Finite Group Databasebeta

← #23775871

Subgroups — #23775871

Order 10112.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099257C211yesmaximal, characteristic, complemented
2#19099214C211yesmaximal, characteristic, complemented
3#19098971C211yesmaximal, characteristic, complemented
4#19098887C211yesmaximal, characteristic, complemented
5#19098883C211yesmaximal, characteristic, complemented
6#19098881C211yesmaximal, characteristic, complemented
7#19098878C211yesmaximal, characteristic, complemented
8#19098866C211yesmaximal, characteristic, complemented
9#19098852C211yesmaximal, characteristic, complemented
10#19098816C211yesmaximal, characteristic, complemented
11#19098800C211yesmaximal, characteristic, complemented
12#19098674C211yesmaximal, characteristic, complemented
13#19098632C211yesmaximal, characteristic, complemented
14#106×D79C211yesmaximal, characteristic, complemented
15#428×C79C211yesmaximal, characteristic, complemented
16C2×#11929624—21no—
17C2×D632C2211yescharacteristic
18C2×C8×D79C2211yescharacteristic
19#14579160C2211yescharacteristic
20#14579155—21no—
21#14579152C2211yescharacteristic
22#14579146—21no—
23#14579144—21no—
24#14579143—21no—
25#14579139—21no—
26#14579136C2211yescharacteristic
27#14579136C2211yescharacteristic
28#14579135C2211yescharacteristic
29#14579135C2211yescharacteristic
30#14579134—21no—
31C4×D316—21no—
32#14579123C2211yescharacteristic
33#14579123C2211yescharacteristic
34C4×C22⋊D79C2211yescharacteristic
35C4⋊C4×D79C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic
37#14579094C2211yescharacteristic
38#14579093C2211yescharacteristic
39#14579092C2211yescharacteristic
40#14579092C2211yescharacteristic
41#14579092C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579081C2211yescharacteristic
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic
52C2×M16×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic
54C2×C4⋊C4×C79C2211yescharacteristic
55#107×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic
57#106×C79C2211yescharacteristic
58#106×C79C2211yescharacteristic
59#11929624—44no—
60C2×Dic158—21no—
61C2×D316—21no—
62C2×D316—21no—
63C2×D316C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79D411yescharacteristic
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79C2311yescharacteristic
73D632—22no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C8×D79—22no—
77C4⋊Dic79—21no—
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4D411yescharacteristic
85C22⋊Dic79D411yescharacteristic
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4D411yescharacteristic
93C4×Dic79C2311yescharacteristic
94C22×C4×C79—21no—
95C22×C4×C79C2311yescharacteristic
96M16×C79—22no—
97C2×C8×C79C2311yescharacteristic
98C2×C8×C79C2311yescharacteristic
99C4⋊C4×C79—21no—
100C4⋊C4×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C42×C79—21no—
106C23×C79C2×D411yescharacteristic
107C22×D79—21no—
108C22×D79—21no—
109C22×D79C2×D411yescharacteristic
110C2×C4×C79—21no—
111C2×C4×C79—21no—
112C2×C4×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—42no—
117C2×C4×C79C2×D411yescharacteristic
118C2×C4×C79C2411yescharacteristic
119C22⋊D79—22no—
120C22⋊D79—42no—
121C22⋊D79—81no—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79C2×D411yescharacteristic
125C2×Dic79C2×D411yescharacteristic
126C2×Dic79C2×D411yescharacteristic
127D316—21no—
128D316—21no—
129D316—21no—
130D316—21no—
131D316—42no—
132D316—42no—
133C4×D79—21no—
134C4×D79—21no—
135C4×D79—42no—
136C4×D79—42no—
137C4×D79—81no—
138C4×D79—81no—
139Dic158—42no—
140C8×C79—21no—
141C8×C79#4112yescomplemented
142C79⋊C8—21no—
143C79⋊C8—21no—
144C22×C79—21no—
145C22×C79—21no—
146C22×C79—21no—
147C22×C79C22×D411yescharacteristic
148C2×D79—21no—
149C2×D79—21no—
150C2×D79—41no—
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79—41no—
156C2×D79AGL(1,ℤ/8)12yes—
157C4×C79—21no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79C2×#4111yescharacteristic
163C4×C792−1+411yescharacteristic
164Dic79—21no—
165Dic79—21no—
166Dic79—21no—
167Dic79—41no—
168Dic79—41no—
169C2×C79—41no—
170C2×C79#54711yescharacteristic
171C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C79#57711yescharacteristic
173D79—22no—
174D79—81no—
175D79—81no—
176#3345—791nomaximal, Sylow
177C79#334511yescharacteristic, complemented, Sylow
178#553—791no—
179#547—791no—
180#501—791no—
181#482—791no—
182#481—791no—
183#481—791no—
184#480—791no—
185#478—791no—
186#476—791no—
187#469—791no—
188#466—791no—
189#442—791no—
190#435—791no—
191#428D7911yescharacteristic, complemented
192C2×#106—791no—
193C2×#41—1581no—
194C2×D8—791no—
195C2×M16C2×D7911yescharacteristic
196C22×C8—791no—
197C4⋊Q8—791no—
198#126—1581no—
199#125—791no—
200#123—1581no—
201#123—1581no—
202#123—1581no—
203C22⋊Q8—1581no—
204#121—791no—
205#121—791no—
206#121—791no—
207#121—791no—
208#121—1581no—
209C4×D4—791no—
210C4×D4—791no—
211C4×D4—791no—
212C4×D4—1581no—
213#117C2×D7911yescharacteristic
214C2×C4⋊C4—791no—
215C2×C4⋊C4—791no—
216C2×C4⋊C4C2×D7911yescharacteristic
217#107—791no—
218#107C2×D7911yescharacteristic
219#107C2×D7911yescharacteristic
220#106—791no—
221#106—791no—
222#106—791no—
223#106—791no—
224#106C2×D7911yescharacteristic
225#106C2×D7911yescharacteristic
226C4⋊C8—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230#102—791no—
231#102—791no—
232#102—791no—
233C22⋊C8—791no—
234C22⋊C8—791no—
235#97—791no—
236#41—3164no—
237C2×Q8—1581no—
238C2×D4—791no—
239C2×D4—791no—
240C2×D4—791no—
241C2×D4—1581no—
242C2×D4—1581no—
243C2×D4—1581no—
244C2×D4—1581no—
245C22×C4—21no—
246C22×C4—791no—
247C22×C4—1581no—
248C22×C4—1581no—
249C22×C4—1581no—
250C22×C4—1581no—
251C22×C4C22×D7911yescharacteristic
252D8—1582no—
253M16—22no—
254C2×C8—791no—
255C2×C8—791no—
256C2×C8—1582no—
257C2×C8C22×D7911yescharacteristic
258C2×C8C22×D7911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—791no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4C22×D7911yescharacteristic
269C4⋊C4C22×D7911yescharacteristic
270C4⋊C4C22×D7911yescharacteristic
271C4⋊C4C22×D7911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—791no—
274C22⋊C4—791no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C42—21no—
282C42—791no—
283C23—791no—
284C23—1581no—
285C23—1581no—
286C23D4×D7911yescharacteristic
287Q8—3162no—
288D4—3162no—
289D4—3162no—
290D4—3162no—
291D4—6321no—
292D4—1582no—
293D4—1581no—
294D4—1581no—
295D4—1581no—
296D4—1581no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—3162no—
305C2×C4—3162no—
306C2×C4—791no—
307C2×C4—791no—
308C2×C4—791no—
309C2×C4—6321no—
310C2×C4—6321no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4D4×D7911yescharacteristic
316C2×C4C23×D7911yescharacteristic
317C8—21no—
318C8—1581no—
319C8—1581no—
320C8#1192962412yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—3161no—
325C22—3161no—
326C22—3161no—
327C22—3161no—
328C22—3161no—
329C22—3161no—
330C22—792no—
331C22—1581no—
332C22—1581no—
333C22C2×D4×D7911yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—3161no—
340C4—3161no—
341C4—1581no—
342C4—1581no—
343C4—1581no—
344C4C2×#1192962411yescharacteristic
345C4#1457920911yescharacteristic
346C2—41no—
347C2—6321no—
348C2—6321no—
349C2—1582no—
350C2#1909921411yescharacteristic
351C2AGL(1,ℤ/8)×D7911yescharacteristic
352C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#428×C79C2
socleC22×C79C22×D4
hypercenter#428D79
hypocenterC79#3345
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #19099257C2semidirect
2. #19099214C2semidirect
3. #19098971C2semidirect
4. #19098887C2semidirect
5. #19098883C2semidirect
6. #19098881C2semidirect
7. #19098878C2semidirect
8. #19098866C2semidirect
9. #19098852C2semidirect
10. #19098816C2semidirect
11. #19098800C2semidirect
12. #19098674C2semidirect
13. #19098632C2semidirect
14. #106×D79C2semidirect
15. #428×C79C2semidirect
141. C8×C79#41semidirect
177. C79#3345semidirect
191. #428D79semidirect
320. C8#11929624semidirect