Finite Group Databasebeta

← #21454862

Subgroups — #21454862

Order 7808.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840269C211yesmaximal, characteristic
2#16839838C211yesmaximal, characteristic, complemented
3#16839837C211yesmaximal, characteristic, complemented
4#16839836C211yesmaximal, characteristic, complemented
5#16839833C211yesmaximal, characteristic, complemented
6#16839831C211yesmaximal, characteristic, complemented
7#16839830C211yesmaximal, characteristic, complemented
8C8×C22⋊D61C211yesmaximal, characteristic, complemented
9#16839825C211yesmaximal, characteristic, complemented
10#16839820C211yesmaximal, characteristic, complemented
11#16839820C211yesmaximal, characteristic, complemented
12#16839729C211yesmaximal, characteristic, complemented
13#16839724C211yesmaximal, characteristic, complemented
14C22⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#408C211yesmaximal, characteristic, complemented
16C22×C4×D61C2211yescharacteristic
17C2×#11758194C2211yescharacteristic, complemented
18C2×#11758189C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20C22×#92418C2211yescharacteristic, complemented
21C2×C8×D61C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic
23#14519758C411yescharacteristic
24#14519758C411yescharacteristic
25#14519753C411yescharacteristic
26#14519753C411yescharacteristic
27#14519748C411yescharacteristic
28#14519748C411yescharacteristic
29#14519745C411yescharacteristic
30#14519745C411yescharacteristic
31C4×C22⋊D61C2211yescharacteristic
32C4×C22⋊D61C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35#14519736C2211yescharacteristic
36#14519706C2211yescharacteristic, complemented
37#14519706C2211yescharacteristic, complemented
38#14519706C2211yescharacteristic, complemented
39#14519706C2211yescharacteristic, complemented
40C22⋊#92418C2211yescharacteristic
41C22⋊#92418C2211yescharacteristic
42C22⋊#92418C2211yescharacteristic, complemented
43C22⋊#92418C2211yescharacteristic, complemented
44#14519689C2211yescharacteristic
45#14519689C2211yescharacteristic
46#14519689C2211yescharacteristic
47#14519689C2211yescharacteristic
48#14519687C2211yescharacteristic, complemented
49#14519687C2211yescharacteristic, complemented
50C8×Dic61C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×#41×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic, complemented
54C22×C8×C61C2211yescharacteristic, complemented
55C22⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61C2×C411yescharacteristic
60#41×C61—41no—
61#41×C61—41no—
62C2×Q8×C61C2×C411yescharacteristic
63C2×D4×C61C2×C411yescharacteristic
64C2×D4×C61C2×C411yescharacteristic
65C2×D4×C61C2×C411yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61C2×C411yescharacteristic
70C2×C22⋊D61C2×C411yescharacteristic
71C2×C22⋊D61C2×C411yescharacteristic
72C2×C22⋊D61C2×C411yescharacteristic
73C22×Dic61C2×C411yescharacteristic
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61C2×C411yescharacteristic
77C2×C4×D61C2×C411yescharacteristic
78C2×C4×D61C2311yescharacteristic
79C2×C4×D61C2311yescharacteristic
80M16×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C22⋊Dic61C2×C411yescharacteristic
87C22⋊Dic61C2×C411yescharacteristic
88C22⋊Dic61C2×C411yescharacteristic
89C22⋊Dic61C2×C411yescharacteristic
90C22⋊Dic61C2×C411yescharacteristic
91C22⋊Dic61C2×C411yescharacteristic
92#11758198C2×C411yescharacteristic
93#11758198C2×C411yescharacteristic
94#11758198C2×C411yescharacteristic
95#11758198C2×C411yescharacteristic
96C4⋊Dic61C2×C411yescharacteristic
97C4⋊Dic61C2×C411yescharacteristic
98#11758196C2×C411yescharacteristic
99#11758196C2×C411yescharacteristic
100#11758196C2×C411yescharacteristic
101#11758196C2×C411yescharacteristic
102C4×Dic61C2311yescharacteristic
103C4×Dic61C2311yescharacteristic
104#11758194—41no—
105C2×#92418—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111#11758189—41no—
112C8×D61—41no—
113C8×D61—41no—
114C23×C61C22×C411yescharacteristic
115C23×C61C22×C411yescharacteristic
116C23×C61C22×C411yescharacteristic
117C22×D61—22no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61C22×C411yescharacteristic
121C22×D61C22×C411yescharacteristic
122Q8×C61—41no—
123D4×C61—41no—
124D4×C61—41no—
125D4×C61—41no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61C22×C411yescharacteristic
133C2×C4×C61C22×C411yescharacteristic
134C2×C4×C61C22×C411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—22no—
137C22⋊D61—22no—
138C22⋊D61—41no—
139C22⋊D61—41no—
140C2×Dic61—41no—
141C2×Dic61C22×C411yescharacteristic
142C2×Dic61C22×C411yescharacteristic
143C2×Dic61C22×C411yescharacteristic
144C2×Dic61C22×C411yescharacteristic
145C2×Dic61C22×C411yescharacteristic
146C2×Dic61C22×C411yescharacteristic
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—21no—
151C4×D61—41no—
152C4×D61—41no—
153C8×C61—21no—
154C8×C61—21no—
155C8×C61—21no—
156C8×C61—21no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61C23×C411yescharacteristic
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—44no—
177C2×D61#13112yes—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61H(5,𝔽2)11yescharacteristic
182C4×C61H(5,𝔽2)11yescharacteristic
183Dic61—21no—
184Dic61—21no—
185Dic61—21no—
186Dic61—21no—
187Dic61—21no—
188Dic61—21no—
189#2976—611nomaximal, Sylow
190C2×C61—41no—
191C2×C61—41no—
192C2×C61—41no—
193C2×C61#51811yescharacteristic
194C2×C61C2×#13111yescharacteristic
195C2×C61#56811yescharacteristic
196D61—22no—
197D61—41no—
198#525—611no—
199#436—611no—
200#436—611no—
201#435—611no—
202#435—611no—
203#435—611no—
204#435—611no—
205C8×D4—611no—
206C8×D4—611no—
207#433—611no—
208#433—611no—
209#408—611no—
210#408D6111yescharacteristic, complemented
211#407—611no—
212C2×C22⋊C8—611no—
213C61#297611yescharacteristic, complemented, Sylow
214C2×#41C2×D6111yescharacteristic
215C23×C4—611no—
216C2×M16—611no—
217C2×M16—611no—
218C2×M16—611no—
219C2×M16C2×D6111yescharacteristic, complemented
220C22×C8—611no—
221C22×C8—611no—
222C22×C8—611no—
223C22×C8C2×D6111yescharacteristic, complemented
224#123—611no—
225#123—611no—
226C22⋊Q8—611no—
227C22⋊Q8—611no—
228#121—611no—
229#121—611no—
230#120—611no—
231#120—611no—
232C4×D4—611no—
233C4×D4—611no—
234C4×D4—611no—
235C4×D4—611no—
236#117—611no—
237C4⋊C8—611no—
238C4⋊C8—611no—
239C4⋊C8—611no—
240C4⋊C8—611no—
241C22⋊C8—611no—
242C22⋊C8—611no—
243C22⋊C8—611no—
244C22⋊C8—611no—
245C22⋊C8—611no—
246C22⋊C8—611no—
247C22⋊C8—611no—
248C22⋊C8—611no—
249C22⋊C8C2×D6111yescharacteristic
250C22⋊C8C2×D6111yescharacteristic
251C22⋊C8C2×D6111yescharacteristic, complemented
252C22⋊C8C2×D6111yescharacteristic, complemented
253#97—611no—
254#97—611no—
255C4×C8—611no—
256C4×C8—611no—
257C24—611no—
258#41—41no—
259#41—41no—
260C2×Q8C4×D6111yescharacteristic
261C2×D4—611no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4C4×D6111yescharacteristic
266C2×D4C4×D6111yescharacteristic
267C2×D4C4×D6111yescharacteristic
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4C22×D6111yescharacteristic
276C22×C4C22×D6111yescharacteristic
277C22×C4C22×D6111yescharacteristic
278M16—41no—
279M16—2441no—
280M16—2441no—
281M16—2441no—
282C2×C8—41no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—611no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8C22×D6111yescharacteristic
291C2×C8C22×D6111yescharacteristic
292C2×C8C22×D6111yescharacteristic
293C2×C8C22×D6111yescharacteristic
294C4⋊C4—611no—
295C4⋊C4—611no—
296C4⋊C4—611no—
297C4⋊C4—611no—
298C4⋊C4—611no—
299C4⋊C4—611no—
300C22⋊C4—611no—
301C22⋊C4—611no—
302C22⋊C4—611no—
303C22⋊C4—611no—
304C22⋊C4—611no—
305C22⋊C4—611no—
306C22⋊C4—611no—
307C22⋊C4—611no—
308C22⋊C4—611no—
309C22⋊C4—611no—
310C42—611no—
311C42—611no—
312C23—611no—
313C23—611no—
314C23—1222no—
315C23—2441no—
316C23—2441no—
317C23C2×C4×D6111yescharacteristic
318C23C2×C4×D6111yescharacteristic
319C23C2×C4×D6111yescharacteristic
320Q8—41no—
321D4—41no—
322D4—41no—
323D4—41no—
324D4—1222no—
325D4—1222no—
326D4—2441no—
327D4—2441no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4C2×C4×D6111yescharacteristic
348C2×C4C2×C4×D6111yescharacteristic
349C2×C4C2×C4×D6111yescharacteristic
350C2×C4C23×D6111yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C8—1221no—
356C8—1221no—
357C8—1221no—
358C8—1221no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—612no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—2444no—
375C22C22×C4×D6111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—1221no—
380C4—1221no—
381C4—1221no—
382C4—1221no—
383C4—1221no—
384C4—1221no—
385C4#1451982211yescharacteristic
386C4#1451982211yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—1222no—
391C2—2441no—
392C2#1684023511yescharacteristic
393C2#131×D6111yescharacteristic
394C2#1684052711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D61
commutator, socleC22×C61C23×C4
FittingC61×#408C2
hypercenter#408D61
hypocenterC61#2976
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #16839838C2semidirect
3. #16839837C2semidirect
4. #16839836C2semidirect
5. #16839833C2semidirect
6. #16839831C2semidirect
7. #16839830C2semidirect
8. C8×C22⋊D61C2semidirect
9. #16839825C2semidirect
10. #16839820C2semidirect
11. #16839820C2semidirect
12. #16839729C2semidirect
13. #16839724C2semidirect
14. C22⋊C8×D61C2semidirect
15. C61×#408C2semidirect
17. C2×#11758194C22semidirect
20. C22×#92418C22semidirect
36. #14519706C22semidirect
37. #14519706C22semidirect
38. #14519706C22semidirect
39. #14519706C22semidirect
42. C22⋊#92418C22semidirect
43. C22⋊#92418C22semidirect
48. #14519687C22semidirect
49. #14519687C22semidirect
50. C8×Dic61C22semidirect
51. C8×Dic61C22semidirect
53. C2×M16×C61C22semidirect
54. C22×C8×C61C22semidirect
57. C22⋊C8×C61C22semidirect
58. C22⋊C8×C61C22semidirect
210. #408D61semidirect
213. C61#2976semidirect
219. C2×M16C2×D61semidirect
223. C22×C8C2×D61semidirect
251. C22⋊C8C2×D61semidirect
252. C22⋊C8C2×D61semidirect