dic122—21no—
52C2×Dic122—21no—
53C2×Dic122—21no—
54C2×Dic122—21no—
55C2×Dic122—21no—
56C2×Dic122D412yescomplemented
57C2×C8×C61—21no—
58C2×C8×C61—21no—
59C2×C8×C61D412yescomplemented
60C4⋊C4×C61—21no—
61C4⋊C4×C61—21no—
62C4⋊C4×C61D412yes—
63C4⋊C4×C61D412yescomplemented
64#11758198—24no—
65#11758198—24no—
66C4⋊Dic61—24no—
67C2×#92418—21no—
68C2×#92418—21no—
69C2×#92418—21no—
70#11758190—28no—
71C23×C61C2×D411yescharacteristic
72C22×D61—21no—
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—22no—
79C22×D61—41no—
80C22×D61—41no—
81C22×D61—41no—
82C22×D61—41no—
83C22×D61—41no—
84C22×D61—41no—
85C22×D61SD1612yescomplemented
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61#4111yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104D244—22no—
105D244—22no—
106D244—48no—
107D244—41no—
108D244—41no—
109C4×D61—41no—
110C4×D61—41no—
111C4×D61—41no—
112C4×D61—41no—
113Dic122—22no—
114Dic122—22no—
115Dic122—41no—
116Dic122—41no—
117C8×C61—22no—
118#92418—41no—
119C22×C61#12011yescharacteristic
120C22×C61#12011yescharacteristic
121C22×C61#12111yescharacteristic
122C22×C61C2×SD1611yescharacteristic
123C22×C61#13511yescharacteristic
124C22×C61AGL(1,ℤ/8)11yescharacteristic
125C22×C61#13711yescharacteristic
126C2×D61—22no—
127C2×D61—22no—
128C2×D61—22no—
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—41no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—81no—
137C2×D61—81no—
138C2×D61—81no—
139C2×D61—81no—
140C4×C61—42no—
141C4×C61—42no—
142C4×C61#12011yescharacteristic
143C4×C61#12111yescharacteristic
144C4×C61#12111yescharacteristic
145C4×C61#12711yescharacteristic
146Dic61—42no—
147Dic61—41no—
148#2000—611nomaximal, Sylow
149C2×C61#39211yescharacteristic
150C2×C61#44811yescharacteristic
151C2×C61#44911yescharacteristic
152C2×C61#45011yescharacteristic
153C2×C61#45211yescharacteristic
154C2×C61#46511yescharacteristic
155C2×C61#46811yescharacteristic
156D61—42no—
157D61—82no—
158C22×SD16—611no—
159C2×C22⋊Q8—611no—
160C2×#121—611no—
161C2×#103—611no—
162C2×#102—611no—
163C2×C22⋊C8—611no—
164#340D6111yescharacteristic, complemented
165C61#200011yescharacteristic, complemented, Sylow
166C22×Q8—611no—
167C22×D4—611no—
168C22×D4—1221no—
169C23×C4—611no—
170C2×SD16—1222no—
171C2×SD16—1222no—
172C2×SD16—1222no—
173C22×C8—611no—
174C22×C8C2×D6111yescharacteristic
175C22⋊Q8—1222no—
176C22⋊Q8—1222no—
177#121—1222no—
178#121—1222no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4C2×D6111yescharacteristic
181C2×C4⋊C4C2×D6111yescharacteristic
182C2×C22⋊C4—1221no—
183C2×C22⋊C4—1221no—
184#103—1222no—
185#102—1222no—
186C22⋊C8—1222no—
187C24—611no—
188C24—1221no—
189C2×Q8—612no—
190C2×Q8—1221no—
191C2×Q8—1221no—
192C2×Q8—1221no—
193C2×Q8—1221no—
194C2×Q8—1221no—
195C2×D4—612no—
196C2×D4—1224no—
197C2×D4—1221no—
198C2×D4—1221no—
199C2×D4—1221no—
200C2×D4—1221no—
201C2×D4—1221no—
202C2×D4—2442no—
203C2×D4—2442no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—611no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4C22×D6111yescharacteristic
215SD16—1228no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—1221no—
219C2×C8—1221no—
220C2×C8—1221no—
221C2×C8D24412yescomplemented
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—1224no—
225C4⋊C4D24412yes—
226C4⋊C4D24412yescomplemented
227C22⋊C4—1224no—
228C22⋊C4—1224no—
229C23—612no—
230C23—1221no—
231C23—1221no—
232C23—1221no—
233C23—1221no—
234C23—1221no—
235C23—1221no—
236C23—1222no—
237C23—2441no—
238C23—2441no—
239C23—2441no—
240C23—2441no—
241C23—2441no—
242C23—2441no—
243C23D4×D6111yescharacteristic
244Q8—1222no—
245Q8—1222no—
246Q8—2441no—
247Q8—2441no—
248D4—1222no—
249D4—1222no—
250D4—2448no—
251D4—2441no—
252D4—2441no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—1221no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4C2×D24411yescharacteristic
270C2×C4C2×D24411yescharacteristic
271C2×C4C2×D24411yescharacteristic
272C2×C4D4×D6111yescharacteristic
273C2×C4D4×D6111yescharacteristic
274C2×C4#1175822611yescharacteristic
275C8—22no—
276C8—2441no—
277C22—1222no—
278C22—1222no—
279C22—1222no—
280C22—4881no—
281C22—4881no—
282C22—4881no—
283C22—4881no—
284C22—2442no—
285C22—2442no—
286C22—2442no—
287C22—2441no—
288C22—2441no—
289C22—2441no—
290C22—2441no—
291C22#1451974711yescharacteristic
292C22#1451974711yescharacteristic
293C22#1451975211yescharacteristic
294C22SD16×D6111yescharacteristic
295C22#1451979811yescharacteristic
296C22#1451980111yescharacteristic
297C22#1451980911yescharacteristic
298C4—42no—
299C4—42no—
300C4—2441no—
301C4—2442no—
302C4#1451974711yescharacteristic
303C4#1451975211yescharacteristic
304C4#1451975211yescharacteristic
305C4#1451977411yescharacteristic
306C2—4882no—
307C2—2442no—
308C2#1683967211yescharacteristic
309C2#1683990211yescharacteristic
310C2#1683990811yescharacteristic
311C2#1683991411yescharacteristic
312C2#1683992711yescharacteristic
313C2#1683999211yescharacteristic
314C2#1684000911yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#2000
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C22×#11758190C2semidirect
2. C2×#14519757C2semidirect
4. C2×#14519700C2semidirect
5. C2×#14519697C2semidirect
6. C2×#14519689C2semidirect
7. C61×#340C2semidirect
56. C2×Dic122D4semidirect
59. C2×C8×C61D4semidirect
63. C4⋊C4×C61D4semidirect
85. C22×D61SD16semidirect
164. #340D61semidirect
165. C61#2000semidirect
221. C2×C8D244semidirect
226. C4⋊C4D244semidirect