Finite Group Databasebeta

← #23775742

Subgroups — #23775742

Order 10112.

420 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#19099214C211yesmaximal, characteristic, complemented
2#19099213C211yesmaximal, characteristic, complemented
3#19098967C211yesmaximal, characteristic, complemented
4#19098878C211yesmaximal, characteristic, complemented
5#19098877C211yesmaximal, characteristic, complemented
6#19098875C211yesmaximal, characteristic, complemented
7#19098842C211yesmaximal, characteristic, complemented
8#19098841C211yesmaximal, characteristic, complemented
9#19098798C211yesmaximal, characteristic, complemented
10#19098797C211yesmaximal, characteristic, complemented
11#19098643C211yesmaximal, characteristic, complemented
12(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
13C2×#14579094C211yesmaximal, characteristic, complemented
14#107×D79C211yesmaximal, characteristic, complemented
15#480×C79C211yesmaximal, characteristic, complemented
16C2×#11929624—21no—
17C2×#11929623—21no—
18C2×#11929609C2211yescharacteristic
19C22×C79⋊C8C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic
21#14579160C2211yescharacteristic
22#14579160C2211yescharacteristic
23#14579146—21no—
24#14579144—21no—
25#14579143—21no—
26#14579142—21no—
27#14579139—21no—
28#14579138—21no—
29#14579136C2211yescharacteristic
30#14579135C2211yescharacteristic
31#14579132C2211yescharacteristic
32D4×Dic79C2211yescharacteristic
33#14579123C2211yescharacteristic
34C4×C22⋊D79C2211yescharacteristic
35C2×C4⋊Dic79C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic
37C4⋊C4×D79C2211yescharacteristic
38#14579095C2211yescharacteristic
39#14579095C2211yescharacteristic
40#14579094C2211yescharacteristic
41#14579094C2211yescharacteristic
42#14579094C2211yescharacteristic
43#14579094C2211yescharacteristic
44#14579094C2211yescharacteristic
45Dic79⋊C8C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52#121×C79C2211yescharacteristic
53C2×C4⋊C4×C79C2211yescharacteristic
54#107×C79C2211yescharacteristic
55#107×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929624—44no—
60#11929623—44no—
61C2×Dic158—21no—
62C2×Dic158—21no—
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79D411yescharacteristic
68C22×Dic79—21no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79C2311yescharacteristic
74#11929609—22no—
75C2×C79⋊C8—22no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C8×D79—22no—
79C4⋊Dic79—21no—
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4D411yescharacteristic
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79D411yescharacteristic
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79C2311yescharacteristic
96C2×D4×C79—21no—
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99C22×C4×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C4⋊C4×C79—21no—
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C23×C79—21no—
108C23×C79C2×D411yescharacteristic
109C22×D79—21no—
110C22×D79C2×D411yescharacteristic
111D4×C79—21no—
112D4×C79—21no—
113D4×C79—42no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—42no—
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2411yescharacteristic
122C22⋊D79—42no—
123C22⋊D79—42no—
124C22⋊D79D814yescomplemented
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—42no—
129C2×Dic79—42no—
130C2×Dic79C2×D411yescharacteristic
131C2×Dic79C2×D411yescharacteristic
132C2×Dic79C2×D411yescharacteristic
133D316—21no—
134D316—21no—
135D316—42no—
136C4×D79—21no—
137C4×D79—21no—
138C4×D79—42no—
139C4×D79—42no—
140C4×D79—42no—
141Dic158—42no—
142Dic158—42no—
143C8×C79—21no—
144C8×C79—21no—
145C79⋊C8—21no—
146C79⋊C8#4112yescomplemented
147C22×C79—21no—
148C22×C79—21no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79C2×D812yes—
153C22×C79C22×D411yescharacteristic
154C2×D79—21no—
155C2×D79—21no—
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C2×D79C2×D812yes—
160C4×C79—21no—
161C4×C79—41no—
162C4×C79—41no—
163C4×C79—41no—
164C4×C79C2×#4111yescharacteristic
165C4×C792−1+411yescharacteristic
166Dic79—21no—
167Dic79—21no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171Dic79C2×D812yes—
172C2×C79—22no—
173C2×C79—81no—
174C2×C79#54711yescharacteristic
175C2×C79C22×D811yescharacteristic
176C2×C79#57811yescharacteristic
177D79—22no—
178D79—81no—
179#3334—791nomaximal, Sylow
180C79#333411yescharacteristic, complemented, Sylow
181#547—791no—
182#547—791no—
183#500—791no—
184#480—791no—
185#480—791no—
186#480—791no—
187#480D7911yescharacteristic, complemented
188#474—791no—
189#474—791no—
190#466—791no—
191#466—791no—
192C4×D8—791no—
193C8×D4—791no—
194C2×#107—791no—
195C2×#107—791no—
196C2×#41—1581no—
197C2×#41—1581no—
198C2×D8—791no—
199C22×C8—791no—
200C22×C8—791no—
201C4⋊Q8—791no—
202C4⋊Q8—791no—
203#123—1581no—
204#123—1581no—
205#123—1581no—
206#123—1581no—
207C22⋊Q8—1581no—
208C22⋊Q8—1581no—
209#121—791no—
210#121—791no—
211#121—791no—
212#121C2×D7911yescharacteristic
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—791no—
216C2×C4⋊C4—791no—
217C2×C4⋊C4—791no—
218C2×C4⋊C4—791no—
219C2×C4⋊C4C2×D7911yescharacteristic
220#107—791no—
221#107—791no—
222#107—791no—
223#107—791no—
224#107—791no—
225#107—791no—
226#107—791no—
227#107C2×D7911yescharacteristic
228#107C2×D7911yescharacteristic
229C4⋊C8—791no—
230#102—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102C2×D7911yescharacteristic
235#102C2×D7911yescharacteristic
236C22⋊C8—791no—
237C22⋊C8C2×D7911yescharacteristic
238C4×C8—791no—
239#41—3164no—
240#41—3164no—
241C2×Q8—1581no—
242C2×Q8—1581no—
243C2×D4—21no—
244C2×D4—791no—
245C2×D4—791no—
246C2×D4—1581no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4C22×D7911yescharacteristic
250C22×C4—21no—
251C22×C4—791no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4C22×D7911yescharacteristic
258D8—1582no—
259C2×C8—791no—
260C2×C8—791no—
261C2×C8—1582no—
262C2×C8—1582no—
263C2×C8C22×D7911yescharacteristic
264C2×C8C22×D7911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4C22×D7911yescharacteristic
276C4⋊C4C22×D7911yescharacteristic
277C4⋊C4C22×D7911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—791no—
280C22⋊C4—791no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C42—791no—
287C23—21no—
288C23—791no—
289C23—1581no—
290C23D4×D7911yescharacteristic
291Q8—3162no—
292Q8—3162no—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—3162no—
297D4—3162no—
298D4—3162no—
299D4—794no—
300D4—1581no—
301D4—1581no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—3162no—
309C2×C4—3162no—
310C2×C4—3162no—
311C2×C4—3162no—
312C2×C4—3162no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—791no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4D4×D7911yescharacteristic
322C2×C4C23×D7911yescharacteristic
323C8—21no—
324C8—21no—
325C8—792no—
326C8—1581no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—3161no—
333C22—3161no—
334C22—3161no—
335C22—792no—
336C22—1581no—
337C22—1581no—
338C22D8×D7912yes—
339C22C2×D4×D7911yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—3161no—
345C4—3161no—
346C4—3161no—
347C4—792no—
348C4—1581no—
349C4—1581no—
350C4#41×D7911yescharacteristic
351C4#1457920811yescharacteristic
352C2—22no—
353C2—81no—
354C2—6321no—
355C2—1582no—
356C2#1909921111yescharacteristic
357C2C2×D8×D7911yescharacteristic
358C2#1909937911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#480×C79C2
socleC22×C79C22×D4
hypercenter#480D79
hypocenterC79#3334
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #19099214C2semidirect
2. #19099213C2semidirect
3. #19098967C2semidirect
4. #19098878C2semidirect
5. #19098877C2semidirect
6. #19098875C2semidirect
7. #19098842C2semidirect
8. #19098841C2semidirect
9. #19098798C2semidirect
10. #19098797C2semidirect
11. #19098643C2semidirect
12. (C22⋊D79)⋊C8C2semidirect
13. C2×#14579094C2semidirect
14. #107×D79C2semidirect
15. #480×C79C2semidirect
124. C22⋊D79D8semidirect
146. C79⋊C8#41semidirect
180. C79#3334semidirect
187. #480D79semidirect