Finite Group Databasebeta

← #21461812

Subgroups — #21461812

Order 7808.

402 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 80 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×D4×#6923C211yesmaximal, characteristic
2C2×#14519840C211yesmaximal, characteristic, complemented
3C2×#14519839C211yesmaximal, characteristic
4(C2×#6923)⋊Q8C211yesmaximal, characteristic, complemented
5#16840636C211yesmaximal, characteristic, complemented
6(C2×#6923)⋊C8C211yesmaximal, characteristic, complemented
7C2×SD16×D61C211yesmaximal, characteristic
8C23×#6923—21no—
9C2×D61⋊C8C2211yescharacteristic
10D4×#6923—22no—
11D4×#6923—22no—
12C2×C4⋊#6923C2211yescharacteristic
13C2×C4⋊#6923C2211yescharacteristic
14C2×C22⋊#6923—21no—
15C2×C4×#6923C2211yescharacteristic
16#14519840—22no—
17#14519839—22no—
18(C2×#6923)⋊C4—21no—
19(C2×#6923)⋊C4—21no—
20C2×Q8×D61C2211yescharacteristic
21C2×D4×D61C2211yescharacteristic
22C2×#11758190C411yescharacteristic, complemented
23C2×#11758200C411yescharacteristic, complemented
24C2×#11758201C411yescharacteristic, complemented
25SD16×D61—22no—
26SD16×D61—22no—
27C2×C8×D61C2211yescharacteristic
28C2×SD16×C61C411yescharacteristic, complemented
29C23×D61—21no—
30C22×#6923—24no—
31C22×#6923—21no—
32C22×#6923—21no—
33C22×#6923—42no—
34C22×#6923—42no—
35C22×#6923D411yescharacteristic
36C22×#6923D411yescharacteristic
37C2×Q8×C61C2×C411yescharacteristic, complemented
38C2×D4×C61C2×C411yescharacteristic
39C2×C22⋊D61—21no—
40Q8×D61—21no—
41Q8×D61—21no—
42Q8×D61—21no—
43Q8×D61—21no—
44D4×D61—21no—
45D4×D61—21no—
46D4×D61D412yes—
47D4×D61D412yes—
48C2×D244C2×C411yescharacteristic
49C2×C4×D61—21no—
50C2×C4×D61C2311yescharacteristic
51C2×Dic122—21no—
52C2×Dic122C2×C411yescharacteristic, complemented
53C22⋊#6923—24no—
54C2×#92420—21no—
55C4⋊#6923—21no—
56C4⋊#6923—21no—
57C4⋊#6923—21no—
58C4⋊#6923D412yes—
59C4×#6923—21no—
60C4×#6923—21no—
61D61⋊C8—21no—
62D61⋊C8—21no—
63SD16×C61—22no—
64C2×C8×C61C2×C411yescharacteristic, complemented
65#11758201—22no—
66#11758200—22no—
67C2×#92418C2×C411yescharacteristic, complemented
68#11758190—22no—
69C8×D61—21no—
70C8×D61—21no—
71C23×C61—21no—
72C22×D61—21no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—41no—
76C22×D61—41no—
77C22×D61—41no—
78C22×D61—41no—
79C22×D61C2×D411yescharacteristic
80C2×#6923—21no—
81C2×#6923—21no—
82C2×#6923—21no—
83C2×#6923—22no—
84C2×#6923—21no—
85C2×#6923—21no—
86C2×#6923—48no—
87C2×#6923—41no—
88C2×#6923—41no—
89C2×#6923—41no—
90C2×#6923—41no—
91C2×#6923—41no—
92C2×#6923SD1612yescomplemented
93Q8×C61—21no—
94Q8×C61—21no—
95D4×C61—21no—
96D4×C61C22⋊C412yes—
97C2×C4×C61—21no—
98C2×C4×C61C22×C411yescharacteristic
99C22⋊D61—22no—
100C22⋊D61—22no—
101C2×Dic61—21no—
102C2×Dic61#4111yescharacteristic
103D244—21no—
104D244C22⋊C412yes—
105C4×D61—41no—
106C4×D61—41no—
107C4×D61C2×D411yescharacteristic
108C4×D61C2×D411yescharacteristic
109C4×D61C2×D411yescharacteristic
110C4×D61#4111yescharacteristic
111Dic122—21no—
112Dic122—21no—
113Dic122—41no—
114Dic122—41no—
115#92420—41no—
116C8×C61—21no—
117#92418—21no—
118C22×C61—22no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61C4×D411yescharacteristic
122C2×D61—22no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—42no—
128C2×D61—42no—
129C2×D61#12011yescharacteristic
130C2×D61#12111yescharacteristic
131C2×D61C2×SD1611yescharacteristic
132C2×D61#13511yescharacteristic
133C2×D61AGL(1,ℤ/8)11yescharacteristic
134C2×D61#13711yescharacteristic
135#6923—22no—
136#6923—42no—
137#6923—41no—
138#6923—81no—
139C4×C61—41no—
140C4×C61C2×C22⋊C411yescharacteristic
141C4×C61C4×D411yescharacteristic
142Dic61—41no—
143Dic61#12111yescharacteristic
144Dic61#12311yescharacteristic
145#1877—611nomaximal, Sylow
146C2×C61—42no—
147C2×C61#38611yescharacteristic
148C2×C61C4×SD1611yescharacteristic
149C2×C61#44011yescharacteristic
150D61—42no—
151D61#45011yescharacteristic
152D61#45211yescharacteristic
153D61#46111yescharacteristic
154D61#46311yescharacteristic
155C22×SD16—611no—
156C2×C4×D4—611no—
157C2×#103—611no—
158C2×#102—611no—
159#391—611no—
160#340—611no—
161#336—611no—
162C61#187711yescharacteristic, complemented, Sylow
163C22×Q8—611no—
164C22×D4—611no—
165C23×C4—1221no—
166C2×SD16—611no—
167C2×SD16—611no—
168C2×SD16—611no—
169C2×SD16—1222no—
170C2×SD16—1222no—
171C2×SD16#692311yescharacteristic, complemented
172C22×C8—611no—
173C22×C8—611no—
174C4×D4—1222no—
175C4×D4—1222no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—611no—
178C2×C22⋊C4—1221no—
179C2×C42—611no—
180#103—1222no—
181#102—1222no—
182#95—1221no—
183#95—1221no—
184C24—1221no—
185C2×Q8—611no—
186C2×Q8—1221no—
187C2×Q8—1221no—
188C2×Q8—1221no—
189C2×Q8—1221no—
190C2×Q8—1221no—
191C2×Q8C2×#692311yescharacteristic, complemented
192C2×D4—612no—
193C2×D4—612no—
194C2×D4—611no—
195C2×D4—1221no—
196C2×D4—1221no—
197C2×D4—1221no—
198C2×D4C2×#692311yescharacteristic
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4—1224no—
205C22×C4—1221no—
206C22×C4—2442no—
207C22×C4—2442no—
208SD16—22no—
209SD16—1222no—
210SD16—1222no—
211SD16—1222no—
212C2×C8—611no—
213C2×C8—1221no—
214C2×C8—1221no—
215C2×C8—1221no—
216C2×C8—1221no—
217C2×C8—1221no—
218C2×C8C2×#692311yescharacteristic, complemented
219C4⋊C4—612no—
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C22⋊C4—1224no—
224C42—1221no—
225C42—1221no—
226C23—21no—
227C23—611no—
228C23—1222no—
229C23—1222no—
230C23—1221no—
231C23—2441no—
232C23—2441no—
233C23—2441no—
234C23—2441no—
235Q8—21no—
236Q8—21no—
237Q8—1221no—
238Q8—1221no—
239Q8—2441no—
240Q8—2441no—
241D4—21no—
242D4—612no—
243D4—1222no—
244D4—1222no—
245D4—1221no—
246D4C22⋊#692312yes—
247C2×C4—21no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—611no—
252C2×C4—611no—
253C2×C4—612no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1222no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2448no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4C22×#692311yescharacteristic
270C8—21no—
271C8—1221no—
272C8—2441no—
273C22—22no—
274C22—41no—
275C22—41no—
276C22—611no—
277C22—611no—
278C22—611no—
279C22—611no—
280C22—611no—
281C22—611no—
282C22—1222no—
283C22—2442no—
284C22—2442no—
285C22—2442no—
286C22—2442no—
287C22—2441no—
288C22—2441no—
289C22D4×#692311yescharacteristic
290C4—41no—
291C4—611no—
292C4—611no—
293C4—1222no—
294C4—4881no—
295C4—2441no—
296C4—2442no—
297C4—2441no—
298C4C2×C22⋊#692311yescharacteristic
299C4D4×#692311yescharacteristic
300C2—42no—
301C2—611no—
302C2—611no—
303C2—611no—
304C2—611no—
305C2—2442no—
306C2#1684071011yescharacteristic
307C2SD16×#692311yescharacteristic
308C2#1684080111yescharacteristic
subgroupG/H
centerC22D4×#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×SD16×C61C4
socleC22×C61C4×D4
hypercenterC2×SD16#6923
hypocenterC61#1877
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#14519840C2semidirect
4. (C2×#6923)⋊Q8C2semidirect
5. #16840636C2semidirect
6. (C2×#6923)⋊C8C2semidirect
22. C2×#11758190C4semidirect
23. C2×#11758200C4semidirect
24. C2×#11758201C4semidirect
28. C2×SD16×C61C4semidirect
37. C2×Q8×C61C2×C4semidirect
52. C2×Dic122C2×C4semidirect
64. C2×C8×C61C2×C4semidirect
67. C2×#92418C2×C4semidirect
92. C2×#6923SD16semidirect
162. C61#1877semidirect
171. C2×SD16#6923semidirect
191. C2×Q8C2×#6923semidirect
218. C2×C8C2×#6923semidirect