Finite Group Databasebeta

← #21457805

Subgroups — #21457805

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#16840422C211yesmaximal, characteristic, complemented
2#16840412C211yesmaximal, characteristic, complemented
3#16840123C211yesmaximal, characteristic, complemented
4#16840095C211yesmaximal, characteristic, complemented
5#16840077C211yesmaximal, characteristic, complemented
6#16840056C211yesmaximal, characteristic, complemented
7#16839997C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839905C211yesmaximal, characteristic, complemented
10#16839899C211yesmaximal, characteristic, complemented
11#16839859C211yesmaximal, characteristic, complemented
12#16839831C211yesmaximal, characteristic, complemented
13#16839764C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224—21no—
18C2×Q8×D61C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519766C2211yescharacteristic
24#14519763—21no—
25#14519759—21no—
26#14519758—21no—
27#14519755—21no—
28#14519754—21no—
29#14519752C2211yescharacteristic
30#14519750—21no—
31#14519748C2211yescharacteristic
32#14519742C2211yescharacteristic
33D4×Dic61C2211yescharacteristic
34#14519739—21no—
35C4×C22⋊D61C2211yescharacteristic
36C2×C4⋊Dic61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61D411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68Q8×D61—22no—
69Q8×D61—41no—
70#11758224—44no—
71#11758222—22no—
72#11758222—41no—
73C2×D244—21no—
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122C2311yescharacteristic
82SD16×C61—41no—
83M16×C61—41no—
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61—21no—
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61D411yescharacteristic
94#11758200—22no—
95#11758199—41no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198D411yescharacteristic
100C4⋊Dic61—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107C4×Dic61—21no—
108C4×Dic61C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C8×D61—41no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—42no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—22no—
129C22⋊D61—42no—
130C22⋊D61—42no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139D244—21no—
140D244—21no—
141D244—42no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—42no—
145C4×D61—42no—
146C4×D61—42no—
147Dic122—21no—
148Dic122—42no—
149Dic122—42no—
150Dic122#4112yescomplemented
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61AGL(1,ℤ/8)12yes—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C2×#4111yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—22no—
175Dic61—21no—
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179Dic61—41no—
180#3308—611nomaximal, Sylow
181C2×C61—41no—
182C2×C61—81no—
183C2×C61#54611yescharacteristic
184C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C61#57811yescharacteristic
186D61—22no—
187D61—81no—
188#548—611no—
189#547—611no—
190#489—611no—
191#484—611no—
192#480—611no—
193#477—611no—
194#468D6111yescharacteristic, complemented
195#466—611no—
196#463—611no—
197#449—611no—
198#448—611no—
199#440—611no—
200#435—611no—
201#417—611no—
202C2×#103—611no—
203C61#330811yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C2×#41—1221no—
206C22×Q8—611no—
207C2×SD16—611no—
208C2×SD16C2×D6111yescharacteristic
209C2×D8—611no—
210C2×M16C2×D6111yescharacteristic
211C22×C8—611no—
212C4⋊Q8—611no—
213#124—611no—
214#124—1221no—
215#123—1221no—
216#123—1221no—
217C22⋊Q8—1221no—
218C22⋊Q8—1221no—
219C22⋊Q8C2×D6111yescharacteristic
220#121—611no—
221#121—611no—
222#121—1221no—
223#121C2×D6111yescharacteristic
224C4×Q8—611no—
225C4×D4—611no—
226C4×D4—611no—
227C4×D4—1221no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230#107—611no—
231#107—611no—
232#107C2×D6111yescharacteristic
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⋊C8—611no—
246#97—611no—
247#41—1222no—
248#41—2441no—
249#41—2444no—
250C2×Q8—611no—
251C2×Q8—1221no—
252C2×Q8—1221no—
253C2×Q8—1222no—
254C2×Q8—2441no—
255C2×Q8C22×D6111yescharacteristic
256C2×D4—21no—
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4C22×D6111yescharacteristic
263C22×C4—611no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4C22×D6111yescharacteristic
270SD16—41no—
271SD16—1222no—
272D8—2441no—
273M16—41no—
274C2×C8—611no—
275C2×C8—611no—
276C2×C8—2441no—
277C2×C8C22×D6111yescharacteristic
278C2×C8C22×D6111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—611no—
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4C22×D6111yescharacteristic
288C4⋊C4C22×D6111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—611no—
292C22⋊C4—611no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C42—611no—
299C42—1221no—
300C23—21no—
301C23—611no—
302C23—1221no—
303C23D4×D6111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—612no—
307Q8—1221no—
308Q8—2442no—
309Q8—2442no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—1222no—
314D4—1221no—
315D4—1221no—
316D4—2442no—
317D4—2442no—
318D4—2442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
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—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—41no—
347C22—41no—
348C22—41no—
349C22—612no—
350C22—1221no—
351C22—1221no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—1221no—
361C4—1221no—
362C4—1221no—
363C4—1222no—
364C4—2441no—
365C4—2441no—
366C4#41×D6111yescharacteristic
367C4#1451982211yescharacteristic
368C2—41no—
369C2—81no—
370C2—1222no—
371C2—4881no—
372C2#1684040111yescharacteristic
373C2AGL(1,ℤ/8)×D6111yescharacteristic
374C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3308
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #16840422C2semidirect
2. #16840412C2semidirect
3. #16840123C2semidirect
4. #16840095C2semidirect
5. #16840077C2semidirect
6. #16840056C2semidirect
7. #16839997C2semidirect
8. #16839979C2semidirect
9. #16839905C2semidirect
10. #16839899C2semidirect
11. #16839859C2semidirect
12. #16839831C2semidirect
13. #16839764C2semidirect
14. #103×D61C2semidirect
15. C61×#468C2semidirect
150. Dic122#41semidirect
194. #468D61semidirect
203. C61#3308semidirect