Finite Group Databasebeta

← #21457342

Subgroups — #21457342

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×#14519803C211yesmaximal, characteristic, complemented
2C2×#14519798C211yesmaximal, characteristic, complemented
3#16840414C211yesmaximal, characteristic, complemented
4#16840406C211yesmaximal, characteristic, complemented
5#16840153C211yesmaximal, characteristic, complemented
6#16840018C211yesmaximal, characteristic, complemented
7#16839990C211yesmaximal, characteristic, complemented
8#16839976C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839925C211yesmaximal, characteristic, complemented
12#16839906C211yesmaximal, characteristic, complemented
13#16839871C211yesmaximal, characteristic, complemented
14#16839836C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic, complemented
17C2×#11758222C2211yescharacteristic
18C2×#11758224C2211yescharacteristic
19#14519803—24no—
20#14519798—24no—
21C2×Dic244C2211yescharacteristic, complemented
22C2×#11758202C2211yescharacteristic, complemented
23C2×#11758190C2211yescharacteristic, complemented
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C2×#11758194C2211yescharacteristic
29C2×C8×D61C2211yescharacteristic, complemented
30#14519775C2211yescharacteristic, complemented
31#14519764C2211yescharacteristic
32#14519762—21no—
33#14519759—21no—
34#14519758—21no—
35#14519757C2211yescharacteristic, complemented
36#14519756C2211yescharacteristic
37#14519750—21no—
38#14519749—21no—
39#14519748C2211yescharacteristic
40#14519746—21no—
41D4×Dic61C2211yescharacteristic
42#14519739C2211yescharacteristic, complemented
43C4×C22⋊D61C2211yescharacteristic
44C4⋊C4×D61—21no—
45C2×C22⋊Dic61—21no—
46#14519708C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519701C2211yescharacteristic, complemented
50#14519700C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519687C2211yescharacteristic, complemented
54C22×D4×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56C2×SD16×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59#102×C61C2211yescharacteristic
60C22⋊C8×C61C2211yescharacteristic
61C24×C61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—22no—
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75#11758226—22no—
76#11758226—41no—
77#11758224—22no—
78#11758224—41no—
79#11758222—22no—
80#11758222—41no—
81C2×D244—21no—
82C2×D244C2311yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88C2×Dic122C2311yescharacteristic
89SD16×C61—22no—
90SD16×C61—41no—
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C4⋊C4×C61—21no—
94C4⋊C4×C61C2311yescharacteristic
95C22⋊C4×C61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61D411yescharacteristic
102#11758202—22no—
103#11758200—22no—
104#11758200—22no—
105#11758199—22no—
106#11758199D414yescomplemented
107#11758198—21no—
108#11758198—21no—
109#11758198D411yescharacteristic
110C4⋊Dic61—21no—
111C4⋊Dic61C2311yescharacteristic
112#11758196—21no—
113#11758196—21no—
114#11758196—21no—
115#11758196D411yescharacteristic
116C4×Dic61C2311yescharacteristic
117#11758194—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120Dic244—41no—
121#11758190—22no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—42no—
126C23×C61—42no—
127C23×C61—81no—
128C23×C61C2×D411yescharacteristic
129C22×D61—21no—
130C22×D61C2×D411yescharacteristic
131Q8×C61—21no—
132Q8×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—42no—
137D4×C61C2×D412yes—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2411yescharacteristic
144C22⋊D61—41no—
145C22⋊D61—42no—
146C22⋊D61—42no—
147C22⋊D61—81no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61—81no—
153C2×Dic61C2×D411yescharacteristic
154C2×Dic61C2×D411yescharacteristic
155C2×Dic61C2×D411yescharacteristic
156D244—21no—
157D244—42no—
158D244C2×D412yes—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—42no—
162C4×D61—42no—
163C4×D61—42no—
164Dic122—21no—
165Dic122—21no—
166Dic122—21no—
167Dic122—21no—
168C8×C61—21no—
169C8×C61—21no—
170#92418—21no—
171#92418C2×D412yes—
172C22×C61—22no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—84no—
182C22×C61C22×D411yescharacteristic
183C2×D61—21no—
184C2×D61—22no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—41no—
188C2×D61—41no—
189C4×C61—21no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61C22×D411yescharacteristic
193C4×C61H(5,𝔽2)11yescharacteristic
194Dic61—21no—
195Dic61—21no—
196Dic61—21no—
197Dic61—41no—
198Dic61—41no—
199Dic61—41no—
200#3267—611nomaximal, Sylow
201C2×C61—41no—
202C2×C61—42no—
203C2×C61—81no—
204C2×C61D4211yescharacteristic
205C2×C61#57511yescharacteristic
206C2×C61#57711yescharacteristic
207D61—41no—
208D61—42no—
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#450D6111yescharacteristic, complemented
221#449—611no—
222#442—611no—
223#435—611no—
224C61#326711yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C2×#41—611no—
227C2×#41—611no—
228C22×D4C2×D6111yescharacteristic
229AGL(1,ℤ/8)—1224no—
230#135—1224no—
231C2×Q16—611no—
232C2×Q16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—611no—
236C2×SD16C2×D6111yescharacteristic
237C2×SD16C2×D6111yescharacteristic
238C2×D8—611no—
239C2×D8—611no—
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⋊Q8C2×D6111yescharacteristic
250#121—611no—
251#121—1221no—
252#121—1221no—
253#120—1221no—
254C4×D4—611no—
255C4×D4—611no—
256C4×D4—611no—
257C2×C4⋊C4—1221no—
258C2×C22⋊C4—1221no—
259#106—611no—
260C4⋊C8—611no—
261#103—611no—
262#103—611no—
263#103—611no—
264#102—611no—
265#102C2×D6111yescharacteristic
266#102C2×D6111yescharacteristic
267C22⋊C8—611no—
268C22⋊C8C2×D6111yescharacteristic
269#97—611no—
270C24—21no—
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×Q8C22×D6111yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—611no—
284C2×D4—611no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4C22×D6111yescharacteristic
290C2×D4C22×D6111yescharacteristic
291C22×C4—611no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4C22×D6111yescharacteristic
298Q16—1222no—
299Q16—2441no—
300SD16—22no—
301SD16—41no—
302SD16—1222no—
303SD16—1222no—
304SD16—1222no—
305D8—614no—
306D8—1222no—
307M16—1222no—
308C2×C8—611no—
309C2×C8—611no—
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⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4C22×D6111yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—611no—
323C22⋊C4—611no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C22⋊C4—1221no—
331C42—611no—
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—611no—
338C23—1221no—
339C23D4×D6111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—1221no—
343Q8—1221no—
344Q8—1221no—
345Q8—1221no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—612no—
351D4—1221no—
352D4—4881no—
353D4—2442no—
354D4—2441no—
355D4—2442no—
356D4—2442no—
357D4D4×D6112yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—4881no—
371C2×C4—2442no—
372C2×C4—2442no—
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—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—1221no—
392C22—1221no—
393C22—1221no—
394C22—1222no—
395C22—2441no—
396C22—2441no—
397C22C2×D4×D6111yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—1221no—
402C4—1221no—
403C4—1221no—
404C4—2441no—
405C4—2441no—
406C4—2441no—
407C4C2×D4×D6111yescharacteristic
408C4#1451982211yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—2441no—
413C2—2442no—
414C2#1684039411yescharacteristic
415C2#1684055811yescharacteristic
416C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3267
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#14519803C2semidirect
2. C2×#14519798C2semidirect
3. #16840414C2semidirect
4. #16840406C2semidirect
5. #16840153C2semidirect
6. #16840018C2semidirect
7. #16839990C2semidirect
8. #16839976C2semidirect
9. #16839965C2semidirect
10. #16839926C2semidirect
11. #16839925C2semidirect
12. #16839906C2semidirect
13. #16839871C2semidirect
14. #16839836C2semidirect
15. C61×#450C2semidirect
16. C2×#11758226C22semidirect
21. C2×Dic244C22semidirect
22. C2×#11758202C22semidirect
23. C2×#11758190C22semidirect
29. C2×C8×D61C22semidirect
30. #14519775C22semidirect
35. #14519757C22semidirect
42. #14519739C22semidirect
46. #14519708C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519701C22semidirect
50. #14519700C22semidirect
51. #14519699C22semidirect
52. #14519689C22semidirect
53. #14519687C22semidirect
106. #11758199D4semidirect
220. #450D61semidirect
224. C61#3267semidirect