Finite Group Databasebeta

← #21456673

Subgroups — #21456673

Order 7808.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840340C211yesmaximal, characteristic, complemented
2#16840326C211yesmaximal, characteristic, complemented
3#16840104C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840081C211yesmaximal, characteristic, complemented
6#16840076C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16840008C211yesmaximal, characteristic, complemented
9#16839998C211yesmaximal, characteristic, complemented
10#16839991C211yesmaximal, characteristic, complemented
11#16839915C211yesmaximal, characteristic, complemented
12#16839909C211yesmaximal, characteristic, complemented
13#16839909C211yesmaximal, characteristic, complemented
14#16839898C211yesmaximal, characteristic, complemented
15C61×#408C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic, complemented
17C22×D244C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×D488C2211yescharacteristic
22#14519773—21no—
23#14519766—21no—
24#14519756C2211yescharacteristic
25#14519756C2211yescharacteristic, complemented
26#14519753—21no—
27#14519751C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519751C2211yescharacteristic
30#14519751C2211yescharacteristic
31#14519751C2211yescharacteristic
32#14519751C2211yescharacteristic, complemented
33#14519749—21no—
34#14519749—21no—
35#14519748—21no—
36#14519745—21no—
37#14519745—21no—
38#14519736C2211yescharacteristic
39C2×C4⋊Dic61C2211yescharacteristic, complemented
40#14519711C2211yescharacteristic, complemented
41#14519711C2211yescharacteristic, complemented
42#14519709C2211yescharacteristic, complemented
43#14519709C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519702C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, 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×D61—21no—
60#41×C61—41no—
61#41×C61—41no—
62C2×Q8×C61D411yescharacteristic
63C2×D4×C61D411yescharacteristic
64C2×D4×C61D411yescharacteristic
65C2×D4×C61D411yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C22×Dic61—21no—
77#11758222—41no—
78#11758222—41no—
79C2×D244—21no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244C2311yescharacteristic
83C2×D244C2311yescharacteristic
84C2×D244C2311yescharacteristic
85C2×C4×D61—21no—
86C2×Dic122C2311yescharacteristic
87M16×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61C2311yescharacteristic
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110D488—41no—
111D488—41no—
112#11758190—41no—
113#11758190—41no—
114C23×C61C2×D411yescharacteristic
115C23×C61C2×D411yescharacteristic
116C23×C61C2×D411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—42no—
121C22×D61—81no—
122C22×D61—81no—
123Q8×C61—41no—
124D4×C61—41no—
125D4×C61—41no—
126D4×C61—41no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—42no—
138C22⋊D61—81no—
139C22⋊D61—81no—
140C22⋊D61—81no—
141C22⋊D61—81no—
142C22⋊D61—81no—
143C22⋊D61—81no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—81no—
150D244—21no—
151D244—21no—
152D244—21no—
153D244—21no—
154D244—21no—
155D244—21no—
156D244—42no—
157C4×D61—42no—
158Dic122—21no—
159Dic122—21no—
160C8×C61—21no—
161C8×C61—21no—
162C8×C61—21no—
163C8×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61C22×D411yescharacteristic
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—84no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61H(5,𝔽2)11yescharacteristic
188C4×C61H(5,𝔽2)11yescharacteristic
189Dic61—41no—
190Dic61—41no—
191Dic61—41no—
192Dic61—41no—
193Dic61—41no—
194#3198—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61—41no—
197C2×C61—41no—
198C2×C61#53411yescharacteristic
199C2×C61#57611yescharacteristic
200C2×C61#57711yescharacteristic
201D61—81no—
202D61—81no—
203D61—81no—
204#537—611no—
205#535—611no—
206#485—611no—
207#482—611no—
208#481—611no—
209#480—611no—
210#469—611no—
211#468—611no—
212#466—611no—
213#465—611no—
214#450—611no—
215#449—611no—
216#449—611no—
217#447—611no—
218#408D6111yescharacteristic, complemented
219C61#319811yescharacteristic, complemented, Sylow
220C2×#41—611no—
221C2×#41C2×D6111yescharacteristic
222C22×D4—611no—
223C2×SD16—611no—
224C2×SD16—611no—
225C2×D8—611no—
226C2×D8—611no—
227C2×M16C2×D6111yescharacteristic, complemented
228C22×C8C2×D6111yescharacteristic, complemented
229#127—1221no—
230#124—1221no—
231C22⋊Q8—611no—
232C22⋊Q8—611no—
233C22⋊Q8—1221no—
234#121—611no—
235#121—611no—
236#121—611no—
237#121—611no—
238#121—611no—
239#121—611no—
240#121—1221no—
241#121—1221no—
242#121—1221no—
243#120—1221no—
244#120—1221no—
245#117—611no—
246C2×C4⋊C4—611no—
247#107—611no—
248#107—611no—
249#106—611no—
250#106—611no—
251#103—611no—
252#103—611no—
253#102—611no—
254#102—611no—
255#102—611no—
256#102—611no—
257#102—611no—
258#102—611no—
259C22⋊C8C2×D6111yescharacteristic
260C22⋊C8C2×D6111yescharacteristic
261C22⋊C8C2×D6111yescharacteristic, complemented
262C22⋊C8C2×D6111yescharacteristic, complemented
263C24—1221no—
264#41—41no—
265#41—41no—
266#41—2441no—
267#41—2441no—
268C2×Q8—611no—
269C2×Q8D24411yescharacteristic
270C2×D4—611no—
271C2×D4—611no—
272C2×D4—611no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4D24411yescharacteristic
284C2×D4D24411yescharacteristic
285C2×D4D24411yescharacteristic
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4C22×D6111yescharacteristic
289C22×C4C22×D6111yescharacteristic
290C22×C4C22×D6111yescharacteristic
291SD16—2441no—
292SD16—2441no—
293D8—2441no—
294D8—2441no—
295M16—41no—
296C2×C8—41no—
297C2×C8C22×D6111yescharacteristic
298C2×C8C22×D6111yescharacteristic
299C2×C8C22×D6111yescharacteristic
300C2×C8C22×D6111yescharacteristic
301C4⋊C4—611no—
302C4⋊C4—611no—
303C4⋊C4—611no—
304C4⋊C4—611no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C42—1221no—
318C23—1221no—
319C23—1221no—
320C23—1221no—
321C23—4881no—
322C23—4881no—
323C23—2442no—
324C23C2×D24411yescharacteristic
325C23C2×D24411yescharacteristic
326C23C2×D24411yescharacteristic
327Q8—41no—
328Q8—1221no—
329Q8—1221no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—1221no—
334D4—1221no—
335D4—1221no—
336D4—1221no—
337D4—1221no—
338D4—1221no—
339D4—4881no—
340D4—4881no—
341D4—4881no—
342D4—4881no—
343D4—4881no—
344D4—4881no—
345D4—2442no—
346D4—2442no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—4881no—
359C2×C4—2442no—
360C2×C4C2×D24411yescharacteristic
361C2×C4C2×D24411yescharacteristic
362C2×C4C2×D24411yescharacteristic
363C2×C4C23×D6111yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—4884no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22C22×D24411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—2441no—
392C4—2441no—
393C4—2441no—
394C4—2441no—
395C4—2441no—
396C4#1451982211yescharacteristic
397C4#1451982211yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—4881no—
402C2—4881no—
403C2—4881no—
404C2#1684032411yescharacteristic
405C2#1684056711yescharacteristic
406C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #16840340C2semidirect
2. #16840326C2semidirect
3. #16840104C2semidirect
4. #16840087C2semidirect
5. #16840081C2semidirect
6. #16840076C2semidirect
7. #16840015C2semidirect
8. #16840008C2semidirect
9. #16839998C2semidirect
10. #16839991C2semidirect
11. #16839915C2semidirect
12. #16839909C2semidirect
13. #16839909C2semidirect
14. #16839898C2semidirect
15. C61×#408C2semidirect
16. C2×#11758222C22semidirect
25. #14519756C22semidirect
32. #14519751C22semidirect
39. C2×C4⋊Dic61C22semidirect
40. #14519711C22semidirect
41. #14519711C22semidirect
42. #14519709C22semidirect
43. #14519709C22semidirect
44. #14519702C22semidirect
45. #14519702C22semidirect
50. #14519699C22semidirect
51. #14519699C22semidirect
53. C2×M16×C61C22semidirect
54. C22×C8×C61C22semidirect
57. C22⋊C8×C61C22semidirect
58. C22⋊C8×C61C22semidirect
218. #408D61semidirect
219. C61#3198semidirect
227. C2×M16C2×D61semidirect
228. C22×C8C2×D61semidirect
261. C22⋊C8C2×D61semidirect
262. C22⋊C8C2×D61semidirect