Finite Group Databasebeta

← #23775894

Subgroups — #23775894

Order 10112.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099278C211yesmaximal, characteristic, complemented
2#19098973C211yesmaximal, characteristic, complemented
3#19098887C211yesmaximal, characteristic, complemented
4#19098884C211yesmaximal, characteristic, complemented
5#19098884C211yesmaximal, characteristic, complemented
6#19098876C211yesmaximal, characteristic, complemented
7#19098860C211yesmaximal, characteristic, complemented
8#19098843C211yesmaximal, characteristic, complemented
9#19098814C211yesmaximal, characteristic, complemented
10#19098797C211yesmaximal, characteristic, complemented
11#19098673C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098603C211yesmaximal, characteristic, complemented
14#19098599C211yesmaximal, characteristic, complemented
15#553×C79C211yesmaximal, characteristic, complemented
16C2×#11929609C2211yescharacteristic
17C2×#11929608C2211yescharacteristic
18C22×C79⋊C8C2211yescharacteristic
19#14579161C2211yescharacteristic
20#14579147—21no—
21#14579147—21no—
22#14579135C2211yescharacteristic
23#14579135C2211yescharacteristic
24#14579132—21no—
25C4×D316C2211yescharacteristic
26#14579120C2211yescharacteristic
27#14579120C2211yescharacteristic
28#14579119—21no—
29#14579094C2211yescharacteristic
30#14579094C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579094C2211yescharacteristic
34#14579092C2211yescharacteristic
35#14579092C2211yescharacteristic
36#14579092C2211yescharacteristic
37#14579092C2211yescharacteristic
38C4⋊(C79⋊C8)C2211yescharacteristic
39#14579082C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48#126×C79—21no—
49#125×C79C2211yescharacteristic
50#123×C79—21no—
51#121×C79—21no—
52#121×C79C2211yescharacteristic
53#121×C79C2211yescharacteristic
54C4×D4×C79—21no—
55C4×D4×C79C2211yescharacteristic
56C4×D4×C79C2211yescharacteristic
57#117×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×D316C2311yescharacteristic
61C2×C22⋊D79—21no—
62C2×C22⋊D79—21no—
63C2×C4×D79—21no—
64#11929609—22no—
65#11929608—22no—
66C2×C79⋊C8—22no—
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C4⋊Dic79—21no—
72C4⋊Dic79C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75C22⋊Dic79—21no—
76C22⋊Dic79—21no—
77(C2×D79)⋊C4—21no—
78(C2×D79)⋊C4—21no—
79(C2×D79)⋊C4—21no—
80C4×Dic79—21no—
81C4×Dic79—21no—
82C2×D4×C79—21no—
83C2×D4×C79—21no—
84C2×D4×C79D411yescharacteristic
85C2×D4×C79C2311yescharacteristic
86C22×C4×C79—21no—
87C22×C4×C79—21no—
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C4⋊C4×C79—21no—
91C4⋊C4×C79—21no—
92C4⋊C4×C79—21no—
93C4⋊C4×C79D411yescharacteristic
94C4⋊C4×C79C2311yescharacteristic
95C4⋊C4×C79C2311yescharacteristic
96C4⋊C4×C79C2311yescharacteristic
97C22⋊C4×C79—21no—
98C22⋊C4×C79—21no—
99C22⋊C4×C79—21no—
100C22⋊C4×C79—21no—
101C22⋊C4×C79D411yescharacteristic
102C22⋊C4×C79D411yescharacteristic
103C42×C79—21no—
104C42×C79C2311yescharacteristic
105C23×C79—21no—
106C23×C79C2×D411yescharacteristic
107C23×C79C2×D411yescharacteristic
108C22×D79—21no—
109D4×C79—21no—
110D4×C79—21no—
111D4×C79—41no—
112D4×C79—42no—
113D4×C79—81no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—81no—
122C2×C4×C79—81no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2411yescharacteristic
128C22⋊D79—81no—
129C22⋊D79—81no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133D316—21no—
134D316—21no—
135C4×D79—42no—
136Dic158—81no—
137C79⋊C8—21no—
138C79⋊C8—21no—
139C79⋊C8—21no—
140C79⋊C8#4112yes—
141C22×C79—21no—
142C22×C79—21no—
143C22×C79—21no—
144C22×C79—21no—
145C22×C79—21no—
146C22×C79—21no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79C22×D411yescharacteristic
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C4×C79—21no—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79C2×#4111yescharacteristic
162C4×C792−1+411yescharacteristic
163Dic79—41no—
164Dic79—41no—
165Dic79—41no—
166C2×C79—41no—
167C2×C79—41no—
168C2×C79—81no—
169C2×C79#54711yescharacteristic
170C2×C79#57511yescharacteristic
171C2×C79#57611yescharacteristic
172D79—81no—
173#3347—791nomaximal, Sylow
174C79#334711yescharacteristic, complemented, Sylow
175#555—791no—
176#553D7911yescharacteristic, complemented
177#501—791no—
178#482—791no—
179#482—791no—
180#482—791no—
181#480—791no—
182#478—791no—
183#474—791no—
184#469—791no—
185#466—791no—
186#442—791no—
187#435—791no—
188#428—791no—
189#427—791no—
190C2×D8—791no—
191C2×M16—791no—
192C22×C8—791no—
193C4⋊Q8—791no—
194#126—21no—
195#125C2×D7911yescharacteristic
196#124—1581no—
197#124—1581no—
198#123—21no—
199#121—21no—
200#121—791no—
201#121—791no—
202#121—1581no—
203#121C2×D7911yescharacteristic
204#121C2×D7911yescharacteristic
205C4×D4—21no—
206C4×D4—791no—
207C4×D4C2×D7911yescharacteristic
208C4×D4C2×D7911yescharacteristic
209#117—791no—
210#117—791no—
211#117—1581no—
212#117C2×D7911yescharacteristic
213C2×C4⋊C4C2×D7911yescharacteristic
214#107—791no—
215#107—791no—
216#107—791no—
217#107—791no—
218#107—791no—
219#106—791no—
220#106—791no—
221#106—791no—
222#106—791no—
223C4⋊C8—791no—
224#102—791no—
225#102—791no—
226#102—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230C22⋊C8—791no—
231C22⋊C8—791no—
232#97—791no—
233C2×Q8—1581no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—791no—
237C2×D4—1581no—
238C2×D4—1581no—
239C2×D4C22⋊D7911yescharacteristic
240C2×D4C22×D7911yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—1581no—
244C22×C4C22×D7911yescharacteristic
245C22×C4C22×D7911yescharacteristic
246D8—1582no—
247M16—1582no—
248C2×C8—791no—
249C2×C8—791no—
250C2×C8—791no—
251C2×C8—791no—
252C2×C8—1582no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—791no—
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—1581no—
260C4⋊C4C22⋊D7911yescharacteristic
261C4⋊C4C22×D7911yescharacteristic
262C4⋊C4C22×D7911yescharacteristic
263C4⋊C4C22×D7911yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—1581no—
269C22⋊C4—1581no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4C22⋊D7911yescharacteristic
274C22⋊C4C22⋊D7911yescharacteristic
275C42—21no—
276C42—1581no—
277C42—1581no—
278C42C22×D7911yescharacteristic
279C23—21no—
280C23—1581no—
281C23C2×C22⋊D7911yescharacteristic
282C23C2×C22⋊D7911yescharacteristic
283Q8—6321no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—42no—
288D4—81no—
289D4—6321no—
290D4—6321no—
291D4—1581no—
292D4—1581no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—3162no—
303C2×C4—1581no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4C2×C22⋊D7911yescharacteristic
307C2×C4C2×C22⋊D7911yescharacteristic
308C2×C4C2×C22⋊D7911yescharacteristic
309C2×C4C2×C22⋊D7911yescharacteristic
310C2×C4C23×D7911yescharacteristic
311C8—792no—
312C8—1581no—
313C8—1581no—
314C8—1581no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—3161no—
325C22—3161no—
326C22—3161no—
327C22C22×C22⋊D7911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—3161no—
336C4—3161no—
337C4—3161no—
338C4#41×D7911yescharacteristic
339C4#1457920811yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—6321no—
344C2#1909921211yescharacteristic
345C2#1909936111yescharacteristic
346C2#1909936611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#553×C79C2
socleC22×C79C22×D4
hypercenter#553D79
hypocenterC79#3347
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #19099278C2semidirect
2. #19098973C2semidirect
3. #19098887C2semidirect
4. #19098884C2semidirect
5. #19098884C2semidirect
6. #19098876C2semidirect
7. #19098860C2semidirect
8. #19098843C2semidirect
9. #19098814C2semidirect
10. #19098797C2semidirect
11. #19098673C2semidirect
12. #19098635C2semidirect
13. #19098603C2semidirect
14. #19098599C2semidirect
15. #553×C79C2semidirect
174. C79#3347semidirect
176. #553D79semidirect