Finite Group Databasebeta

← #21458117

Subgroups — #21458117

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#16840412C211yesmaximal, characteristic, complemented
2#16840411C211yesmaximal, characteristic, complemented
3#16840111C211yesmaximal, characteristic, complemented
4#16840098C211yesmaximal, characteristic, complemented
5#16840096C211yesmaximal, characteristic, complemented
6#16840040C211yesmaximal, characteristic, complemented
7#16840006C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839904C211yesmaximal, characteristic, complemented
11D8×Dic61C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839763C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×#11758224C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21#14519776C2211yescharacteristic
22#14519775C2211yescharacteristic
23#14519760—21no—
24#14519759—21no—
25#14519758—21no—
26#14519758—21no—
27#14519756C2211yescharacteristic
28#14519754—21no—
29#14519753C2211yescharacteristic
30#14519749—21no—
31#14519748C2211yescharacteristic
32D4×Dic61C2211yescharacteristic
33D4×Dic61C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35C2×C4⋊Dic61C2211yescharacteristic
36C2×#11758196—21no—
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
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—
74C22×Dic61—21no—
75#11758224—22no—
76#11758224—41no—
77#11758224—44no—
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81C2×Dic122C2311yescharacteristic
82SD16×C61—41no—
83D8×C61—22no—
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61D411yescharacteristic
93#11758200—41no—
94#11758198—21no—
95#11758198D411yescharacteristic
96C4⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107C4×Dic61C2311yescharacteristic
108#11758194—41no—
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111#11758189—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61C2×D411yescharacteristic
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—42no—
122D4×C61—42no—
123D4×C61#4112yescomplemented
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—22no—
132C22⋊D61—42no—
133C22⋊D61—42no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—42no—
148Dic122—21no—
149Dic122—21no—
150Dic122—42no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—22no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61C2×#4111yescharacteristic
172C4×C61H(5,𝔽2)11yescharacteristic
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178Dic61—41no—
179Dic61AGL(1,ℤ/8)12yes—
180#3330—611nomaximal, Sylow
181C2×C61—41no—
182C2×C61—42no—
183C2×C61—81no—
184C2×C61#54611yescharacteristic
185C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C61#57811yescharacteristic
187D61—41no—
188#547—611no—
189#547—611no—
190#487—611no—
191#484—611no—
192#484—611no—
193#474—611no—
194#468—611no—
195#468—611no—
196#461—611no—
197#449—611no—
198#449D6111yescharacteristic, complemented
199C4×D8—611no—
200#436—611no—
201#417—611no—
202#417—611no—
203C61#333011yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C2×#41—1221no—
206C2×#41C2×D6111yescharacteristic
207C2×SD16—611no—
208C2×SD16C2×D6111yescharacteristic
209C2×D8C2×D6111yescharacteristic
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—611no—
220C22⋊Q8—1221no—
221#121—611no—
222#121—1221no—
223#121C2×D6111yescharacteristic
224C4×D4—611no—
225C4×D4—611no—
226C4×D4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230#107—611no—
231#107—611no—
232#107—611no—
233C4⋊C8—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#103—611no—
238#103—611no—
239#103C2×D6111yescharacteristic
240#102—611no—
241#102—611no—
242#102—611no—
243#102C2×D6111yescharacteristic
244C22⋊C8—611no—
245C22⋊C8C2×D6111yescharacteristic
246C4×C8—611no—
247#41—22no—
248#41—41no—
249#41—1222no—
250#41—2441no—
251#41—2444no—
252C2×Q8—611no—
253C2×Q8—1221no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4C22×D6111yescharacteristic
261C2×D4C22×D6111yescharacteristic
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—41no—
271SD16—2441no—
272D8—22no—
273M16—2441no—
274M16—2441no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8C22×D6111yescharacteristic
278C2×C8C22×D6111yescharacteristic
279C4⋊C4—611no—
280C4⋊C4—611no—
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
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—21no—
301C23—21no—
302C23—611no—
303C23D4×D6111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1221no—
307Q8—1221no—
308Q8—2442no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—1222no—
315D4—2442no—
316D4—2442no—
317D4#1175822412yescomplemented
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—1221no—
327C2×C4—1221no—
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—22no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—1221no—
353C22—1221no—
354C22—1221no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—612no—
360C4—1221no—
361C4—1221no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C4—2441no—
366C4C2×#1175822411yescharacteristic
367C4#1451982211yescharacteristic
368C2—41no—
369C2—42no—
370C2—81no—
371C2—2441no—
372C2#1684039911yescharacteristic
373C2AGL(1,ℤ/8)×D6111yescharacteristic
374C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3330
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. #16840412C2semidirect
2. #16840411C2semidirect
3. #16840111C2semidirect
4. #16840098C2semidirect
5. #16840096C2semidirect
6. #16840040C2semidirect
7. #16840006C2semidirect
8. #16840005C2semidirect
9. #16839965C2semidirect
10. #16839904C2semidirect
11. D8×Dic61C2semidirect
12. #16839837C2semidirect
13. #16839763C2semidirect
14. #16839760C2semidirect
15. C61×#449C2semidirect
123. D4×C61#41semidirect
198. #449D61semidirect
203. C61#3330semidirect
317. D4#11758224semidirect