Finite Group Databasebeta

← #21456796

Subgroups — #21456796

Order 7808.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840311C211yesmaximal, characteristic, complemented
2#16840297C211yesmaximal, characteristic, complemented
3#16840146C211yesmaximal, characteristic, complemented
4#16840144C211yesmaximal, characteristic, complemented
5#16840119C211yesmaximal, characteristic, complemented
6#16839971C211yesmaximal, characteristic, complemented
7#16839966C211yesmaximal, characteristic, complemented
8#16839961C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839927C211yesmaximal, characteristic, complemented
11#16839925C211yesmaximal, characteristic, complemented
12#16839910C211yesmaximal, characteristic, complemented
13#16839908C211yesmaximal, characteristic, complemented
14#16839813C211yesmaximal, characteristic, complemented
15C61×#488C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Dic244C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758190C2211yescharacteristic
22C2×#11758200C2211yescharacteristic
23C2×#11758201C2211yescharacteristic
24C2×D488C2211yescharacteristic
25C2×#11758199C2211yescharacteristic
26#14519775C2211yescharacteristic
27#14519773C2211yescharacteristic
28#14519772—21no—
29#14519765C2211yescharacteristic
30#14519765C2211yescharacteristic
31#14519762—21no—
32#14519757C2211yescharacteristic
33#14519752C2211yescharacteristic
34#14519750—21no—
35#14519750—21no—
36#14519742C2211yescharacteristic
37#14519739—21no—
38#14519739C2211yescharacteristic
39#14519737—21no—
40#14519737—21no—
41#14519735—21no—
42C42×D61C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52#125×C61C2211yescharacteristic
53#124×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65#11758226—41no—
66#11758226—41no—
67#11758224—41no—
68#11758224—41no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244C2311yescharacteristic
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61D411yescharacteristic
76C2×C4×D61D411yescharacteristic
77C2×C4×D61C2311yescharacteristic
78C2×Dic122C2311yescharacteristic
79C2×Dic122C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C42×C61C2311yescharacteristic
89#11758202—41no—
90#11758201—41no—
91#11758200—41no—
92#11758199—41no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61D411yescharacteristic
106C4×Dic61D411yescharacteristic
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110Dic244—41no—
111D488—41no—
112#11758190—41no—
113#11758190—41no—
114C23×C61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61C2×D411yescharacteristic
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—42no—
130C22⋊D61—42no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—42no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—21no—
138D244—21no—
139D244—21no—
140D244—21no—
141D244—42no—
142D244—42no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—22no—
146C4×D61—41no—
147C4×D61—42no—
148C4×D61—42no—
149Dic122—21no—
150Dic122—21no—
151Dic122—21no—
152Dic122—21no—
153C8×C61—21no—
154C8×C61—21no—
155#92418—21no—
156#92418—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61C22×D411yescharacteristic
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61H(5,𝔽2)11yescharacteristic
176C4×C61H(5,𝔽2)11yescharacteristic
177Dic61—21no—
178Dic61—21no—
179Dic61—41no—
180Dic61—41no—
181Dic61#13512yes—
182#3212—611nomaximal, Sylow
183C2×C61—81no—
184C2×C61#53511yescharacteristic
185C2×C61C2×#13511yescharacteristic
186C2×C61#57511yescharacteristic
187D61—41no—
188D61—81no—
189D61—81no—
190#532—611no—
191#529—611no—
192#495—611no—
193#495—611no—
194#488—611no—
195#488D6111yescharacteristic, complemented
196#462—611no—
197#461—611no—
198#460—611no—
199#459—611no—
200#452—611no—
201#452—611no—
202#449—611no—
203#449—611no—
204#431—611no—
205C61#321211yescharacteristic, complemented, Sylow
206C2×#41—611no—
207C2×#41—611no—
208C2×Q16—611no—
209C2×Q16—611no—
210C2×SD16—611no—
211C2×SD16—611no—
212C2×SD16—611no—
213C2×SD16—611no—
214C2×D8—611no—
215C2×D8—611no—
216C4⋊Q8—611no—
217#127—611no—
218#126—1221no—
219#125C2×D6111yescharacteristic
220#124—611no—
221#124—611no—
222#124C2×D6111yescharacteristic
223#123—1221no—
224C22⋊Q8—611no—
225#121—611no—
226#121—1221no—
227#121—1221no—
228C4×Q8—611no—
229C4×D4—611no—
230C4×D4—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233#117—1221no—
234C2×C42—611no—
235C4⋊C8—611no—
236C4⋊C8—611no—
237#103—611no—
238#103—611no—
239#103C2×D6111yescharacteristic
240#103C2×D6111yescharacteristic
241#102—611no—
242#102—611no—
243#102C2×D6111yescharacteristic
244#102C2×D6111yescharacteristic
245C22⋊C8—611no—
246C22⋊C8—611no—
247C4×C8—611no—
248C4×C8C2×D6111yescharacteristic
249#41—2441no—
250#41—2441no—
251#41—2441no—
252#41—2441no—
253C2×Q8—611no—
254C2×Q8—611no—
255C2×Q8C22×D6111yescharacteristic
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4C22×D6111yescharacteristic
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270Q16—2441no—
271Q16—2441no—
272SD16—2441no—
273SD16—2441no—
274SD16—2441no—
275SD16—2441no—
276D8—2441no—
277D8—2441no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8C22×D6111yescharacteristic
281C2×C8C22×D6111yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4C22×D6111yescharacteristic
289C4⋊C4C22×D6111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—611no—
300C42—611no—
301C42—611no—
302C42—1221no—
303C42C22×D6111yescharacteristic
304C23—21no—
305C23—611no—
306C23—1221no—
307C23—1221no—
308Q8—21no—
309Q8—21no—
310Q8—1221no—
311Q8—1221no—
312Q8—1221no—
313Q8—1221no—
314D4—21no—
315D4—21no—
316D4—1221no—
317D4—1221no—
318D4—1221no—
319D4—1221no—
320D4—2442no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324D4—2442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—1222no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2441no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4D4×D6111yescharacteristic
341C2×C4D4×D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1221no—
346C8—1221no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—1221no—
351C22—1221no—
352C22—1221no—
353C22—2441no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22C2×D4×D6111yescharacteristic
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—612no—
366C4—1221no—
367C4—1221no—
368C4—2441no—
369C4—2441no—
370C4#1451982311yescharacteristic
371C4#1451982311yescharacteristic
372C2—81no—
373C2—4881no—
374C2—4881no—
375C2—2441no—
376C2#1684033011yescharacteristic
377C2#135×D6111yescharacteristic
378C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#488C2
socleC22×C61C22×D4
hypercenter#488D61
hypocenterC61#3212
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16840311C2semidirect
2. #16840297C2semidirect
3. #16840146C2semidirect
4. #16840144C2semidirect
5. #16840119C2semidirect
6. #16839971C2semidirect
7. #16839966C2semidirect
8. #16839961C2semidirect
9. #16839956C2semidirect
10. #16839927C2semidirect
11. #16839925C2semidirect
12. #16839910C2semidirect
13. #16839908C2semidirect
14. #16839813C2semidirect
15. C61×#488C2semidirect
195. #488D61semidirect
205. C61#3212semidirect