Finite Group Databasebeta

← #21456804

Subgroups — #21456804

Order 7808.

444 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840309C211yesmaximal, characteristic, complemented
2#124×D61C211yesmaximal, characteristic, complemented
3#16840150C211yesmaximal, characteristic, complemented
4#16840148C211yesmaximal, characteristic, complemented
5#16840123C211yesmaximal, characteristic, complemented
6#16840120C211yesmaximal, characteristic, complemented
7#16839978C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839974C211yesmaximal, characteristic, complemented
10#16839902C211yesmaximal, characteristic, complemented
11#16839899C211yesmaximal, characteristic, complemented
12#16839897C211yesmaximal, characteristic, complemented
13#16839894C211yesmaximal, characteristic, complemented
14#16839818C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×Q8×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19C2×#11758190C2211yescharacteristic, complemented
20C2×#11758200C2211yescharacteristic, complemented
21C2×#11758201C2211yescharacteristic, complemented
22C2×D488C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×#11758199C2211yescharacteristic
25#14519776C2211yescharacteristic, complemented
26#14519773C2211yescharacteristic, complemented
27#14519766C2211yescharacteristic
28#14519765C2211yescharacteristic
29#14519764C2211yescharacteristic
30#14519763—21no—
31#14519763—21no—
32#14519763—21no—
33#14519752C2211yescharacteristic
34#14519750—21no—
35#14519748C2211yescharacteristic
36C4×D244C2211yescharacteristic, complemented
37C4×C22⋊D61—21no—
38C22⋊C4×D61—21no—
39C22⋊C4×D61—21no—
40C42×D61C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51#14519687C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic, complemented
53C2×D8×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68Q8×D61—41no—
69Q8×D61—41no—
70D4×D61—41no—
71D4×D61—41no—
72#11758222—44no—
73C2×D244—21no—
74C2×D244C2311yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61D411yescharacteristic
79C2×C4×D61D411yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—21no—
82C2×Dic122—21no—
83C2×Dic122C2311yescharacteristic
84SD16×C61—41no—
85D8×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C22⋊C4×C61—21no—
92C42×C61C2311yescharacteristic
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96#11758201—41no—
97#11758200—41no—
98#11758199—41no—
99#11758199—41no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108C4×Dic61D411yescharacteristic
109C4×Dic61D411yescharacteristic
110C4×Dic61C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113D488—41no—
114#11758190—41no—
115C23×C61—21no—
116C23×C61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—21no—
145D244—21no—
146D244—21no—
147D244—21no—
148D244—42no—
149C4×D61—22no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—41no—
153C4×D61—42no—
154C4×D61—42no—
155Dic122—21no—
156Dic122—21no—
157Dic122—42no—
158Dic122—42no—
159C8×C61—21no—
160C8×C61—21no—
161#92418—21no—
162#92418—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61C22×D411yescharacteristic
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—84no—
179C2×D61AGL(1,ℤ/8)12yes—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61H(5,𝔽2)11yescharacteristic
185C4×C61H(5,𝔽2)11yescharacteristic
186Dic61—21no—
187Dic61—21no—
188Dic61—21no—
189Dic61—41no—
190Dic61—41no—
191#3213—611nomaximal, Sylow
192C2×C61—81no—
193C2×C61—81no—
194C2×C61#53511yescharacteristic
195C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C61#57511yescharacteristic
197D61—22no—
198D61—81no—
199D61—81no—
200#532—611no—
201C2×#124—611no—
202#496—611no—
203#496—611no—
204#489—611no—
205#489—611no—
206#463—611no—
207#463—611no—
208#463—611no—
209#463D6111yescharacteristic, complemented
210#448—611no—
211#448—611no—
212#447—611no—
213#447—611no—
214#432—611no—
215C61#321311yescharacteristic, complemented, Sylow
216C2×#41—1221no—
217C22×Q8—611no—
218C22×D4—611no—
219C2×SD16—611no—
220C2×SD16—611no—
221C2×SD16—611no—
222C2×SD16C2×D6111yescharacteristic, complemented
223C2×D8—611no—
224C2×D8—611no—
225C2×D8—611no—
226C2×D8C2×D6111yescharacteristic
227C4⋊Q8—611no—
228#127—611no—
229#124—611no—
230#124—611no—
231#124—611no—
232#124—1221no—
233#124—1221no—
234#124—1221no—
235#124C2×D6111yescharacteristic
236#121—611no—
237#121—611no—
238#121—1221no—
239C4×D4—611no—
240C4×D4—1221no—
241C4×D4C2×D6111yescharacteristic, complemented
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C4⋊C8—611no—
246C4⋊C8C2×D6111yescharacteristic, complemented
247#103—611no—
248#103—611no—
249#103—611no—
250#103C2×D6111yescharacteristic, complemented
251#102—611no—
252#102—611no—
253#102—611no—
254#102C2×D6111yescharacteristic
255C22⋊C8—611no—
256C22⋊C8—611no—
257#97—611no—
258#97—611no—
259C24—1221no—
260#41—2444no—
261C2×Q8—611no—
262C2×Q8—1221no—
263C2×Q8—1221no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8C22×D6111yescharacteristic
267C2×D4—611no—
268C2×D4—611no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—2441no—
275C2×D4—2441no—
276C2×D4C22×D6111yescharacteristic
277C2×D4C22×D6111yescharacteristic
278C22×C4—21no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—1221no—
283C22×C4—1221no—
284SD16—41no—
285SD16—2441no—
286SD16—2441no—
287SD16—2441no—
288D8—41no—
289D8—2441no—
290D8—2441no—
291D8—2441no—
292C2×C8—611no—
293C2×C8—611no—
294C2×C8C22×D6111yescharacteristic
295C2×C8C22×D6111yescharacteristic
296C4⋊C4—611no—
297C4⋊C4—1221no—
298C4⋊C4C22×D6111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C42—611no—
312C42—611no—
313C42—611no—
314C42C22×D6111yescharacteristic
315C23—21no—
316C23—21no—
317C23—611no—
318C23—1221no—
319C23—1221no—
320C23—2442no—
321C23—2442no—
322C23—2442no—
323Q8—21no—
324Q8—21no—
325Q8—1221no—
326Q8—1221no—
327Q8—2442no—
328Q8—2442no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—1221no—
334D4—1221no—
335D4—1221no—
336D4—1221no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340D4—2442no—
341D4—2442no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—1222no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—2441no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4D4×D6111yescharacteristic
357C2×C4D4×D6111yescharacteristic
358C2×C4C23×D6111yescharacteristic
359C8—21no—
360C8—21no—
361C8—1221no—
362C8—1221no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—612no—
370C22—1221no—
371C22—1221no—
372C22—4884no—
373C22—2441no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22C2×D4×D6111yescharacteristic
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—1221no—
385C4—1221no—
386C4—1221no—
387C4—2441no—
388C4—2441no—
389C4#1451982211yescharacteristic
390C4#1451982311yescharacteristic
391C2—81no—
392C2—81no—
393C2—1222no—
394C2—4881no—
395C2—4881no—
396C2#1684032811yescharacteristic
397C2AGL(1,ℤ/8)×D6111yescharacteristic
398C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3213
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16840309C2semidirect
2. #124×D61C2semidirect
3. #16840150C2semidirect
4. #16840148C2semidirect
5. #16840123C2semidirect
6. #16840120C2semidirect
7. #16839978C2semidirect
8. #16839977C2semidirect
9. #16839974C2semidirect
10. #16839902C2semidirect
11. #16839899C2semidirect
12. #16839897C2semidirect
13. #16839894C2semidirect
14. #16839818C2semidirect
15. C61×#463C2semidirect
19. C2×#11758190C22semidirect
20. C2×#11758200C22semidirect
21. C2×#11758201C22semidirect
25. #14519776C22semidirect
26. #14519773C22semidirect
36. C4×D244C22semidirect
41. C4⋊#92418C22semidirect
42. #14519702C22semidirect
43. #14519701C22semidirect
44. #14519700C22semidirect
50. #14519687C22semidirect
51. #14519687C22semidirect
52. C2×SD16×C61C22semidirect
55. C4×D4×C61C22semidirect
56. C4⋊C8×C61C22semidirect
57. #103×C61C22semidirect
209. #463D61semidirect
215. C61#3213semidirect
222. C2×SD16C2×D61semidirect
241. C4×D4C2×D61semidirect
246. C4⋊C8C2×D61semidirect
250. #103C2×D61semidirect