Finite Group Databasebeta

← #21458648

Subgroups — #21458648

Order 7808.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840485C211yesmaximal, characteristic, complemented
2#16840472C211yesmaximal, characteristic, complemented
3#16840131C211yesmaximal, characteristic, complemented
4#16840122C211yesmaximal, characteristic, complemented
5#16840117C211yesmaximal, characteristic, complemented
6#16840070C211yesmaximal, characteristic, complemented
7#16840063C211yesmaximal, characteristic, complemented
8#16840048C211yesmaximal, characteristic, complemented
9#16839978C211yesmaximal, characteristic
10#16839978C211yesmaximal, characteristic
11#16839968C211yesmaximal, characteristic, complemented
12#16839875C211yesmaximal, characteristic
13#16839864C211yesmaximal, characteristic, complemented
14C4×#11758190C211yesmaximal, characteristic, complemented
15C61×#446C211yesmaximal, characteristic, complemented
16C2×#11758190C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×D488C2211yescharacteristic
19#14519777C2211yescharacteristic
20#14519777C2211yescharacteristic
21#14519772—21no—
22#14519772—21no—
23#14519769C2211yescharacteristic
24#14519769C2211yescharacteristic
25#14519765C2211yescharacteristic
26#14519765C2211yescharacteristic
27#14519755—21no—
28#14519755—21no—
29#14519753—21no—
30#14519753—21no—
31C4×Dic122C2211yescharacteristic
32C4×Dic122C2211yescharacteristic
33C4×D244C2211yescharacteristic
34C4×D244C2211yescharacteristic
35C4×D244C2211yescharacteristic
36C4×D244C2211yescharacteristic
37#14519735—21no—
38C4⋊C4×D61—21no—
39#14519711C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52C4×Q8×C61C2211yescharacteristic
53C4⋊C8×C61C2211yescharacteristic
54C4⋊C8×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic
56#97×C61C2211yescharacteristic
57#97×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61D411yescharacteristic
60C2×D244C2311yescharacteristic
61C2×D244C2311yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×Dic122—21no—
67C2×Dic122C2311yescharacteristic
68C2×Dic122C2311yescharacteristic
69C2×C8×C61C2311yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C2×C8×C61C2311yescharacteristic
72C2×C8×C61C2311yescharacteristic
73C4⋊C4×C61D411yescharacteristic
74C4⋊C4×C61D411yescharacteristic
75C4⋊C4×C61D411yescharacteristic
76C42×C61C2311yescharacteristic
77C42×C61C2311yescharacteristic
78C42×C61C2311yescharacteristic
79#11758198—21no—
80#11758198—21no—
81#11758198—21no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61C2311yescharacteristic
91C4⋊Dic61C2311yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102D488—22no—
103#11758190—22no—
104#11758190—22no—
105C22×D61—21no—
106C22×D61—21no—
107Q8×C61—41no—
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2×D411yescharacteristic
110C2×C4×C61C2×D411yescharacteristic
111C2×C4×C61C2×D411yescharacteristic
112C2×C4×C61C2×D411yescharacteristic
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2411yescharacteristic
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121D244—21no—
122D244—21no—
123D244—21no—
124D244#4112yes—
125C4×D61—42no—
126C4×D61—42no—
127C4×D61—81no—
128C4×D61—81no—
129Dic122—21no—
130Dic122—21no—
131Dic122—21no—
132Dic122—21no—
133Dic122—81no—
134C8×C61—21no—
135C8×C61—21no—
136C8×C61—21no—
137C8×C61—21no—
138C22×C61C22×D411yescharacteristic
139C2×D61—22no—
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—41no—
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61C2×#4111yescharacteristic
152C4×C612−1+411yescharacteristic
153Dic61—41no—
154Dic61—41no—
155Dic61—41no—
156Dic61—41no—
157Dic61—41no—
158Dic61—41no—
159#3376—611nomaximal, Sylow
160C2×C61#54811yescharacteristic
161C2×C61#57511yescharacteristic
162C2×C61#57711yescharacteristic
163D61—42no—
164D61—81no—
165#556—611no—
166#554—611no—
167#491—611no—
168#489—611no—
169#488—611no—
170#479—611no—
171#478—611no—
172#475—611no—
173#463—611no—
174#463—611no—
175#461—611no—
176#446D6111yescharacteristic, complemented
177#442—611no—
178#440—611no—
179C4×SD16—611no—
180C61#337611yescharacteristic, complemented, Sylow
181C2×SD16—611no—
182C2×SD16—611no—
183C2×D8—611no—
184C4⋊Q8—611no—
185C4⋊Q8—611no—
186#126—1221no—
187#126—1221no—
188#125—611no—
189#125—611no—
190#124—611no—
191#124—611no—
192C22⋊Q8—1221no—
193C22⋊Q8—1221no—
194C22⋊Q8—1221no—
195C22⋊Q8—1221no—
196C4×Q8—611no—
197C4×Q8—611no—
198C4×Q8C2×D6111yescharacteristic
199C4×D4—611no—
200C4×D4—611no—
201C4×D4—611no—
202C4×D4—611no—
203#117—1221no—
204C2×C4⋊C4—1221no—
205#107—611no—
206#106—611no—
207#106—611no—
208C4⋊C8C2×D6111yescharacteristic
209C4⋊C8C2×D6111yescharacteristic
210C4⋊C8C2×D6111yescharacteristic
211#103—611no—
212#103—611no—
213#103—611no—
214#103—611no—
215#103—611no—
216#103—611no—
217#102—611no—
218#102—611no—
219#102—611no—
220#102—611no—
221#97C2×D6111yescharacteristic
222#97C2×D6111yescharacteristic
223C4×C8C2×D6111yescharacteristic
224C2×Q8—611no—
225C2×Q8—611no—
226C2×Q8—1221no—
227C2×Q8D24411yescharacteristic
228C2×D4—611no—
229C2×D4—611no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234SD16—1222no—
235SD16—1222no—
236D8—1222no—
237C2×C8C22×D6111yescharacteristic
238C2×C8C22×D6111yescharacteristic
239C2×C8C22×D6111yescharacteristic
240C2×C8C22×D6111yescharacteristic
241C4⋊C4—611no—
242C4⋊C4—611no—
243C4⋊C4—611no—
244C4⋊C4—611no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4D24411yescharacteristic
255C4⋊C4D24411yescharacteristic
256C4⋊C4D24411yescharacteristic
257C22⋊C4—1221no—
258C22⋊C4—1221no—
259C22⋊C4—1221no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C42—1221no—
266C42—1221no—
267C42C22×D6111yescharacteristic
268C42C22×D6111yescharacteristic
269C42C22×D6111yescharacteristic
270C23—1221no—
271C23—1221no—
272Q8—41no—
273Q8—1221no—
274Q8—1221no—
275Q8—1221no—
276Q8—1221no—
277Q8—4881no—
278D4—612no—
279D4—1221no—
280D4—1221no—
281D4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—4881no—
289C2×C4—4881no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4C2×D24411yescharacteristic
293C2×C4C2×D24411yescharacteristic
294C2×C4C2×D24411yescharacteristic
295C2×C4C2×D24411yescharacteristic
296C2×C4C2×D24411yescharacteristic
297C2×C4C2×D24411yescharacteristic
298C2×C4C23×D6111yescharacteristic
299C8—21no—
300C8—21no—
301C8—21no—
302C8—21no—
303C22—1222no—
304C22—2441no—
305C22—2441no—
306C22—2441no—
307C22—2441no—
308C22—2441no—
309C22C22×D24411yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—2441no—
317C4—2441no—
318C4—2441no—
319C4—2441no—
320C4—2441no—
321C4—2441no—
322C4#41×D6111yescharacteristic
323C4#1451982511yescharacteristic
324C2—4881no—
325C2—2442no—
326C2#1684042411yescharacteristic
327C2#1684056211yescharacteristic
328C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3376
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #16840485C2semidirect
2. #16840472C2semidirect
3. #16840131C2semidirect
4. #16840122C2semidirect
5. #16840117C2semidirect
6. #16840070C2semidirect
7. #16840063C2semidirect
8. #16840048C2semidirect
11. #16839968C2semidirect
13. #16839864C2semidirect
14. C4×#11758190C2semidirect
15. C61×#446C2semidirect
176. #446D61semidirect
180. C61#3376semidirect