Finite Group Databasebeta

← #21456040

Subgroups — #21456040

Order 7808.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840375C211yesmaximal, characteristic, complemented
2#16840244C211yesmaximal, characteristic
3#16840099C211yesmaximal, characteristic, complemented
4#16840094C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16839972C211yesmaximal, characteristic, complemented
7#16839968C211yesmaximal, characteristic, complemented
8#16839927C211yesmaximal, characteristic
9#16839927C211yesmaximal, characteristic
10#16839866C211yesmaximal, characteristic, complemented
11#16839861C211yesmaximal, characteristic, complemented
12#16839854C211yesmaximal, characteristic, complemented
13#16839849C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#479C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21#14519777C2211yescharacteristic
22#14519772—21no—
23#14519772—21no—
24#14519768—21no—
25#14519768—21no—
26#14519757C2211yescharacteristic
27#14519757C2211yescharacteristic
28Q8×Dic61C2211yescharacteristic
29#14519742C2211yescharacteristic
30#14519742C2211yescharacteristic
31C4×D244—21no—
32C4×D244C2211yescharacteristic
33#14519739—21no—
34#14519739C2211yescharacteristic
35#14519734—21no—
36#14519734C2211yescharacteristic
37C4⋊C4×D61—21no—
38C4⋊C4×D61C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519708C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60#11758226—22no—
61#11758226—22no—
62C2×D244—21no—
63C2×D244C2311yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61C2311yescharacteristic
69C2×Dic122C2311yescharacteristic
70C2×Dic122C2311yescharacteristic
71C2×C8×C61C2311yescharacteristic
72C2×C8×C61C2311yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C42×C61—21no—
80C42×C61C2311yescharacteristic
81#11758202—22no—
82#11758202—22no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198D411yescharacteristic
88#11758198D411yescharacteristic
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
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#11758190—22no—
107#11758190—22no—
108C22×D61—21no—
109C22×D61C2×D411yescharacteristic
110Q8×C61—21no—
111Q8×C61#4112yes—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2411yescharacteristic
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61C2×D411yescharacteristic
123C2×Dic61C2×D411yescharacteristic
124C2×Dic61C2×D411yescharacteristic
125D244—24no—
126D244—21no—
127D244#4112yes—
128C4×D61—24no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—81no—
132C4×D61—81no—
133C4×D61—81no—
134Dic122—21no—
135Dic122—21no—
136Dic122—21no—
137Dic122—21no—
138C8×C61—21no—
139C8×C61—21no—
140#92418—21no—
141#92418—21no—
142C22×C61C22×D411yescharacteristic
143C2×D61—21no—
144C2×D61—22no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—41no—
148C2×D61—41no—
149C4×C61—22no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61C2×#4111yescharacteristic
156C4×C61C2×#4111yescharacteristic
157Dic61—21no—
158Dic61—21no—
159Dic61—21no—
160Dic61—41no—
161Dic61—41no—
162Dic61—41no—
163#3120—611nomaximal, Sylow
164C2×C61#52511yescharacteristic
165C2×C61#57711yescharacteristic
166C2×C61#57811yescharacteristic
167D61—41no—
168D61—42no—
169#541—611no—
170#520—611no—
171#484—611no—
172#483—611no—
173#479D6111yescharacteristic, complemented
174#478—611no—
175#462—611no—
176#461—611no—
177#452—611no—
178#452—611no—
179#441—611no—
180#440—611no—
181C4×Q16—611no—
182C4×SD16—611no—
183#433—611no—
184C61#312011yescharacteristic, complemented, Sylow
185C2×#41—611no—
186C2×Q16—611no—
187C2×Q16—611no—
188C2×SD16—611no—
189C2×SD16—611no—
190C4⋊Q8—611no—
191#126—1221no—
192#126—1221no—
193#125—1221no—
194#125—1221no—
195#125C2×D6111yescharacteristic
196C22⋊Q8—611no—
197C22⋊Q8—611no—
198C4×Q8—611no—
199C4×Q8—611no—
200C4×Q8—611no—
201C4×Q8C2×D6111yescharacteristic
202C4×D4—611no—
203C4×D4—611no—
204C4×D4—1221no—
205C4×D4—1221no—
206#117—611no—
207#117—1221no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—1221no—
210#107—611no—
211#107C2×D6111yescharacteristic
212#106—611no—
213#106C2×D6111yescharacteristic
214C4⋊C8—611no—
215C4⋊C8C2×D6111yescharacteristic
216#103—611no—
217#103—611no—
218#103—611no—
219#103—611no—
220#103C2×D6111yescharacteristic
221#103C2×D6111yescharacteristic
222#102—611no—
223#102—611no—
224C22⋊C8—611no—
225C22⋊C8—611no—
226#97—611no—
227C4×C8—611no—
228#41—1222no—
229#41—1222no—
230C2×Q8—611no—
231C2×Q8—611no—
232C2×Q8C22×D6111yescharacteristic
233C2×D4—611no—
234C2×D4—1221no—
235C22×C4—611no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240Q16—1222no—
241Q16—1222no—
242SD16—1222no—
243SD16—1222no—
244C2×C8—611no—
245C2×C8—611no—
246C2×C8C22×D6111yescharacteristic
247C2×C8C22×D6111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—611no—
252C4⋊C4—611no—
253C4⋊C4—611no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4C22×D6111yescharacteristic
263C4⋊C4C22×D6111yescharacteristic
264C4⋊C4C22×D6111yescharacteristic
265C22⋊C4—611no—
266C22⋊C4—611no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C42—21no—
272C42—611no—
273C42—1221no—
274C42—1221no—
275C42—1221no—
276C42C22×D6111yescharacteristic
277C23—611no—
278C23—1221no—
279Q8—21no—
280Q8—1221no—
281Q8—1221no—
282Q8—1221no—
283Q8—1221no—
284Q8#1175822612yes—
285D4—612no—
286D4—1224no—
287D4—1221no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—1224no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—4881no—
302C2×C4—4881no—
303C2×C4—4881no—
304C2×C4D4×D6111yescharacteristic
305C2×C4D4×D6111yescharacteristic
306C2×C4C23×D6111yescharacteristic
307C8—21no—
308C8—21no—
309C8—1221no—
310C8—1221no—
311C22—1222no—
312C22—1221no—
313C22—1221no—
314C22—1221no—
315C22—2441no—
316C22—2441no—
317C22C2×D4×D6111yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—1221no—
325C4—1221no—
326C4—1221no—
327C4—2441no—
328C4—2441no—
329C4—2441no—
330C4#41×D6111yescharacteristic
331C4C2×#1175822611yescharacteristic
332C2—2441no—
333C2—2442no—
334C2#1684027511yescharacteristic
335C2#1684056911yescharacteristic
336C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3120
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #16840375C2semidirect
3. #16840099C2semidirect
4. #16840094C2semidirect
5. #16840059C2semidirect
6. #16839972C2semidirect
7. #16839968C2semidirect
10. #16839866C2semidirect
11. #16839861C2semidirect
12. #16839854C2semidirect
13. #16839849C2semidirect
14. #16839822C2semidirect
15. C61×#479C2semidirect
173. #479D61semidirect
184. C61#3120semidirect