Finite Group Databasebeta

← #21458122

Subgroups — #21458122

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840414C211yesmaximal, characteristic, complemented
2#16840413C211yesmaximal, characteristic, complemented
3#16840111C211yesmaximal, characteristic, complemented
4#16840099C211yesmaximal, characteristic, complemented
5#16840041C211yesmaximal, characteristic, complemented
6#16840010C211yesmaximal, characteristic, complemented
7#16840009C211yesmaximal, characteristic, complemented
8#16839966C211yesmaximal, characteristic, complemented
9#16839910C211yesmaximal, characteristic, complemented
10#16839909C211yesmaximal, characteristic, complemented
11#16839844C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#16839761C211yesmaximal, characteristic, complemented
15C61×#484C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222—21no—
18C2×#11758222C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×D488C2211yescharacteristic
22C2×#11758194C2211yescharacteristic
23C2×#11758189C2211yescharacteristic
24#14519776C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519762—21no—
27#14519762—21no—
28#14519760—21no—
29#14519759—21no—
30#14519757C2211yescharacteristic
31#14519755—21no—
32#14519752C2211yescharacteristic
33#14519751C2211yescharacteristic
34#14519750—21no—
35#14519739C2211yescharacteristic
36#14519739C2211yescharacteristic
37C4×C22⋊D61C2211yescharacteristic
38C4⋊C4×D61—21no—
39C4⋊C4×D61C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61D411yescharacteristic
65#11758226—22no—
66#11758226—41no—
67#11758222—22no—
68#11758222—41no—
69#11758222—44no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81C2×Dic122C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊Dic61D411yescharacteristic
91#11758201—41no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198D411yescharacteristic
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196D411yescharacteristic
105C4×Dic61C2311yescharacteristic
106#11758194—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109D488—22no—
110#11758190—41no—
111#11758189—41no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—42no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—22no—
128C22⋊D61—42no—
129C22⋊D61—42no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—21no—
136D244—21no—
137D244—21no—
138D244—42no—
139D244—42no—
140D244#4112yescomplemented
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—42no—
144C4×D61—42no—
145C4×D61—42no—
146C4×D61—42no—
147C4×D61—42no—
148Dic122—21no—
149Dic122—21no—
150Dic122—42no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—22no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61C2×#4111yescharacteristic
174C4×C61H(5,𝔽2)11yescharacteristic
175Dic61—21no—
176Dic61—21no—
177Dic61—41no—
178Dic61—41no—
179Dic61AGL(1,ℤ/8)12yes—
180#3330—611nomaximal, Sylow
181C2×C61—41no—
182C2×C61#54611yescharacteristic
183C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C61#57811yescharacteristic
185D61—41no—
186D61—42no—
187D61—81no—
188#547—611no—
189#547—611no—
190#487—611no—
191#484—611no—
192#484D6111yescharacteristic, complemented
193#474—611no—
194#468—611no—
195#468—611no—
196#461—611no—
197#449—611no—
198#449—611no—
199C4×D8—611no—
200#436—611no—
201#417—611no—
202#417—611no—
203C61#333011yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C2×#41—611no—
206C2×#41—1221no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×D8—611no—
210C2×M16—611no—
211C2×M16—611no—
212C4⋊Q8—611no—
213C4⋊Q8—611no—
214#123—1221no—
215#123—1221no—
216#123—1221no—
217#123—1221no—
218C22⋊Q8—611no—
219C22⋊Q8—1221no—
220C22⋊Q8C2×D6111yescharacteristic
221#121—611no—
222#121—611no—
223#121—1221no—
224C4×D4—611no—
225C4×D4—611no—
226C4×D4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4C2×D6111yescharacteristic
230#107—611no—
231#107C2×D6111yescharacteristic
232#107C2×D6111yescharacteristic
233C4⋊C8—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#103—611no—
238#103C2×D6111yescharacteristic
239#103C2×D6111yescharacteristic
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244C22⋊C8—611no—
245C22⋊C8C2×D6111yescharacteristic
246C4×C8—611no—
247#41—1222no—
248#41—1222no—
249#41—2441no—
250#41—2444no—
251#41—2441no—
252C2×Q8—611no—
253C2×Q8—1221no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—611no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C22×C4—21no—
263C22×C4—611no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4C22×D6111yescharacteristic
270SD16—2441no—
271SD16—2441no—
272D8—1222no—
273M16—2441no—
274M16—2441no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8C22×D6111yescharacteristic
278C2×C8C22×D6111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4C22×D6111yescharacteristic
289C4⋊C4C22×D6111yescharacteristic
290C4⋊C4C22×D6111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—611no—
293C22⋊C4—611no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—611no—
300C23—611no—
301C23—1221no—
302C23—1221no—
303C23D4×D6111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1221no—
307Q8—1221no—
308Q8—2442no—
309D4—612no—
310D4—1222no—
311D4—1221no—
312D4—1221no—
313D4—1221no—
314D4—2442no—
315D4—2442no—
316D4—2442no—
317D4—2442no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4D4×D6111yescharacteristic
338C2×C4C23×D6111yescharacteristic
339C8—21no—
340C8—21no—
341C8—1221no—
342C8—1221no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—1221no—
347C22—1221no—
348C22—1221no—
349C22—1222no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—612no—
362C4—1221no—
363C4—1221no—
364C4—2441no—
365C4—2441no—
366C4#41×D6111yescharacteristic
367C4#1451982311yescharacteristic
368C2—41no—
369C2—4881no—
370C2—2441no—
371C2—2442no—
372C2#1684040411yescharacteristic
373C2AGL(1,ℤ/8)×D6111yescharacteristic
374C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#484C2
socleC22×C61C22×D4
hypercenter#484D61
hypocenterC61#3330
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #16840414C2semidirect
2. #16840413C2semidirect
3. #16840111C2semidirect
4. #16840099C2semidirect
5. #16840041C2semidirect
6. #16840010C2semidirect
7. #16840009C2semidirect
8. #16839966C2semidirect
9. #16839910C2semidirect
10. #16839909C2semidirect
11. #16839844C2semidirect
12. #16839837C2semidirect
13. #16839762C2semidirect
14. #16839761C2semidirect
15. C61×#484C2semidirect
140. D244#41semidirect
192. #484D61semidirect
203. C61#3330semidirect