Finite Group Databasebeta

← #21456023

Subgroups — #21456023

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#16840368C211yesmaximal, characteristic, complemented
2#16840241C211yesmaximal, characteristic, complemented
3#16840082C211yesmaximal, characteristic, complemented
4#16840077C211yesmaximal, characteristic, complemented
5#16840066C211yesmaximal, characteristic, complemented
6#16839963C211yesmaximal, characteristic, complemented
7#16839957C211yesmaximal, characteristic, complemented
8#16839908C211yesmaximal, characteristic, complemented
9#16839908C211yesmaximal, characteristic, complemented
10#16839871C211yesmaximal, characteristic, complemented
11#16839861C211yesmaximal, characteristic, complemented
12#16839849C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#478C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21#14519774C2211yescharacteristic
22#14519762—21no—
23#14519762—21no—
24#14519752—21no—
25#14519752—21no—
26#14519752C2211yescharacteristic
27#14519752C2211yescharacteristic
28C4×Dic122C2211yescharacteristic
29#14519742C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31#14519739C2211yescharacteristic
32#14519739C2211yescharacteristic
33C4×C22⋊D61—21no—
34#14519737—21no—
35#14519734C2211yescharacteristic
36#14519733—21no—
37C2×#11758196—21no—
38C4⋊C4×D61C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519708C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519700C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×D4×C61C2311yescharacteristic
60C22×C4×C61—21no—
61C2×C22⋊D61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64#11758224—22no—
65#11758224—22no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244C2311yescharacteristic
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C42×C61C2311yescharacteristic
86C22⋊Dic61—21no—
87#11758199—22no—
88#11758199—22no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94#11758198D411yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196D411yescharacteristic
100#11758196D411yescharacteristic
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758190—22no—
107#11758190—22no—
108C23×C61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61C2×D411yescharacteristic
112D4×C61—21no—
113D4×C61#4112yes—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—81no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2411yescharacteristic
121C22⋊D61—24no—
122C2×Dic61—24no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—81no—
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129D244—21no—
130D244—21no—
131D244—21no—
132D244—21no—
133D244—81no—
134D244—81no—
135D244—81no—
136D244—81no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—81no—
140C4×D61—81no—
141C4×D61—81no—
142Dic122—21no—
143Dic122#4112yes—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—22no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61C22×D411yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
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—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61C2×#4111yescharacteristic
168Dic61—22no—
169Dic61—21no—
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173#3119—611nomaximal, Sylow
174C2×C61—42no—
175C2×C61#52511yescharacteristic
176C2×C61#57611yescharacteristic
177C2×C61#57711yescharacteristic
178D61—41no—
179D61—81no—
180D61—81no—
181#540—611no—
182#520—611no—
183#481—611no—
184#480—611no—
185#479—611no—
186#478D6111yescharacteristic, complemented
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#433—611no—
196C61#311911yescharacteristic, complemented, Sylow
197C2×#41—611no—
198C2×SD16—611no—
199C2×SD16—611no—
200C2×D8—611no—
201C2×D8—611no—
202#127—611no—
203#125C2×D6111yescharacteristic
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—1221no—
216C4×D4—1221no—
217C4×D4C2×D6111yescharacteristic
218#117—611no—
219#117—1221no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222#107—611no—
223#107C2×D6111yescharacteristic
224#106—611no—
225#106C2×D6111yescharacteristic
226C4⋊C8—611no—
227C4⋊C8C2×D6111yescharacteristic
228#103—611no—
229#103—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102C2×D6111yescharacteristic
235#102C2×D6111yescharacteristic
236C22⋊C8—611no—
237C22⋊C8—611no—
238#97—611no—
239C4×C8—611no—
240#41—1222no—
241#41—1222no—
242C2×Q8—611no—
243C2×D4—611no—
244C2×D4—611no—
245C2×D4—1221no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4C22×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—611no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258SD16—1222no—
259SD16—1222no—
260D8—1222no—
261D8—1222no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8C22×D6111yescharacteristic
265C2×C8C22×D6111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4C22×D6111yescharacteristic
275C4⋊C4C22×D6111yescharacteristic
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—611no—
279C22⋊C4—611no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C42—611no—
286C42—1221no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C23—21no—
290C23—611no—
291C23—1221no—
292C23—1221no—
293Q8—612no—
294Q8—1221no—
295D4—21no—
296D4—1224no—
297D4—1221no—
298D4—1221no—
299D4—1221no—
300D4—1221no—
301D4—4881no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305D4#1175822612yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—1224no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4D4×D6111yescharacteristic
323C2×C4D4×D6111yescharacteristic
324C2×C4C23×D6111yescharacteristic
325C8—21no—
326C8—21no—
327C8—1221no—
328C8—1221no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—1221no—
333C22—1221no—
334C22—1221no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—1221no—
348C4—1222no—
349C4—1221no—
350C4—1221no—
351C4—2441no—
352C4#41×D6111yescharacteristic
353C4C2×#1175822611yescharacteristic
354C2—42no—
355C2—4881no—
356C2—4881no—
357C2—2441no—
358C2#1684027511yescharacteristic
359C2#1684056611yescharacteristic
360C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3119
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16840368C2semidirect
2. #16840241C2semidirect
3. #16840082C2semidirect
4. #16840077C2semidirect
5. #16840066C2semidirect
6. #16839963C2semidirect
7. #16839957C2semidirect
8. #16839908C2semidirect
9. #16839908C2semidirect
10. #16839871C2semidirect
11. #16839861C2semidirect
12. #16839849C2semidirect
13. #16839842C2semidirect
14. #16839822C2semidirect
15. C61×#478C2semidirect
186. #478D61semidirect
196. C61#3119semidirect