Finite Group Databasebeta

← #21458523

Subgroups — #21458523

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#16840432C211yesmaximal, characteristic, complemented
3#16840125C211yesmaximal, characteristic, complemented
4#16840107C211yesmaximal, characteristic, complemented
5#16840064C211yesmaximal, characteristic, complemented
6#16840059C211yesmaximal, characteristic, complemented
7#16840050C211yesmaximal, characteristic, complemented
8#16839956C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839954C211yesmaximal, characteristic, complemented
11#16839890C211yesmaximal, characteristic, complemented
12#16839875C211yesmaximal, characteristic, complemented
13#16839871C211yesmaximal, characteristic, complemented
14#16839842C211yesmaximal, characteristic, complemented
15C61×#490C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×D488C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519773C2211yescharacteristic
22#14519773C2211yescharacteristic
23#14519768C2211yescharacteristic
24#14519757—21no—
25#14519755—21no—
26#14519755—21no—
27#14519749—21no—
28#14519749—21no—
29#14519748—21no—
30C4×Dic122C2211yescharacteristic
31C4×D244C2211yescharacteristic
32C4×D244C2211yescharacteristic
33D4×Dic61C2211yescharacteristic
34D4×Dic61C2211yescharacteristic
35#14519739C2211yescharacteristic
36#14519739C2211yescharacteristic
37C4⋊C4×D61—21no—
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#127×C61C2211yescharacteristic
53#125×C61C2211yescharacteristic
54#102×C61C2211yescharacteristic
55#102×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69#11758224—44no—
70C2×D244C2311yescharacteristic
71C2×D244C2311yescharacteristic
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
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87#11758199—22no—
88#11758199—22no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61D411yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196D411yescharacteristic
100#11758196D411yescharacteristic
101C4×Dic61C2311yescharacteristic
102C4×Dic61C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105D488—22no—
106C23×C61—21no—
107C23×C61—21no—
108C22×D61—21no—
109C22×D61—21no—
110D4×C61—21no—
111D4×C61—21no—
112D4×C61—21no—
113D4×C61—21no—
114D4×C61—42no—
115D4×C61—81no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2411yescharacteristic
121C22⋊D61—42no—
122C22⋊D61—42no—
123C22⋊D61—81no—
124C22⋊D61—81no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—21no—
135D244—21no—
136D244#4112yescomplemented
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×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61C22×D411yescharacteristic
154C2×D61—22no—
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×C61C2×#4111yescharacteristic
165C4×C612−1+411yescharacteristic
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171Dic61AGL(1,ℤ/8)12yes—
172#3366—611nomaximal, Sylow
173C2×C61—81no—
174C2×C61—81no—
175C2×C61#54811yescharacteristic
176C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C61#57611yescharacteristic
178D61—42no—
179D61—81no—
180#554—611no—
181#550—611no—
182#490—611no—
183#490D6111yescharacteristic, complemented
184#486—611no—
185#478—611no—
186#478—611no—
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#127C2×D6111yescharacteristic
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×D4—611no—
219C2×C4⋊C4—1221no—
220#107—611no—
221#106—611no—
222#106—611no—
223C4⋊C8—611no—
224C4⋊C8—611no—
225C4⋊C8—611no—
226#102—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102C2×D6111yescharacteristic
233#102C2×D6111yescharacteristic
234#102C2×D6111yescharacteristic
235#102C2×D6111yescharacteristic
236#97—611no—
237#97C2×D6111yescharacteristic
238C4×C8—611no—
239#41—2444no—
240C2×Q8—611no—
241C2×Q8—1221no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4C22×D6111yescharacteristic
251C2×D4C22×D6111yescharacteristic
252C22×C4—1221no—
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—611no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4C22×D6111yescharacteristic
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C42—611no—
284C42—611no—
285C42C22×D6111yescharacteristic
286C23—21no—
287C23—21no—
288C23—1221no—
289C23—1221no—
290Q8—1222no—
291Q8—4881no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—42no—
297D4—81no—
298D4—612no—
299D4—1221no—
300D4—1221no—
301D4—1221no—
302D4—4881no—
303D4—4881no—
304D4—2442no—
305D4—2442no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—4881no—
315C2×C4—4881no—
316C2×C4—2442no—
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—41no—
331C22—41no—
332C22—41no—
333C22—1222no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22C2×D4×D6111yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—612no—
345C4—1221no—
346C4—1221no—
347C4—1221no—
348C4—2441no—
349C4—2441no—
350C4#41×D6111yescharacteristic
351C4#1451982411yescharacteristic
352C2—81no—
353C2—81no—
354C2—4881no—
355C2—2442no—
356C2#1684042011yescharacteristic
357C2AGL(1,ℤ/8)×D6111yescharacteristic
358C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#490C2
socleC22×C61C22×D4
hypercenter#490D61
hypocenterC61#3366
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #16840468C2semidirect
2. #16840432C2semidirect
3. #16840125C2semidirect
4. #16840107C2semidirect
5. #16840064C2semidirect
6. #16840059C2semidirect
7. #16840050C2semidirect
8. #16839956C2semidirect
9. #16839956C2semidirect
10. #16839954C2semidirect
11. #16839890C2semidirect
12. #16839875C2semidirect
13. #16839871C2semidirect
14. #16839842C2semidirect
15. C61×#490C2semidirect
136. D244#41semidirect
183. #490D61semidirect
195. C61#3366semidirect