Finite Group Databasebeta

← #21456486

Subgroups — #21456486

Order 7808.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840381C211yesmaximal, characteristic
2#16840375C211yesmaximal, characteristic, complemented
3#16840172C211yesmaximal, characteristic, complemented
4#16840157C211yesmaximal, characteristic, complemented
5#16840113C211yesmaximal, characteristic, complemented
6#16840019C211yesmaximal, characteristic, complemented
7#16840007C211yesmaximal, characteristic
8#16840002C211yesmaximal, characteristic, complemented
9#16839990C211yesmaximal, characteristic
10#16839866C211yesmaximal, characteristic, complemented
11#16839859C211yesmaximal, characteristic, complemented
12#16839854C211yesmaximal, characteristic, complemented
13#16839853C211yesmaximal, characteristic, complemented
14#16839716C211yesmaximal, characteristic, complemented
15C61×#488C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519777C2211yescharacteristic
23#14519777C2211yescharacteristic
24#14519772—21no—
25#14519772—21no—
26#14519770—21no—
27#14519768—21no—
28#14519768—21no—
29#14519763—21no—
30#14519761—21no—
31#14519757C2211yescharacteristic
32#14519757C2211yescharacteristic
33#14519754—21no—
34#14519753C2211yescharacteristic
35#14519748C2211yescharacteristic
36Q8×Dic61C2211yescharacteristic
37#14519742C2211yescharacteristic
38#14519742C2211yescharacteristic
39D4×Dic61C2211yescharacteristic
40#14519734C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519710C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519708C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519688C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#125×C61C2211yescharacteristic
53#124×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C22×Dic61—21no—
63C2×C4×D61C2311yescharacteristic
64C2×Dic122—21no—
65C2×Dic122C2311yescharacteristic
66C2×Dic122C2311yescharacteristic
67C2×C8×C61C2311yescharacteristic
68C2×C8×C61C2311yescharacteristic
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61C2311yescharacteristic
72C4⋊C4×C61C2311yescharacteristic
73C22⋊C4×C61—21no—
74C22⋊C4×C61—21no—
75C42×C61C2311yescharacteristic
76C22⋊Dic61—21no—
77C22⋊Dic61—21no—
78#11758202—22no—
79#11758202—22no—
80#11758200—22no—
81#11758200—22no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198D411yescharacteristic
86#11758198D411yescharacteristic
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196D411yescharacteristic
99#11758196D411yescharacteristic
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758189—22no—
107C8×D61—22no—
108C23×C61—21no—
109C22×D61C2×D411yescharacteristic
110Q8×C61—21no—
111Q8×C61—21no—
112D4×C61—21no—
113D4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C22⋊D61—81no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—81no—
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C4×D61—21no—
130C4×D61—21no—
131Dic122—21no—
132Dic122—21no—
133Dic122—21no—
134Dic122—21no—
135Dic122—81no—
136C8×C61—21no—
137C8×C61—21no—
138#92418#4112yes—
139#92418#4112yes—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61C22×D411yescharacteristic
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61C2×#4111yescharacteristic
153C4×C61C2×#4111yescharacteristic
154Dic61—21no—
155Dic61—21no—
156Dic61—21no—
157Dic61—41no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161#3178—611nomaximal, Sylow
162C2×C61—81no—
163C2×C61#53211yescharacteristic
164C2×C61#57711yescharacteristic
165C2×C61#57811yescharacteristic
166D61—41no—
167#542—611no—
168#541—611no—
169#501—611no—
170#497—611no—
171#488D6111yescharacteristic, complemented
172#487—611no—
173#470—611no—
174#468—611no—
175#467—611no—
176#465—611no—
177#441—611no—
178#440—611no—
179C4×Q16—611no—
180C4×SD16—611no—
181#405—611no—
182C61#317811yescharacteristic, complemented, Sylow
183C2×Q16—611no—
184C2×Q16—611no—
185C2×SD16—611no—
186C2×SD16—611no—
187C2×M16—611no—
188C22×C8—611no—
189C4⋊Q8—611no—
190C4⋊Q8—611no—
191#126—1221no—
192#126—1221no—
193#126—1221no—
194#125—1221no—
195#125—1221no—
196#125C2×D6111yescharacteristic
197#124—1221no—
198#124C2×D6111yescharacteristic
199#123—1221no—
200C22⋊Q8—611no—
201C22⋊Q8—611no—
202C22⋊Q8—611no—
203C22⋊Q8—1221no—
204#121—611no—
205C4×Q8—611no—
206C4×Q8—611no—
207C4×Q8—611no—
208C4×D4—611no—
209#117—611no—
210#107—611no—
211#107—611no—
212#106—611no—
213#106—611no—
214#103—611no—
215#103—611no—
216#103—611no—
217#103—611no—
218#103C2×D6111yescharacteristic
219#103C2×D6111yescharacteristic
220#102C2×D6111yescharacteristic
221#102C2×D6111yescharacteristic
222#97—611no—
223#97—611no—
224C4×C8—611no—
225C4×C8C2×D6111yescharacteristic
226C2×Q8—611no—
227C2×Q8—611no—
228C2×Q8—1221no—
229C2×Q8C22×D6111yescharacteristic
230C2×D4—1221no—
231C2×D4C22×D6111yescharacteristic
232C22×C4—611no—
233C22×C4—1221no—
234Q16—1222no—
235Q16—1222no—
236SD16—1222no—
237SD16—1222no—
238M16—1222no—
239C2×C8—611no—
240C2×C8—611no—
241C2×C8—1222no—
242C2×C8C22×D6111yescharacteristic
243C2×C8C22×D6111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—611no—
247C4⋊C4—611no—
248C4⋊C4—611no—
249C4⋊C4—611no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4C22×D6111yescharacteristic
260C4⋊C4C22×D6111yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—611no—
264C22⋊C4—611no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C42—611no—
271C42—1221no—
272C42—1221no—
273C42—1221no—
274C42C22×D6111yescharacteristic
275C23—21no—
276C23—611no—
277Q8—21no—
278Q8—21no—
279Q8—1221no—
280Q8—1221no—
281Q8—1221no—
282Q8—1221no—
283Q8—4881no—
284D4—21no—
285D4—21no—
286D4—4881no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—611no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—4881no—
300C2×C4D4×D6111yescharacteristic
301C2×C4D4×D6111yescharacteristic
302C2×C4C23×D6111yescharacteristic
303C8—21no—
304C8—21no—
305C8—612no—
306C8—612no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—1221no—
311C22—1221no—
312C22—1221no—
313C22C2×D4×D6111yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—1221no—
320C4—1221no—
321C4—1221no—
322C4—2441no—
323C4—2441no—
324C4—2441no—
325C4—2441no—
326C4#41×D6111yescharacteristic
327C4#41×D6111yescharacteristic
328C2—81no—
329C2—2441no—
330C2#1684031111yescharacteristic
331C2#1684056911yescharacteristic
332C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#488C2
socleC22×C61C22×D4
hypercenter#488D61
hypocenterC61#3178
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #16840375C2semidirect
3. #16840172C2semidirect
4. #16840157C2semidirect
5. #16840113C2semidirect
6. #16840019C2semidirect
8. #16840002C2semidirect
10. #16839866C2semidirect
11. #16839859C2semidirect
12. #16839854C2semidirect
13. #16839853C2semidirect
14. #16839716C2semidirect
15. C61×#488C2semidirect
171. #488D61semidirect
182. C61#3178semidirect