Finite Group Databasebeta

← #21458887

Subgroups — #21458887

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#16840497C211yesmaximal, characteristic, complemented
2#16840485C211yesmaximal, characteristic, complemented
3#16840156C211yesmaximal, characteristic, complemented
4#16840151C211yesmaximal, characteristic
5#16840146C211yesmaximal, characteristic, complemented
6#16839985C211yesmaximal, characteristic, complemented
7#16839985C211yesmaximal, characteristic, complemented
8#16839978C211yesmaximal, characteristic, complemented
9#16839978C211yesmaximal, characteristic, complemented
10#16839968C211yesmaximal, characteristic, complemented
11#16839963C211yesmaximal, characteristic, complemented
12#16839875C211yesmaximal, characteristic, complemented
13#16839870C211yesmaximal, characteristic, complemented
14C4×#11758190C211yesmaximal, characteristic, complemented
15C61×#446C211yesmaximal, characteristic, complemented
16C2×Dic244C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758190C2211yescharacteristic
22C2×#11758190C2211yescharacteristic
23C2×D488C2211yescharacteristic
24C2×D488C2211yescharacteristic
25#14519777C2211yescharacteristic
26#14519774C2211yescharacteristic
27#14519772—21no—
28#14519772—21no—
29#14519766—21no—
30#14519765C2211yescharacteristic
31#14519765C2211yescharacteristic
32#14519765C2211yescharacteristic
33#14519765C2211yescharacteristic
34#14519762—21no—
35#14519762—21no—
36#14519753—21no—
37C4×Dic122C2211yescharacteristic
38C4×Dic122C2211yescharacteristic
39C4×Dic122C2211yescharacteristic
40C4×D244C2211yescharacteristic
41C4×D244C2211yescharacteristic
42C4×D244C2211yescharacteristic
43#14519739—21no—
44#14519735—21no—
45#14519709C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52C4×Q8×C61C2211yescharacteristic
53C4⋊C8×C61C2211yescharacteristic
54C4⋊C8×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic
56#97×C61C2211yescharacteristic
57#97×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61D411yescharacteristic
60C2×D244—21no—
61C2×D244—21no—
62C2×D244C2311yescharacteristic
63C2×D244C2311yescharacteristic
64C2×D244C2311yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×Dic122C2311yescharacteristic
69C2×Dic122C2311yescharacteristic
70C2×Dic122C2311yescharacteristic
71C2×C8×C61C2311yescharacteristic
72C2×C8×C61C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C4⋊C4×C61D411yescharacteristic
76C4⋊C4×C61D411yescharacteristic
77C4⋊C4×C61D411yescharacteristic
78C42×C61C2311yescharacteristic
79C42×C61C2311yescharacteristic
80C42×C61C2311yescharacteristic
81#11758198—21no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102Dic244—22no—
103Dic244—41no—
104D488—22no—
105D488—41no—
106#11758190—22no—
107#11758190—41no—
108#11758190—41no—
109#11758190—41no—
110#11758190—41no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114Q8×C61—41no—
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127D244—21no—
128D244—21no—
129D244—21no—
130D244—21no—
131D244—21no—
132D244—21no—
133D244—42no—
134D244—81no—
135C4×D61—42no—
136C4×D61—81no—
137C4×D61—81no—
138Dic122—21no—
139Dic122—21no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—21no—
144C8×C61—21no—
145C8×C61—21no—
146C8×C61—21no—
147C8×C61#4112yes—
148C22×C61C22×D411yescharacteristic
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—41no—
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—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61C2×#4111yescharacteristic
165C4×C61H(5,𝔽2)11yescharacteristic
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171#3401—611nomaximal, Sylow
172C2×C61#55011yescharacteristic
173C2×C61#57511yescharacteristic
174C2×C61#57711yescharacteristic
175D61—81no—
176D61—81no—
177D61—81no—
178#559—611no—
179#556—611no—
180#497—611no—
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#446D6111yescharacteristic, complemented
190#442—611no—
191#441—611no—
192C4×SD16—611no—
193C61#340111yescharacteristic, complemented, Sylow
194C2×Q16—611no—
195C2×Q16—611no—
196C2×SD16—611no—
197C2×SD16—611no—
198C2×SD16—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×D8—611no—
202C2×D8—611no—
203C4⋊Q8—611no—
204#127—611no—
205#126—1221no—
206#126—1221no—
207#124—611no—
208#124—611no—
209#124—611no—
210#124—611no—
211#124—1221no—
212#123—1221no—
213#123—1221no—
214C22⋊Q8—1221no—
215C4×Q8—611no—
216C4×Q8—611no—
217C4×Q8—611no—
218C4×Q8C2×D6111yescharacteristic
219C4×D4—611no—
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—1221no—
223#117—1221no—
224#106—611no—
225C4⋊C8C2×D6111yescharacteristic
226C4⋊C8C2×D6111yescharacteristic
227C4⋊C8C2×D6111yescharacteristic
228#103—611no—
229#103—611no—
230#103—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#97C2×D6111yescharacteristic
235#97C2×D6111yescharacteristic
236C4×C8C2×D6111yescharacteristic
237C2×Q8—611no—
238C2×Q8—611no—
239C2×Q8—611no—
240C2×Q8D24411yescharacteristic
241C2×D4—611no—
242C2×D4—611no—
243C2×D4—611no—
244C2×D4—1221no—
245C2×D4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249Q16—1222no—
250Q16—2441no—
251SD16—1222no—
252SD16—2441no—
253SD16—2441no—
254SD16—2441no—
255SD16—2441no—
256D8—1222no—
257D8—2441no—
258C2×C8C22×D6111yescharacteristic
259C2×C8C22×D6111yescharacteristic
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—611no—
263C4⋊C4—611no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4D24411yescharacteristic
270C4⋊C4D24411yescharacteristic
271C4⋊C4D24411yescharacteristic
272C22⋊C4—1221no—
273C22⋊C4—1221no—
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—1221no—
284C42—1221no—
285C42—1221no—
286C42C22×D6111yescharacteristic
287C42C22×D6111yescharacteristic
288C42C22×D6111yescharacteristic
289C23—1221no—
290C23—1221no—
291C23—1221no—
292Q8—41no—
293Q8—1221no—
294Q8—1221no—
295Q8—1221no—
296Q8—1221no—
297Q8—1221no—
298Q8—1221no—
299D4—1221no—
300D4—1221no—
301D4—1221no—
302D4—1221no—
303D4—1221no—
304D4—1221no—
305D4—4881no—
306D4—2442no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—4881no—
313C2×C4—4881no—
314C2×C4—2442no—
315C2×C4C2×D24411yescharacteristic
316C2×C4C2×D24411yescharacteristic
317C2×C4C2×D24411yescharacteristic
318C2×C4C2×D24411yescharacteristic
319C2×C4C2×D24411yescharacteristic
320C2×C4C2×D24411yescharacteristic
321C2×C4C23×D6111yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#1175822612yes—
326C22—2441no—
327C22—2441no—
328C22—2441no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22C22×D24411yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—2441no—
343C4—2441no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4C2×#1175822611yescharacteristic
348C4#1451982311yescharacteristic
349C2—4881no—
350C2—4881no—
351C2—4881no—
352C2#1684043411yescharacteristic
353C2#1684056211yescharacteristic
354C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3401
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #16840497C2semidirect
2. #16840485C2semidirect
3. #16840156C2semidirect
5. #16840146C2semidirect
6. #16839985C2semidirect
7. #16839985C2semidirect
8. #16839978C2semidirect
9. #16839978C2semidirect
10. #16839968C2semidirect
11. #16839963C2semidirect
12. #16839875C2semidirect
13. #16839870C2semidirect
14. C4×#11758190C2semidirect
15. C61×#446C2semidirect
189. #446D61semidirect
193. C61#3401semidirect