Finite Group Databasebeta

← #21458288

Subgroups — #21458288

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#16840465C211yesmaximal, characteristic, complemented
2#16840415C211yesmaximal, characteristic, complemented
3#16840089C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic, complemented
5#16840082C211yesmaximal, characteristic, complemented
6#16840077C211yesmaximal, characteristic, complemented
7#16840059C211yesmaximal, characteristic, complemented
8#16840049C211yesmaximal, characteristic, complemented
9#16840016C211yesmaximal, characteristic, complemented
10#16839999C211yesmaximal, characteristic, complemented
11#16839875C211yesmaximal, characteristic, complemented
12#16839835C211yesmaximal, characteristic, complemented
13#16839803C211yesmaximal, characteristic, complemented
14#106×D61C211yesmaximal, characteristic, complemented
15C61×#501C211yesmaximal, characteristic, complemented
16C2×#11758226—21no—
17C2×D488C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519772—21no—
21#14519762—21no—
22#14519762—21no—
23#14519762—21no—
24#14519753—21no—
25#14519752—21no—
26#14519752C2211yescharacteristic
27#14519752C2211yescharacteristic
28#14519752C2211yescharacteristic
29#14519752C2211yescharacteristic
30C4×D244C2211yescharacteristic
31C4×D244C2211yescharacteristic
32C4×D244C2211yescharacteristic
33#14519739—21no—
34#14519735C2211yescharacteristic
35C4⋊C4×D61C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519708C2211yescharacteristic
43C4⋊#92418C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C4⋊Q8×C61C2211yescharacteristic
53#125×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic
57#106×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60#11758226—44no—
61C2×D244—21no—
62C2×D244—21no—
63C2×D244—21no—
64C2×D244—21no—
65C2×D244D411yescharacteristic
66C2×D244C2311yescharacteristic
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61C2311yescharacteristic
74C2×C4×D61C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C42×C61C2311yescharacteristic
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198D411yescharacteristic
93#11758198D411yescharacteristic
94C4⋊Dic61D411yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103D488—22no—
104#11758189—22no—
105C8×D61—22no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61C2×D411yescharacteristic
109C22×D61C2×D411yescharacteristic
110Q8×C61—42no—
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×C61C2411yescharacteristic
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61C2×D411yescharacteristic
121C2×Dic61C2×D411yescharacteristic
122D244—22no—
123D244—21no—
124D244—21no—
125D244—21no—
126D244—21no—
127D244—42no—
128D244—42no—
129D244—42no—
130D244—81no—
131C4×D61—21no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—42no—
136C4×D61—42no—
137C4×D61—42no—
138C4×D61—81no—
139C4×D61—81no—
140C8×C61—21no—
141C8×C61#4112yescomplemented
142#92418—21no—
143#92418—21no—
144C22×C61C22×D411yescharacteristic
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61AGL(1,ℤ/8)12yes—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61C2×#4111yescharacteristic
164C4×C612−1+411yescharacteristic
165Dic61—21no—
166Dic61—21no—
167Dic61—41no—
168Dic61—41no—
169#3345—611nomaximal, Sylow
170C2×C61#54711yescharacteristic
171C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C61#57711yescharacteristic
173D61—22no—
174D61—41no—
175D61—81no—
176D61—81no—
177#553—611no—
178#547—611no—
179#501D6111yescharacteristic, complemented
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#435—611no—
190#428—611no—
191C2×#106—611no—
192C61#334511yescharacteristic, complemented, Sylow
193C2×#41—1221no—
194C2×D8—611no—
195C2×M16—611no—
196C22×C8—611no—
197C4⋊Q8C2×D6111yescharacteristic
198#126—1221no—
199#125C2×D6111yescharacteristic
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—611no—
212C4×D4—1221no—
213#117—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217#107—611no—
218#107C2×D6111yescharacteristic
219#107C2×D6111yescharacteristic
220#106—611no—
221#106—611no—
222#106—611no—
223#106—611no—
224#106C2×D6111yescharacteristic
225#106C2×D6111yescharacteristic
226C4⋊C8—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233C22⋊C8—611no—
234C22⋊C8—611no—
235#97C2×D6111yescharacteristic
236#41—2444no—
237C2×Q8—21no—
238C2×D4—611no—
239C2×D4—611no—
240C2×D4—611no—
241C2×D4—1221no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4—1221no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252D8—1222no—
253M16—1222no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8—1222no—
257C2×C8C22×D6111yescharacteristic
258C2×C8C22×D6111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—611no—
263C4⋊C4—611no—
264C4⋊C4—611no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4C22×D6111yescharacteristic
269C4⋊C4C22×D6111yescharacteristic
270C4⋊C4C22×D6111yescharacteristic
271C4⋊C4C22×D6111yescharacteristic
272C22⋊C4—611no—
273C22⋊C4—611no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C42—1221no—
282C42C22×D6111yescharacteristic
283C23—611no—
284C23—611no—
285C23—1221no—
286C23—1221no—
287Q8—42no—
288D4—1222no—
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—611no—
302C2×C4—611no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—4881no—
310C2×C4—4881no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2442no—
314C2×C4D4×D6111yescharacteristic
315C2×C4D4×D6111yescharacteristic
316C2×C4C23×D6111yescharacteristic
317C8—21no—
318C8—1221no—
319C8—1221no—
320C8#1175822612yescomplemented
321C22—612no—
322C22—1221no—
323C22—1221no—
324C22—1221no—
325C22—1221no—
326C22—1221no—
327C22—2441no—
328C22—2441no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22C2×D4×D6111yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—1221no—
341C4—1221no—
342C4—2441no—
343C4—2441no—
344C4C2×#1175822611yescharacteristic
345C4#1451982511yescharacteristic
346C2—1222no—
347C2—4881no—
348C2—4881no—
349C2—2441no—
350C2#1684041511yescharacteristic
351C2AGL(1,ℤ/8)×D6111yescharacteristic
352C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#501C2
socleC22×C61C22×D4
hypercenter#501D61
hypocenterC61#3345
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #16840465C2semidirect
2. #16840415C2semidirect
3. #16840089C2semidirect
4. #16840082C2semidirect
5. #16840082C2semidirect
6. #16840077C2semidirect
7. #16840059C2semidirect
8. #16840049C2semidirect
9. #16840016C2semidirect
10. #16839999C2semidirect
11. #16839875C2semidirect
12. #16839835C2semidirect
13. #16839803C2semidirect
14. #106×D61C2semidirect
15. C61×#501C2semidirect
141. C8×C61#41semidirect
179. #501D61semidirect
192. C61#3345semidirect
320. C8#11758226semidirect