Finite Group Databasebeta

← #21454872

Subgroups — #21454872

Order 7808.

422 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#16840271C211yesmaximal, characteristic
2#16839836C211yesmaximal, characteristic, complemented
3#16839834C211yesmaximal, characteristic, complemented
4#16839833C211yesmaximal, characteristic, complemented
5#16839832C211yesmaximal, characteristic, complemented
6C8×D244C211yesmaximal, characteristic, complemented
7C8×C22⋊D61C211yesmaximal, characteristic, complemented
8#16839825C211yesmaximal, characteristic, complemented
9#16839822C211yesmaximal, characteristic, complemented
10#16839821C211yesmaximal, characteristic, complemented
11#16839728C211yesmaximal, characteristic, complemented
12#16839727C211yesmaximal, characteristic, complemented
13C2×#14519689C211yesmaximal, characteristic, complemented
14C22⋊C8×D61C211yesmaximal, characteristic, complemented
15C8×D4×C61C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C2×#11758194C2211yescharacteristic, complemented
19C2×#11758189C2211yescharacteristic, complemented
20C22×#92418C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic
23C2×C8×D61C2211yescharacteristic, complemented
24#14519762C411yescharacteristic
25#14519759C411yescharacteristic
26#14519755C411yescharacteristic
27#14519754C411yescharacteristic
28#14519750C411yescharacteristic
29#14519749C411yescharacteristic
30#14519747C411yescharacteristic
31#14519745C411yescharacteristic
32C4×D244C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35#14519734C2211yescharacteristic
36C4⋊#92418C2211yescharacteristic, complemented
37#14519706C2211yescharacteristic, complemented
38#14519706C2211yescharacteristic, complemented
39C22⋊#92418C2211yescharacteristic
40C22⋊#92418C2211yescharacteristic, complemented
41#14519689C2211yescharacteristic
42#14519689C2211yescharacteristic
43#14519689C2211yescharacteristic
44#14519689C2211yescharacteristic
45#14519689C2211yescharacteristic
46#14519689C2211yescharacteristic
47#14519689C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic, complemented
49#14519688C2211yescharacteristic, complemented
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22×C8×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic, complemented
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic, complemented
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic, complemented
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61C2×C411yescharacteristic
60C2×D4×C61C2×C411yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61C2×C411yescharacteristic
64C2×C22⋊D61C2×C411yescharacteristic
65C2×C22⋊D61C2×C411yescharacteristic
66C2×C22⋊D61C2×C411yescharacteristic
67C22×Dic61C2×C411yescharacteristic
68#11758222—41no—
69#11758222—41no—
70C2×D244C2×C411yescharacteristic
71C2×D244C2×C411yescharacteristic
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×C4×D61C2×C411yescharacteristic
75C2×C4×D61C2×C411yescharacteristic
76C2×C4×D61C2311yescharacteristic
77C2×C4×D61C2311yescharacteristic
78C2×C4×D61C2311yescharacteristic
79C2×Dic122C2×C411yescharacteristic
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61C2×C411yescharacteristic
87C22⋊C4×C61C2×C411yescharacteristic
88C22⋊C4×C61C2×C411yescharacteristic
89C42×C61C2311yescharacteristic
90C22⋊Dic61C2×C411yescharacteristic
91C22⋊Dic61C2×C411yescharacteristic
92#11758198C2×C411yescharacteristic
93#11758198C2×C411yescharacteristic
94#11758198C2×C411yescharacteristic
95#11758198C2×C411yescharacteristic
96#11758198C2×C411yescharacteristic
97#11758198C2×C411yescharacteristic
98C4⋊Dic61C2×C411yescharacteristic
99#11758196C2×C411yescharacteristic
100#11758196C2×C411yescharacteristic
101#11758196C2×C411yescharacteristic
102#11758196C2×C411yescharacteristic
103C4×Dic61C2311yescharacteristic
104#11758194—41no—
105C2×#92418—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C8×D61—41no—
112C8×D61—41no—
113C8×D61—41no—
114C23×C61C22×C411yescharacteristic
115C23×C61C22×C411yescharacteristic
116C22×D61—22no—
117C22×D61—22no—
118C22×D61—41no—
119C22×D61C22×C411yescharacteristic
120C22×D61C22×C411yescharacteristic
121C22×D61C22×C411yescharacteristic
122D4×C61—22no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61C22×C411yescharacteristic
128C2×C4×C61C22×C411yescharacteristic
129C2×C4×C61C22×C411yescharacteristic
130C2×C4×C61C22×C411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—22no—
133C22⋊D61—22no—
134C22⋊D61—41no—
135C22⋊D61—41no—
136C2×Dic61—41no—
137C2×Dic61C22×C411yescharacteristic
138C2×Dic61C22×C411yescharacteristic
139C2×Dic61C22×C411yescharacteristic
140C2×Dic61C22×C411yescharacteristic
141C2×Dic61C22×C411yescharacteristic
142D244—22no—
143D244—41no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—41no—
151C4×D61—41no—
152Dic122—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#13112yes—
167C22×C61C23×C411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
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×C61—21no—
182C4×C61H(5,𝔽2)11yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—21no—
187Dic61—21no—
188Dic61—21no—
189#2977—611nomaximal, Sylow
190C2×C61—22no—
191C2×C61—41no—
192C2×C61#51811yescharacteristic
193C2×C61C2×#13111yescharacteristic
194C2×C61C2×#13111yescharacteristic
195D61—22no—
196D61—41no—
197D61—41no—
198#525—611no—
199#435—611no—
200#435—611no—
201#435—611no—
202#435—611no—
203C8×D4—611no—
204C8×D4—611no—
205C8×D4—611no—
206C8×D4D6111yescharacteristic, complemented
207#433—611no—
208#433—611no—
209#408—611no—
210#408—611no—
211C2×C22⋊C8—611no—
212C2×C22⋊C8—611no—
213C61#297711yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C23×C4—611no—
216C2×M16—611no—
217C2×M16—611no—
218C22×C8—611no—
219C22×C8—611no—
220C22×C8—611no—
221C22×C8—611no—
222C22×C8C2×D6111yescharacteristic
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×D4C2×D6111yescharacteristic
236#117—611no—
237C4⋊C8—611no—
238C4⋊C8—611no—
239C4⋊C8—611no—
240C4⋊C8C2×D6111yescharacteristic, complemented
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⋊C8—611no—
250C22⋊C8—611no—
251C22⋊C8C2×D6111yescharacteristic
252C22⋊C8C2×D6111yescharacteristic, complemented
253#97—611no—
254#97—611no—
255C4×C8—611no—
256C4×C8C2×D6111yescharacteristic, complemented
257C24—611no—
258#41—2441no—
259#41—2441no—
260C2×Q8—611no—
261C2×D4—611no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4C4×D6111yescharacteristic
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4C22×D6111yescharacteristic
277C22×C4C22×D6111yescharacteristic
278M16—2441no—
279M16—2441no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—2441no—
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⋊C4C4×D6111yescharacteristic
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⋊C4C4×D6111yescharacteristic
309C22⋊C4C4×D6111yescharacteristic
310C42—611no—
311C42C22×D6111yescharacteristic
312C23—611no—
313C23—611no—
314C23—611no—
315C23—1222no—
316C23—1222no—
317C23—2441no—
318C23C2×C4×D6111yescharacteristic
319C23C2×C4×D6111yescharacteristic
320Q8—2441no—
321D4—22no—
322D4—1222no—
323D4—1222no—
324D4—1222no—
325D4—2441no—
326D4—2441no—
327D4—2441no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4C2×C4×D6111yescharacteristic
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—612no—
365C22—1221no—
366C22—1221no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—1221no—
373C22—2444no—
374C22#1451978312yes—
375C22C22×C4×D6111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—1221no—
381C4—1221no—
382C4—1221no—
383C4—1221no—
384C4—1221no—
385C4#1451982211yescharacteristic
386C4#1451982311yescharacteristic
387C2—22no—
388C2—41no—
389C2—1222no—
390C2—2441no—
391C2—2441no—
392C2#1684023411yescharacteristic
393C2#131×D6111yescharacteristic
394C2C2×#1451978311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D61
commutator, socleC22×C61C23×C4
FittingC8×D4×C61C2
hypercenterC8×D4D61
hypocenterC61#2977
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #16839836C2semidirect
3. #16839834C2semidirect
4. #16839833C2semidirect
5. #16839832C2semidirect
6. C8×D244C2semidirect
7. C8×C22⋊D61C2semidirect
8. #16839825C2semidirect
9. #16839822C2semidirect
10. #16839821C2semidirect
11. #16839728C2semidirect
12. #16839727C2semidirect
13. C2×#14519689C2semidirect
14. C22⋊C8×D61C2semidirect
15. C8×D4×C61C2semidirect
18. C2×#11758194C22semidirect
19. C2×#11758189C22semidirect
23. C2×C8×D61C22semidirect
36. C4⋊#92418C22semidirect
37. #14519706C22semidirect
38. #14519706C22semidirect
40. C22⋊#92418C22semidirect
47. #14519689C22semidirect
48. #14519689C22semidirect
49. #14519688C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
53. C22×C8×C61C22semidirect
55. C4⋊C8×C61C22semidirect
57. C22⋊C8×C61C22semidirect
58. C4×C8×C61C22semidirect
206. C8×D4D61semidirect
213. C61#2977semidirect
223. C22×C8C2×D61semidirect
240. C4⋊C8C2×D61semidirect
252. C22⋊C8C2×D61semidirect
256. C4×C8C2×D61semidirect