Finite Group Databasebeta

← #21458291

Subgroups — #21458291

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840458C211yesmaximal, characteristic, complemented
2#16840416C211yesmaximal, characteristic, complemented
3#16840171C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840081C211yesmaximal, characteristic, complemented
6#16840081C211yesmaximal, characteristic, complemented
7#16840076C211yesmaximal, characteristic, complemented
8#16840063C211yesmaximal, characteristic, complemented
9#16840053C211yesmaximal, characteristic, complemented
10#16840015C211yesmaximal, characteristic, complemented
11#16839998C211yesmaximal, characteristic, complemented
12#16839875C211yesmaximal, characteristic, complemented
13#16839804C211yesmaximal, characteristic, complemented
14C2×#14519709C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×D488C2211yescharacteristic
18#14519777C2211yescharacteristic
19#14519772—21no—
20#14519769C2211yescharacteristic
21#14519761—21no—
22#14519761—21no—
23#14519759—21no—
24#14519757—21no—
25#14519751C2211yescharacteristic
26#14519751C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519749—21no—
30C4×D244C2211yescharacteristic
31C4×D244C2211yescharacteristic
32#14519737—21no—
33#14519736C2211yescharacteristic
34C2×C4⋊Dic61C2211yescharacteristic
35C2×C4⋊Dic61C2211yescharacteristic
36C2×C4⋊Dic61C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519709C2211yescharacteristic
44#14519709C2211yescharacteristic
45#14519709C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52C2×M16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×D4×C61D411yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69#11758224—44no—
70C2×D244C2311yescharacteristic
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×Dic122—21no—
75M16×C61—22no—
76C2×C8×C61—22no—
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61D411yescharacteristic
82C22⋊C4×C61D411yescharacteristic
83C22⋊C4×C61D411yescharacteristic
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105D488—22no—
106C23×C61C2×D411yescharacteristic
107C23×C61C2×D411yescharacteristic
108C22×D61—21no—
109C22×D61—21no—
110D4×C61—22no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C22⋊D61—42no—
121C22⋊D61—42no—
122C22⋊D61—42no—
123C22⋊D61—81no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—81no—
133D244—21no—
134D244—21no—
135D244—21no—
136D244—21no—
137C4×D61—42no—
138C4×D61—81no—
139Dic122—42no—
140C8×C61—21no—
141C8×C61—21no—
142C8×C61—21no—
143C8×C61#4112yescomplemented
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61AGL(1,ℤ/8)12yes—
150C22×C61C22×D411yescharacteristic
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61C2×#4111yescharacteristic
162C4×C612−1+411yescharacteristic
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169#3345—611nomaximal, Sylow
170C2×C61—22no—
171C2×C61—41no—
172C2×C61#54711yescharacteristic
173C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C61#57711yescharacteristic
175D61—81no—
176D61—81no—
177#553—611no—
178#547—611no—
179#501—611no—
180#482—611no—
181#481—611no—
182#481—611no—
183#480—611no—
184#478—611no—
185#476—611no—
186#469—611no—
187#466—611no—
188#442—611no—
189#435D6111yescharacteristic, complemented
190#428—611no—
191C2×#106—611no—
192C61#334511yescharacteristic, complemented, Sylow
193C2×#41—1221no—
194C2×D8—611no—
195C2×M16C2×D6111yescharacteristic
196C22×C8C2×D6111yescharacteristic
197C4⋊Q8—611no—
198#126—1221no—
199#125—611no—
200#123—1221no—
201#123—1221no—
202#123—1221no—
203C22⋊Q8—1221no—
204#121—611no—
205#121—611no—
206#121—611no—
207#121—611no—
208#121—1221no—
209C4×D4—611no—
210C4×D4—611no—
211C4×D4—1221no—
212C4×D4C2×D6111yescharacteristic
213#117—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217#107—611no—
218#107—611no—
219#107—611no—
220#106—611no—
221#106—611no—
222#106—611no—
223#106—611no—
224#106—611no—
225#106—611no—
226C4⋊C8C2×D6111yescharacteristic
227#102—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233C22⋊C8C2×D6111yescharacteristic
234C22⋊C8C2×D6111yescharacteristic
235#97C2×D6111yescharacteristic
236#41—2444no—
237C2×Q8—1221no—
238C2×D4—611no—
239C2×D4—611no—
240C2×D4—1221no—
241C2×D4—1221no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4D24411yescharacteristic
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4C22×D6111yescharacteristic
251C22×C4C22×D6111yescharacteristic
252D8—1222no—
253M16—22no—
254C2×C8—22no—
255C2×C8C22×D6111yescharacteristic
256C2×C8C22×D6111yescharacteristic
257C2×C8C22×D6111yescharacteristic
258C2×C8C22×D6111yescharacteristic
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—611no—
263C4⋊C4—611no—
264C4⋊C4—611no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4D24411yescharacteristic
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4D24411yescharacteristic
280C22⋊C4D24411yescharacteristic
281C42—1221no—
282C42C22×D6111yescharacteristic
283C23—1221no—
284C23—1221no—
285C23C2×D24411yescharacteristic
286C23C2×D24411yescharacteristic
287Q8—2442no—
288D4—22no—
289D4—1221no—
290D4—1221no—
291D4—1221no—
292D4—1221no—
293D4—4881no—
294D4—2442no—
295D4—2442no—
296D4—2442no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—4881no—
308C2×C4—4881no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4C2×D24411yescharacteristic
313C2×C4C2×D24411yescharacteristic
314C2×C4C2×D24411yescharacteristic
315C2×C4C2×D24411yescharacteristic
316C2×C4C23×D6111yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8#1175822412yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—2441no—
327C22—2441no—
328C22—2441no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22#1451980512yes—
333C22C22×D24411yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—2441no—
339C4—2441no—
340C4—2441no—
341C4—2441no—
342C4—2441no—
343C4—2441no—
344C4C2×#1175822411yescharacteristic
345C4#1451982411yescharacteristic
346C2—22no—
347C2—41no—
348C2—4881no—
349C2—4881no—
350C2#1684041611yescharacteristic
351C2C2×#1451980511yescharacteristic
352C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3345
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16840458C2semidirect
2. #16840416C2semidirect
3. #16840171C2semidirect
4. #16840087C2semidirect
5. #16840081C2semidirect
6. #16840081C2semidirect
7. #16840076C2semidirect
8. #16840063C2semidirect
9. #16840053C2semidirect
10. #16840015C2semidirect
11. #16839998C2semidirect
12. #16839875C2semidirect
13. #16839804C2semidirect
14. C2×#14519709C2semidirect
15. C61×#435C2semidirect
143. C8×C61#41semidirect
189. #435D61semidirect
192. C61#3345semidirect
320. C8#11758224semidirect