Finite Group Databasebeta

← #21457144

Subgroups — #21457144

Order 7808.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840309C211yesmaximal, characteristic, complemented
2#16840297C211yesmaximal, characteristic, complemented
3#16840059C211yesmaximal, characteristic, complemented
4#16840056C211yesmaximal, characteristic, complemented
5#16840051C211yesmaximal, characteristic, complemented
6#16839999C211yesmaximal, characteristic, complemented
7#16839997C211yesmaximal, characteristic, complemented
8#16839992C211yesmaximal, characteristic, complemented
9#16839990C211yesmaximal, characteristic, complemented
10#16839978C211yesmaximal, characteristic, complemented
11#16839977C211yesmaximal, characteristic, complemented
12#16839961C211yesmaximal, characteristic, complemented
13#16839956C211yesmaximal, characteristic, complemented
14C4⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#478C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758190C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic
23#14519776C2211yescharacteristic
24#14519773C2211yescharacteristic
25#14519772—21no—
26#14519765C2211yescharacteristic
27#14519763—21no—
28#14519762—21no—
29#14519757C2211yescharacteristic
30#14519752C2211yescharacteristic
31#14519752C2211yescharacteristic
32#14519750—21no—
33#14519748C2211yescharacteristic
34#14519742C2211yescharacteristic
35C4×D244C2211yescharacteristic
36#14519739—21no—
37#14519739C2211yescharacteristic
38C4×C22⋊D61—21no—
39#14519735—21no—
40C42×D61C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519708C2211yescharacteristic
43C4⋊#92418C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519697C2211yescharacteristic
51#14519697C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×D4×C61C2311yescharacteristic
60C22×C4×C61—21no—
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64#11758222—44no—
65C2×D244—21no—
66C2×D244—21no—
67C2×D244C2311yescharacteristic
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61D411yescharacteristic
72C2×C4×D61D411yescharacteristic
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86#11758200—41no—
87#11758199—41no—
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⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99C4×Dic61—21no—
100C4×Dic61D411yescharacteristic
101C4×Dic61D411yescharacteristic
102C4×Dic61C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105D488—41no—
106#11758190—41no—
107C8×D61—41no—
108C8×D61—41no—
109C23×C61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61C2×D411yescharacteristic
113D4×C61—21no—
114D4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—42no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C22⋊D61—42no—
123C22⋊D61—42no—
124C22⋊D61—42no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—21no—
131D244—21no—
132D244—21no—
133D244—21no—
134D244—42no—
135D244—42no—
136C4×D61—22no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—22no—
140C4×D61—42no—
141C4×D61—42no—
142Dic122—21no—
143Dic122—21no—
144Dic122—42no—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61C22×D411yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61AGL(1,ℤ/8)12yes—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61H(5,𝔽2)11yescharacteristic
168C4×C612−1+411yescharacteristic
169Dic61—21no—
170Dic61—21no—
171Dic61—41no—
172Dic61—41no—
173Dic61#13512yes—
174#3247—611nomaximal, Sylow
175C2×C61—81no—
176C2×C61#53711yescharacteristic
177C2×C61C2×#13511yescharacteristic
178C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
179D61—22no—
180D61—81no—
181D61—81no—
182#532—611no—
183#529—611no—
184#478—611no—
185#478D6111yescharacteristic, complemented
186#477—611no—
187#476—611no—
188#466—611no—
189#466—611no—
190#465—611no—
191#465—611no—
192#463—611no—
193#463—611no—
194#460—611no—
195#459—611no—
196C2×C4⋊C8—611no—
197C61#324711yescharacteristic, complemented, Sylow
198C2×#41—1221no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×D8—611no—
202C2×D8—611no—
203C22×C8—611no—
204C22×C8—611no—
205C4⋊Q8—611no—
206#127—611no—
207#126—1221no—
208#125C2×D6111yescharacteristic
209#124—611no—
210#124—1221no—
211#123—1221no—
212C22⋊Q8—611no—
213#121—611no—
214#121—611no—
215#121—611no—
216#121—1221no—
217C4×Q8—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—1221no—
221C4×D4—1221no—
222C4×D4C2×D6111yescharacteristic
223#117—1221no—
224C2×C42—611no—
225#107—611no—
226#107C2×D6111yescharacteristic
227#106—611no—
228#106C2×D6111yescharacteristic
229C4⋊C8—611no—
230C4⋊C8—611no—
231C4⋊C8—611no—
232C4⋊C8C2×D6111yescharacteristic
233#103—611no—
234#103—611no—
235#102—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102C2×D6111yescharacteristic
240#102C2×D6111yescharacteristic
241#41—2444no—
242C2×Q8—611no—
243C2×Q8—1221no—
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4C22×D6111yescharacteristic
252C22×C4—21no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258SD16—2441no—
259SD16—2441no—
260D8—2441no—
261D8—2441no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—2441no—
265C2×C8—2441no—
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4C22×D6111yescharacteristic
275C4⋊C4C22×D6111yescharacteristic
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—611no—
287C42—611no—
288C42—611no—
289C42—1221no—
290C42C22×D6111yescharacteristic
291C23—21no—
292C23—611no—
293C23—1221no—
294C23—1221no—
295Q8—1221no—
296Q8—1221no—
297Q8—2442no—
298D4—21no—
299D4—21no—
300D4—1221no—
301D4—1221no—
302D4—1221no—
303D4—1221no—
304D4—2442no—
305D4—2442no—
306D4—2442no—
307D4—2442no—
308D4—2442no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4D4×D6111yescharacteristic
325C2×C4D4×D6111yescharacteristic
326C2×C4C23×D6111yescharacteristic
327C8—21no—
328C8—21no—
329C8—1221no—
330C8—1221no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—612no—
335C22—1221no—
336C22—1221no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22C2×D4×D6111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—612no—
350C4—1221no—
351C4—1221no—
352C4—2441no—
353C4—2441no—
354C4#1451982311yescharacteristic
355C4#1451982511yescharacteristic
356C2—81no—
357C2—1222no—
358C2—4881no—
359C2—4881no—
360C2#1684034211yescharacteristic
361C2#135×D6111yescharacteristic
362C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3247
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16840309C2semidirect
2. #16840297C2semidirect
3. #16840059C2semidirect
4. #16840056C2semidirect
5. #16840051C2semidirect
6. #16839999C2semidirect
7. #16839997C2semidirect
8. #16839992C2semidirect
9. #16839990C2semidirect
10. #16839978C2semidirect
11. #16839977C2semidirect
12. #16839961C2semidirect
13. #16839956C2semidirect
14. C4⋊C8×D61C2semidirect
15. C61×#478C2semidirect
185. #478D61semidirect
197. C61#3247semidirect