Finite Group Databasebeta

← #21457346

Subgroups — #21457346

Order 7808.

500 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×#14519801C211yesmaximal, characteristic, complemented
2C2×#14519796C211yesmaximal, characteristic, complemented
3#16840416C211yesmaximal, characteristic, complemented
4#16840407C211yesmaximal, characteristic, complemented
5#16840156C211yesmaximal, characteristic, complemented
6#16840021C211yesmaximal, characteristic, complemented
7#16839992C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839967C211yesmaximal, characteristic, complemented
10#16839925C211yesmaximal, characteristic, complemented
11#16839925C211yesmaximal, characteristic, complemented
12#16839914C211yesmaximal, characteristic, complemented
13#16839908C211yesmaximal, characteristic, complemented
14#16839835C211yesmaximal, characteristic, complemented
15C61×#442C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758224C2211yescharacteristic, complemented
19C2×D4×D61C2211yescharacteristic
20#14519801—24no—
21#14519796—24no—
22C2×Dic244C2211yescharacteristic, complemented
23C2×Dic244C2211yescharacteristic, complemented
24C2×#11758190C2211yescharacteristic
25C2×#11758190C2211yescharacteristic
26C2×#11758200C2211yescharacteristic
27C2×#11758200C2211yescharacteristic
28C2×#11758200C2211yescharacteristic, complemented
29C2×#11758199C2211yescharacteristic
30C2×#11758189C2211yescharacteristic
31C2×C8×D61C2211yescharacteristic, complemented
32#14519777C2211yescharacteristic, complemented
33#14519765C2211yescharacteristic
34#14519761—21no—
35#14519761—21no—
36#14519761—21no—
37#14519757C2211yescharacteristic
38#14519757C2211yescharacteristic
39#14519757C2211yescharacteristic, complemented
40#14519752C2211yescharacteristic
41#14519751—21no—
42#14519751—21no—
43#14519747—21no—
44C4×D244C2211yescharacteristic
45C2×C4⋊Dic61—21no—
46C2×#11758198—21no—
47C4⋊#92418C2211yescharacteristic, complemented
48#14519700C2211yescharacteristic, complemented
49#14519700C2211yescharacteristic, complemented
50#14519700C2211yescharacteristic, complemented
51#14519697C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519689C2211yescharacteristic, complemented
54C2×D8×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic, complemented
57#106×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59#102×C61C2211yescharacteristic, complemented
60#97×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
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—
72C22×Dic61—21no—
73#11758224—22no—
74#11758224—22no—
75#11758224—22no—
76#11758224—41no—
77#11758224—41no—
78#11758224—41no—
79D4×D61—22no—
80D4×D61—41no—
81C2×D244—21no—
82C2×D244D411yescharacteristic
83C2×D244C2311yescharacteristic
84C2×C4×D61C2311yescharacteristic
85C2×C4×D61C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88C2×Dic122C2311yescharacteristic
89D8×C61D414yescomplemented
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C4⋊C4×C61C2311yescharacteristic
94C22⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C42×C61C2311yescharacteristic
97#11758200—22no—
98#11758200—22no—
99#11758200—22no—
100#11758199—22no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198D411yescharacteristic
108#11758198D411yescharacteristic
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61D411yescharacteristic
115C2×#92418C2311yescharacteristic
116C2×#92418C2311yescharacteristic
117Dic244—22no—
118Dic244—41no—
119#11758190—22no—
120#11758190—41no—
121#11758189—22no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61—21no—
125C22×D61—21no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—81no—
129C22×D61C2×D411yescharacteristic
130C22×D61C2×D411yescharacteristic
131D4×C61—21no—
132D4×C61—21no—
133D4×C61C2×D412yes—
134D4×C61C2×D412yes—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—42no—
138C2×C4×C61—81no—
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2×D411yescharacteristic
141C2×C4×C61C2411yescharacteristic
142C22⋊D61—42no—
143C22⋊D61—42no—
144C22⋊D61—42no—
145C22⋊D61—42no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61C2×D411yescharacteristic
153C2×Dic61C2×D411yescharacteristic
154D244—21no—
155D244—21no—
156D244—41no—
157D244—81no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—21no—
162Dic122—21no—
163Dic122—21no—
164Dic122—21no—
165Dic122—21no—
166Dic122—21no—
167Dic122—21no—
168C8×C61—21no—
169C8×C61C2×D412yes—
170#92418—21no—
171#92418—21no—
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61C22×D411yescharacteristic
179C2×D61—21no—
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—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61C22×D411yescharacteristic
194C4×C61H(5,𝔽2)11yescharacteristic
195Dic61—21no—
196Dic61—21no—
197Dic61—41no—
198Dic61—41no—
199Dic61—41no—
200#3267—611nomaximal, Sylow
201C2×C61—42no—
202C2×C61—42no—
203C2×C61D4211yescharacteristic
204C2×C61#57511yescharacteristic
205C2×C61#57711yescharacteristic
206D61—41no—
207D61—41no—
208D61—81no—
209C2×AGL(1,ℤ/8)—611no—
210C2×#135—611no—
211#547—611no—
212#546—611no—
213#497—611no—
214#470—611no—
215#465—611no—
216#463—611no—
217#461—611no—
218#452—611no—
219#452—611no—
220#450—611no—
221#449—611no—
222#442D6111yescharacteristic, complemented
223#435—611no—
224C61#326711yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C2×#41—611no—
227C2×#41—611no—
228C22×D4—611no—
229AGL(1,ℤ/8)—1224no—
230#135—1224no—
231C2×Q16—611no—
232C2×Q16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—611no—
236C2×SD16—611no—
237C2×SD16—611no—
238C2×D8—611no—
239C2×D8C2×D6111yescharacteristic
240C2×M16—611no—
241C22×C8—611no—
242C4⋊Q8—611no—
243#124—611no—
244#123—1221no—
245#123—1221no—
246#123—1221no—
247C22⋊Q8—611no—
248C22⋊Q8—611no—
249C22⋊Q8—611no—
250#121—611no—
251#121—1221no—
252#121—1221no—
253#120—1221no—
254C4×D4—611no—
255C4×D4C2×D6111yescharacteristic
256C4×D4C2×D6111yescharacteristic, complemented
257C2×C4⋊C4—1221no—
258C2×C22⋊C4—1221no—
259#106C2×D6111yescharacteristic, complemented
260C4⋊C8—611no—
261#103—611no—
262#103—611no—
263#103—611no—
264#102—611no—
265#102C2×D6111yescharacteristic
266#102C2×D6111yescharacteristic, complemented
267C22⋊C8—611no—
268C22⋊C8—611no—
269#97C2×D6111yescharacteristic, complemented
270C24—1221no—
271#41—1222no—
272#41—1222no—
273#41—1222no—
274#41—2441no—
275#41—2441no—
276#41—2441no—
277C2×Q8—611no—
278C2×Q8—611no—
279C2×Q8—611no—
280C2×D4—611no—
281C2×D4—611no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1222no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—2441no—
289C2×D4C22×D6111yescharacteristic
290C2×D4C22×D6111yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298Q16—1222no—
299Q16—2441no—
300SD16—1222no—
301SD16—1222no—
302SD16—1222no—
303SD16—1222no—
304SD16—2441no—
305D8—1222no—
306D8D24414yescomplemented
307M16—1222no—
308C2×C8—611no—
309C2×C8—611no—
310C2×C8—1222no—
311C2×C8C22×D6111yescharacteristic
312C2×C8C22×D6111yescharacteristic
313C4⋊C4—611no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4C22×D6111yescharacteristic
320C4⋊C4C22×D6111yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—611no—
324C22⋊C4—611no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C22⋊C4—1221no—
331C42C22×D6111yescharacteristic
332C23—21no—
333C23—21no—
334C23—611no—
335C23—611no—
336C23—1221no—
337C23—4881no—
338C23—2442no—
339C23—2442no—
340Q8—1221no—
341Q8—1221no—
342Q8—1221no—
343Q8—1221no—
344Q8—1221no—
345Q8—1221no—
346D4—21no—
347D4—21no—
348D4—1221no—
349D4—1221no—
350D4—4881no—
351D4—2441no—
352D4—2442no—
353D4—2442no—
354D4—2442no—
355D4—2442no—
356D4C2×D24412yes—
357D4C2×D24412yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4—2442no—
374C2×C4D4×D6111yescharacteristic
375C2×C4D4×D6111yescharacteristic
376C2×C4C23×D6111yescharacteristic
377C8—21no—
378C8—1221no—
379C8—1221no—
380C8C2×D24412yes—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—1221no—
388C22—1221no—
389C22—1221no—
390C22—1221no—
391C22—1221no—
392C22—1221no—
393C22—4884no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22C2×D4×D6111yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—1221no—
403C4—1221no—
404C4—2441no—
405C4—2441no—
406C4—2441no—
407C4C22×D24411yescharacteristic
408C4#1451982311yescharacteristic
409C2—42no—
410C2—42no—
411C2—4881no—
412C2—2441no—
413C2—2441no—
414C2D4×D24411yescharacteristic
415C2#1684055811yescharacteristic
416C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#3267
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. C2×#14519796C2semidirect
3. #16840416C2semidirect
4. #16840407C2semidirect
5. #16840156C2semidirect
6. #16840021C2semidirect
7. #16839992C2semidirect
8. #16839977C2semidirect
9. #16839967C2semidirect
10. #16839925C2semidirect
11. #16839925C2semidirect
12. #16839914C2semidirect
13. #16839908C2semidirect
14. #16839835C2semidirect
15. C61×#442C2semidirect
18. C2×#11758224C22semidirect
22. C2×Dic244C22semidirect
23. C2×Dic244C22semidirect
28. C2×#11758200C22semidirect
31. C2×C8×D61C22semidirect
32. #14519777C22semidirect
39. #14519757C22semidirect
47. C4⋊#92418C22semidirect
48. #14519700C22semidirect
49. #14519700C22semidirect
50. #14519700C22semidirect
53. #14519689C22semidirect
56. C4×D4×C61C22semidirect
57. #106×C61C22semidirect
59. #102×C61C22semidirect
60. #97×C61C22semidirect
89. D8×C61D4semidirect
222. #442D61semidirect
224. C61#3267semidirect
256. C4×D4C2×D61semidirect
259. #106C2×D61semidirect
266. #102C2×D61semidirect
269. #97C2×D61semidirect
306. D8D244semidirect