Finite Group Databasebeta

← #21458150

Subgroups — #21458150

Order 7808.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840470C211yesmaximal, characteristic, complemented
2#16840431C211yesmaximal, characteristic
3#16840107C211yesmaximal, characteristic, complemented
4#16840076C211yesmaximal, characteristic, complemented
5#16840074C211yesmaximal, characteristic, complemented
6#16840055C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16839960C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11Q16×Dic61C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839763C211yesmaximal, characteristic, complemented
14#16839762C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758194C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519773—21no—
22#14519773C2211yescharacteristic
23#14519767—21no—
24#14519757—21no—
25#14519754—21no—
26#14519753C2211yescharacteristic
27#14519751—21no—
28#14519751C2211yescharacteristic
29#14519748—21no—
30#14519748C2211yescharacteristic
31Q8×Dic61C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33C4×C22⋊D61—21no—
34C4×C22⋊D61C2211yescharacteristic
35#14519737—21no—
36C2×C4⋊Dic61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61D411yescharacteristic
72C22×Dic61—21no—
73#11758226—22no—
74#11758226—41no—
75C2×D244—21no—
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81Q16×C61—22no—
82SD16×C61—41no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61—21no—
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61D411yescharacteristic
90#11758201—41no—
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107#11758194—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61#4112yes—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—42no—
122C2×C4×C61—21no—
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—22no—
131C22⋊D61—42no—
132C22⋊D61—81no—
133C22⋊D61—81no—
134C22⋊D61—81no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—81no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142D244—21no—
143D244—21no—
144D244—42no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—42no—
148C4×D61—81no—
149Dic122—81no—
150C8×C61—21no—
151C8×C61—21no—
152#92418—21no—
153#92418—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—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—
167C4×C61—22no—
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#13712yes—
179#3333—611nomaximal, Sylow
180C2×C61—41no—
181C2×C61—81no—
182C2×C61#54611yescharacteristic
183C2×C61C2×#13711yescharacteristic
184C2×C61#57611yescharacteristic
185D61—41no—
186D61—81no—
187#554—611no—
188#550—611no—
189#486—611no—
190#480—611no—
191#480—611no—
192#477—611no—
193#468—611no—
194#468—611no—
195#460—611no—
196#452—611no—
197#452D6111yescharacteristic, complemented
198C4×Q16—611no—
199#436—611no—
200#417—611no—
201#417—611no—
202C61#333311yescharacteristic, complemented, Sylow
203C2×#41—611no—
204C2×#41C2×D6111yescharacteristic
205C2×Q16C2×D6111yescharacteristic
206C2×SD16—611no—
207C2×SD16C2×D6111yescharacteristic
208C2×M16—611no—
209C2×M16—611no—
210C4⋊Q8—611no—
211#127—611no—
212#127—1221no—
213#125—1221no—
214C22⋊Q8—611no—
215C22⋊Q8—1221no—
216C22⋊Q8—1221no—
217C22⋊Q8C2×D6111yescharacteristic
218#121—611no—
219#121—611no—
220#121—1221no—
221#121—1221no—
222C4×Q8—611no—
223C4×Q8—611no—
224C4×D4—611no—
225C4×D4—1221no—
226C4×D4—1221no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229#107—611no—
230#107—611no—
231#107—611no—
232C4⋊C8—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103C2×D6111yescharacteristic
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242#102C2×D6111yescharacteristic
243C22⋊C8—611no—
244C22⋊C8C2×D6111yescharacteristic
245C4×C8—611no—
246#41—22no—
247#41—41no—
248#41—1222no—
249#41—2441no—
250C2×Q8—1221no—
251C2×Q8C22×D6111yescharacteristic
252C2×Q8C22×D6111yescharacteristic
253C2×D4—21no—
254C2×D4—611no—
255C2×D4—611no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4C22×D6111yescharacteristic
262C22×C4—21no—
263C22×C4—611no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4C22×D6111yescharacteristic
268Q16—22no—
269SD16—41no—
270SD16—2441no—
271M16—2441no—
272M16—2441no—
273C2×C8—611no—
274C2×C8—611no—
275C2×C8C22×D6111yescharacteristic
276C2×C8C22×D6111yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—611no—
279C4⋊C4—611no—
280C4⋊C4—611no—
281C4⋊C4—611no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4C22×D6111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—611no—
291C22⋊C4—611no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C42—611no—
296C42—1221no—
297C42—1221no—
298C23—21no—
299C23—611no—
300C23—1221no—
301C23D4×D6111yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—4881no—
306Q8#1175822412yes—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—1222no—
311D4—1221no—
312D4—1221no—
313D4—4881no—
314D4—4881no—
315D4—4881no—
316D4—2442no—
317D4—2442no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—2442no—
335C2×C4D4×D6111yescharacteristic
336C2×C4C23×D6111yescharacteristic
337C8—21no—
338C8—21no—
339C8—1221no—
340C8—1221no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—1221no—
348C22—1221no—
349C22—1221no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22C2×D4×D6111yescharacteristic
354C4—21no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—612no—
359C4—1221no—
360C4—1221no—
361C4—2441no—
362C4—2441no—
363C4—2441no—
364C4C2×#1175822411yescharacteristic
365C4#1451982211yescharacteristic
366C2—41no—
367C2—81no—
368C2—4881no—
369C2—2441no—
370C2#1684039911yescharacteristic
371C2#137×D6111yescharacteristic
372C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3333
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16840470C2semidirect
3. #16840107C2semidirect
4. #16840076C2semidirect
5. #16840074C2semidirect
6. #16840055C2semidirect
7. #16840010C2semidirect
8. #16840005C2semidirect
9. #16839960C2semidirect
10. #16839923C2semidirect
11. Q16×Dic61C2semidirect
12. #16839837C2semidirect
13. #16839763C2semidirect
14. #16839762C2semidirect
15. C61×#452C2semidirect
197. #452D61semidirect
202. C61#3333semidirect