Finite Group Databasebeta

← #21456070

Subgroups — #21456070

Order 7808.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840370C211yesmaximal, characteristic, complemented
2#16840234C211yesmaximal, characteristic
3#16840105C211yesmaximal, characteristic, complemented
4#16840102C211yesmaximal, characteristic, complemented
5#16840065C211yesmaximal, characteristic, complemented
6#16840060C211yesmaximal, characteristic, complemented
7#16839966C211yesmaximal, characteristic, complemented
8#16839965C211yesmaximal, characteristic, complemented
9#16839914C211yesmaximal, characteristic
10#16839911C211yesmaximal, characteristic
11#16839864C211yesmaximal, characteristic, complemented
12C4×#11758201C211yesmaximal, characteristic, complemented
13C4×#11758200C211yesmaximal, characteristic, complemented
14#16839824C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20#14519775C2211yescharacteristic, complemented
21#14519772—21no—
22#14519771—21no—
23#14519769—21no—
24#14519768C2211yescharacteristic, complemented
25#14519767—21no—
26#14519757C2211yescharacteristic
27#14519753C2211yescharacteristic
28C4×Dic122C2211yescharacteristic, complemented
29C4×D244C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519735C2211yescharacteristic
35#14519734C2211yescharacteristic
36C2×#11758198—21no—
37C22⋊C4×D61—21no—
38#14519711C2211yescharacteristic, complemented
39#14519708C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic, complemented
54C4×D4×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65D4×D61—22no—
66D4×D61—22no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61C2311yescharacteristic
71C2×Dic122C2311yescharacteristic
72SD16×C61—22no—
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C22⋊C4×C61—21no—
79C42×C61—21no—
80C42×C61C2311yescharacteristic
81C22⋊Dic61—21no—
82#11758201—22no—
83#11758200—22no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198D411yescharacteristic
90#11758198D411yescharacteristic
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107#11758190—22no—
108C23×C61—21no—
109C22×D61—21no—
110C22×D61—24no—
111C22×D61—81no—
112C22×D61—81no—
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116D4×C61—21no—
117D4×C61#4112yes—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—81no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—24no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—81no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244#4112yes—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—81no—
138C4×D61—81no—
139Dic122—21no—
140Dic122—21no—
141C8×C61—21no—
142C8×C61—21no—
143#92418—21no—
144#92418—21no—
145C22×C61—22no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61C22×D411yescharacteristic
149C2×D61—21no—
150C2×D61—22no—
151C2×D61—21no—
152C2×D61—21no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—84no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61C2×#4111yescharacteristic
162C4×C61C2×#4111yescharacteristic
163Dic61—21no—
164Dic61—21no—
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169#3123—611nomaximal, Sylow
170C2×C61—42no—
171C2×C61#52511yescharacteristic
172C2×C61#57711yescharacteristic
173C2×C61#57711yescharacteristic
174D61—41no—
175D61—42no—
176#541—611no—
177#518—611no—
178#485—611no—
179#485—611no—
180#478—611no—
181#478—611no—
182#461—611no—
183#461—611no—
184#450—611no—
185#450—611no—
186#440—611no—
187#440D6111yescharacteristic, complemented
188C4×SD16—611no—
189C4×SD16—611no—
190#433—611no—
191C61#312311yescharacteristic, complemented, Sylow
192C22×D4—611no—
193C2×SD16—611no—
194C2×SD16—611no—
195C2×SD16—611no—
196C2×SD16C2×D6111yescharacteristic
197C4⋊Q8—611no—
198#126—1221no—
199#126—1221no—
200#125—611no—
201#125—1221no—
202#125—1221no—
203C22⋊Q8—611no—
204C22⋊Q8—611no—
205C4×Q8—611no—
206C4×Q8C2×D6111yescharacteristic, complemented
207C4×D4—611no—
208C4×D4—611no—
209C4×D4—611no—
210C4×D4—1221no—
211C4×D4—1221no—
212C4×D4C2×D6111yescharacteristic
213#117—611no—
214#117—611no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217#107—611no—
218#107C2×D6111yescharacteristic, complemented
219#106—611no—
220#106—611no—
221C4⋊C8—611no—
222C4⋊C8—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#103C2×D6111yescharacteristic, complemented
227#102—611no—
228#102—611no—
229#102—611no—
230#102C2×D6111yescharacteristic
231C22⋊C8—611no—
232C22⋊C8—611no—
233#97C2×D6111yescharacteristic, complemented
234C4×C8—611no—
235C24—1221no—
236C2×Q8—611no—
237C2×Q8C22×D6111yescharacteristic
238C2×D4—611no—
239C2×D4—1221no—
240C2×D4—1222no—
241C2×D4—1222no—
242C2×D4C22×D6111yescharacteristic
243C22×C4—21no—
244C22×C4—611no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248SD16—22no—
249SD16—1222no—
250SD16—1222no—
251SD16—1222no—
252C2×C8—611no—
253C2×C8—611no—
254C2×C8C22×D6111yescharacteristic
255C2×C8C22×D6111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4C22×D6111yescharacteristic
269C4⋊C4C22×D6111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—611no—
272C22⋊C4—611no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C42—21no—
280C42—611no—
281C42—1221no—
282C42—1221no—
283C42C22×D6111yescharacteristic
284C23—21no—
285C23—611no—
286C23—1224no—
287C23—1221no—
288C23—4881no—
289C23—4881no—
290Q8—21no—
291Q8—21no—
292Q8—1221no—
293Q8—1221no—
294D4—21no—
295D4—612no—
296D4—1224no—
297D4—1221no—
298D4#1175822212yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—4881no—
314C2×C4D4×D6111yescharacteristic
315C2×C4D4×D6111yescharacteristic
316C2×C4C23×D6111yescharacteristic
317C8—21no—
318C8—21no—
319C8—1221no—
320C8—1221no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—1221no—
325C22—1222no—
326C22—1221no—
327C22—1221no—
328C22—4884no—
329C22—2441no—
330C22—2441no—
331C22C2×D4×D6111yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1221no—
338C4—1221no—
339C4—1221no—
340C4—2441no—
341C4—2441no—
342C4—2441no—
343C4#41×D6111yescharacteristic
344C4C2×#1175822211yescharacteristic
345C2—42no—
346C2—2441no—
347C2—2442no—
348C2#1684027111yescharacteristic
349C2#1684057111yescharacteristic
350C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#3123
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16840370C2semidirect
3. #16840105C2semidirect
4. #16840102C2semidirect
5. #16840065C2semidirect
6. #16840060C2semidirect
7. #16839966C2semidirect
8. #16839965C2semidirect
11. #16839864C2semidirect
12. C4×#11758201C2semidirect
13. C4×#11758200C2semidirect
14. #16839824C2semidirect
15. C61×#440C2semidirect
20. #14519775C22semidirect
24. #14519768C22semidirect
28. C4×Dic122C22semidirect
38. #14519711C22semidirect
39. #14519708C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519702C22semidirect
44. #14519701C22semidirect
45. #14519700C22semidirect
51. C4×#92418C22semidirect
53. C4×Q8×C61C22semidirect
55. #107×C61C22semidirect
56. #103×C61C22semidirect
58. #97×C61C22semidirect
187. #440D61semidirect
191. C61#3123semidirect
206. C4×Q8C2×D61semidirect
218. #107C2×D61semidirect
226. #103C2×D61semidirect
233. #97C2×D61semidirect