Finite Group Databasebeta

← #21456020

Subgroups — #21456020

Order 7808.

396 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#16840367C211yesmaximal, characteristic, complemented
2#16840242C211yesmaximal, characteristic, complemented
3#16840081C211yesmaximal, characteristic, complemented
4#16840076C211yesmaximal, characteristic, complemented
5#16840070C211yesmaximal, characteristic, complemented
6#16840063C211yesmaximal, characteristic, complemented
7#16839963C211yesmaximal, characteristic, complemented
8#16839958C211yesmaximal, characteristic, complemented
9#16839909C211yesmaximal, characteristic, complemented
10#16839909C211yesmaximal, characteristic, complemented
11#16839875C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13C4×#11758190C211yesmaximal, characteristic, complemented
14C4×D488C211yesmaximal, characteristic, complemented
15C61×#433C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic
21#14519774C2211yescharacteristic
22#14519769C2211yescharacteristic
23#14519762—21no—
24#14519762—21no—
25#14519751C2211yescharacteristic
26#14519751C2211yescharacteristic
27#14519750—21no—
28#14519750—21no—
29C4×Dic122C2211yescharacteristic
30C4×Dic122C2211yescharacteristic
31C4×D244C2211yescharacteristic
32C4×D244C2211yescharacteristic
33C4×D244C2211yescharacteristic
34C4×D244C2211yescharacteristic
35#14519737—21no—
36#14519737—21no—
37#14519735—21no—
38C2×C4⋊Dic61C2211yescharacteristic
39C4⋊C4×D61—21no—
40#14519711C2211yescharacteristic
41#14519711C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519709C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52#117×C61C2211yescharacteristic
53C4⋊C8×C61C2211yescharacteristic
54C4⋊C8×C61C2211yescharacteristic
55C22⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57#97×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C2×C22⋊D61—21no—
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63C22×Dic61—21no—
64#11758222—22no—
65#11758222—22no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244C2311yescharacteristic
69C2×D244C2311yescharacteristic
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×Dic122C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61D411yescharacteristic
82C4⋊C4×C61D411yescharacteristic
83C22⋊C4×C61D411yescharacteristic
84C22⋊C4×C61D411yescharacteristic
85C42×C61C2311yescharacteristic
86C42×C61C2311yescharacteristic
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104D488—22no—
105D488—22no—
106#11758190—22no—
107#11758190—22no—
108C23×C61C2×D411yescharacteristic
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C22⋊D61—24no—
121C22⋊D61—81no—
122C22⋊D61—81no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—81no—
129D244—21no—
130D244—21no—
131D244—21no—
132D244—21no—
133D244—21no—
134D244—81no—
135D244—81no—
136D244#4112yes—
137C4×D61—24no—
138C4×D61—81no—
139C4×D61—81no—
140C4×D61—81no—
141C4×D61—81no—
142Dic122—21no—
143Dic122#4112yes—
144C8×C61—21no—
145C8×C61—21no—
146C8×C61—21no—
147C8×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C22×D411yescharacteristic
152C2×D61—22no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61C2×#4111yescharacteristic
167C4×C61C2×#4111yescharacteristic
168Dic61—22no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173#3119—611nomaximal, Sylow
174C2×C61—41no—
175C2×C61#52511yescharacteristic
176C2×C61#57611yescharacteristic
177C2×C61#57711yescharacteristic
178D61—42no—
179D61—81no—
180D61—81no—
181#540—611no—
182#520—611no—
183#481—611no—
184#480—611no—
185#479—611no—
186#478—611no—
187#460—611no—
188#459—611no—
189#449—611no—
190#449—611no—
191#442—611no—
192#440—611no—
193C4×SD16—611no—
194C4×D8—611no—
195#433D6111yescharacteristic, complemented
196C61#311911yescharacteristic, complemented, Sylow
197C2×#41—611no—
198C2×SD16—611no—
199C2×SD16—611no—
200C2×D8—611no—
201C2×D8—611no—
202#127—611no—
203#125—611no—
204#123—1221no—
205#123—1221no—
206#121—611no—
207#121—611no—
208#121—1221no—
209#121—1221no—
210C4×Q8—611no—
211C4×Q8—611no—
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—1221no—
217C4×D4—1221no—
218#117—1221no—
219#117C2×D6111yescharacteristic
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222#107—611no—
223#107—611no—
224#106—611no—
225#106—611no—
226C4⋊C8C2×D6111yescharacteristic
227C4⋊C8C2×D6111yescharacteristic
228#103—611no—
229#103—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102—611no—
236C22⋊C8C2×D6111yescharacteristic
237C22⋊C8C2×D6111yescharacteristic
238#97C2×D6111yescharacteristic
239C4×C8C2×D6111yescharacteristic
240#41—1222no—
241#41—1222no—
242C2×Q8—611no—
243C2×D4—611no—
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C22×D6111yescharacteristic
258SD16—1222no—
259SD16—1222no—
260D8—1222no—
261D8—1222no—
262C2×C8C22×D6111yescharacteristic
263C2×C8C22×D6111yescharacteristic
264C2×C8C22×D6111yescharacteristic
265C2×C8C22×D6111yescharacteristic
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4D24411yescharacteristic
276C4⋊C4D24411yescharacteristic
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4D24411yescharacteristic
284C22⋊C4D24411yescharacteristic
285C42—1221no—
286C42—1221no—
287C42C22×D6111yescharacteristic
288C42C22×D6111yescharacteristic
289C23—1221no—
290C23—1221no—
291C23—1221no—
292C23C2×D24411yescharacteristic
293Q8—612no—
294Q8—1221no—
295D4—612no—
296D4—1224no—
297D4—1221no—
298D4—1221no—
299D4—1221no—
300D4—1221no—
301D4—1221no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305D4—4881no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—1224no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—4881no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4C2×D24411yescharacteristic
320C2×C4C2×D24411yescharacteristic
321C2×C4C2×D24411yescharacteristic
322C2×C4C2×D24411yescharacteristic
323C2×C4C2×D24411yescharacteristic
324C2×C4C23×D6111yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—1222no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22C22×D24411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—1222no—
348C4—2441no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4#41×D6111yescharacteristic
353C4#41×D6111yescharacteristic
354C2—41no—
355C2—4881no—
356C2—4881no—
357C2—2442no—
358C2#1684027411yescharacteristic
359C2#1684056711yescharacteristic
360C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3119
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16840367C2semidirect
2. #16840242C2semidirect
3. #16840081C2semidirect
4. #16840076C2semidirect
5. #16840070C2semidirect
6. #16840063C2semidirect
7. #16839963C2semidirect
8. #16839958C2semidirect
9. #16839909C2semidirect
10. #16839909C2semidirect
11. #16839875C2semidirect
12. #16839864C2semidirect
13. C4×#11758190C2semidirect
14. C4×D488C2semidirect
15. C61×#433C2semidirect
195. #433D61semidirect
196. C61#3119semidirect