Finite Group Databasebeta

← #21457155

Subgroups — #21457155

Order 7808.

354 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#16840316C211yesmaximal, characteristic, complemented
2#16840297C211yesmaximal, characteristic
3#16840066C211yesmaximal, characteristic, complemented
4#16840046C211yesmaximal, characteristic, complemented
5#16840041C211yesmaximal, characteristic, complemented
6#16840004C211yesmaximal, characteristic, complemented
7#16840002C211yesmaximal, characteristic, complemented
8#16839994C211yesmaximal, characteristic
9#16839992C211yesmaximal, characteristic
10#16839985C211yesmaximal, characteristic, complemented
11#16839984C211yesmaximal, characteristic, complemented
12#16839971C211yesmaximal, characteristic, complemented
13#16839966C211yesmaximal, characteristic, complemented
14C4⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#479C211yesmaximal, characteristic, complemented
16C2×Dic244C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519775C2211yescharacteristic
24#14519772—21no—
25#14519767—21no—
26#14519765C2211yescharacteristic
27#14519762—21no—
28#14519757C2211yescharacteristic
29#14519757C2211yescharacteristic
30#14519755—21no—
31#14519753C2211yescharacteristic
32#14519752C2211yescharacteristic
33C4×Dic122—21no—
34C4×Dic122C2211yescharacteristic
35#14519742C2211yescharacteristic
36#14519739—21no—
37#14519739C2211yescharacteristic
38#14519735—21no—
39#14519734—21no—
40C42×D61C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519708C2211yescharacteristic
43C4⋊#92418C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519700C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519697C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D244—21no—
61C2×D244C2311yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61D411yescharacteristic
64C2×C4×D61D411yescharacteristic
65C2×C4×D61C2311yescharacteristic
66C2×Dic122—21no—
67C2×Dic122C2311yescharacteristic
68C2×Dic122C2311yescharacteristic
69C2×C8×C61C2311yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C42×C61—21no—
78C42×C61C2311yescharacteristic
79#11758202—41no—
80#11758201—41no—
81#11758198—21no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61C2311yescharacteristic
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61D411yescharacteristic
100C4×Dic61D411yescharacteristic
101C4×Dic61C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104Dic244—41no—
105#11758190—41no—
106C8×D61—41no—
107C8×D61—41no—
108C22×D61—21no—
109C22×D61C2×D411yescharacteristic
110Q8×C61—21no—
111Q8×C61—21no—
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—21no—
126D244—21no—
127D244—42no—
128C4×D61—22no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—22no—
132C4×D61—42no—
133Dic122—21no—
134Dic122—21no—
135Dic122—21no—
136Dic122—21no—
137Dic122—42no—
138C8×C61—21no—
139C8×C61—21no—
140#92418—21no—
141#92418—21no—
142C22×C61C22×D411yescharacteristic
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—41no—
148C2×D61#13712yes—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61H(5,𝔽2)11yescharacteristic
156C4×C612−1+411yescharacteristic
157Dic61—21no—
158Dic61—21no—
159Dic61—41no—
160Dic61—41no—
161Dic61—41no—
162Dic61#13512yes—
163#3248—611nomaximal, Sylow
164C2×C61#53711yescharacteristic
165C2×C61C2×#13511yescharacteristic
166C2×C61C2×#13711yescharacteristic
167D61—22no—
168D61—81no—
169#533—611no—
170#529—611no—
171#479—611no—
172#479D6111yescharacteristic, complemented
173#475—611no—
174#474—611no—
175#467—611no—
176#467—611no—
177#465—611no—
178#465—611no—
179#464—611no—
180#464—611no—
181#462—611no—
182#461—611no—
183C2×C4⋊C8—611no—
184C61#324811yescharacteristic, complemented, Sylow
185C2×Q16—611no—
186C2×Q16—611no—
187C2×SD16—611no—
188C2×SD16—611no—
189C22×C8—611no—
190C22×C8—611no—
191C4⋊Q8—611no—
192C4⋊Q8—611no—
193#126—1221no—
194#125—1221no—
195#125C2×D6111yescharacteristic
196#124—611no—
197#123—1221no—
198C22⋊Q8—611no—
199C22⋊Q8—611no—
200C22⋊Q8—611no—
201C22⋊Q8—1221no—
202#121—611no—
203C4×Q8—611no—
204C4×Q8—611no—
205C4×Q8—1221no—
206C4×Q8C2×D6111yescharacteristic
207C4×D4—611no—
208C4×D4—1221no—
209#117—1221no—
210#117—1221no—
211C2×C42—611no—
212#107—611no—
213#107C2×D6111yescharacteristic
214#106—611no—
215#106C2×D6111yescharacteristic
216C4⋊C8—611no—
217C4⋊C8—611no—
218C4⋊C8—611no—
219C4⋊C8C2×D6111yescharacteristic
220#103—611no—
221#103—611no—
222#103—611no—
223#103—611no—
224#103C2×D6111yescharacteristic
225#103C2×D6111yescharacteristic
226#102—611no—
227#102—611no—
228C2×Q8—611no—
229C2×Q8—611no—
230C2×Q8—1221no—
231C2×Q8C22×D6111yescharacteristic
232C2×D4—611no—
233C2×D4—1221no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—1221no—
238Q16—2441no—
239Q16—2441no—
240SD16—2441no—
241SD16—2441no—
242C2×C8—611no—
243C2×C8—611no—
244C2×C8—2441no—
245C2×C8—2441no—
246C2×C8C22×D6111yescharacteristic
247C2×C8C22×D6111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—611no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4C22×D6111yescharacteristic
261C4⋊C4C22×D6111yescharacteristic
262C4⋊C4C22×D6111yescharacteristic
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C42—21no—
271C42—611no—
272C42—611no—
273C42—611no—
274C42—1221no—
275C42—1221no—
276C42C22×D6111yescharacteristic
277C23—611no—
278C23—1221no—
279Q8—21no—
280Q8—21no—
281Q8—1221no—
282Q8—1221no—
283Q8—1221no—
284Q8—1221no—
285Q8—2442no—
286D4—1221no—
287D4—1221no—
288D4—2442no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—611no—
296C2×C4—1222no—
297C2×C4—1222no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—2442no—
304C2×C4D4×D6111yescharacteristic
305C2×C4D4×D6111yescharacteristic
306C2×C4C23×D6111yescharacteristic
307C8—21no—
308C8—21no—
309C8—1221no—
310C8—1221no—
311C22—612no—
312C22—1221no—
313C22—1221no—
314C22—2441no—
315C22—2441no—
316C22—2441no—
317C22C2×D4×D6111yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—612no—
325C4—1221no—
326C4—1221no—
327C4—2441no—
328C4—2441no—
329C4—2441no—
330C4#1451982311yescharacteristic
331C4#1451982511yescharacteristic
332C2—1222no—
333C2—4881no—
334C2#1684034211yescharacteristic
335C2#135×D6111yescharacteristic
336C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3248
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. #16840316C2semidirect
3. #16840066C2semidirect
4. #16840046C2semidirect
5. #16840041C2semidirect
6. #16840004C2semidirect
7. #16840002C2semidirect
10. #16839985C2semidirect
11. #16839984C2semidirect
12. #16839971C2semidirect
13. #16839966C2semidirect
14. C4⋊C8×D61C2semidirect
15. C61×#479C2semidirect
172. #479D61semidirect
184. C61#3248semidirect