Finite Group Databasebeta

← #23764465

Subgroups — #23764465

Order 10112.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099361C211yesmaximal, characteristic, complemented
2#19099074C211yesmaximal, characteristic, complemented
3#19098581C211yesmaximal, characteristic, complemented
4#19098580C211yesmaximal, characteristic, complemented
5#19098527C211yesmaximal, characteristic, complemented
6#19098319C211yesmaximal, characteristic, complemented
7#525×C79C211yesmaximal, characteristic, complemented
8C2×#11929624C2211yescharacteristic
9#14579192—21no—
10#14579191—21no—
11#14579187—21no—
12#14579186—21no—
13#14579181—22no—
14C2×#11929608C2211yescharacteristic
15C2×#11929608C2211yescharacteristic
16#14579144—21no—
17#14579140—21no—
18#14579135—21no—
19#14579130—21no—
20C4×C22⋊D79—22no—
21#14579120C2211yescharacteristic
22#14579089—22no—
23#14579088—22no—
24C22⋊(C79⋊C8)—22no—
25C2×#41×C79C2211yescharacteristic
26C23×C4×C79C2211yescharacteristic
27#123×C79—21no—
28C22⋊Q8×C79—21no—
29#121×C79—21no—
30#120×C79—21no—
31C4×D4×C79—22no—
32#117×C79C2211yescharacteristic
33#11929624—21no—
34#11929624—21no—
35#11929624—21no—
36#11929624—21no—
37C2×Dic158D411yescharacteristic, complemented
38C2×D316D411yescharacteristic, complemented
39C2×C22⋊D79—22no—
40C2×C22⋊D79—21no—
41C2×C4×D79—21no—
42#11929614—22no—
43#11929612—22no—
44#11929611—22no—
45#11929609—22no—
46#11929608—21no—
47#11929608—21no—
48#11929608—21no—
49#11929608—21no—
50C2×C79⋊C8—21no—
51C2×C79⋊C8D412yescomplemented
52C4⋊Dic79—21no—
53Dic79⋊C4—22no—
54C22⋊Dic79—22no—
55C22⋊Dic79—21no—
56(C2×D79)⋊C4—22no—
57C4×Dic79D412yescomplemented
58C24×C79D411yescharacteristic
59#41×C79—21no—
60#41×C79—21no—
61#41×C79—21no—
62#41×C79—21no—
63C2×Q8×C79D411yescharacteristic, complemented
64C2×D4×C79—22no—
65C2×D4×C79—21no—
66C2×D4×C79D411yescharacteristic, complemented
67C22×C4×C79—21no—
68C22×C4×C79—21no—
69C22×C4×C79—21no—
70C22×C4×C79—21no—
71C22×C4×C79—21no—
72C22×C4×C79—21no—
73C22×C4×C79—21no—
74C22×C4×C79D411yescharacteristic
75C22×C4×C79C2311yescharacteristic
76C4⋊C4×C79—22no—
77C4⋊C4×C79—21no—
78C22⋊C4×C79—22no—
79C22⋊C4×C79—22no—
80C22⋊C4×C79—21no—
81C42×C79D412yescomplemented
82C23×C79—21no—
83C23×C79—21no—
84C23×C79—21no—
85C23×C79—21no—
86C23×C79—42no—
87C23×C79C2×D411yescharacteristic
88C22×D79—21no—
89Q8×C79—21no—
90Q8×C79—21no—
91D4×C79—21no—
92D4×C79—21no—
93D4×C79—44no—
94D4×C79—41no—
95D4×C79—41no—
96C2×C4×C79—21no—
97C2×C4×C79—22no—
98C2×C4×C79—21no—
99C2×C4×C79—21no—
100C2×C4×C79—21no—
101C2×C4×C79—41no—
102C2×C4×C79—41no—
103C2×C4×C79—41no—
104C2×C4×C79—41no—
105C2×C4×C79—41no—
106C2×C4×C79—41no—
107C2×C4×C79C2×D411yescharacteristic
108C2×C4×C79C2×D411yescharacteristic
109C2×C4×C79C2×D411yescharacteristic
110C2×C4×C79C2×D411yescharacteristic
111C2×C4×C79C2×D411yescharacteristic
112C2×C4×C79#4111yescharacteristic
113C22⋊D79—44no—
114C22⋊D79—41no—
115C22⋊D79—41no—
116C2×Dic79—22no—
117C2×Dic79—21no—
118D316—21no—
119D316—21no—
120C4×D79—41no—
121C4×D79—41no—
122Dic158—21no—
123Dic158—21no—
124C79⋊C8—22no—
125C79⋊C8—41no—
126C22×C79—22no—
127C22×C79—22no—
128C22×C79—22no—
129C22×C79—41no—
130C22×C79—41no—
131C22×C79—41no—
132C22×C79—41no—
133C22×C79—42no—
134C22×C79—41no—
135C22×C79—41no—
136C22×C79#12011yescharacteristic
137C22×C79#12011yescharacteristic
138C22×C79#12111yescharacteristic
139C2×D79—42no—
140C2×D79—41no—
141C4×C79—42no—
142C4×C79—41no—
143C4×C79—41no—
144C4×C79#12011yescharacteristic
145C4×C79#12111yescharacteristic
146C4×C79#12111yescharacteristic
147C4×C79#12711yescharacteristic
148Dic79—42no—
149Dic79—41no—
150C2×C79—21no—
151C2×C79—21no—
152C2×C79—21no—
153C2×C79—42no—
154C2×C79—81no—
155C2×C79#39211yescharacteristic
156D79—81no—
157#2010—791nomaximal, Sylow
158C79#201011yescharacteristic, complemented, Sylow
159#575—791no—
160#525—791no—
161#525D7911yescharacteristic, complemented
162#421—791no—
163#421—791no—
164#407—791no—
165H(3,ℤ/4)—791no—
166C2×#41—791no—
167C2×#41C2×D7911yescharacteristic
168C23×C4C2×D7911yescharacteristic
169#137—1581no—
170#137—1581no—
171AGL(1,ℤ/8)—1581no—
172AGL(1,ℤ/8)—1581no—
173#135—1582no—
174C2×M16—791no—
175C2×M16—791no—
176#123—21no—
177#123—1581no—
178C22⋊Q8—21no—
179C22⋊Q8—1581no—
180#121—21no—
181#121—1581no—
182#120—21no—
183#120—1581no—
184C4×D4—22no—
185C4×D4—1582no—
186#117—791no—
187#117C2×D7911yescharacteristic
188#104—1582no—
189#104—1582no—
190C22⋊C8—1582no—
191C24C22⋊D7911yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—1581no—
197#41—1581no—
198#41—1581no—
199#41—1581no—
200C2×Q8—791no—
201C2×Q8C22⋊D7911yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—791no—
205C2×D4—1582no—
206C2×D4—1581no—
207C2×D4C22⋊D7911yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—1581no—
216C22×C4C22⋊D7911yescharacteristic
217C22×C4C22×D7911yescharacteristic
218Q16—1582no—
219SD16—1582no—
220SD16—1582no—
221D8—1582no—
222M16—1581no—
223M16—1581no—
224M16—1581no—
225M16—1581no—
226C2×C8—792no—
227C2×C8—1581no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—1582no—
231C4⋊C4—1581no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—1582no—
236C22⋊C4—1582no—
237C22⋊C4—1581no—
238C42—792no—
239C42C22⋊D7912yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—1581no—
246C23C2×C22⋊D7911yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—1581no—
250Q8—1581no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—3164no—
257D4—3161no—
258D4—3161no—
259D4—1581no—
260D4—1581no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—3161no—
273C2×C4—3161no—
274C2×C4—1582no—
275C2×C4—1581no—
276C2×C4D4×D7911yescharacteristic
277C2×C4D4×D7911yescharacteristic
278C2×C4D4×D7911yescharacteristic
279C2×C4C2×C22⋊D7911yescharacteristic
280C2×C4C2×C22⋊D7911yescharacteristic
281C2×C4#1192962311yescharacteristic
282C8—3161no—
283C8—1582no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—3162no—
295C22—3161no—
296C22#1457912911yescharacteristic
297C22#1457913011yescharacteristic
298C22#1457913311yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—3162no—
303C4—3161no—
304C4#1457912911yescharacteristic
305C4#1457913211yescharacteristic
306C4#1457913311yescharacteristic
307C4#1457915711yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—6321no—
314C2#1909847111yescharacteristic
subgroupG/H
centerC4#14579157
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#525×C79C2
socleC2×C79#392
hypercenter#525D79
hypocenterC79#2010
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #19099361C2semidirect
2. #19099074C2semidirect
3. #19098581C2semidirect
4. #19098580C2semidirect
5. #19098527C2semidirect
6. #19098319C2semidirect
7. #525×C79C2semidirect
37. C2×Dic158D4semidirect
38. C2×D316D4semidirect
51. C2×C79⋊C8D4semidirect
57. C4×Dic79D4semidirect
63. C2×Q8×C79D4semidirect
66. C2×D4×C79D4semidirect
81. C42×C79D4semidirect
158. C79#2010semidirect
161. #525D79semidirect
201. C2×Q8C22⋊D79semidirect
207. C2×D4C22⋊D79semidirect
239. C42C22⋊D79semidirect