Finite Group Databasebeta

← #21455281

Subgroups — #21455281

Order 7808.

548 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic, complemented
2C2×#14519801C211yesmaximal, characteristic, complemented
3#16840311C211yesmaximal, characteristic, complemented
4C4×D4×D61C211yesmaximal, characteristic, complemented
5#16839978C211yesmaximal, characteristic, complemented
6#16839977C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839966C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839956C211yesmaximal, characteristic, complemented
11#16839955C211yesmaximal, characteristic, complemented
12#16839784C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19C22×C4×D61—21no—
20#14519804—24no—
21#14519801—24no—
22C2×#11758190C2211yescharacteristic
23C2×#11758200C2211yescharacteristic
24C2×#11758201C2211yescharacteristic
25C2×D488C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C2×#11758189C2211yescharacteristic
29C2×#11758189C2211yescharacteristic
30#14519775C2211yescharacteristic, complemented
31#14519773C2211yescharacteristic, complemented
32#14519765C2211yescharacteristic, complemented
33#14519750—21no—
34#14519750—21no—
35C4×D244C2211yescharacteristic
36D4×Dic61C2211yescharacteristic
37#14519739C2211yescharacteristic
38C4×C22⋊D61—21no—
39#14519737—21no—
40#14519737—21no—
41#14519737—21no—
42C4⋊C4×D61C2211yescharacteristic
43C22⋊C4×D61—21no—
44C42×D61C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic, complemented
46#14519706C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519701C2211yescharacteristic, complemented
50#14519700C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, complemented
52#14519698C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic, complemented
57C4×D4×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72#11758226—22no—
73#11758226—22no—
74#11758224—22no—
75#11758224—22no—
76D4×D61—22no—
77D4×D61D414yescomplemented
78C2×D244—21no—
79C2×D244C2311yescharacteristic
80C2×D244C2311yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—44no—
86C2×C4×D61D411yescharacteristic
87C2×C4×D61D411yescharacteristic
88C2×C4×D61C2311yescharacteristic
89C2×Dic122C2311yescharacteristic
90SD16×C61—22no—
91D8×C61—22no—
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C4⋊C4×C61C2311yescharacteristic
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊C4×C61—21no—
98C42×C61C2311yescharacteristic
99C22⋊Dic61—21no—
100#11758201—22no—
101#11758200—22no—
102#11758199—22no—
103#11758199—22no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112C4×Dic61D411yescharacteristic
113C4×Dic61D411yescharacteristic
114C4×Dic61C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116C2×#92418C2311yescharacteristic
117D488—22no—
118#11758190—22no—
119#11758189—22no—
120#11758189—22no—
121C23×C61—21no—
122C23×C61—21no—
123C22×D61—21no—
124C22×D61—24no—
125C22×D61—21no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61C2×D411yescharacteristic
129Q8×C61—21no—
130Q8×C61—21no—
131D4×C61—21no—
132D4×C61—21no—
133D4×C61—21no—
134D4×C61C2×D412yes—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—42no—
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2411yescharacteristic
141C22⋊D61—24no—
142C22⋊D61—42no—
143C22⋊D61—42no—
144C22⋊D61—42no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151C2×Dic61C2×D411yescharacteristic
152D244—21no—
153D244—21no—
154D244—21no—
155D244—42no—
156D244C2×D412yes—
157C4×D61—22no—
158C4×D61—41no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—42no—
163C4×D61C2×D412yes—
164C4×D61#4112yes—
165Dic122—21no—
166Dic122—21no—
167C8×C61—21no—
168C8×C61—21no—
169#92418—21no—
170#92418—21no—
171C22×C61—22no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61C22×D411yescharacteristic
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—22no—
181C2×D61—48no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61#12112yes—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61C22×D411yescharacteristic
193C4×C61C2×#4111yescharacteristic
194Dic61—21no—
195Dic61—41no—
196Dic61—41no—
197Dic61#12112yes—
198Dic61AGL(1,ℤ/8)12yescomplemented
199#3036—611nomaximal, Sylow
200C2×C61—42no—
201C2×C61—81no—
202C2×C61C2×#12111yescharacteristic
203C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
204C2×C61#57511yescharacteristic
205D61—22no—
206D61—42no—
207D61—81no—
208C2×AGL(1,ℤ/8)—611no—
209C2×AGL(1,ℤ/8)—611no—
210#532—611no—
211C2×C4×D4—611no—
212#463—611no—
213#463—611no—
214#463—611no—
215#463D6111yescharacteristic, complemented
216#461—611no—
217#461—611no—
218#459—611no—
219#459—611no—
220#423—611no—
221#417—611no—
222#417—611no—
223C61#303611yescharacteristic, complemented, Sylow
224C2×#41—611no—
225C2×#41—611no—
226C22×D4—611no—
227C23×C4—1221no—
228AGL(1,ℤ/8)—1224no—
229AGL(1,ℤ/8)—1224no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×SD16—611no—
233C2×SD16C2×D6111yescharacteristic
234C2×D8—611no—
235C2×D8—611no—
236C2×D8—611no—
237C2×D8C2×D6111yescharacteristic
238C2×M16—611no—
239C2×M16—611no—
240C4⋊Q8—611no—
241#127—611no—
242#124—611no—
243#124C2×D6111yescharacteristic, complemented
244#121—1221no—
245#121—1221no—
246C4×D4—611no—
247C4×D4—611no—
248C4×D4—611no—
249C4×D4—1221no—
250C4×D4—1221no—
251C4×D4—1221no—
252C4×D4—1221no—
253C4×D4C2×D6111yescharacteristic
254C2×C4⋊C4—611no—
255C2×C22⋊C4—1221no—
256C2×C42—611no—
257C4⋊C8—611no—
258C4⋊C8—611no—
259C4⋊C8—611no—
260C4⋊C8C2×D6111yescharacteristic, complemented
261#103—611no—
262#103—611no—
263#103—611no—
264#103C2×D6111yescharacteristic, complemented
265#102—611no—
266#102—611no—
267#102—611no—
268#102C2×D6111yescharacteristic, complemented
269C24—1221no—
270#41—1222no—
271#41—1222no—
272#41—1222no—
273#41—1222no—
274C2×Q8—611no—
275C2×Q8C22×D6111yescharacteristic
276C2×D4—614no—
277C2×D4—611no—
278C2×D4—611no—
279C2×D4—1221no—
280C2×D4—1222no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4C22×D6111yescharacteristic
286C2×D4C22×D6111yescharacteristic
287C22×C4—21no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—2444no—
298SD16—22no—
299SD16—1222no—
300SD16—1222no—
301SD16—1222no—
302D8—22no—
303D8—1222no—
304D8—1222no—
305D8—1222no—
306M16—1222no—
307M16—1222no—
308C2×C8—611no—
309C2×C8—611no—
310C2×C8C22×D6111yescharacteristic
311C2×C8C22×D6111yescharacteristic
312C4⋊C4—611no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4C22×D6111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C42—611no—
326C42—611no—
327C42—611no—
328C42C22×D6111yescharacteristic
329C23—21no—
330C23—21no—
331C23—611no—
332C23—1224no—
333C23—1221no—
334C23—1221no—
335C23—2442no—
336C23—2442no—
337Q8—21no—
338Q8—21no—
339Q8—1221no—
340Q8—1221no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—612no—
345D4—1224no—
346D4—1221no—
347D4—1221no—
348D4—1221no—
349D4—2442no—
350D4—2442no—
351D4—2442no—
352D4—2442no—
353D4D4×D6112yes—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—611no—
358C2×C4—611no—
359C2×C4—612no—
360C2×C4—612no—
361C2×C4—611no—
362C2×C4—1222no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—2441no—
366C2×C4—2442no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4D4×D6111yescharacteristic
373C2×C4D4×D6111yescharacteristic
374C2×C4C23×D6111yescharacteristic
375C8—21no—
376C8—21no—
377C8—1221no—
378C8—1221no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—612no—
386C22—1221no—
387C22—1221no—
388C22—1222no—
389C22—2448no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22C2×D4×D6111yescharacteristic
396C4—21no—
397C4—21no—
398C4—41no—
399C4—41no—
400C4—612no—
401C4—612no—
402C4—1221no—
403C4—2441no—
404C4—2441no—
405C4C2×D4×D6111yescharacteristic
406C4#41×D6111yescharacteristic
407C2—42no—
408C2—81no—
409C2—1222no—
410C2—4881no—
411C2—2442no—
412C2#121×D6111yescharacteristic
413C2AGL(1,ℤ/8)×D6111yescharacteristic
414C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3036
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. C2×#14519804C2semidirect
2. C2×#14519801C2semidirect
3. #16840311C2semidirect
4. C4×D4×D61C2semidirect
5. #16839978C2semidirect
6. #16839977C2semidirect
7. #16839974C2semidirect
8. #16839966C2semidirect
9. #16839965C2semidirect
10. #16839956C2semidirect
11. #16839955C2semidirect
12. #16839784C2semidirect
13. #16839762C2semidirect
14. #16839760C2semidirect
15. C61×#463C2semidirect
30. #14519775C22semidirect
31. #14519773C22semidirect
32. #14519765C22semidirect
45. C4⋊#92418C22semidirect
46. #14519706C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519701C22semidirect
50. #14519700C22semidirect
51. #14519699C22semidirect
52. #14519698C22semidirect
53. #14519697C22semidirect
56. #124×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
77. D4×D61D4semidirect
198. Dic61AGL(1,ℤ/8)semidirect
215. #463D61semidirect
223. C61#3036semidirect
243. #124C2×D61semidirect
260. C4⋊C8C2×D61semidirect
264. #103C2×D61semidirect
268. #102C2×D61semidirect