Finite Group Databasebeta

← #21455792

Subgroups — #21455792

Order 7808.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840341C211yesmaximal, characteristic
2#16840243C211yesmaximal, characteristic, complemented
3#16840105C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840099C211yesmaximal, characteristic, complemented
6#16840097C211yesmaximal, characteristic, complemented
7#16840085C211yesmaximal, characteristic, complemented
8#16840083C211yesmaximal, characteristic, complemented
9#16840074C211yesmaximal, characteristic, complemented
10#16839803C211yesmaximal, characteristic, complemented
11#107×D61C211yesmaximal, characteristic, complemented
12#16839760C211yesmaximal, characteristic, complemented
13#16839755C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#480C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519757C2211yescharacteristic
21#14519756C2211yescharacteristic
22#14519754—21no—
23#14519750—21no—
24#14519749—21no—
25#14519748—21no—
26#14519748C2211yescharacteristic
27#14519742—21no—
28#14519739—21no—
29C4×C22⋊D61—21no—
30C4×C22⋊D61—21no—
31#14519736C2211yescharacteristic
32#14519735C2211yescharacteristic
33#14519735C2211yescharacteristic
34C4⋊C4×D61C2211yescharacteristic
35C4⋊C4×D61C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52#121×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61D411yescharacteristic
66C2×C22⋊D61D411yescharacteristic
67C22×Dic61—21no—
68#11758224—22no—
69#11758224—22no—
70#11758222—22no—
71#11758222—22no—
72C2×D244D411yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61C2311yescharacteristic
77C2×C4×D61C2311yescharacteristic
78C2×Dic122D411yescharacteristic
79C2×Dic122C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758189—22no—
107C8×D61—22no—
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61C2×D411yescharacteristic
111C22×D61C2×D411yescharacteristic
112D4×C61—21no—
113D4×C61—21no—
114D4×C61—81no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—81no—
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2411yescharacteristic
123C22⋊D61—22no—
124C22⋊D61—22no—
125C22⋊D61—42no—
126C22⋊D61—81no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—42no—
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134D244—22no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—81no—
138C4×D61—81no—
139C4×D61—81no—
140C4×D61#4112yes—
141C4×D61#4112yes—
142Dic122—22no—
143Dic122—21no—
144Dic122—21no—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61C22×D411yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61#12312yes—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61C2×#4111yescharacteristic
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61#12312yes—
174#3098—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61—81no—
177C2×C61C2×#12311yescharacteristic
178C2×C61#57611yescharacteristic
179C2×C61#57811yescharacteristic
180D61—22no—
181D61—41no—
182#537—611no—
183#520—611no—
184#485—611no—
185#485—611no—
186#484—611no—
187#484—611no—
188#482—611no—
189#482—611no—
190#480—611no—
191#480D6111yescharacteristic, complemented
192#428—611no—
193C2×#107—611no—
194#417—611no—
195#416—611no—
196#408—611no—
197C61#309811yescharacteristic, complemented, Sylow
198C2×#41—611no—
199C2×#41—611no—
200C2×M16—611no—
201C22×C8—611no—
202C22⋊Q8—611no—
203C22⋊Q8—611no—
204C22⋊Q8—1221no—
205#121—611no—
206#121—1221no—
207#121—1221no—
208#121—1221no—
209#121C2×D6111yescharacteristic
210C4×Q8—1221no—
211C4×D4—1221no—
212C4×D4—1221no—
213C4×D4—1221no—
214#117—611no—
215#117—611no—
216#117—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4C2×D6111yescharacteristic
221#107—611no—
222#107—611no—
223#107—611no—
224#107—611no—
225#107C2×D6111yescharacteristic
226#107C2×D6111yescharacteristic
227#106—611no—
228#106—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103—611no—
233#102—611no—
234#102—611no—
235#102C2×D6111yescharacteristic
236#102C2×D6111yescharacteristic
237C22⋊C8—611no—
238C22⋊C8—611no—
239C22⋊C8—611no—
240C22⋊C8C2×D6111yescharacteristic
241#41—1222no—
242#41—1222no—
243#41—1222no—
244#41—1222no—
245C2×Q8—611no—
246C2×Q8—611no—
247C2×D4—21no—
248C2×D4—611no—
249C2×D4—611no—
250C2×D4—611no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4C22×D6111yescharacteristic
254C22×C4—21no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4C22×D6111yescharacteristic
262M16—1222no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—1222no—
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—611no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4C22×D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C4⋊C4C22×D6111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C23—21no—
291C23—611no—
292C23—611no—
293C23D4×D6111yescharacteristic
294Q8—1222no—
295Q8—1221no—
296Q8—1221no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—1222no—
301D4—1222no—
302D4—1222no—
303D4—4881no—
304D4—2442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—611no—
312C2×C4—612no—
313C2×C4—612no—
314C2×C4—611no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—2442no—
325C2×C4D4×D6111yescharacteristic
326C2×C4C23×D6111yescharacteristic
327C8—21no—
328C8—21no—
329C8—1221no—
330C8—1221no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—612no—
338C22—1221no—
339C22—1221no—
340C22—1221no—
341C22—1221no—
342C22—1221no—
343C22C2×D4×D6111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—612no—
349C4—1221no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4—2441no—
354C4#41×D6111yescharacteristic
355C4#41×D6111yescharacteristic
356C2—41no—
357C2—81no—
358C2—1222no—
359C2—2441no—
360C2#123×D6111yescharacteristic
361C2#1684056311yescharacteristic
362C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3098
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #16840243C2semidirect
3. #16840105C2semidirect
4. #16840104C2semidirect
5. #16840099C2semidirect
6. #16840097C2semidirect
7. #16840085C2semidirect
8. #16840083C2semidirect
9. #16840074C2semidirect
10. #16839803C2semidirect
11. #107×D61C2semidirect
12. #16839760C2semidirect
13. #16839755C2semidirect
14. #16839727C2semidirect
15. C61×#480C2semidirect
191. #480D61semidirect
197. C61#3098semidirect