Finite Group Databasebeta

← #21458529

Subgroups — #21458529

Order 7808.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840468C211yesmaximal, characteristic, complemented
2#16840433C211yesmaximal, characteristic, complemented
3#16840128C211yesmaximal, characteristic, complemented
4#16840125C211yesmaximal, characteristic, complemented
5#16840107C211yesmaximal, characteristic, complemented
6#16840065C211yesmaximal, characteristic, complemented
7#16840051C211yesmaximal, characteristic, complemented
8#16839958C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839956C211yesmaximal, characteristic, complemented
11#16839891C211yesmaximal, characteristic, complemented
12#16839873C211yesmaximal, characteristic, complemented
13#16839872C211yesmaximal, characteristic, complemented
14#16839844C211yesmaximal, characteristic, complemented
15C61×#478C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×D488C2211yescharacteristic
18C2×D488C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519774C2211yescharacteristic
22#14519773C2211yescharacteristic
23#14519773C2211yescharacteristic
24#14519768C2211yescharacteristic
25#14519757—21no—
26#14519755—21no—
27#14519755—21no—
28#14519751—21no—
29#14519750—21no—
30#14519750—21no—
31C4×Dic122C2211yescharacteristic
32C4×D244C2211yescharacteristic
33#14519739C2211yescharacteristic
34#14519739C2211yescharacteristic
35#14519739C2211yescharacteristic
36#14519739C2211yescharacteristic
37C4⋊C4×D61—21no—
38#14519708C2211yescharacteristic
39#14519706C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519699C2211yescharacteristic
42#14519699C2211yescharacteristic
43#14519698C2211yescharacteristic
44#14519697C2211yescharacteristic
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519688C2211yescharacteristic
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—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65#11758222—44no—
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×Dic122—21no—
77C2×Dic122D411yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C42×C61C2311yescharacteristic
87#11758199—22no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61D411yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196D411yescharacteristic
99#11758196D411yescharacteristic
100C4×Dic61C2311yescharacteristic
101C4×Dic61C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104D488—22no—
105D488—22no—
106C23×C61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110D4×C61—21no—
111D4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—42no—
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2411yescharacteristic
119C22⋊D61—42no—
120C22⋊D61—42no—
121C22⋊D61—81no—
122C22⋊D61—81no—
123C2×Dic61—21no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128D244—21no—
129D244—21no—
130D244—21no—
131D244—21no—
132D244—21no—
133D244—42no—
134D244—81no—
135D244#4112yescomplemented
136C4×D61—42no—
137C4×D61—42no—
138C4×D61—42no—
139C4×D61—81no—
140C4×D61—81no—
141Dic122—22no—
142Dic122—81no—
143C8×C61—21no—
144C8×C61—21no—
145#92418—21no—
146#92418—21no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61C22×D411yescharacteristic
151C2×D61—22no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61C2×#4111yescharacteristic
166C4×C612−1+411yescharacteristic
167Dic61—21no—
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61AGL(1,ℤ/8)12yes—
172#3366—611nomaximal, Sylow
173C2×C61—81no—
174C2×C61#54811yescharacteristic
175C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C61#57611yescharacteristic
177D61—42no—
178D61—81no—
179D61—81no—
180#554—611no—
181#550—611no—
182#490—611no—
183#490—611no—
184#486—611no—
185#478—611no—
186#478D6111yescharacteristic, complemented
187#476—611no—
188#459—611no—
189#459—611no—
190#459—611no—
191#446—611no—
192#442—611no—
193#442—611no—
194C4×D8—611no—
195C61#336611yescharacteristic, complemented, Sylow
196C2×#41—1221no—
197C2×D8—611no—
198C2×D8—611no—
199C2×D8—611no—
200C4⋊Q8—611no—
201#127—611no—
202#127—611no—
203#127—611no—
204#125—611no—
205#125C2×D6111yescharacteristic
206C22⋊Q8—1221no—
207C22⋊Q8—1221no—
208C22⋊Q8—1221no—
209#121—1221no—
210#121—1221no—
211#121—1221no—
212C4×Q8—611no—
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—611no—
217C4×D4—611no—
218C4×D4C2×D6111yescharacteristic
219C2×C4⋊C4—1221no—
220#107C2×D6111yescharacteristic
221#106—611no—
222#106C2×D6111yescharacteristic
223C4⋊C8—611no—
224C4⋊C8—611no—
225C4⋊C8C2×D6111yescharacteristic
226#102—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102C2×D6111yescharacteristic
235#102C2×D6111yescharacteristic
236#97—611no—
237#97—611no—
238C4×C8—611no—
239#41—2444no—
240C2×Q8—611no—
241C2×Q8—1221no—
242C2×D4—611no—
243C2×D4—611no—
244C2×D4—611no—
245C2×D4—1221no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4C22×D6111yescharacteristic
252C22×C4—21no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258D8—1222no—
259D8—1222no—
260D8—1222no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8C22×D6111yescharacteristic
264C2×C8C22×D6111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—611no—
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—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C42—611no—
284C42—611no—
285C42C22×D6111yescharacteristic
286C23—21no—
287C23—1221no—
288C23—1221no—
289C23—1221no—
290Q8—1222no—
291Q8—4881no—
292D4—21no—
293D4—21no—
294D4—612no—
295D4—1221no—
296D4—1221no—
297D4—1221no—
298D4—1221no—
299D4—1221no—
300D4—4881no—
301D4—4881no—
302D4—4881no—
303D4—2442no—
304D4—2442no—
305D4—2442no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1221no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4D4×D6111yescharacteristic
321C2×C4D4×D6111yescharacteristic
322C2×C4C23×D6111yescharacteristic
323C8—21no—
324C8—21no—
325C8—1221no—
326C8—1221no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—1222no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22C2×D4×D6111yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—612no—
346C4—1221no—
347C4—1221no—
348C4—1221no—
349C4—2441no—
350C4#41×D6111yescharacteristic
351C4#1451982511yescharacteristic
352C2—81no—
353C2—4881no—
354C2—4881no—
355C2—2442no—
356C2#1684042211yescharacteristic
357C2AGL(1,ℤ/8)×D6111yescharacteristic
358C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3366
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. #16840468C2semidirect
2. #16840433C2semidirect
3. #16840128C2semidirect
4. #16840125C2semidirect
5. #16840107C2semidirect
6. #16840065C2semidirect
7. #16840051C2semidirect
8. #16839958C2semidirect
9. #16839956C2semidirect
10. #16839956C2semidirect
11. #16839891C2semidirect
12. #16839873C2semidirect
13. #16839872C2semidirect
14. #16839844C2semidirect
15. C61×#478C2semidirect
135. D244#41semidirect
186. #478D61semidirect
195. C61#3366semidirect