Finite Group Databasebeta

← #21455787

Subgroups — #21455787

Order 7808.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840335C211yesmaximal, characteristic
2#16840243C211yesmaximal, characteristic
3#16840105C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840102C211yesmaximal, characteristic, complemented
6#16840100C211yesmaximal, characteristic, complemented
7#16840099C211yesmaximal, characteristic, complemented
8#16840092C211yesmaximal, characteristic, complemented
9#16840091C211yesmaximal, characteristic, complemented
10#16839803C211yesmaximal, characteristic, complemented
11#16839799C211yesmaximal, characteristic, complemented
12#16839769C211yesmaximal, characteristic, complemented
13#103×D61C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic
15C61×#484C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519776—21no—
21#14519763—21no—
22#14519762—21no—
23#14519759—21no—
24#14519757C2211yescharacteristic
25#14519756C2211yescharacteristic
26#14519753C2211yescharacteristic
27#14519742—21no—
28#14519739—21no—
29C4×C22⋊D61—21no—
30C4×C22⋊D61—21no—
31#14519736C2211yescharacteristic
32#14519735C2211yescharacteristic
33#14519735C2211yescharacteristic
34#14519735C2211yescharacteristic
35C4⋊C4×D61C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
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⋊D61D411yescharacteristic
63C2×C22⋊D61D411yescharacteristic
64Q8×D61—22no—
65Q8×D61—22no—
66#11758222—22no—
67#11758222—22no—
68C2×D244D411yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61C2311yescharacteristic
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122D411yescharacteristic
76C2×Dic122C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758189—22no—
107C8×D61—22no—
108C23×C61C2×D411yescharacteristic
109C22×D61C2×D411yescharacteristic
110C22×D61C2×D411yescharacteristic
111Q8×C61—21no—
112Q8×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—81no—
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C22⋊D61—22no—
123C22⋊D61—22no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—22no—
131C4×D61—21no—
132C4×D61—21no—
133C4×D61—42no—
134C4×D61—81no—
135C4×D61—81no—
136C4×D61#4112yes—
137C4×D61#4112yes—
138Dic122—22no—
139Dic122—21no—
140Dic122—21no—
141Dic122—42no—
142C8×C61—21no—
143C8×C61—21no—
144#92418—21no—
145#92418—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61C22×D411yescharacteristic
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
155C2×D61#12312yes—
156C4×C61—21no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61C2×#4111yescharacteristic
162C4×C61C2×#4111yescharacteristic
163Dic61—21no—
164Dic61—41no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61#12312yes—
169#3097—611nomaximal, Sylow
170C2×C61—41no—
171C2×C61C2×#12311yescharacteristic
172C2×C61#57711yescharacteristic
173C2×C61#57811yescharacteristic
174D61—22no—
175D61—41no—
176#536—611no—
177#520—611no—
178#485—611no—
179#485—611no—
180#485—611no—
181#485—611no—
182#484—611no—
183#484D6111yescharacteristic, complemented
184#483—611no—
185#483—611no—
186#428—611no—
187#427—611no—
188#419—611no—
189C2×#103—611no—
190#408—611no—
191C61#309711yescharacteristic, complemented, Sylow
192C2×#41—611no—
193C22×Q8—611no—
194C2×M16—611no—
195C22×C8—611no—
196C4⋊Q8—1221no—
197#124—1221no—
198#123—1221no—
199#123—1221no—
200C22⋊Q8—611no—
201C22⋊Q8—611no—
202C22⋊Q8—611no—
203C22⋊Q8C2×D6111yescharacteristic
204C4×Q8—1221no—
205C4×D4—1221no—
206C4×D4—1221no—
207C4×D4—1221no—
208#117—611no—
209#117—611no—
210#117—611no—
211#117—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4C2×D6111yescharacteristic
215#107—611no—
216#107—611no—
217#107C2×D6111yescharacteristic
218#107C2×D6111yescharacteristic
219#106—611no—
220#106—611no—
221#106—611no—
222#106—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103C2×D6111yescharacteristic
230#103C2×D6111yescharacteristic
231C22⋊C8—611no—
232C22⋊C8—611no—
233C22⋊C8—611no—
234C22⋊C8C2×D6111yescharacteristic
235#41—1222no—
236#41—1222no—
237C2×Q8—611no—
238C2×Q8—611no—
239C2×Q8—1221no—
240C2×Q8—1222no—
241C2×Q8—1222no—
242C2×Q8C22×D6111yescharacteristic
243C2×D4—611no—
244C2×D4—611no—
245C2×D4—611no—
246C22×C4—21no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4C22×D6111yescharacteristic
253M16—1222no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8—1222no—
257C2×C8C22×D6111yescharacteristic
258C2×C8C22×D6111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—611no—
262C4⋊C4—611no—
263C4⋊C4—611no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4C22×D6111yescharacteristic
270C4⋊C4C22×D6111yescharacteristic
271C4⋊C4C22×D6111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C42—1221no—
281C42—1221no—
282C42—1221no—
283C42—1221no—
284C23—611no—
285C23—611no—
286C23D4×D6111yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—1222no—
290Q8—1221no—
291Q8—1221no—
292Q8—2442no—
293D4—1222no—
294D4—1222no—
295D4—1222no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—611no—
304C2×C4—612no—
305C2×C4—612no—
306C2×C4—611no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—4881no—
314C2×C4—4881no—
315C2×C4—2442no—
316C2×C4D4×D6111yescharacteristic
317C2×C4C23×D6111yescharacteristic
318C8—21no—
319C8—21no—
320C8—1221no—
321C8—1221no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—612no—
326C22—1221no—
327C22—1221no—
328C22—1221no—
329C22—1221no—
330C22—1221no—
331C22C2×D4×D6111yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—612no—
338C4—1221no—
339C4—2441no—
340C4—2441no—
341C4—2441no—
342C4—2441no—
343C4#41×D6111yescharacteristic
344C4#41×D6111yescharacteristic
345C2—41no—
346C2—1222no—
347C2—2441no—
348C2#123×D6111yescharacteristic
349C2#1684057211yescharacteristic
350C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#484C2
socleC22×C61C22×D4
hypercenter#484D61
hypocenterC61#3097
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
3. #16840105C2semidirect
4. #16840104C2semidirect
5. #16840102C2semidirect
6. #16840100C2semidirect
7. #16840099C2semidirect
8. #16840092C2semidirect
9. #16840091C2semidirect
10. #16839803C2semidirect
11. #16839799C2semidirect
12. #16839769C2semidirect
13. #103×D61C2semidirect
15. C61×#484C2semidirect
183. #484D61semidirect
191. C61#3097semidirect