Finite Group Databasebeta

← #21456294

Subgroups — #21456294

Order 7808.

564 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic, complemented
2C2×#14519804C211yesmaximal, characteristic, complemented
3C2×#14519800C211yesmaximal, characteristic, complemented
4C2×SD16×D61C211yesmaximal, characteristic, complemented
5#16840337C211yesmaximal, characteristic, complemented
6#16840330C211yesmaximal, characteristic, complemented
7#16840155C211yesmaximal, characteristic, complemented
8#16840151C211yesmaximal, characteristic, complemented
9#16840148C211yesmaximal, characteristic, complemented
10#16840147C211yesmaximal, characteristic, complemented
11#16840144C211yesmaximal, characteristic, complemented
12#16840136C211yesmaximal, characteristic, complemented
13#16840133C211yesmaximal, characteristic, complemented
14#16839719C211yesmaximal, characteristic, complemented
15C61×#497C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758226C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×D4×D61C2211yescharacteristic
20#14519809—24no—
21#14519804—24no—
22#14519800—24no—
23C2×#11758202C2211yescharacteristic, complemented
24C2×#11758190C2211yescharacteristic
25C2×#11758190C2211yescharacteristic, complemented
26C2×#11758200C2211yescharacteristic
27C2×#11758201C2211yescharacteristic
28C2×#11758201C2211yescharacteristic
29C2×#11758201C2211yescharacteristic, complemented
30C2×#11758201C2211yescharacteristic, complemented
31C2×#11758201C2211yescharacteristic, complemented
32SD16×D61—24no—
33C2×D488C2211yescharacteristic
34C2×D488C2211yescharacteristic, complemented
35C2×#11758199C2211yescharacteristic
36C2×#11758189C2211yescharacteristic
37C2×C8×D61C2211yescharacteristic
38#14519775C2211yescharacteristic, complemented
39#14519774C2211yescharacteristic
40#14519773C2211yescharacteristic
41#14519766C2211yescharacteristic
42#14519766C2211yescharacteristic, complemented
43#14519765C2211yescharacteristic, complemented
44#14519762—22no—
45#14519755—22no—
46#14519750—22no—
47#14519747—22no—
48#14519734C2211yescharacteristic
49#14519687C2211yescharacteristic, complemented
50C4×#92418C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×Q16×C61C2211yescharacteristic, complemented
53C2×Q16×C61C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56C4⋊Q8×C61C2211yescharacteristic, complemented
57#124×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—22no—
66#11758226—22no—
67#11758226—22no—
68#11758226—22no—
69#11758226—22no—
70Q8×D61—22no—
71Q8×D61—22no—
72D4×D61—22no—
73D4×D61—22no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—22no—
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61C2311yescharacteristic
84C2×Dic122—21no—
85C2×Dic122C2311yescharacteristic
86Q16×C61—22no—
87Q16×C61—22no—
88SD16×C61—22no—
89SD16×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—22no—
93C22⋊C4×C61—22no—
94C42×C61C2311yescharacteristic
95#11758202—22no—
96#11758201—22no—
97#11758201—22no—
98#11758201—22no—
99#11758201—22no—
100#11758201—22no—
101#11758200—22no—
102#11758199—22no—
103#11758198—22no—
104#11758198—22no—
105#11758198—22no—
106#11758198D412yes—
107#11758196—22no—
108#11758196D412yes—
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112D488—22no—
113D488—22no—
114#11758190—22no—
115#11758190—22no—
116#11758189D414yescomplemented
117C8×D61D414yescomplemented
118C23×C61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—42no—
123C22×D61—82no—
124C22×D61C2×D411yescharacteristic
125Q8×C61—21no—
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131D4×C61—21no—
132D4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61C2×D412yes—
137C2×C4×C61C2411yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—82no—
140C2×Dic61—21no—
141C2×Dic61C2×D412yes—
142C2×Dic61C2×D411yescharacteristic
143D244—21no—
144D244—21no—
145D244—21no—
146D244—21no—
147D244—21no—
148D244—21no—
149D244—42no—
150D244—42no—
151D244—82no—
152C4×D61—42no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61C2×D412yes—
156C4×D61C2×D412yes—
157Dic122—21no—
158Dic122—21no—
159Dic122—42no—
160C8×C61C2×D412yes—
161C8×C61C2×D412yes—
162#92418C2×D412yes—
163#92418C2×D412yes—
164C22×C61—41no—
165C22×C61—42no—
166C22×C61C22×D411yescharacteristic
167C2×D61—22no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—42no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61—84no—
175C2×D61#12712yes—
176C4×C61—22no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61C22×D411yescharacteristic
181C4×C61C22×D411yescharacteristic
182Dic61—22no—
183Dic61—41no—
184Dic61#12712yes—
185#3154—611nomaximal, Sylow
186C2×C61—81no—
187C2×C61C2×#12711yescharacteristic
188C2×C61#57712yes—
189D61—22no—
190D61—81no—
191D61—81no—
192D61—81no—
193C2×#137—611no—
194C2×AGL(1,ℤ/8)—611no—
195C2×#135—611no—
196C22×SD16—611no—
197#536—611no—
198#535—611no—
199#497—611no—
200#497D6111yescharacteristic, complemented
201#496—611no—
202#496—611no—
203#495—611no—
204#495—611no—
205#492—611no—
206#492—611no—
207#405—611no—
208C61#315411yescharacteristic, complemented, Sylow
209C2×#41—611no—
210C2×#41—611no—
211C22×Q8—611no—
212C22×D4—611no—
213#137—1224no—
214AGL(1,ℤ/8)—1224no—
215#135—1224no—
216C2×Q16—611no—
217C2×Q16C2×D6111yescharacteristic, complemented
218C2×Q16C2×D6111yescharacteristic, complemented
219C2×SD16—611no—
220C2×SD16—611no—
221C2×SD16—611no—
222C2×SD16—611no—
223C2×SD16—611no—
224C2×SD16—611no—
225C2×SD16—611no—
226C2×SD16—611no—
227C2×SD16—1224no—
228C2×SD16C2×D6111yescharacteristic
229C2×SD16C2×D6111yescharacteristic
230C2×D8—611no—
231C2×D8—611no—
232C2×D8—611no—
233C2×M16—611no—
234C22×C8—611no—
235C4⋊Q8—611no—
236C4⋊Q8C2×D6111yescharacteristic, complemented
237#127—611no—
238#127—611no—
239#124—611no—
240#124—611no—
241#124—611no—
242#124C2×D6111yescharacteristic
243#123—1222no—
244C22⋊Q8—1222no—
245#121—1222no—
246#120—1222no—
247#117—611no—
248#97—611no—
249#97C2×D6111yescharacteristic, complemented
250C4×C8—611no—
251C4×C8—611no—
252C24—1221no—
253#41—1222no—
254#41—1222no—
255#41—1222no—
256#41—1222no—
257C2×Q8—611no—
258C2×Q8—1221no—
259C2×Q8—1222no—
260C2×Q8—1222no—
261C2×Q8C22×D6111yescharacteristic
262C2×Q8C22×D6111yescharacteristic
263C2×Q8C22×D6111yescharacteristic
264C2×D4—611no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1222no—
270C2×D4—1222no—
271C2×D4—1222no—
272C2×D4—1221no—
273C2×D4—1222no—
274C2×D4C22×D6111yescharacteristic
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279Q16—22no—
280Q16—22no—
281Q16—1222no—
282SD16—22no—
283SD16—22no—
284SD16—1222no—
285SD16—1222no—
286SD16—1222no—
287SD16—1222no—
288SD16—1222no—
289SD16—1222no—
290SD16—1222no—
291SD16—1222no—
292D8—1222no—
293D8—1222no—
294D8—1222no—
295M16—614no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—614no—
299C2×C8C22×D6111yescharacteristic
300C2×C8C22×D6111yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—612no—
303C4⋊C4—1222no—
304C22⋊C4—22no—
305C22⋊C4—612no—
306C22⋊C4—1222no—
307C22⋊C4—1222no—
308C22⋊C4—1222no—
309C42—611no—
310C42C22×D6111yescharacteristic
311C23—21no—
312C23—611no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—4882no—
317C23—2442no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—1221no—
325Q8—1221no—
326Q8—2442no—
327D4—21no—
328D4—21no—
329D4—1221no—
330D4—1221no—
331D4—1221no—
332D4—1221no—
333D4—1221no—
334D4—1221no—
335D4—4882no—
336D4—4882no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—611no—
344C2×C4—612no—
345C2×C4—612no—
346C2×C4—612no—
347C2×C4—1221no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4D4×D6112yes—
352C2×C4C23×D6111yescharacteristic
353C8—612no—
354C8—612no—
355C8D4×D6112yes—
356C8D4×D6112yes—
357C22—41no—
358C22—42no—
359C22—612no—
360C22—1222no—
361C22—4884no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2442no—
366C22—2442no—
367C22—2442no—
368C22C2×D4×D6111yescharacteristic
369C4—22no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—612no—
374C4—1222no—
375C4—2441no—
376C4C2×D4×D6111yescharacteristic
377C4C2×D4×D6111yescharacteristic
378C2—81no—
379C2—1222no—
380C2—4881no—
381C2—4881no—
382C2—4881no—
383C2#127×D6111yescharacteristic
384C2#1684057112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#497C2
socleC22×C61C22×D4
hypercenter#497D61
hypocenterC61#3154
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×#14519804C2semidirect
3. C2×#14519800C2semidirect
4. C2×SD16×D61C2semidirect
5. #16840337C2semidirect
6. #16840330C2semidirect
7. #16840155C2semidirect
8. #16840151C2semidirect
9. #16840148C2semidirect
10. #16840147C2semidirect
11. #16840144C2semidirect
12. #16840136C2semidirect
13. #16840133C2semidirect
14. #16839719C2semidirect
15. C61×#497C2semidirect
23. C2×#11758202C22semidirect
25. C2×#11758190C22semidirect
29. C2×#11758201C22semidirect
30. C2×#11758201C22semidirect
31. C2×#11758201C22semidirect
34. C2×D488C22semidirect
38. #14519775C22semidirect
42. #14519766C22semidirect
43. #14519765C22semidirect
49. #14519687C22semidirect
50. C4×#92418C22semidirect
51. C8×Dic61C22semidirect
52. C2×Q16×C61C22semidirect
53. C2×Q16×C61C22semidirect
56. C4⋊Q8×C61C22semidirect
58. #97×C61C22semidirect
116. #11758189D4semidirect
117. C8×D61D4semidirect
200. #497D61semidirect
208. C61#3154semidirect
217. C2×Q16C2×D61semidirect
218. C2×Q16C2×D61semidirect
236. C4⋊Q8C2×D61semidirect
249. #97C2×D61semidirect