Finite Group Databasebeta

← #21457519

Subgroups — #21457519

Order 7808.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519800C211yesmaximal, characteristic, complemented
2C22×#11758201C211yesmaximal, characteristic, complemented
3#16840423C211yesmaximal, characteristic, complemented
4#16840403C211yesmaximal, characteristic, complemented
5#16840147C211yesmaximal, characteristic, complemented
6#16839994C211yesmaximal, characteristic, complemented
7#16839993C211yesmaximal, characteristic, complemented
8#16839986C211yesmaximal, characteristic, complemented
9#16839980C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11#16839910C211yesmaximal, characteristic, complemented
12#16839898C211yesmaximal, characteristic, complemented
13#16839847C211yesmaximal, characteristic, complemented
14#16839825C211yesmaximal, characteristic, complemented
15C61×#451C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758226C2211yescharacteristic, complemented
18C22×D244C2211yescharacteristic
19#14519800—24no—
20C2×#11758201—24no—
21C2×#11758201C2211yescharacteristic
22C2×#11758201C2211yescharacteristic
23C2×#11758201C2211yescharacteristic
24C2×#11758201C2211yescharacteristic
25C2×#11758201C2211yescharacteristic, complemented
26C2×D488C2211yescharacteristic
27C2×D488C2211yescharacteristic
28C22×#92418C2211yescharacteristic
29C2×C8×D61C2211yescharacteristic, complemented
30#14519766—21no—
31#14519766C2211yescharacteristic
32#14519766C2211yescharacteristic, complemented
33#14519762—21no—
34#14519753—21no—
35#14519753C2211yescharacteristic, complemented
36#14519752—21no—
37#14519752C2211yescharacteristic
38#14519751—21no—
39#14519751C2211yescharacteristic
40#14519747—21no—
41Q8×Dic61C2211yescharacteristic, complemented
42#14519739C2211yescharacteristic
43C4×C22⋊D61—21no—
44C4×C22⋊D61C2211yescharacteristic
45C22⋊C4×D61—21no—
46#14519708C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519701C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519697C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53C8×Dic61C2211yescharacteristic, complemented
54C22×Q8×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic, complemented
56C2×Q16×C61C2211yescharacteristic, complemented
57C22⋊Q8×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60C22⋊C8×C61C2211yescharacteristic
61C23×D61—21no—
62C2×Q8×C61—21no—
63C2×Q8×C61—22no—
64C2×Q8×C61—41no—
65C2×Q8×C61C2311yescharacteristic
66C2×Q8×C61C2311yescharacteristic
67C2×Q8×C61C2311yescharacteristic
68C22×C4×C61—21no—
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61D411yescharacteristic
72#11758226—22no—
73#11758226—22no—
74#11758226—41no—
75#11758226—41no—
76C2×D244—22no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—41no—
82C2×D244C2311yescharacteristic
83C2×D244C2311yescharacteristic
84C2×D244C2311yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61C2311yescharacteristic
89Q16×C61—22no—
90Q16×C61—41no—
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C4⋊C4×C61—21no—
94C4⋊C4×C61C2311yescharacteristic
95C22⋊C4×C61—21no—
96C22⋊Dic61D411yescharacteristic
97#11758201—22no—
98#11758201—22no—
99#11758201—22no—
100#11758201—22no—
101#11758201D414yescomplemented
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198D411yescharacteristic
111C4⋊Dic61—21no—
112C4⋊Dic61C2311yescharacteristic
113#11758196—21no—
114#11758196D411yescharacteristic
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117C2×#92418—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120D488—22no—
121D488—41no—
122C8×D61—22no—
123C23×C61C2×D411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—81no—
130C22×D61C2×D411yescharacteristic
131Q8×C61—21no—
132Q8×C61—21no—
133Q8×C61—21no—
134Q8×C61—21no—
135Q8×C61—21no—
136Q8×C61—42no—
137Q8×C61C2×D412yes—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—42no—
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2411yescharacteristic
147C22⋊D61—22no—
148C22⋊D61—42no—
149C2×Dic61—21no—
150C2×Dic61C2×D411yescharacteristic
151C2×Dic61C2×D411yescharacteristic
152C2×Dic61C2×D411yescharacteristic
153D244—21no—
154D244—21no—
155D244—21no—
156D244—21no—
157D244—21no—
158D244—42no—
159D244—42no—
160D244—42no—
161D244—81no—
162D244C2×D412yes—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—81no—
168C8×C61—21no—
169C8×C61—21no—
170#92418—21no—
171#92418C2×D412yes—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#13512yescomplemented
175C22×C61C22×D411yescharacteristic
176C2×D61—21no—
177C2×D61—22no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—84no—
189C4×C61—22no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61C22×D411yescharacteristic
195C4×C61H(5,𝔽2)11yescharacteristic
196Dic61—21no—
197Dic61—21no—
198Dic61—21no—
199Dic61—41no—
200#3282—611nomaximal, Sylow
201C2×C61—22no—
202C2×C61D4211yescharacteristic
203C2×C61C2×#13511yescharacteristic
204C2×C61#57711yescharacteristic
205D61—41no—
206D61—42no—
207D61—81no—
208D61—81no—
209C2×#135—611no—
210C22×SD16—611no—
211#548—611no—
212#546—611no—
213#495—611no—
214#465—611no—
215#465—611no—
216#464—611no—
217#463—611no—
218#452—611no—
219#451D6111yescharacteristic, complemented
220#449—611no—
221#447—611no—
222C4×SD16—611no—
223C8×D4—611no—
224C61#328211yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C2×#41—611no—
227C22×Q8C2×D6111yescharacteristic
228C22×D4—611no—
229#135—1224no—
230C2×Q16C2×D6111yescharacteristic, complemented
231C2×Q16C2×D6111yescharacteristic, complemented
232C2×SD16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—611no—
236C2×SD16—611no—
237C2×SD16—1224no—
238C2×D8—611no—
239C2×D8—611no—
240C22×C8—611no—
241C22×C8—611no—
242#124—611no—
243#124—611no—
244#124—1221no—
245#123—1221no—
246C22⋊Q8—611no—
247C22⋊Q8—1221no—
248C22⋊Q8C2×D6111yescharacteristic
249#121—611no—
250#121—611no—
251#121—1221no—
252#121—1221no—
253#120—1221no—
254C4×Q8—611no—
255C4×D4—611no—
256C4×D4—611no—
257C4×D4—1221no—
258C2×C22⋊C4—1221no—
259#106—611no—
260C4⋊C8—611no—
261#103—611no—
262#103C2×D6111yescharacteristic, complemented
263#103C2×D6111yescharacteristic, complemented
264#102—611no—
265#102—611no—
266#102—611no—
267C22⋊C8—611no—
268C22⋊C8C2×D6111yescharacteristic
269C4×C8—611no—
270C24—1221no—
271#41—1222no—
272#41—1222no—
273#41—2441no—
274#41—2441no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D6111yescharacteristic
279C2×Q8C22×D6111yescharacteristic
280C2×Q8C22×D6111yescharacteristic
281C2×D4—611no—
282C2×D4—611no—
283C2×D4—611no—
284C2×D4—611no—
285C2×D4—1222no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—2441no—
292C22×C4—21no—
293C22×C4—611no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4C22×D6111yescharacteristic
298Q16—22no—
299Q16—41no—
300SD16—614no—
301SD16—1222no—
302SD16—1222no—
303SD16—1222no—
304SD16—1222no—
305D8—1222no—
306D8—2441no—
307C2×C8—611no—
308C2×C8—611no—
309C2×C8—1222no—
310C2×C8—1222no—
311C2×C8C22×D6111yescharacteristic
312C2×C8C22×D6111yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4C22×D6111yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—611no—
321C22⋊C4—611no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C42—611no—
331C42—1221no—
332C23—611no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336C23—4881no—
337C23—2442no—
338C23—2442no—
339C23D4×D6111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8D4×D6112yes—
347D4—612no—
348D4—1222no—
349D4—1221no—
350D4—1221no—
351D4—1221no—
352D4—1221no—
353D4—1221no—
354D4—4881no—
355D4—2442no—
356D4—2442no—
357D4—2442no—
358D4—2442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—4881no—
373C2×C4—2442no—
374C2×C4—2442no—
375C2×C4D4×D6111yescharacteristic
376C2×C4C23×D6111yescharacteristic
377C8—21no—
378C8—21no—
379C8—612no—
380C8—1221no—
381C22—21no—
382C22—21no—
383C22—1221no—
384C22—1221no—
385C22—1221no—
386C22—1222no—
387C22—4884no—
388C22—2441no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22#1451980012yescomplemented
397C22C2×D4×D6111yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—1221no—
404C4—1221no—
405C4—1221no—
406C4—2441no—
407C4C2×D4×D6111yescharacteristic
408C4#1451982211yescharacteristic
409C2—22no—
410C2—4881no—
411C2—4881no—
412C2—2441no—
413C2—2442no—
414C2#1684039411yescharacteristic
415C2C2×#1451980011yescharacteristic
416C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3282
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#14519800C2semidirect
2. C22×#11758201C2semidirect
3. #16840423C2semidirect
4. #16840403C2semidirect
5. #16840147C2semidirect
6. #16839994C2semidirect
7. #16839993C2semidirect
8. #16839986C2semidirect
9. #16839980C2semidirect
10. #16839923C2semidirect
11. #16839910C2semidirect
12. #16839898C2semidirect
13. #16839847C2semidirect
14. #16839825C2semidirect
15. C61×#451C2semidirect
17. C2×#11758226C22semidirect
25. C2×#11758201C22semidirect
29. C2×C8×D61C22semidirect
32. #14519766C22semidirect
35. #14519753C22semidirect
41. Q8×Dic61C22semidirect
46. #14519708C22semidirect
47. #14519706C22semidirect
48. #14519701C22semidirect
51. #14519697C22semidirect
52. #14519689C22semidirect
53. C8×Dic61C22semidirect
55. C2×Q16×C61C22semidirect
56. C2×Q16×C61C22semidirect
58. #103×C61C22semidirect
59. #103×C61C22semidirect
101. #11758201D4semidirect
174. C22×C61#135semidirect
219. #451D61semidirect
224. C61#3282semidirect
230. C2×Q16C2×D61semidirect
231. C2×Q16C2×D61semidirect
262. #103C2×D61semidirect
263. #103C2×D61semidirect
396. C22#14519800semidirect