Finite Group Databasebeta

← #21458295

Subgroups — #21458295

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#16840464C211yesmaximal, characteristic, complemented
2#16840412C211yesmaximal, characteristic, complemented
3#16840170C211yesmaximal, characteristic, complemented
4#16840085C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840078C211yesmaximal, characteristic, complemented
7#16840073C211yesmaximal, characteristic, complemented
8#16840064C211yesmaximal, characteristic, complemented
9#16840050C211yesmaximal, characteristic, complemented
10#16840012C211yesmaximal, characteristic, complemented
11#16839874C211yesmaximal, characteristic, complemented
12#16839833C211yesmaximal, characteristic, complemented
13#16839803C211yesmaximal, characteristic, complemented
14C2×#14519709C211yesmaximal, characteristic, complemented
15C61×#466C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×#11758189C2211yescharacteristic
18#14519776C2211yescharacteristic
19#14519770—21no—
20#14519768C2211yescharacteristic
21#14519761—21no—
22#14519759—21no—
23#14519758—21no—
24#14519754—21no—
25#14519749—21no—
26#14519748C2211yescharacteristic
27#14519748C2211yescharacteristic
28D4×Dic61—21no—
29D4×Dic61C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31C4×C22⋊D61C2211yescharacteristic
32#14519735C2211yescharacteristic
33C2×C4⋊Dic61C2211yescharacteristic
34C2×C4⋊Dic61C2211yescharacteristic
35C4⋊C4×D61C2211yescharacteristic
36#14519710C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519709C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×D8×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54#121×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71#11758224—44no—
72C2×C4×D61—21no—
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75D8×C61—22no—
76C2×C8×C61—22no—
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61D411yescharacteristic
88#11758198—21no—
89#11758198D411yescharacteristic
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101C4×Dic61—21no—
102C4×Dic61C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105#11758189—22no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61C2×D411yescharacteristic
109C22×D61C2×D411yescharacteristic
110D4×C61—21no—
111D4×C61—21no—
112D4×C61—21no—
113D4×C61—21no—
114D4×C61—42no—
115D4×C61—42no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C22⋊D61—22no—
123C22⋊D61—42no—
124C22⋊D61—81no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61—81no—
132C2×Dic61—81no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—42no—
139Dic122—42no—
140C8×C61—21no—
141C8×C61#4112yescomplemented
142#92418—21no—
143#92418—21no—
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61AGL(1,ℤ/8)12yes—
153C22×C61C22×D411yescharacteristic
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61C2×#4111yescharacteristic
161C4×C612−1+411yescharacteristic
162Dic61—21no—
163Dic61—21no—
164Dic61—21no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169#3345—611nomaximal, Sylow
170C2×C61—22no—
171C2×C61—81no—
172C2×C61—81no—
173C2×C61#54711yescharacteristic
174C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C61#57711yescharacteristic
176D61—41no—
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#466D6111yescharacteristic, complemented
188#442—611no—
189#435—611no—
190#428—611no—
191C2×#106—611no—
192C61#334511yescharacteristic, complemented, Sylow
193C2×#41—1221no—
194C2×D8C2×D6111yescharacteristic
195C2×M16—611no—
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—1221no—
207#121C2×D6111yescharacteristic
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⋊C4—611no—
217#107—611no—
218#107—611no—
219#107C2×D6111yescharacteristic
220#106—611no—
221#106—611no—
222#106—611no—
223#106—611no—
224#106—611no—
225#106—611no—
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⋊C8—611no—
235#97—611no—
236#41—2444no—
237C2×Q8—1221no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—611no—
241C2×D4—1221no—
242C2×D4—1221no—
243C2×D4C22×D6111yescharacteristic
244C2×D4C22×D6111yescharacteristic
245C22×C4—611no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4C22×D6111yescharacteristic
252D8—22no—
253M16—1222no—
254C2×C8—22no—
255C2×C8—611no—
256C2×C8—611no—
257C2×C8C22×D6111yescharacteristic
258C2×C8C22×D6111yescharacteristic
259C4⋊C4—611no—
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⋊C4—1221no—
270C4⋊C4C22×D6111yescharacteristic
271C4⋊C4C22×D6111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—611no—
275C22⋊C4—611no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C42—611no—
282C42—1221no—
283C23—21no—
284C23—21no—
285C23—611no—
286C23D4×D6111yescharacteristic
287Q8—2442no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—42no—
294D4—1222no—
295D4—4881no—
296D4—2442no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—4881no—
311C2×C4—4881no—
312C2×C4—2442no—
313C2×C4—2442no—
314C2×C4—2442no—
315C2×C4D4×D6111yescharacteristic
316C2×C4C23×D6111yescharacteristic
317C8—21no—
318C8—1221no—
319C8—1221no—
320C8#1175822412yescomplemented
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1221no—
330C22—1221no—
331C22—1221no—
332C22#1451980112yes—
333C22C2×D4×D6111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—1221no—
338C4—1221no—
339C4—1221no—
340C4—2441no—
341C4—2441no—
342C4—2441no—
343C4—2441no—
344C4C2×#1175822411yescharacteristic
345C4#1451982411yescharacteristic
346C2—22no—
347C2—81no—
348C2—81no—
349C2—2441no—
350C2#1684041211yescharacteristic
351C2C2×#1451980111yescharacteristic
352C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#466C2
socleC22×C61C22×D4
hypercenter#466D61
hypocenterC61#3345
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #16840464C2semidirect
2. #16840412C2semidirect
3. #16840170C2semidirect
4. #16840085C2semidirect
5. #16840079C2semidirect
6. #16840078C2semidirect
7. #16840073C2semidirect
8. #16840064C2semidirect
9. #16840050C2semidirect
10. #16840012C2semidirect
11. #16839874C2semidirect
12. #16839833C2semidirect
13. #16839803C2semidirect
14. C2×#14519709C2semidirect
15. C61×#466C2semidirect
141. C8×C61#41semidirect
187. #466D61semidirect
192. C61#3345semidirect
320. C8#11758224semidirect