Finite Group Databasebeta

← #21455498

Subgroups — #21455498

Order 7808.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519801C211yesmaximal, characteristic, complemented
2C2×#14519783C211yesmaximal, characteristic, complemented
3#16840341C211yesmaximal, characteristic, complemented
4#16840328C211yesmaximal, characteristic, complemented
5#16840013C211yesmaximal, characteristic, complemented
6#16840012C211yesmaximal, characteristic, complemented
7#16840009C211yesmaximal, characteristic, complemented
8#16840006C211yesmaximal, characteristic, complemented
9#16839997C211yesmaximal, characteristic, complemented
10#16839991C211yesmaximal, characteristic, complemented
11#16839990C211yesmaximal, characteristic, complemented
12#16839803C211yesmaximal, characteristic, complemented
13#16839755C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#466C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19#14519801—24no—
20C2×#11758190C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23#14519783—24no—
24C2×#11758194C2211yescharacteristic, complemented
25C2×#11758189C2211yescharacteristic
26C2×#11758189C2211yescharacteristic, complemented
27C2×C8×D61C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic, complemented
29#14519773—21no—
30#14519763—21no—
31#14519757C2211yescharacteristic, complemented
32#14519756C2211yescharacteristic, complemented
33#14519754—21no—
34#14519752C2211yescharacteristic
35#14519751C2211yescharacteristic
36#14519750—21no—
37#14519749—21no—
38#14519748—21no—
39#14519748C2211yescharacteristic
40#14519748C2211yescharacteristic, complemented
41#14519747—21no—
42#14519745—21no—
43#14519735C2211yescharacteristic
44C4⋊C4×D61C2211yescharacteristic
45#14519710C2211yescharacteristic, complemented
46#14519709C2211yescharacteristic, complemented
47#14519708C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519700C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic
51#14519698C2211yescharacteristic
52#14519698C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55C22×C8×C61C2211yescharacteristic, complemented
56#121×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic, complemented
58#107×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—21no—
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
74C22×Dic61—21no—
75#11758224—22no—
76#11758224—22no—
77D4×D61—22no—
78D4×D61—22no—
79#11758222—22no—
80#11758222—22no—
81C2×D244—21no—
82C2×D244D411yescharacteristic
83C2×D244C2311yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61C2311yescharacteristic
86C2×C4×D61C2311yescharacteristic
87C2×Dic122D411yescharacteristic
88C2×Dic122C2311yescharacteristic
89D8×C61—22no—
90C2×C8×C61—22no—
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C4⋊C4×C61C2311yescharacteristic
94C4⋊C4×C61C2311yescharacteristic
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100#11758200—22no—
101#11758199—22no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61C2311yescharacteristic
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196—21no—
111C4×Dic61—21no—
112#11758194—22no—
113C2×#92418C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115#11758190—22no—
116#11758189—22no—
117#11758189D414yescomplemented
118C8×D61—22no—
119C8×D61—22no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61C2×D411yescharacteristic
123C22×D61—21no—
124C22×D61—42no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61C2×D411yescharacteristic
128C22×D61C2×D411yescharacteristic
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×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2411yescharacteristic
141C22⋊D61—22no—
142C22⋊D61—22no—
143C22⋊D61—42no—
144C22⋊D61—42no—
145C22⋊D61—81no—
146C22⋊D61—81no—
147C22⋊D61—81no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61C2×D411yescharacteristic
153C2×Dic61C2×D411yescharacteristic
154D244—22no—
155D244—21no—
156D244—21no—
157D244—81no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—81no—
161C4×D61C2×D412yes—
162C4×D61#4112yes—
163Dic122—22no—
164Dic122—21no—
165Dic122—21no—
166C8×C61—21no—
167C8×C61C2×D412yes—
168#92418—21no—
169#92418C2×D412yes—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61C22×D411yescharacteristic
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—84no—
189C2×D61#12112yes—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61C22×D411yescharacteristic
194C4×C61C2×#4111yescharacteristic
195Dic61—21no—
196Dic61—41no—
197Dic61—41no—
198Dic61—41no—
199Dic61#12112yes—
200#3062—611nomaximal, Sylow
201C2×C61—41no—
202C2×C61—81no—
203C2×C61—81no—
204C2×C61C2×#12111yescharacteristic
205C2×C61#57611yescharacteristic
206C2×C61#57711yescharacteristic
207D61—22no—
208D61—41no—
209D61—81no—
210C2×AGL(1,ℤ/8)—611no—
211C2×#131—611no—
212#537—611no—
213#535—611no—
214#469—611no—
215#469—611no—
216#468—611no—
217#468—611no—
218#466—611no—
219#466D6111yescharacteristic, complemented
220#465—611no—
221#465—611no—
222#428—611no—
223#416—611no—
224C2×#102—611no—
225C61#306211yescharacteristic, complemented, Sylow
226C2×#41—611no—
227C2×#41—611no—
228C22×D4—611no—
229AGL(1,ℤ/8)—1224no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×D8—611no—
233C2×D8C2×D6111yescharacteristic
234#131—1224no—
235C2×M16—611no—
236C2×M16—611no—
237C2×M16—611no—
238C22×C8—611no—
239C22×C8—611no—
240C22×C8C2×D6111yescharacteristic, complemented
241#127—1221no—
242#124—1221no—
243C22⋊Q8—611no—
244C22⋊Q8—611no—
245C22⋊Q8—1221no—
246#121—611no—
247#121—611no—
248#121—611no—
249#121—611no—
250#121—1221no—
251#121—1221no—
252#121—1221no—
253#121C2×D6111yescharacteristic
254#121C2×D6111yescharacteristic, complemented
255#120—1221no—
256#120—1221no—
257#117—611no—
258C2×C4⋊C4—611no—
259#107—611no—
260#107C2×D6111yescharacteristic, complemented
261#106—611no—
262#106—611no—
263#103—611no—
264#103—611no—
265#102—611no—
266#102—611no—
267#102—611no—
268#102—611no—
269#102C2×D6111yescharacteristic
270#102C2×D6111yescharacteristic, complemented
271C24—1221no—
272#41—1222no—
273#41—1222no—
274#41—1222no—
275#41—1222no—
276C2×Q8—611no—
277C2×Q8—611no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—611no—
281C2×D4—611no—
282C2×D4—611no—
283C2×D4—611no—
284C2×D4—1221no—
285C2×D4—1222no—
286C2×D4—1222no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4C22×D6111yescharacteristic
293C2×D4C22×D6111yescharacteristic
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4C22×D6111yescharacteristic
299SD16—1222no—
300SD16—1222no—
301D8—22no—
302D8—1222no—
303M16—614no—
304M16—1222no—
305M16—1222no—
306C2×C8—22no—
307C2×C8—611no—
308C2×C8—611no—
309C2×C8—1222no—
310C2×C8—1222no—
311C2×C8C22×D6111yescharacteristic
312C2×C8C22×D6111yescharacteristic
313C4⋊C4—611no—
314C4⋊C4—611no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4C22×D6111yescharacteristic
319C4⋊C4C22×D6111yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C42—1221no—
330C23—21no—
331C23—21no—
332C23—611no—
333C23—611no—
334C23—1221no—
335C23—4881no—
336C23—4881no—
337C23—2442no—
338C23D4×D6111yescharacteristic
339Q8—1222no—
340Q8—1221no—
341Q8—1221no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—81no—
347D4—81no—
348D4—1222no—
349D4—1222no—
350D4—1222no—
351D4—1221no—
352D4—1221no—
353D4—4881no—
354D4—4881no—
355D4—4881no—
356D4—4881no—
357D4—2442no—
358D4—2442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—611no—
364C2×C4—612no—
365C2×C4—612no—
366C2×C4—611no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—4881no—
373C2×C4—2442no—
374C2×C4D4×D6111yescharacteristic
375C2×C4C23×D6111yescharacteristic
376C8—21no—
377C8—612no—
378C8—1221no—
379C8D4×D6112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—612no—
390C22—1221no—
391C22—1221no—
392C22—1221no—
393C22—1221no—
394C22—1221no—
395C22—4884no—
396C22—2441no—
397C22—2441no—
398C22—2441no—
399C22C2×D4×D6111yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—612no—
404C4—1221no—
405C4—2441no—
406C4—2441no—
407C4—2441no—
408C4C2×D4×D6111yescharacteristic
409C4#41×D6111yescharacteristic
410C2—41no—
411C2—81no—
412C2—81no—
413C2—1222no—
414C2—4881no—
415C2—2441no—
416C2#121×D6111yescharacteristic
417C2#1684056311yescharacteristic
418C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#466C2
socleC22×C61C22×D4
hypercenter#466D61
hypocenterC61#3062
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. C2×#14519783C2semidirect
3. #16840341C2semidirect
4. #16840328C2semidirect
5. #16840013C2semidirect
6. #16840012C2semidirect
7. #16840009C2semidirect
8. #16840006C2semidirect
9. #16839997C2semidirect
10. #16839991C2semidirect
11. #16839990C2semidirect
12. #16839803C2semidirect
13. #16839755C2semidirect
14. #102×D61C2semidirect
15. C61×#466C2semidirect
24. C2×#11758194C22semidirect
26. C2×#11758189C22semidirect
28. C2×C8×D61C22semidirect
31. #14519757C22semidirect
32. #14519756C22semidirect
40. #14519748C22semidirect
45. #14519710C22semidirect
46. #14519709C22semidirect
47. #14519708C22semidirect
48. #14519702C22semidirect
49. #14519700C22semidirect
52. #14519698C22semidirect
55. C22×C8×C61C22semidirect
57. #121×C61C22semidirect
58. #107×C61C22semidirect
60. #102×C61C22semidirect
117. #11758189D4semidirect
219. #466D61semidirect
225. C61#3062semidirect
240. C22×C8C2×D61semidirect
254. #121C2×D61semidirect
260. #107C2×D61semidirect
270. #102C2×D61semidirect