Finite Group Databasebeta

← #21455335

Subgroups — #21455335

Order 7808.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519806C211yesmaximal, characteristic, complemented
2C2×SD16×D61C211yesmaximal, characteristic, complemented
3#16840325C211yesmaximal, characteristic
4#16840238C211yesmaximal, characteristic, complemented
5#16839985C211yesmaximal, characteristic, complemented
6#16839984C211yesmaximal, characteristic, complemented
7#16839983C211yesmaximal, characteristic, complemented
8#16839982C211yesmaximal, characteristic, complemented
9#16839961C211yesmaximal, characteristic, complemented
10#16839960C211yesmaximal, characteristic, complemented
11#16839959C211yesmaximal, characteristic, complemented
12#16839787C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#16839755C211yesmaximal, characteristic, complemented
15C61×#460C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19#14519806—24no—
20C2×Dic244C2211yescharacteristic, complemented
21C2×#11758202C2211yescharacteristic, complemented
22C2×#11758190C2211yescharacteristic
23C2×#11758200C2211yescharacteristic
24C2×#11758200C2211yescharacteristic, complemented
25C2×#11758201C2211yescharacteristic
26SD16×D61—24no—
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519773C2211yescharacteristic
30#14519765C2211yescharacteristic
31#14519764C2211yescharacteristic
32#14519749—21no—
33#14519749—21no—
34#14519745—21no—
35#14519745—21no—
36Q8×Dic61C2211yescharacteristic, complemented
37C4×Dic122—21no—
38C4×Dic122C2211yescharacteristic, complemented
39#14519742—21no—
40#14519742C2211yescharacteristic, complemented
41#14519735—21no—
42#14519735C2211yescharacteristic
43#14519734—21no—
44#14519734C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic, complemented
46#14519706C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519700C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic
51#14519698C2211yescharacteristic
52#14519698C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic, complemented
56#127×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic, complemented
58C4⋊C8×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61—21no—
72Q8×D61—22no—
73Q8×D61D414yescomplemented
74#11758224—22no—
75#11758224—22no—
76D4×D61—22no—
77D4×D61—22no—
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—21no—
82C2×Dic122C2311yescharacteristic
83C2×Dic122C2311yescharacteristic
84SD16×C61—22no—
85SD16×C61—22no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61—21no—
89C4⋊C4×C61C2311yescharacteristic
90C42×C61—21no—
91C42×C61C2311yescharacteristic
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94#11758202—22no—
95#11758201—22no—
96#11758200—22no—
97#11758200—22no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198D411yescharacteristic
102#11758198D411yescharacteristic
103C4⋊Dic61—21no—
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107#11758196D411yescharacteristic
108#11758196D411yescharacteristic
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116Dic244—22no—
117#11758190—22no—
118#11758189—22no—
119C8×D61—22no—
120C23×C61—21no—
121C23×C61—21no—
122C22×D61—21no—
123C22×D61—42no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61C2×D412yes—
129D4×C61—21no—
130D4×C61—21no—
131D4×C61—21no—
132D4×C61—21no—
133D4×C61—81no—
134D4×C61—81no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2411yescharacteristic
140C22⋊D61—42no—
141C22⋊D61—42no—
142C22⋊D61—81no—
143C22⋊D61—81no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—42no—
148C2×Dic61C2×D411yescharacteristic
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151D244—21no—
152D244—21no—
153C4×D61—24no—
154C4×D61C2×D412yes—
155C4×D61#4112yes—
156Dic122—21no—
157Dic122—24no—
158Dic122—21no—
159Dic122—21no—
160Dic122C2×D412yes—
161C8×C61—21no—
162C8×C61—21no—
163#92418—21no—
164#92418—21no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61C22×D411yescharacteristic
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—84no—
178C2×D61#12112yes—
179C4×C61—22no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—41no—
183C4×C61C22×D411yescharacteristic
184C4×C61C2×#4111yescharacteristic
185Dic61—22no—
186Dic61—21no—
187Dic61—21no—
188Dic61—41no—
189Dic61—41no—
190Dic61#12112yes—
191#3043—611nomaximal, Sylow
192C2×C61—81no—
193C2×C61—81no—
194C2×C61C2×#12111yescharacteristic
195C2×C61#57711yescharacteristic
196C2×C61#57711yescharacteristic
197D61—22no—
198D61—81no—
199C2×#137—611no—
200C22×SD16—611no—
201#535—611no—
202#519—611no—
203#464—611no—
204#464—611no—
205#464—611no—
206#464—611no—
207#460—611no—
208#460—611no—
209#460—611no—
210#460D6111yescharacteristic, complemented
211#424—611no—
212#418—611no—
213#416—611no—
214C61#304311yescharacteristic, complemented, Sylow
215C2×#41—611no—
216C22×Q8—611no—
217C22×D4—611no—
218#137—1224no—
219C2×Q16—611no—
220C2×Q16—611no—
221C2×SD16—611no—
222C2×SD16—611no—
223C2×SD16—611no—
224C2×SD16—611no—
225C2×SD16—1224no—
226C2×SD16C2×D6111yescharacteristic
227C2×SD16C2×D6111yescharacteristic, complemented
228C2×M16—611no—
229C22×C8—611no—
230#127—611no—
231#127C2×D6111yescharacteristic
232#124—611no—
233#124—611no—
234#121—1221no—
235#121—1221no—
236#120—1221no—
237#120—1221no—
238C4×Q8—611no—
239C4×Q8—611no—
240C4×Q8—611no—
241C4×Q8—1221no—
242C4×Q8—1221no—
243C4×Q8C2×D6111yescharacteristic, complemented
244#117—611no—
245#117—611no—
246#117—1221no—
247#117—1221no—
248C4⋊C8—611no—
249C4⋊C8—611no—
250C4⋊C8—611no—
251C4⋊C8C2×D6111yescharacteristic, complemented
252#103—611no—
253#103—611no—
254#102—611no—
255#102—611no—
256#102—611no—
257#102—611no—
258#102C2×D6111yescharacteristic
259#102C2×D6111yescharacteristic, complemented
260C24—1221no—
261#41—1222no—
262#41—1222no—
263C2×Q8—614no—
264C2×Q8—611no—
265C2×Q8—611no—
266C2×Q8—1221no—
267C2×Q8—1222no—
268C2×Q8C22×D6111yescharacteristic
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—611no—
272C2×D4—1222no—
273C2×D4—1222no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4C22×D6111yescharacteristic
279C2×D4C22×D6111yescharacteristic
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283Q16—1222no—
284Q16—1222no—
285SD16—22no—
286SD16—22no—
287SD16—1222no—
288SD16—1222no—
289SD16—1222no—
290SD16—1222no—
291M16—1222no—
292C2×C8—611no—
293C2×C8—611no—
294C2×C8—1222no—
295C2×C8C22×D6111yescharacteristic
296C2×C8C22×D6111yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—611no—
299C4⋊C4—611no—
300C4⋊C4—611no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4C22×D6111yescharacteristic
305C22⋊C4—611no—
306C22⋊C4—611no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C42—21no—
313C42—611no—
314C42—1221no—
315C42—1221no—
316C42—1221no—
317C42—1221no—
318C42C22×D6111yescharacteristic
319C23—21no—
320C23—21no—
321C23—611no—
322C23—1221no—
323C23—4881no—
324C23—4881no—
325C23—2442no—
326Q8—21no—
327Q8—612no—
328Q8—1224no—
329Q8—1221no—
330Q8—1221no—
331Q8—1221no—
332Q8D4×D6112yes—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—21no—
337D4—81no—
338D4—81no—
339D4—1221no—
340D4—1221no—
341D4—4881no—
342D4—4881no—
343D4—2442no—
344D4—2442no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—611no—
348C2×C4—612no—
349C2×C4—612no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—1224no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—2442no—
357C2×C4D4×D6111yescharacteristic
358C2×C4D4×D6111yescharacteristic
359C2×C4C23×D6111yescharacteristic
360C8—21no—
361C8—21no—
362C8—1221no—
363C8—1221no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—612no—
371C22—1221no—
372C22—1221no—
373C22—4884no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22C2×D4×D6111yescharacteristic
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—612no—
383C4—1222no—
384C4—1221no—
385C4—1221no—
386C4—2441no—
387C4—2441no—
388C4C2×D4×D6111yescharacteristic
389C4#41×D6111yescharacteristic
390C2—81no—
391C2—81no—
392C2—1222no—
393C2—4881no—
394C2#121×D6111yescharacteristic
395C2#1684056811yescharacteristic
396C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#460C2
socleC22×C61C22×D4
hypercenter#460D61
hypocenterC61#3043
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#14519806C2semidirect
2. C2×SD16×D61C2semidirect
4. #16840238C2semidirect
5. #16839985C2semidirect
6. #16839984C2semidirect
7. #16839983C2semidirect
8. #16839982C2semidirect
9. #16839961C2semidirect
10. #16839960C2semidirect
11. #16839959C2semidirect
12. #16839787C2semidirect
13. #16839765C2semidirect
14. #16839755C2semidirect
15. C61×#460C2semidirect
20. C2×Dic244C22semidirect
21. C2×#11758202C22semidirect
24. C2×#11758200C22semidirect
36. Q8×Dic61C22semidirect
38. C4×Dic122C22semidirect
40. #14519742C22semidirect
45. C4⋊#92418C22semidirect
46. #14519706C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519700C22semidirect
52. #14519698C22semidirect
55. C2×SD16×C61C22semidirect
57. C4×Q8×C61C22semidirect
58. C4⋊C8×C61C22semidirect
60. #102×C61C22semidirect
73. Q8×D61D4semidirect
210. #460D61semidirect
214. C61#3043semidirect
227. C2×SD16C2×D61semidirect
243. C4×Q8C2×D61semidirect
251. C4⋊C8C2×D61semidirect
259. #102C2×D61semidirect