Finite Group Databasebeta

← #21457990

Subgroups — #21457990

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840458C211yesmaximal, characteristic
2#16840130C211yesmaximal, characteristic, complemented
3#16840100C211yesmaximal, characteristic, complemented
4#16840095C211yesmaximal, characteristic, complemented
5#16840069C211yesmaximal, characteristic, complemented
6#16840010C211yesmaximal, characteristic, complemented
7#16839993C211yesmaximal, characteristic, complemented
8#16839964C211yesmaximal, characteristic, complemented
9#16839901C211yesmaximal, characteristic, complemented
10#16839901C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839771C211yesmaximal, characteristic, complemented
14C2×#14519701C211yesmaximal, characteristic, complemented
15D4×Q8×C61C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20C22×#92418C2211yescharacteristic
21#14519772—21no—
22#14519769C2211yescharacteristic
23#14519759—21no—
24#14519751C2211yescharacteristic
25#14519751C2211yescharacteristic
26#14519749—21no—
27C4×D244C2211yescharacteristic
28#14519737—21no—
29#14519736C2211yescharacteristic
30C2×C4⋊Dic61C2211yescharacteristic
31#14519710C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519701C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519701C2211yescharacteristic
39#14519701C2211yescharacteristic
40#14519701C2211yescharacteristic
41#14519701C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48C22×Q8×C61C2211yescharacteristic
49C22×Q8×C61C2211yescharacteristic
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61C2211yescharacteristic
52C22⋊Q8×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic
57C4×D4×C61—21no—
58C4×D4×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—21no—
61C2×Q8×C61—22no—
62C2×Q8×C61—22no—
63C2×Q8×C61—41no—
64C2×Q8×C61—41no—
65C2×Q8×C61C2311yescharacteristic
66C2×Q8×C61C2311yescharacteristic
67C2×Q8×C61C2311yescharacteristic
68C2×D4×C61D411yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C22×Dic61—21no—
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61D411yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61D411yescharacteristic
88C22⋊C4×C61D411yescharacteristic
89C42×C61—21no—
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92#11758201—22no—
93#11758201—41no—
94#11758201—41no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—42no—
120Q8×C61—42no—
121Q8×C61#4112yes—
122D4×C61—22no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2411yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—81no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—81no—
144D244—21no—
145D244—21no—
146C4×D61—81no—
147#92418—21no—
148#92418—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61#13712yes—
157C22×C61C22×D411yescharacteristic
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—22no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3320—611nomaximal, Sylow
175C2×C61—22no—
176C2×C61—41no—
177C2×C61#54611yescharacteristic
178C2×C61C2×#13711yescharacteristic
179C2×C61#57711yescharacteristic
180D61—81no—
181#553—611no—
182D4×Q8D6111yescharacteristic, complemented
183#491—611no—
184#485—611no—
185#484—611no—
186#479—611no—
187#468—611no—
188#465—611no—
189#461—611no—
190#448—611no—
191#448—611no—
192#440—611no—
193#435—611no—
194#419—611no—
195C2×#103—611no—
196C61#332011yescharacteristic, complemented, Sylow
197C22×Q8C2×D6111yescharacteristic
198C22×Q8C2×D6111yescharacteristic
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16—611no—
202C2×M16—611no—
203C22×C8—611no—
204C4⋊Q8—21no—
205C4⋊Q8C2×D6111yescharacteristic
206#126—1221no—
207#125—611no—
208#123—1221no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D6111yescharacteristic
212C22⋊Q8C2×D6111yescharacteristic
213#121—611no—
214#121—611no—
215#121—1221no—
216C4×Q8C2×D6111yescharacteristic
217C4×D4—21no—
218C4×D4—611no—
219C4×D4—1221no—
220C4×D4C2×D6111yescharacteristic
221#117—611no—
222C2×C4⋊C4—611no—
223#107—611no—
224#107—611no—
225#106—611no—
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#102—611no—
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97—611no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C22×D6111yescharacteristic
247C2×Q8C22×D6111yescharacteristic
248C2×Q8C22×D6111yescharacteristic
249C2×D4—611no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4C22⋊D6111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C22×D6111yescharacteristic
258C22×C4C22×D6111yescharacteristic
259SD16—1222no—
260SD16—2441no—
261SD16—2441no—
262M16—2441no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—2441no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22⋊D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4C22⋊D6111yescharacteristic
288C22⋊C4C22⋊D6111yescharacteristic
289C42—21no—
290C42—1221no—
291C42C22×D6111yescharacteristic
292C23—1221no—
293C23C2×C22⋊D6111yescharacteristic
294C23C2×C22⋊D6111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—42no—
302Q8#1175822412yes—
303D4—22no—
304D4—1221no—
305D4—1221no—
306D4—4881no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4C2×C22⋊D6111yescharacteristic
324C2×C4C2×C22⋊D6111yescharacteristic
325C2×C4C2×C22⋊D6111yescharacteristic
326C2×C4C2×C22⋊D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—1221no—
329C8—1221no—
330C8—1221no—
331C8—1221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22#1451980812yes—
341C22C22×C22⋊D6111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4C2×#1175822411yescharacteristic
354C4#1451982211yescharacteristic
355C2—22no—
356C2—41no—
357C2—4881no—
358C2#1684040611yescharacteristic
359C2C2×#1451980811yescharacteristic
360C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingD4×Q8×C61C2
socleC22×C61C22×D4
hypercenterD4×Q8D61
hypocenterC61#3320
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #16840130C2semidirect
3. #16840100C2semidirect
4. #16840095C2semidirect
5. #16840069C2semidirect
6. #16840010C2semidirect
7. #16839993C2semidirect
8. #16839964C2semidirect
9. #16839901C2semidirect
10. #16839901C2semidirect
11. #16839860C2semidirect
12. #16839834C2semidirect
13. #16839771C2semidirect
14. C2×#14519701C2semidirect
15. D4×Q8×C61C2semidirect
182. D4×Q8D61semidirect
196. C61#3320semidirect