Finite Group Databasebeta

← #21455830

Subgroups — #21455830

Order 7808.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840293C211yesmaximal, characteristic, complemented
2#41×Dic61C211yesmaximal, characteristic, complemented
3#16840104C211yesmaximal, characteristic, complemented
4#16840083C211yesmaximal, characteristic, complemented
5#16840071C211yesmaximal, characteristic, complemented
6#16840064C211yesmaximal, characteristic, complemented
7#16839982C211yesmaximal, characteristic, complemented
8#16839975C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839854C211yesmaximal, characteristic, complemented
11#16839853C211yesmaximal, characteristic, complemented
12SD16×Dic61C211yesmaximal, characteristic, complemented
13D8×Dic61C211yesmaximal, characteristic, complemented
14#16839812C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic
16C2×#11758202C2211yescharacteristic
17C2×#11758200C2211yescharacteristic
18#14519770—21no—
19#14519768C2211yescharacteristic
20#14519764C2211yescharacteristic
21#14519758—21no—
22#14519756C2211yescharacteristic
23Q8×Dic61C2211yescharacteristic
24Q8×Dic61C2211yescharacteristic
25#14519742C2211yescharacteristic
26D4×Dic61—21no—
27D4×Dic61—21no—
28D4×Dic61—21no—
29D4×Dic61C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31D4×Dic61C2211yescharacteristic
32#14519736—21no—
33#14519736C2211yescharacteristic
34#14519733—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—22no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61D411yescharacteristic
72C22×Dic61D411yescharacteristic
73C2×Dic122C2311yescharacteristic
74SD16×C61—22no—
75D8×C61—22no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C22⋊Dic61—21no—
81C22⋊Dic61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87#11758202—22no—
88#11758200—22no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
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
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61—21no—
110C23×C61C2×D411yescharacteristic
111Q8×C61—21no—
112Q8×C61#4112yes—
113D4×C61—24no—
114D4×C61—21no—
115D4×C61—21no—
116D4×C61—21no—
117D4×C61—42no—
118D4×C61#4112yes—
119C2×C4×C61—24no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139Dic122—21no—
140Dic122—21no—
141C8×C61—21no—
142C8×C61—21no—
143#92418—21no—
144#92418—21no—
145C22×C61—21no—
146C22×C61—22no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C4×C61—21no—
156C4×C61—22no—
157C4×C61—41no—
158C4×C61C2×#4111yescharacteristic
159C4×C61C2×#4111yescharacteristic
160Dic61—21no—
161Dic61—21no—
162Dic61—21no—
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166Dic61—41no—
167Dic61#13512yes—
168#3102—611nomaximal, Sylow
169C2×C61—41no—
170C2×C61—42no—
171C2×C61—81no—
172C2×C61#52511yescharacteristic
173C2×C61C2×#13511yescharacteristic
174C2×C61#57511yescharacteristic
175#529—611no—
176C4×#41—611no—
177#485—611no—
178#482—611no—
179#479—611no—
180#478—611no—
181#464—611no—
182#463—611no—
183#452—611no—
184#449D6111yescharacteristic
185C4×Q16—611no—
186C4×SD16—611no—
187C4×SD16—611no—
188C4×D8—611no—
189#431—611no—
190C61#310211yescharacteristic, complemented, Sylow
191C2×#41C2×D6111yescharacteristic
192C2×Q16—611no—
193C2×SD16—611no—
194C2×SD16C2×D6111yescharacteristic
195C2×D8C2×D6111yescharacteristic
196#126—1221no—
197#125—611no—
198#124—611no—
199#123—1221no—
200C22⋊Q8—611no—
201#121C2×D6111yescharacteristic
202C4×Q8—611no—
203C4×Q8—611no—
204C4×Q8—611no—
205C4×D4—611no—
206C4×D4—611no—
207C4×D4—611no—
208C4×D4—1221no—
209C4×D4—1221no—
210C4×D4—1221no—
211#117—611no—
212#117—1221no—
213#117—1221no—
214C2×C42—611no—
215C2×C42—1221no—
216#107—611no—
217#107—611no—
218#106—611no—
219#106—611no—
220C4⋊C8—611no—
221C4⋊C8—611no—
222#103—611no—
223#103—611no—
224#103—611no—
225#103C2×D6111yescharacteristic
226#102—611no—
227#102—611no—
228#102—611no—
229#102C2×D6111yescharacteristic
230C22⋊C8—611no—
231C22⋊C8C2×D6111yescharacteristic
232C4×C8—611no—
233C4×C8—611no—
234#41—22no—
235#41—22no—
236C2×Q8—611no—
237C2×Q8C22×D6111yescharacteristic
238C2×D4—21no—
239C2×D4—21no—
240C2×D4C22×D6111yescharacteristic
241C2×D4C22×D6111yescharacteristic
242C22×C4—21no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4C22×D6111yescharacteristic
249Q16—1222no—
250SD16—22no—
251SD16—1222no—
252D8—22no—
253C2×C8—611no—
254C2×C8—611no—
255C2×C8C22×D6111yescharacteristic
256C2×C8C22×D6111yescharacteristic
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4C22×D6111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C42—611no—
276C42—611no—
277C42—611no—
278C42—611no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C42—1221no—
283C23—21no—
284C23—21no—
285C23D4×D6111yescharacteristic
286Q8—21no—
287Q8—1221no—
288Q8—1221no—
289Q8#1175822412yes—
290D4—24no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—42no—
295D4#1175822412yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—1222no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4—2441no—
313C2×C4—2442no—
314C2×C4D4×D6111yescharacteristic
315C2×C4C23×D6111yescharacteristic
316C8—21no—
317C8—21no—
318C8—1221no—
319C8—1221no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D6111yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—612no—
334C4—1221no—
335C4—1221no—
336C4—1221no—
337C4—2441no—
338C4—2441no—
339C4—2441no—
340C4—2441no—
341C4C2×#1175822411yescharacteristic
342C4C2×#1175822411yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#1684026811yescharacteristic
347C2#135×D6111yescharacteristic
348C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3102
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16840293C2semidirect
2. #41×Dic61C2semidirect
3. #16840104C2semidirect
4. #16840083C2semidirect
5. #16840071C2semidirect
6. #16840064C2semidirect
7. #16839982C2semidirect
8. #16839975C2semidirect
9. #16839924C2semidirect
10. #16839854C2semidirect
11. #16839853C2semidirect
12. SD16×Dic61C2semidirect
13. D8×Dic61C2semidirect
14. #16839812C2semidirect
190. C61#3102semidirect