Finite Group Databasebeta

← #21458884

Subgroups — #21458884

Order 7808.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840494C211yesmaximal, characteristic, complemented
2#16840486C211yesmaximal, characteristic, complemented
3#16840148C211yesmaximal, characteristic
4#16840147C211yesmaximal, characteristic, complemented
5#16839986C211yesmaximal, characteristic, complemented
6#16839986C211yesmaximal, characteristic, complemented
7#16839979C211yesmaximal, characteristic, complemented
8#16839974C211yesmaximal, characteristic, complemented
9#16839964C211yesmaximal, characteristic, complemented
10#16839960C211yesmaximal, characteristic, complemented
11#16839890C211yesmaximal, characteristic, complemented
12#16839875C211yesmaximal, characteristic, complemented
13#16839869C211yesmaximal, characteristic, complemented
14SD16×Dic61C211yesmaximal, characteristic, complemented
15C61×#497C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21#14519773C2211yescharacteristic
22#14519772—21no—
23#14519772—21no—
24#14519766C2211yescharacteristic
25#14519766C2211yescharacteristic
26#14519766C2211yescharacteristic
27#14519763—21no—
28#14519761—21no—
29#14519759—21no—
30#14519757—21no—
31Q8×Dic61C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33Q8×Dic61C2211yescharacteristic
34C4×Dic122C2211yescharacteristic
35C4×D244C2211yescharacteristic
36C4×D244C2211yescharacteristic
37D4×Dic61C2211yescharacteristic
38#14519737—21no—
39#14519735—21no—
40#14519709C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56C4⋊Q8×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C22×Dic61—21no—
66C2×D244C2311yescharacteristic
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×Dic122D411yescharacteristic
71Q16×C61—22no—
72Q16×C61—41no—
73SD16×C61—22no—
74SD16×C61—41no—
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C42×C61C2311yescharacteristic
82C22⋊Dic61—21no—
83#11758201—41no—
84#11758201—41no—
85#11758201—41no—
86#11758199—41no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61D411yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196D411yescharacteristic
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110D488—22no—
111C23×C61—21no—
112C22×D61—21no—
113C22×D61—21no—
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—42no—
129C22⋊D61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—81no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—21no—
138D244—21no—
139D244—21no—
140D244—21no—
141C4×D61—42no—
142C4×D61—81no—
143Dic122—41no—
144C8×C61—21no—
145C8×C61#4112yes—
146#92418—21no—
147#92418—21no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61C22×D411yescharacteristic
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61C2×#4111yescharacteristic
164C4×C61H(5,𝔽2)11yescharacteristic
165Dic61—21no—
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171#3401—611nomaximal, Sylow
172C2×C61—81no—
173C2×C61#55011yescharacteristic
174C2×C61#57511yescharacteristic
175C2×C61#57711yescharacteristic
176D61—81no—
177D61—81no—
178#559—611no—
179#556—611no—
180#497D6111yescharacteristic, complemented
181#496—611no—
182#495—611no—
183#464—611no—
184#464—611no—
185#463—611no—
186#463—611no—
187#461—611no—
188#460—611no—
189#446—611no—
190#442—611no—
191#441—611no—
192C4×SD16—611no—
193C61#340111yescharacteristic, complemented, Sylow
194C2×Q16C2×D6111yescharacteristic
195C2×Q16C2×D6111yescharacteristic
196C2×SD16—611no—
197C2×SD16—611no—
198C2×SD16—611no—
199C2×SD16C2×D6111yescharacteristic
200C2×SD16C2×D6111yescharacteristic
201C2×D8—611no—
202C2×D8—611no—
203C4⋊Q8C2×D6111yescharacteristic
204#127—611no—
205#126—1221no—
206#126—1221no—
207#124—611no—
208#124—611no—
209#124—611no—
210#124—1221no—
211#124C2×D6111yescharacteristic
212#123—1221no—
213#123—1221no—
214C22⋊Q8—1221no—
215C4×Q8—611no—
216C4×Q8—611no—
217C4×Q8—611no—
218C4×Q8—611no—
219C4×D4—611no—
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—1221no—
223#117—1221no—
224#106—611no—
225C4⋊C8—611no—
226C4⋊C8—611no—
227C4⋊C8—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#97—611no—
235#97C2×D6111yescharacteristic
236C4×C8—611no—
237C2×Q8—611no—
238C2×Q8C22×D6111yescharacteristic
239C2×Q8C22×D6111yescharacteristic
240C2×Q8C22×D6111yescharacteristic
241C2×D4—611no—
242C2×D4—611no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4C22×D6111yescharacteristic
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249Q16—22no—
250Q16—41no—
251SD16—22no—
252SD16—41no—
253SD16—2441no—
254SD16—2441no—
255SD16—2441no—
256D8—1222no—
257D8—2441no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C42—611no—
284C42—611no—
285C42—1221no—
286C42—1221no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C23—21no—
290C23—1221no—
291C23—1221no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—2441no—
299D4—21no—
300D4—21no—
301D4—1221no—
302D4—1221no—
303D4—1221no—
304D4—1221no—
305D4—4881no—
306D4—2442no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—2442no—
319C2×C4D4×D6111yescharacteristic
320C2×C4D4×D6111yescharacteristic
321C2×C4C23×D6111yescharacteristic
322C8—21no—
323C8—1221no—
324C8—1221no—
325C8#1175822412yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22C2×D4×D6111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—1221no—
342C4—1221no—
343C4—1221no—
344C4—1221no—
345C4—2441no—
346C4—2441no—
347C4C2×#1175822411yescharacteristic
348C4#1451982211yescharacteristic
349C2—81no—
350C2—4881no—
351C2—4881no—
352C2#1684043211yescharacteristic
353C2#1684056111yescharacteristic
354C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#497C2
socleC22×C61C22×D4
hypercenter#497D61
hypocenterC61#3401
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. #16840494C2semidirect
2. #16840486C2semidirect
4. #16840147C2semidirect
5. #16839986C2semidirect
6. #16839986C2semidirect
7. #16839979C2semidirect
8. #16839974C2semidirect
9. #16839964C2semidirect
10. #16839960C2semidirect
11. #16839890C2semidirect
12. #16839875C2semidirect
13. #16839869C2semidirect
14. SD16×Dic61C2semidirect
15. C61×#497C2semidirect
180. #497D61semidirect
193. C61#3401semidirect