Finite Group Databasebeta

← #21456513

Subgroups — #21456513

Order 7808.

410 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#16840309C211yesmaximal, characteristic, complemented
2#16840299C211yesmaximal, characteristic, complemented
3#16840170C211yesmaximal, characteristic, complemented
4#16840148C211yesmaximal, characteristic, complemented
5#16840125C211yesmaximal, characteristic, complemented
6#16840123C211yesmaximal, characteristic, complemented
7#16839999C211yesmaximal, characteristic, complemented
8#16839997C211yesmaximal, characteristic, complemented
9#16839994C211yesmaximal, characteristic, complemented
10#16839988C211yesmaximal, characteristic, complemented
11#16839875C211yesmaximal, characteristic, complemented
12#16839872C211yesmaximal, characteristic, complemented
13#16839860C211yesmaximal, characteristic, complemented
14#97×D61C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758201C2211yescharacteristic
18C2×D488C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519773C2211yescharacteristic
24#14519772—21no—
25#14519768C2211yescharacteristic
26#14519766C2211yescharacteristic
27#14519763—21no—
28#14519762—21no—
29#14519753C2211yescharacteristic
30#14519752C2211yescharacteristic
31#14519752C2211yescharacteristic
32#14519750—21no—
33#14519748C2211yescharacteristic
34C4×D244—21no—
35C4×D244C2211yescharacteristic
36C4×D244C2211yescharacteristic
37C4×C22⋊D61—21no—
38#14519734—21no—
39C42×D61C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519688C2211yescharacteristic
50#14519687C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—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×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61D411yescharacteristic
73C2×C4×D61D411yescharacteristic
74C2×C4×D61C2311yescharacteristic
75C2×Dic122—21no—
76SD16×C61—22no—
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C42×C61—21no—
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86#11758201—22no—
87#11758199—22no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101C4×Dic61D411yescharacteristic
102C4×Dic61D411yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106D488—22no—
107C8×D61—22no—
108C8×D61—22no—
109C23×C61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61C2×D411yescharacteristic
113Q8×C61—21no—
114Q8×C61—21no—
115D4×C61—21no—
116D4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—42no—
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C22⋊D61—42no—
125C22⋊D61—42no—
126C22⋊D61—42no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—21no—
133D244—21no—
134D244—21no—
135D244—21no—
136D244—42no—
137D244—42no—
138C4×D61—22no—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—41no—
142C4×D61—42no—
143C4×D61—42no—
144Dic122—42no—
145C8×C61—21no—
146C8×C61#4112yescomplemented
147#92418—21no—
148#92418#4112yescomplemented
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61C22×D411yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61AGL(1,ℤ/8)12yes—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61C2×#4111yescharacteristic
168C4×C61C2×#4111yescharacteristic
169Dic61—21no—
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173Dic61—41no—
174#3180—611nomaximal, Sylow
175C2×C61—81no—
176C2×C61#53211yescharacteristic
177C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C61#57511yescharacteristic
179D61—22no—
180D61—81no—
181D61—81no—
182#532—611no—
183#529—611no—
184#501—611no—
185#496—611no—
186#490—611no—
187#489—611no—
188#466—611no—
189#466—611no—
190#465—611no—
191#465—611no—
192#442—611no—
193#442—611no—
194#440—611no—
195#440D6111yescharacteristic, complemented
196C2×#97—611no—
197C61#318011yescharacteristic, complemented, Sylow
198C2×#41—1221no—
199C2×SD16—611no—
200C2×SD16C2×D6111yescharacteristic
201C2×D8—611no—
202C2×D8—611no—
203C22×C8—611no—
204C22×C8—611no—
205C4⋊Q8—611no—
206#127—611no—
207#126—1221no—
208#125—611no—
209#124—611no—
210#124—1221no—
211#123—1221no—
212C22⋊Q8—611no—
213#121—611no—
214#121—611no—
215#121—611no—
216#121—1221no—
217C4×Q8C2×D6111yescharacteristic
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—1221no—
221C4×D4—1221no—
222C4×D4C2×D6111yescharacteristic
223#117—1221no—
224C2×C42—611no—
225#107—611no—
226#107C2×D6111yescharacteristic
227#106—611no—
228#106—611no—
229#103—611no—
230#103C2×D6111yescharacteristic
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102—611no—
236#102C2×D6111yescharacteristic
237#97—611no—
238#97—611no—
239#97—611no—
240#97C2×D6111yescharacteristic
241#41—2444no—
242C2×Q8—1221no—
243C2×Q8C22×D6111yescharacteristic
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4C22×D6111yescharacteristic
252C22×C4—21no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258SD16—22no—
259SD16—1222no—
260D8—1222no—
261D8—1222no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—1222no—
265C2×C8—1222no—
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4C22×D6111yescharacteristic
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—21no—
287C42—611no—
288C42—611no—
289C42—611no—
290C42C22×D6111yescharacteristic
291C23—21no—
292C23—611no—
293C23—1221no—
294C23—1221no—
295Q8—21no—
296Q8—21no—
297Q8—2442no—
298D4—21no—
299D4—21no—
300D4—1221no—
301D4—1221no—
302D4—1221no—
303D4—1221no—
304D4—2442no—
305D4—2442no—
306D4—2442no—
307D4—2442no—
308D4—2442no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—1222no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—2441no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4D4×D6111yescharacteristic
325C2×C4D4×D6111yescharacteristic
326C2×C4C23×D6111yescharacteristic
327C8—21no—
328C8—612no—
329C8—1221no—
330C8#1175822212yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—612no—
335C22—1221no—
336C22—1221no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22C2×D4×D6111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1221no—
350C4—1221no—
351C4—1221no—
352C4—2441no—
353C4—2441no—
354C4#41×D6111yescharacteristic
355C4C2×#1175822211yescharacteristic
356C2—81no—
357C2—1222no—
358C2—4881no—
359C2—4881no—
360C2#1684030911yescharacteristic
361C2AGL(1,ℤ/8)×D6111yescharacteristic
362C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#3180
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16840309C2semidirect
2. #16840299C2semidirect
3. #16840170C2semidirect
4. #16840148C2semidirect
5. #16840125C2semidirect
6. #16840123C2semidirect
7. #16839999C2semidirect
8. #16839997C2semidirect
9. #16839994C2semidirect
10. #16839988C2semidirect
11. #16839875C2semidirect
12. #16839872C2semidirect
13. #16839860C2semidirect
14. #97×D61C2semidirect
15. C61×#440C2semidirect
146. C8×C61#41semidirect
148. #92418#41semidirect
195. #440D61semidirect
197. C61#3180semidirect
330. C8#11758222semidirect