Finite Group Databasebeta

← #21457799

Subgroups — #21457799

Order 7808.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840459C211yesmaximal, characteristic, complemented
2#16840411C211yesmaximal, characteristic, complemented
3#16840129C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840091C211yesmaximal, characteristic, complemented
6#16840060C211yesmaximal, characteristic, complemented
7#16840005C211yesmaximal, characteristic, complemented
8#16839989C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839904C211yesmaximal, characteristic, complemented
11#16839874C211yesmaximal, characteristic, complemented
12#16839830C211yesmaximal, characteristic, complemented
13#16839760C211yesmaximal, characteristic, complemented
14#16839758C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758200C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C22×#92418C2211yescharacteristic
20#14519775C2211yescharacteristic
21#14519770—21no—
22#14519768C2211yescharacteristic
23#14519760—21no—
24#14519758—21no—
25#14519758—21no—
26#14519756C2211yescharacteristic
27#14519753C2211yescharacteristic
28#14519749—21no—
29#14519748—21no—
30#14519748C2211yescharacteristic
31D4×Dic61C2211yescharacteristic
32D4×Dic61C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34#14519737—21no—
35#14519736C2211yescharacteristic
36C2×#11758196—21no—
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74#11758224—22no—
75#11758224—41no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×Dic122C2311yescharacteristic
79SD16×C61—41no—
80D8×C61—22no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61D411yescharacteristic
91#11758200—41no—
92#11758198—21no—
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196D411yescharacteristic
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—42no—
121D4×C61—81no—
122D4×C61#4112yes—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—42no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—41no—
131C22⋊D61—42no—
132C22⋊D61—42no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—81no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—81no—
146Dic122—21no—
147Dic122—21no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—22no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61C2×#4111yescharacteristic
169C4×C61H(5,𝔽2)11yescharacteristic
170Dic61—21no—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177#3307—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61—42no—
180C2×C61—81no—
181C2×C61#54611yescharacteristic
182C2×C61#57511yescharacteristic
183C2×C61#57711yescharacteristic
184D61—41no—
185#553—611no—
186#547—611no—
187#491—611no—
188#485—611no—
189#483—611no—
190#478—611no—
191#468—611no—
192#465—611no—
193#461—611no—
194#449—611no—
195#449D6111yescharacteristic, complemented
196#442—611no—
197#435—611no—
198#417—611no—
199#416—611no—
200C61#330711yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C2×#41C2×D6111yescharacteristic
203C2×SD16—611no—
204C2×SD16C2×D6111yescharacteristic
205C2×D8C2×D6111yescharacteristic
206C2×M16—611no—
207C22×C8—611no—
208C4⋊Q8—611no—
209#126—1221no—
210#125—611no—
211#123—1221no—
212#123—1221no—
213#123—1221no—
214C22⋊Q8—611no—
215C22⋊Q8—611no—
216#121—611no—
217#121—1221no—
218#121—1221no—
219#121C2×D6111yescharacteristic
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—611no—
223C4×D4—1221no—
224#117—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227#107—611no—
228#106—611no—
229#106—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103C2×D6111yescharacteristic
237#102—611no—
238#102—611no—
239#102—611no—
240#102C2×D6111yescharacteristic
241C22⋊C8—611no—
242C22⋊C8C2×D6111yescharacteristic
243#97—611no—
244#41—22no—
245#41—41no—
246#41—1222no—
247#41—2441no—
248C2×Q8—611no—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—611no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4C22×D6111yescharacteristic
256C2×D4C22×D6111yescharacteristic
257C22×C4—21no—
258C22×C4—611no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4C22×D6111yescharacteristic
264SD16—41no—
265SD16—2441no—
266D8—22no—
267M16—2441no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—2441no—
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4C22×D6111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—611no—
287C22⋊C4—611no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—611no—
295C42—1221no—
296C23—21no—
297C23—21no—
298C23—611no—
299C23D4×D6111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—1221no—
303Q8—1221no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—81no—
309D4—2441no—
310D4—2442no—
311D4—2442no—
312D4#1175822412yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—42no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4D4×D6111yescharacteristic
332C2×C4C23×D6111yescharacteristic
333C8—21no—
334C8—21no—
335C8—1221no—
336C8—1221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—1221no—
347C22—1221no—
348C22—1221no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—1221no—
354C4—1221no—
355C4—1221no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4C2×#1175822411yescharacteristic
361C4#1451982211yescharacteristic
362C2—41no—
363C2—42no—
364C2—81no—
365C2—2441no—
366C2#1684039911yescharacteristic
367C2#1684055911yescharacteristic
368C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3307
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16840459C2semidirect
2. #16840411C2semidirect
3. #16840129C2semidirect
4. #16840104C2semidirect
5. #16840091C2semidirect
6. #16840060C2semidirect
7. #16840005C2semidirect
8. #16839989C2semidirect
9. #16839965C2semidirect
10. #16839904C2semidirect
11. #16839874C2semidirect
12. #16839830C2semidirect
13. #16839760C2semidirect
14. #16839758C2semidirect
15. C61×#449C2semidirect
195. #449D61semidirect
200. C61#3307semidirect