Finite Group Databasebeta

← #21456675

Subgroups — #21456675

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#16840342C211yesmaximal, characteristic, complemented
2#16840329C211yesmaximal, characteristic, complemented
3#16840100C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840074C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16839997C211yesmaximal, characteristic, complemented
10#16839988C211yesmaximal, characteristic, complemented
11#16839906C211yesmaximal, characteristic, complemented
12#16839906C211yesmaximal, characteristic, complemented
13#16839896C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic, complemented
17C2×#11758222C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic, complemented
21C2×C8×D61C2211yescharacteristic, complemented
22#14519773—21no—
23#14519764—21no—
24#14519755—21no—
25#14519753C2211yescharacteristic, complemented
26#14519752—21no—
27#14519752C2211yescharacteristic, complemented
28#14519751C2211yescharacteristic
29#14519750—21no—
30#14519750—21no—
31#14519748C2211yescharacteristic
32#14519748C2211yescharacteristic
33#14519748C2211yescharacteristic
34#14519748C2211yescharacteristic
35#14519746—21no—
36#14519746—21no—
37#14519736C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic, complemented
39#14519711C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C24×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61—21no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61D411yescharacteristic
73C2×C22⋊D61D411yescharacteristic
74#11758226—41no—
75#11758226—41no—
76#11758222—41no—
77#11758222—41no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244D411yescharacteristic
81C2×D244C2311yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61C2311yescharacteristic
85C2×C4×D61C2311yescharacteristic
86C2×Dic122D411yescharacteristic
87SD16×C61—41no—
88SD16×C61—41no—
89C2×C8×C61C2311yescharacteristic
90C2×C8×C61C2311yescharacteristic
91C4⋊C4×C61—21no—
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99#11758199—41no—
100#11758199—41no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112#11758189—41no—
113C8×D61—41no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—42no—
117C23×C61—81no—
118C23×C61—81no—
119C23×C61C2×D411yescharacteristic
120C22×D61—21no—
121C22×D61C2×D411yescharacteristic
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—42no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—41no—
137C22⋊D61—41no—
138C22⋊D61—81no—
139C22⋊D61—81no—
140C22⋊D61—81no—
141C22⋊D61—81no—
142C22⋊D61—81no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148D244—21no—
149D244—21no—
150D244—41no—
151D244—42no—
152D244—81no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—42no—
158C4×D61—81no—
159Dic122—41no—
160C8×C61—21no—
161C8×C61—21no—
162#92418—21no—
163#92418—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—84no—
174C22×C61C22×D411yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61H(5,𝔽2)11yescharacteristic
188C4×C61H(5,𝔽2)11yescharacteristic
189Dic61—21no—
190Dic61—21no—
191Dic61—41no—
192Dic61—41no—
193Dic61—41no—
194#3198—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61—81no—
197C2×C61—81no—
198C2×C61#53411yescharacteristic
199C2×C61#57611yescharacteristic
200C2×C61#57711yescharacteristic
201D61—41no—
202D61—41no—
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#450D6111yescharacteristic, complemented
215#449—611no—
216#449—611no—
217#447—611no—
218#408—611no—
219C61#319811yescharacteristic, complemented, Sylow
220C2×#41—611no—
221C2×#41—611no—
222C22×D4C2×D6111yescharacteristic
223C2×SD16C2×D6111yescharacteristic
224C2×SD16C2×D6111yescharacteristic
225C2×D8—611no—
226C2×D8—611no—
227C2×M16—611no—
228C22×C8—611no—
229#127—1221no—
230#124—1221no—
231C22⋊Q8—611no—
232C22⋊Q8—1221no—
233C22⋊Q8C2×D6111yescharacteristic
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#102C2×D6111yescharacteristic
258#102C2×D6111yescharacteristic
259C22⋊C8—611no—
260C22⋊C8—611no—
261C22⋊C8—611no—
262C22⋊C8C2×D6111yescharacteristic
263C24—21no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267#41—2441no—
268C2×Q8—611no—
269C2×Q8C22×D6111yescharacteristic
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—611no—
274C2×D4—611no—
275C2×D4—611no—
276C2×D4—611no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4C22×D6111yescharacteristic
285C2×D4C22×D6111yescharacteristic
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4C22×D6111yescharacteristic
291SD16—41no—
292SD16—41no—
293D8—2441no—
294D8—2441no—
295M16—2441no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—2441no—
299C2×C8C22×D6111yescharacteristic
300C2×C8C22×D6111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—611no—
303C4⋊C4—611no—
304C4⋊C4—611no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4C22×D6111yescharacteristic
308C22⋊C4—21no—
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—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—611no—
324C23—611no—
325C23—1221no—
326C23D4×D6111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—2441no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—1221no—
336D4—1221no—
337D4—4881no—
338D4—4881no—
339D4—4881no—
340D4—4881no—
341D4—4881no—
342D4—4881no—
343D4—2441no—
344D4—2442no—
345D4—2441no—
346D4—2441no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—4881no—
361C2×C4—2442no—
362C2×C4D4×D6111yescharacteristic
363C2×C4C23×D6111yescharacteristic
364C8—21no—
365C8—21no—
366C8—1221no—
367C8—1221no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—1221no—
379C22—1221no—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22C2×D4×D6111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—1221no—
392C4—1221no—
393C4—2441no—
394C4—2441no—
395C4—2441no—
396C4#1451982211yescharacteristic
397C4#1451982211yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—4881no—
402C2—2441no—
403C2—2441no—
404C2#1684032211yescharacteristic
405C2#1684056611yescharacteristic
406C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #16840342C2semidirect
2. #16840329C2semidirect
3. #16840100C2semidirect
4. #16840087C2semidirect
5. #16840079C2semidirect
6. #16840074C2semidirect
7. #16840014C2semidirect
8. #16840005C2semidirect
9. #16839997C2semidirect
10. #16839988C2semidirect
11. #16839906C2semidirect
12. #16839906C2semidirect
13. #16839896C2semidirect
14. #16839727C2semidirect
15. C61×#450C2semidirect
16. C2×#11758226C22semidirect
20. C2×#11758189C22semidirect
21. C2×C8×D61C22semidirect
25. #14519753C22semidirect
27. #14519752C22semidirect
38. C4⋊C4×D61C22semidirect
39. #14519711C22semidirect
40. #14519710C22semidirect
41. #14519709C22semidirect
42. #14519708C22semidirect
43. #14519701C22semidirect
44. #14519701C22semidirect
45. #14519699C22semidirect
46. #14519699C22semidirect
50. #14519689C22semidirect
51. #14519689C22semidirect
214. #450D61semidirect
219. C61#3198semidirect