Finite Group Databasebeta

← #21455886

Subgroups — #21455886

Order 7808.

390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840316C211yesmaximal, characteristic, complemented
2C4×#11758224C211yesmaximal, characteristic
3#16840106C211yesmaximal, characteristic, complemented
4#16840102C211yesmaximal, characteristic, complemented
5#16840046C211yesmaximal, characteristic, complemented
6#16840040C211yesmaximal, characteristic, complemented
7#16839971C211yesmaximal, characteristic, complemented
8#16839965C211yesmaximal, characteristic, complemented
9#16839925C211yesmaximal, characteristic
10#16839921C211yesmaximal, characteristic
11C4×Dic244C211yesmaximal, characteristic, complemented
12C4×#11758202C211yesmaximal, characteristic, complemented
13C4×#11758200C211yesmaximal, characteristic, complemented
14#16839813C211yesmaximal, characteristic, complemented
15C4×SD16×C61C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519775C2211yescharacteristic
22#14519767—21no—
23#14519757C2211yescharacteristic
24#14519755—21no—
25#14519753C2211yescharacteristic
26C4×Dic122—21no—
27C4×Dic122C2211yescharacteristic
28C4×Dic122C2211yescharacteristic
29#14519742C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31C4×C22⋊D61—21no—
32#14519737—21no—
33#14519735C2211yescharacteristic
34#14519734—21no—
35#14519733—21no—
36C2×C4×Dic61—21no—
37C42×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65#11758224—22no—
66#11758224—22no—
67C2×C4×D61D411yescharacteristic
68C2×C4×D61D411yescharacteristic
69C2×C4×D61C2311yescharacteristic
70C2×Dic122—21no—
71C2×Dic122C2311yescharacteristic
72C2×Dic122C2311yescharacteristic
73SD16×C61—22no—
74C2×C8×C61C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C4⋊C4×C61—21no—
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C42×C61—21no—
81C42×C61C2311yescharacteristic
82C22⋊Dic61—21no—
83#11758202—22no—
84#11758200—22no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61C2311yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61D411yescharacteristic
103C4×Dic61D411yescharacteristic
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107Dic244—22no—
108C23×C61—21no—
109C22×D61C2×D411yescharacteristic
110Q8×C61—21no—
111Q8×C61—21no—
112D4×C61—21no—
113D4×C61#4112yes—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—42no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2411yescharacteristic
121C22⋊D61—24no—
122C2×Dic61—24no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—42no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C4×D61—22no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—22no—
135Dic122—21no—
136Dic122—21no—
137Dic122—21no—
138Dic122—42no—
139Dic122#4112yes—
140C8×C61—21no—
141C8×C61—21no—
142#92418—21no—
143#92418—21no—
144C22×C61—22no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61C22×D411yescharacteristic
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—21no—
151C4×C61—21no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61#13712yes—
156C4×C61C2×#4111yescharacteristic
157C4×C61C2×#4111yescharacteristic
158Dic61—22no—
159Dic61—21no—
160Dic61—21no—
161Dic61—41no—
162Dic61—41no—
163Dic61—41no—
164Dic61#13512yes—
165#3107—611nomaximal, Sylow
166C2×C61—42no—
167C2×C61#52511yescharacteristic
168C2×C61C2×#13511yescharacteristic
169C2×C61C2×#13711yescharacteristic
170D61—41no—
171#533—611no—
172C4×#41—611no—
173#485—611no—
174#485—611no—
175#475—611no—
176#474—611no—
177#462—611no—
178#461—611no—
179#452—611no—
180#452—611no—
181C4×Q16—611no—
182C4×Q16—611no—
183C4×SD16—611no—
184C4×SD16D6111yescharacteristic, complemented
185#431—611no—
186C61#310711yescharacteristic, complemented, Sylow
187C2×#41—611no—
188C2×Q16—611no—
189C2×Q16—611no—
190C2×SD16—611no—
191C2×SD16C2×D6111yescharacteristic
192C4⋊Q8—611no—
193C4⋊Q8—611no—
194#125—1221no—
195C22⋊Q8—611no—
196C22⋊Q8—611no—
197C22⋊Q8—1221no—
198C4×Q8—611no—
199C4×Q8—611no—
200C4×Q8—611no—
201C4×Q8—1221no—
202C4×Q8C2×D6111yescharacteristic
203C4×D4—611no—
204C4×D4—1221no—
205C4×D4—1221no—
206C4×D4C2×D6111yescharacteristic
207#117—611no—
208#117—1221no—
209#117—1221no—
210C2×C42—611no—
211C2×C42—1221no—
212#107—611no—
213#107—611no—
214#106—611no—
215#106C2×D6111yescharacteristic
216C4⋊C8—611no—
217C4⋊C8—611no—
218#103—611no—
219#103—611no—
220#103—611no—
221#103—611no—
222#103—611no—
223#103C2×D6111yescharacteristic
224#102—611no—
225#102C2×D6111yescharacteristic
226C22⋊C8—611no—
227C22⋊C8—611no—
228C4×C8—611no—
229C4×C8C2×D6111yescharacteristic
230#41—1222no—
231#41—1222no—
232C2×Q8—611no—
233C2×Q8—611no—
234C2×Q8—1221no—
235C2×Q8C22×D6111yescharacteristic
236C2×D4—1221no—
237C2×D4C22×D6111yescharacteristic
238C22×C4—21no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—1221no—
243C22×C4—1221no—
244Q16—1222no—
245Q16—1222no—
246SD16—22no—
247SD16—1222no—
248C2×C8—611no—
249C2×C8—611no—
250C2×C8C22×D6111yescharacteristic
251C2×C8C22×D6111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—611no—
254C4⋊C4—611no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4C22×D6111yescharacteristic
264C4⋊C4C22×D6111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C42—21no—
271C42—611no—
272C42—611no—
273C42—611no—
274C42—1221no—
275C42—1221no—
276C42—1221no—
277C42—1221no—
278C42C22×D6111yescharacteristic
279C23—21no—
280C23—611no—
281Q8—21no—
282Q8—21no—
283Q8—612no—
284Q8—1221no—
285Q8—1221no—
286Q8—1221no—
287Q8—2442no—
288D4—21no—
289D4—1224no—
290D4#1175822212yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—611no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—1222no—
299C2×C4—1224no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1222no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—2442no—
308C2×C4D4×D6111yescharacteristic
309C2×C4D4×D6111yescharacteristic
310C2×C4C23×D6111yescharacteristic
311C8—21no—
312C8—21no—
313C8—1221no—
314C8—1221no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—1221no—
319C22—1221no—
320C22—1221no—
321C22C2×D4×D6111yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—612no—
327C4—1221no—
328C4—1222no—
329C4—1221no—
330C4—2441no—
331C4—2441no—
332C4—2441no—
333C4#1451980612yes—
334C4#41×D6111yescharacteristic
335C4C2×#1175822211yescharacteristic
336C2—42no—
337C2—2441no—
338C2#1684027111yescharacteristic
339C2#135×D6111yescharacteristic
340C2C2×#1451980611yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×SD16×C61C2
socleC22×C61C22×D4
hypercenterC4×SD16D61
hypocenterC61#3107
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #16840316C2semidirect
3. #16840106C2semidirect
4. #16840102C2semidirect
5. #16840046C2semidirect
6. #16840040C2semidirect
7. #16839971C2semidirect
8. #16839965C2semidirect
11. C4×Dic244C2semidirect
12. C4×#11758202C2semidirect
13. C4×#11758200C2semidirect
14. #16839813C2semidirect
15. C4×SD16×C61C2semidirect
184. C4×SD16D61semidirect
186. C61#3107semidirect