Finite Group Databasebeta

← #21457451

Subgroups — #21457451

Order 7808.

498 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×#14519808C211yesmaximal, characteristic, complemented
2C2×#14519802C211yesmaximal, characteristic, complemented
3#16840408C211yesmaximal, characteristic, complemented
4#16840144C211yesmaximal, characteristic, complemented
5#16840018C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16839984C211yesmaximal, characteristic, complemented
8#16839974C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839912C211yesmaximal, characteristic, complemented
11#16839905C211yesmaximal, characteristic, complemented
12#16839901C211yesmaximal, characteristic, complemented
13C4×#11758201C211yesmaximal, characteristic, complemented
14#16839840C211yesmaximal, characteristic, complemented
15C61×#548C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×D244C2211yescharacteristic
18#14519808—24no—
19#14519802—24no—
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758202C2211yescharacteristic, complemented
22C2×#11758200C2211yescharacteristic, complemented
23C2×#11758201C2211yescharacteristic
24C2×#11758201C2211yescharacteristic
25C2×#11758201C2211yescharacteristic
26C2×#11758201C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C2×#11758199C2211yescharacteristic
29C2×#11758194C2211yescharacteristic
30C2×#11758194C2211yescharacteristic, complemented
31#14519765C2211yescharacteristic
32#14519762—21no—
33#14519756C2211yescharacteristic
34#14519751C2211yescharacteristic
35#14519750—21no—
36#14519745—21no—
37C4×D244C2211yescharacteristic
38C22⋊C4×D61—21no—
39#14519708C2211yescharacteristic, complemented
40C4⋊#92418C2211yescharacteristic, complemented
41#14519701C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519698C2211yescharacteristic, complemented
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47C22⋊#92418C2211yescharacteristic
48C22⋊#92418C2211yescharacteristic, complemented
49C4×#92418C2211yescharacteristic, complemented
50C2×#41×C61C2211yescharacteristic
51C22×Q8×C61C2211yescharacteristic, complemented
52#124×C61—21no—
53#124×C61C2211yescharacteristic, complemented
54C22⋊Q8×C61—21no—
55C22⋊Q8×C61C2211yescharacteristic
56#121×C61—21no—
57#121×C61C2211yescharacteristic, complemented
58C4×Q8×C61C2211yescharacteristic, complemented
59C4×D4×C61—21no—
60C4×D4×C61C2211yescharacteristic
61C23×D61—21no—
62#41×C61—22no—
63#41×C61—41no—
64C2×Q8×C61—21no—
65C2×Q8×C61—22no—
66C2×Q8×C61—41no—
67C2×Q8×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C2×D4×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61D411yescharacteristic
72C2×D4×C61C2311yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C2×C22⋊D61—21no—
78C2×C22⋊D61—21no—
79#11758222—22no—
80#11758222—41no—
81C2×D244—22no—
82C2×D244—21no—
83C2×D244—41no—
84C2×D244C2311yescharacteristic
85C2×D244C2311yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×Dic122C2311yescharacteristic
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61D411yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊C4×C61D411yescharacteristic
98C22⋊C4×C61D411yescharacteristic
99C42×C61—21no—
100C42×C61C2311yescharacteristic
101C22⋊Dic61—21no—
102#11758202—22no—
103#11758202—22no—
104#11758201—22no—
105#11758201—22no—
106#11758201—41no—
107#11758201D414yescomplemented
108#11758200—41no—
109#11758199—22no—
110#11758199—22no—
111#11758198—21no—
112#11758198—21no—
113#11758198—21no—
114#11758198—21no—
115C4⋊Dic61C2311yescharacteristic
116#11758196—21no—
117#11758194—22no—
118#11758194—22no—
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121C2×#92418C2311yescharacteristic
122C2×#92418C2311yescharacteristic
123C23×C61—21no—
124C23×C61C2×D411yescharacteristic
125C23×C61C2×D411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—81no—
131Q8×C61—21no—
132Q8×C61—21no—
133Q8×C61—21no—
134Q8×C61—42no—
135Q8×C61C2×D412yes—
136D4×C61—21no—
137D4×C61—21no—
138D4×C61—41no—
139D4×C61—42no—
140D4×C61—42no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61C2×D411yescharacteristic
151C2×C4×C61C2×D411yescharacteristic
152C2×C4×C61C2×D411yescharacteristic
153C2×C4×C61C2×D411yescharacteristic
154C2×C4×C61C2411yescharacteristic
155C22⋊D61—42no—
156C22⋊D61—81no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159D244—21no—
160D244—21no—
161D244—21no—
162D244—42no—
163D244C2×D412yes—
164C4×D61—42no—
165C4×D61—81no—
166Dic122—21no—
167Dic122—21no—
168#92418—21no—
169#92418—21no—
170#92418—21no—
171#92418C2×D412yes—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61C22×D411yescharacteristic
182C2×D61—22no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—84no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—22no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—41no—
195C4×C61—41no—
196C4×C61C22×D411yescharacteristic
197C4×C61H(5,𝔽2)11yescharacteristic
198Dic61—41no—
199Dic61—41no—
200#3275—611nomaximal, Sylow
201C2×C61—41no—
202C2×C61—41no—
203C2×C61—81no—
204C2×C61D4211yescharacteristic
205C2×C61#57511yescharacteristic
206C2×C61#57711yescharacteristic
207D61—42no—
208D61—81no—
209C2×#137—611no—
210C2×AGL(1,ℤ/8)—611no—
211#548D6111yescharacteristic, complemented
212#546—611no—
213#495—611no—
214#470—611no—
215#469—611no—
216#464—611no—
217#463—611no—
218#452—611no—
219#450—611no—
220#449—611no—
221#448—611no—
222C4×SD16—611no—
223#436—611no—
224C61#327511yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C2×#41C2×D6111yescharacteristic
227C22×Q8C2×D6111yescharacteristic, complemented
228C22×D4—611no—
229#137—1224no—
230AGL(1,ℤ/8)—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×D8—611no—
240C2×M16—611no—
241C2×M16—611no—
242#124—21no—
243#124—611no—
244#124C2×D6111yescharacteristic, complemented
245#123—1221no—
246C22⋊Q8—21no—
247C22⋊Q8—611no—
248C22⋊Q8C2×D6111yescharacteristic
249#121—21no—
250#121—611no—
251#121—1221no—
252#121C2×D6111yescharacteristic, complemented
253#120—1221no—
254C4×Q8C2×D6111yescharacteristic, complemented
255C4×D4—21no—
256C4×D4—611no—
257C4×D4C2×D6111yescharacteristic
258C2×C22⋊C4—1221no—
259#106—611no—
260C4⋊C8—611no—
261#103—611no—
262#103—611no—
263#103—611no—
264#102—611no—
265#102—611no—
266#102—611no—
267C22⋊C8—611no—
268C22⋊C8—611no—
269C4×C8—611no—
270C24—1221no—
271#41—22no—
272#41—41no—
273#41—1222no—
274#41—2441no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—611no—
279C2×Q8C22×D6111yescharacteristic
280C2×Q8C22×D6111yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—611no—
284C2×D4—611no—
285C2×D4—1222no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—2441no—
290C2×D4C22⋊D6111yescharacteristic
291C2×D4C22×D6111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4C22×D6111yescharacteristic
297C22×C4C22×D6111yescharacteristic
298Q16—1222no—
299Q16—1222no—
300SD16—614no—
301SD16—1222no—
302SD16—1222no—
303SD16—2441no—
304SD16—2441no—
305D8—1222no—
306D8—1222no—
307M16—1222no—
308M16—1222no—
309C2×C8—611no—
310C2×C8—611no—
311C2×C8—611no—
312C2×C8—611no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—611no—
316C4⋊C4—1221no—
317C4⋊C4C22⋊D6111yescharacteristic
318C4⋊C4C22×D6111yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4C22⋊D6111yescharacteristic
329C22⋊C4C22⋊D6111yescharacteristic
330C42—21no—
331C42C22×D6111yescharacteristic
332C23—21no—
333C23—1221no—
334C23—1221no—
335C23—4881no—
336C23—2442no—
337C23—2442no—
338C23C2×C22⋊D6111yescharacteristic
339C23C2×C22⋊D6111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—1221no—
345Q8—1221no—
346Q8D4×D6112yes—
347D4—21no—
348D4—21no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—612no—
353D4—1221no—
354D4—1221no—
355D4—1221no—
356D4—4881no—
357D4—2442no—
358D4—2442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—4881no—
371C2×C4—2442no—
372C2×C4C2×C22⋊D6111yescharacteristic
373C2×C4C2×C22⋊D6111yescharacteristic
374C2×C4C2×C22⋊D6111yescharacteristic
375C2×C4C2×C22⋊D6111yescharacteristic
376C2×C4C23×D6111yescharacteristic
377C8—612no—
378C8—1221no—
379C8—1221no—
380C8—1221no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—1222no—
391C22—4884no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22C22×C22⋊D6111yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—2441no—
406C4—2441no—
407C4C2×D4×D6111yescharacteristic
408C4#1451982211yescharacteristic
409C2—41no—
410C2—41no—
411C2—81no—
412C2—4881no—
413C2—2442no—
414C2D4×C22⋊D6111yescharacteristic
415C2#1684056011yescharacteristic
416C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#548C2
socleC22×C61C22×D4
hypercenter#548D61
hypocenterC61#3275
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
2. C2×#14519802C2semidirect
3. #16840408C2semidirect
4. #16840144C2semidirect
5. #16840018C2semidirect
6. #16840013C2semidirect
7. #16839984C2semidirect
8. #16839974C2semidirect
9. #16839924C2semidirect
10. #16839912C2semidirect
11. #16839905C2semidirect
12. #16839901C2semidirect
13. C4×#11758201C2semidirect
14. #16839840C2semidirect
15. C61×#548C2semidirect
20. C2×#11758202C22semidirect
21. C2×#11758202C22semidirect
22. C2×#11758200C22semidirect
30. C2×#11758194C22semidirect
39. #14519708C22semidirect
40. C4⋊#92418C22semidirect
41. #14519701C22semidirect
42. #14519701C22semidirect
43. #14519700C22semidirect
44. #14519698C22semidirect
48. C22⋊#92418C22semidirect
49. C4×#92418C22semidirect
51. C22×Q8×C61C22semidirect
53. #124×C61C22semidirect
57. #121×C61C22semidirect
58. C4×Q8×C61C22semidirect
107. #11758201D4semidirect
211. #548D61semidirect
224. C61#3275semidirect
227. C22×Q8C2×D61semidirect
244. #124C2×D61semidirect
252. #121C2×D61semidirect
254. C4×Q8C2×D61semidirect