Finite Group Databasebeta

← #21458259

Subgroups — #21458259

Order 7808.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840416C211yesmaximal, characteristic
2#16840172C211yesmaximal, characteristic, complemented
3#16840095C211yesmaximal, characteristic, complemented
4#16840090C211yesmaximal, characteristic, complemented
5#16840086C211yesmaximal, characteristic, complemented
6#16840075C211yesmaximal, characteristic, complemented
7#16840059C211yesmaximal, characteristic, complemented
8#16840057C211yesmaximal, characteristic, complemented
9#16840010C211yesmaximal, characteristic, complemented
10#16839993C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839805C211yesmaximal, characteristic, complemented
14C2×#14519710C211yesmaximal, characteristic, complemented
15C61×#552C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×#11758201C2211yescharacteristic
18C2×#11758194C2211yescharacteristic
19C22×#92418C2211yescharacteristic
20#14519777C2211yescharacteristic
21#14519761—21no—
22#14519761—21no—
23#14519757—21no—
24#14519751C2211yescharacteristic
25#14519751C2211yescharacteristic
26C4×D244C2211yescharacteristic
27C2×C4⋊Dic61C2211yescharacteristic
28C2×C4⋊Dic61C2211yescharacteristic
29#14519710C2211yescharacteristic
30#14519710C2211yescharacteristic
31#14519710C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519710C2211yescharacteristic
34#14519710C2211yescharacteristic
35#14519708C2211yescharacteristic
36#14519708C2211yescharacteristic
37#14519708C2211yescharacteristic
38C4⋊#92418C2211yescharacteristic
39#14519701C2211yescharacteristic
40#14519701C2211yescharacteristic
41#14519701C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48#126×C61—21no—
49#125×C61—21no—
50#125×C61C2211yescharacteristic
51#123×C61—21no—
52C22⋊Q8×C61C2211yescharacteristic
53C22⋊Q8×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56#117×C61—21no—
57#117×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61D411yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68#11758224—44no—
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×Dic122—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61D411yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61D411yescharacteristic
86C22⋊C4×C61D411yescharacteristic
87C42×C61—21no—
88C42×C61—21no—
89C42×C61C2311yescharacteristic
90#11758201—22no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758194—22no—
101C2×#92418—22no—
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C23×C61C2×D411yescharacteristic
107C23×C61C2×D411yescharacteristic
108C22×D61—21no—
109Q8×C61—21no—
110Q8×C61—21no—
111D4×C61—22no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—42no—
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—42no—
127C22⋊D61—42no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133D244—21no—
134D244—21no—
135C4×D61—42no—
136Dic122—42no—
137#92418—21no—
138#92418—21no—
139#92418—21no—
140#92418#4112yescomplemented
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—21no—
146C22×C61AGL(1,ℤ/8)12yes—
147C22×C61C22×D411yescharacteristic
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—41no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61C2×#4111yescharacteristic
160C4×C612−1+411yescharacteristic
161Dic61—41no—
162Dic61—41no—
163Dic61—41no—
164#3343—611nomaximal, Sylow
165C2×C61—22no—
166C2×C61—41no—
167C2×C61#54711yescharacteristic
168C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C61#57811yescharacteristic
170D61—81no—
171#552D6111yescharacteristic, complemented
172#547—611no—
173#501—611no—
174#484—611no—
175#483—611no—
176#482—611no—
177#480—611no—
178#478—611no—
179#477—611no—
180#468—611no—
181#465—611no—
182#440—611no—
183#435—611no—
184#428—611no—
185C2×#107—611no—
186C61#334311yescharacteristic, complemented, Sylow
187C2×#41—1221no—
188C2×SD16—611no—
189C2×M16—611no—
190C22×C8—611no—
191C4⋊Q8—611no—
192#126—21no—
193#125—21no—
194#125C2×D6111yescharacteristic
195#123—21no—
196#123—1221no—
197#123—1221no—
198C22⋊Q8—1221no—
199C22⋊Q8C2×D6111yescharacteristic
200C22⋊Q8C2×D6111yescharacteristic
201#121—611no—
202#121—611no—
203C4×Q8C2×D6111yescharacteristic
204C4×D4—611no—
205C4×D4C2×D6111yescharacteristic
206#117—21no—
207#117C2×D6111yescharacteristic
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4C2×D6111yescharacteristic
211#107—611no—
212#107—611no—
213#107—611no—
214#107—611no—
215#107—611no—
216#107—611no—
217#106—611no—
218#106—611no—
219#106—611no—
220C4⋊C8—611no—
221#103—611no—
222#103—611no—
223#103—611no—
224#102—611no—
225#102—611no—
226#102—611no—
227C22⋊C8—611no—
228C22⋊C8—611no—
229#97—611no—
230#41—2444no—
231C2×Q8—1221no—
232C2×Q8C22×D6111yescharacteristic
233C2×D4—611no—
234C2×D4—1221no—
235C2×D4—1221no—
236C2×D4C22⋊D6111yescharacteristic
237C22×C4—21no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4C22×D6111yescharacteristic
242C22×C4C22×D6111yescharacteristic
243SD16—1222no—
244M16—1222no—
245C2×C8—611no—
246C2×C8—611no—
247C2×C8—611no—
248C2×C8—611no—
249C2×C8—1222no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—611no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4C22⋊D6111yescharacteristic
263C4⋊C4C22×D6111yescharacteristic
264C4⋊C4C22×D6111yescharacteristic
265C4⋊C4C22×D6111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4C22⋊D6111yescharacteristic
273C22⋊C4C22⋊D6111yescharacteristic
274C42—21no—
275C42—21no—
276C42C22×D6111yescharacteristic
277C23—1221no—
278C23C2×C22⋊D6111yescharacteristic
279C23C2×C22⋊D6111yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—2442no—
283D4—22no—
284D4—1221no—
285D4—1221no—
286D4—2442no—
287D4—2442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—2442no—
301C2×C4—2442no—
302C2×C4—2442no—
303C2×C4C2×C22⋊D6111yescharacteristic
304C2×C4C2×C22⋊D6111yescharacteristic
305C2×C4C2×C22⋊D6111yescharacteristic
306C2×C4C2×C22⋊D6111yescharacteristic
307C2×C4C23×D6111yescharacteristic
308C8—612no—
309C8—1221no—
310C8—1221no—
311C8—1221no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—2441no—
318C22—2441no—
319C22—2441no—
320C22#1451980212yes—
321C22C22×C22⋊D6111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—2441no—
331C4—2441no—
332C4—2441no—
333C4#41×D6111yescharacteristic
334C4#1451982411yescharacteristic
335C2—22no—
336C2—41no—
337C2—4881no—
338C2#1684041111yescharacteristic
339C2C2×#1451980211yescharacteristic
340C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#552C2
socleC22×C61C22×D4
hypercenter#552D61
hypocenterC61#3343
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #16840172C2semidirect
3. #16840095C2semidirect
4. #16840090C2semidirect
5. #16840086C2semidirect
6. #16840075C2semidirect
7. #16840059C2semidirect
8. #16840057C2semidirect
9. #16840010C2semidirect
10. #16839993C2semidirect
11. #16839860C2semidirect
12. #16839834C2semidirect
13. #16839805C2semidirect
14. C2×#14519710C2semidirect
15. C61×#552C2semidirect
140. #92418#41semidirect
171. #552D61semidirect
186. C61#3343semidirect