Finite Group Databasebeta

← #21458282

Subgroups — #21458282

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#16840459C211yesmaximal, characteristic, complemented
2#16840413C211yesmaximal, characteristic, complemented
3#16840169C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840082C211yesmaximal, characteristic, complemented
6#16840074C211yesmaximal, characteristic, complemented
7#16840061C211yesmaximal, characteristic, complemented
8#16840050C211yesmaximal, characteristic, complemented
9#16840013C211yesmaximal, characteristic, complemented
10#16839997C211yesmaximal, characteristic, complemented
11#16839871C211yesmaximal, characteristic, complemented
12#16839836C211yesmaximal, characteristic, complemented
13#16839802C211yesmaximal, characteristic, complemented
14#106×D61C211yesmaximal, characteristic, complemented
15C61×#481C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758199C2211yescharacteristic
18C2×#11758194C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519770—21no—
22#14519768C2211yescharacteristic
23#14519762—21no—
24#14519760—21no—
25#14519758—21no—
26#14519755—21no—
27#14519752C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519748—21no—
30#14519748C2211yescharacteristic
31D4×Dic61C2211yescharacteristic
32#14519739C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34#14519737—21no—
35#14519736C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519708C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52#121×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic
54#106×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61D411yescharacteristic
66C22×Dic61—21no—
67#11758222—44no—
68C2×D244—21no—
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61D411yescharacteristic
86#11758199—22no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198D411yescharacteristic
91C4⋊Dic61—21no—
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196D411yescharacteristic
100C4×Dic61—21no—
101C4×Dic61C2311yescharacteristic
102#11758194—22no—
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C8×D61—22no—
106C23×C61—21no—
107C23×C61C2×D411yescharacteristic
108C22×D61—21no—
109C22×D61C2×D411yescharacteristic
110D4×C61—21no—
111D4×C61—21no—
112D4×C61—81no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—42no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2411yescharacteristic
121C22⋊D61—22no—
122C22⋊D61—42no—
123C22⋊D61—42no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—81no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131D244—21no—
132D244—21no—
133D244—42no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—42no—
137C4×D61—42no—
138C4×D61—81no—
139Dic122—42no—
140C8×C61—21no—
141C8×C61—21no—
142#92418—21no—
143#92418#4112yescomplemented
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61C22×D411yescharacteristic
151C2×D61—21no—
152C2×D61—21no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61AGL(1,ℤ/8)12yes—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61C2×#4111yescharacteristic
162C4×C612−1+411yescharacteristic
163Dic61—21no—
164Dic61—21no—
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169#3345—611nomaximal, Sylow
170C2×C61—41no—
171C2×C61—81no—
172C2×C61#54711yescharacteristic
173C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C61#57711yescharacteristic
175D61—22no—
176D61—81no—
177#553—611no—
178#547—611no—
179#501—611no—
180#482—611no—
181#481—611no—
182#481D6111yescharacteristic, complemented
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⋊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—1221no—
208#121C2×D6111yescharacteristic
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⋊C4C2×D6111yescharacteristic
217#107—611no—
218#107—611no—
219#107—611no—
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#102C2×D6111yescharacteristic
232#102C2×D6111yescharacteristic
233C22⋊C8—611no—
234C22⋊C8C2×D6111yescharacteristic
235#97—611no—
236#41—2444no—
237C2×Q8—1221no—
238C2×D4—21no—
239C2×D4—611no—
240C2×D4—611no—
241C2×D4—1221no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4C22×D6111yescharacteristic
245C22×C4—21no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4C22×D6111yescharacteristic
252D8—1222no—
253M16—1222no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8—1222no—
257C2×C8C22×D6111yescharacteristic
258C2×C8C22×D6111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—611no—
263C4⋊C4—611no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4C22×D6111yescharacteristic
270C4⋊C4C22×D6111yescharacteristic
271C4⋊C4C22×D6111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—611no—
274C22⋊C4—611no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C42—611no—
282C42—1221no—
283C23—21no—
284C23—611no—
285C23—1221no—
286C23D4×D6111yescharacteristic
287Q8—2442no—
288D4—21no—
289D4—21no—
290D4—81no—
291D4—1222no—
292D4—1221no—
293D4—1221no—
294D4—2442no—
295D4—2442no—
296D4—2442no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—2442no—
314C2×C4—2442no—
315C2×C4D4×D6111yescharacteristic
316C2×C4C23×D6111yescharacteristic
317C8—21no—
318C8—21no—
319C8—612no—
320C8—1221no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—612no—
328C22—1221no—
329C22—1221no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22C2×D4×D6111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—1221no—
339C4—1221no—
340C4—1221no—
341C4—2441no—
342C4—2441no—
343C4—2441no—
344C4#41×D6111yescharacteristic
345C4#1451982411yescharacteristic
346C2—41no—
347C2—81no—
348C2—1222no—
349C2—4881no—
350C2#1684041011yescharacteristic
351C2AGL(1,ℤ/8)×D6111yescharacteristic
352C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#481C2
socleC22×C61C22×D4
hypercenter#481D61
hypocenterC61#3345
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #16840459C2semidirect
2. #16840413C2semidirect
3. #16840169C2semidirect
4. #16840087C2semidirect
5. #16840082C2semidirect
6. #16840074C2semidirect
7. #16840061C2semidirect
8. #16840050C2semidirect
9. #16840013C2semidirect
10. #16839997C2semidirect
11. #16839871C2semidirect
12. #16839836C2semidirect
13. #16839802C2semidirect
14. #106×D61C2semidirect
15. C61×#481C2semidirect
143. #92418#41semidirect
182. #481D61semidirect
192. C61#3345semidirect