Finite Group Databasebeta

← #23764404

Subgroups — #23764404

Order 10112.

444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×#11929612C211yesmaximal, characteristic, complemented
2C2×#14579141C211yesmaximal, characteristic, complemented
3C2×#14579132C211yesmaximal, characteristic
4C2×#14579086C211yesmaximal, characteristic, complemented
5C2×(C2×D79)⋊C8C211yesmaximal, characteristic, complemented
6#19098325C211yesmaximal, characteristic, complemented
7C2×#102×C79C211yesmaximal, characteristic, complemented
8C22×Dic158C2211yescharacteristic
9C22×C22⋊D79—21no—
10C22×C4×D79C2211yescharacteristic
11C2×#11929612—22no—
12C2×#11929612—22no—
13C2×#11929612—22no—
14C22×C79⋊C8C2211yescharacteristic
15#14579141—22no—
16#14579141—22no—
17#14579132—22no—
18#14579132—22no—
19C2×C4⋊Dic79—21no—
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C22⋊Dic79—21no—
22C2×(C2×D79)⋊C4—21no—
23#14579086—22no—
24(C2×D79)⋊C8—22no—
25C22×D4×C79C2211yescharacteristic
26C22×C8×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28#102×C79—22no—
29C23×D79D411yescharacteristic
30C2×Dic158—21no—
31C2×Dic158—21no—
32C2×Dic158—21no—
33C2×Dic158—21no—
34C2×Dic158—21no—
35C2×Dic158D412yescomplemented
36C2×C22⋊D79—24no—
37C2×C22⋊D79—42no—
38C2×C22⋊D79—42no—
39C22×Dic79—21no—
40C22×Dic79—21no—
41C22×Dic79D411yescharacteristic
42C2×C4×D79—21no—
43C2×C4×D79—21no—
44C2×C4×D79—21no—
45C2×C4×D79—21no—
46C2×C4×D79—21no—
47C2×C4×D79—21no—
48#11929612—28no—
49C2×C79⋊C8—21no—
50C2×C79⋊C8—21no—
51C2×C79⋊C8D412yescomplemented
52C4⋊Dic79—24no—
53C4⋊Dic79—21no—
54C4⋊Dic79D412yes—
55C22⋊Dic79—24no—
56(C2×D79)⋊C4—24no—
57C24×C79—21no—
58C2×D4×C79—21no—
59C2×D4×C79—21no—
60C2×D4×C79—21no—
61C2×D4×C79—21no—
62C2×D4×C79—21no—
63C2×D4×C79D412yes—
64C22×C4×C79—21no—
65C22×C4×C79C2311yescharacteristic
66C2×C8×C79—21no—
67C2×C8×C79—21no—
68C2×C8×C79—21no—
69C4⋊C4×C79—21no—
70C4⋊C4×C79D412yescomplemented
71C23×C79—22no—
72C23×C79—41no—
73C23×C79—41no—
74C23×C79—41no—
75C23×C79—41no—
76C23×C79—41no—
77C23×C79—41no—
78C23×C79C2×D411yescharacteristic
79C22×D79—21no—
80C22×D79—21no—
81C22×D79—21no—
82C22×D79—21no—
83C22×D79—21no—
84C22×D79—21no—
85C22×D79SD1612yescomplemented
86D4×C79—22no—
87D4×C79—22no—
88D4×C79—41no—
89D4×C79—41no—
90C2×C4×C79—22no—
91C2×C4×C79—41no—
92C2×C4×C79—41no—
93C2×C4×C79C2×D411yescharacteristic
94C2×C4×C79C2×D411yescharacteristic
95C2×C4×C79C2×D411yescharacteristic
96C2×C4×C79C2×D411yescharacteristic
97C2×C4×C79C2×D411yescharacteristic
98C2×C4×C79#4111yescharacteristic
99C22⋊D79—48no—
100C2×Dic79—22no—
101C2×Dic79—21no—
102C2×Dic79—22no—
103C2×Dic79—21no—
104C2×Dic79—21no—
105C2×Dic79—41no—
106C2×Dic79—41no—
107C2×Dic79—41no—
108C2×Dic79—41no—
109C4×D79—41no—
110C4×D79—41no—
111C4×D79—41no—
112C4×D79—41no—
113Dic158—22no—
114Dic158—22no—
115Dic158—41no—
116Dic158—41no—
117C8×C79—41no—
118C79⋊C8—22no—
119C22×C79—42no—
120C22×C79—42no—
121C22×C79—42no—
122C22×C79—81no—
123C22×C79—81no—
124C22×C79—81no—
125C22×C79—81no—
126C22×C79#12011yescharacteristic
127C22×C79#12011yescharacteristic
128C22×C79#12111yescharacteristic
129C22×C79C2×SD1611yescharacteristic
130C22×C79#13511yescharacteristic
131C22×C79AGL(1,ℤ/8)11yescharacteristic
132C22×C79#13711yescharacteristic
133C2×D79—22no—
134C2×D79—22no—
135C2×D79—22no—
136C2×D79—41no—
137C2×D79—41no—
138C2×D79—41no—
139C2×D79—41no—
140C4×C79—42no—
141C4×C79#12011yescharacteristic
142C4×C79#12111yescharacteristic
143C4×C79#12111yescharacteristic
144C4×C79#12711yescharacteristic
145Dic79—42no—
146Dic79—41no—
147Dic79—42no—
148C2×C79—82no—
149C2×C79#39211yescharacteristic
150C2×C79#44811yescharacteristic
151C2×C79#44911yescharacteristic
152C2×C79#45011yescharacteristic
153C2×C79#45211yescharacteristic
154C2×C79#46511yescharacteristic
155C2×C79#46811yescharacteristic
156D79—42no—
157#2000—791nomaximal, Sylow
158C79#200011yescharacteristic, complemented, Sylow
159C22×SD16—791no—
160C2×C22⋊Q8—791no—
161C2×#121—791no—
162C2×#103—791no—
163C2×#102D7911yescharacteristic, complemented
164C2×C22⋊C8—791no—
165#340—791no—
166C22×Q8—791no—
167C22×D4—1581no—
168C22×D4C2×D7911yescharacteristic
169C23×C4—791no—
170C2×SD16—1582no—
171C2×SD16—1582no—
172C2×SD16—1582no—
173C22×C8—791no—
174C22×C8C2×D7911yescharacteristic
175C22⋊Q8—1582no—
176C22⋊Q8—1582no—
177#121—1582no—
178#121—1582no—
179C2×C4⋊C4—791no—
180C2×C4⋊C4—1581no—
181C2×C4⋊C4C2×D7911yescharacteristic
182C2×C22⋊C4—1581no—
183C2×C22⋊C4—1581no—
184#103—1582no—
185#102—22no—
186C22⋊C8—1582no—
187C24—21no—
188C24—791no—
189C2×Q8—792no—
190C2×Q8—1581no—
191C2×Q8—1581no—
192C2×Q8—1581no—
193C2×Q8—1581no—
194C2×Q8—1581no—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—3162no—
201C2×D4—3162no—
202C2×D4—1584no—
203C2×D4D31612yes—
204C22×C4—21no—
205C22×C4—791no—
206C22×C4—1581no—
207C22×C4—1581no—
208C22×C4—1581no—
209C22×C4—1581no—
210C22×C4—1581no—
211C22×C4—1581no—
212C22×C4—1581no—
213C22×C4—1581no—
214C22×C4C22×D7911yescharacteristic
215SD16—1588no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—792no—
220C2×C8—1581no—
221C2×C8—1581no—
222C4⋊C4—21no—
223C4⋊C4—792no—
224C4⋊C4—1584no—
225C4⋊C4—1581no—
226C4⋊C4C22⋊D7912yescomplemented
227C22⋊C4—1584no—
228C22⋊C4—1584no—
229C23—22no—
230C23—41no—
231C23—41no—
232C23—41no—
233C23—41no—
234C23—41no—
235C23—41no—
236C23—792no—
237C23—1581no—
238C23—1581no—
239C23—1581no—
240C23—1581no—
241C23—1581no—
242C23—1581no—
243C23D4×D7911yescharacteristic
244Q8—3161no—
245Q8—3161no—
246Q8—1582no—
247Q8—1582no—
248D4—22no—
249D4—22no—
250D4—41no—
251D4—41no—
252D4—3168no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—3161no—
257C2×C4—3161no—
258C2×C4—3161no—
259C2×C4—3161no—
260C2×C4—3161no—
261C2×C4—3161no—
262C2×C4—3161no—
263C2×C4—3161no—
264C2×C4—1582no—
265C2×C4—1581no—
266C2×C4—1581no—
267C2×C4—1582no—
268C2×C4—1581no—
269C2×C4D4×D7911yescharacteristic
270C2×C4D4×D7911yescharacteristic
271C2×C4D4×D7911yescharacteristic
272C2×C4C2×C22⋊D7911yescharacteristic
273C2×C4C2×D31611yescharacteristic
274C2×C4#1192962411yescharacteristic
275C8—41no—
276C8—1582no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—81no—
281C22—81no—
282C22—81no—
283C22—81no—
284C22—3161no—
285C22—3161no—
286C22—3161no—
287C22—3161no—
288C22—1582no—
289C22—1582no—
290C22—1582no—
291C22#1457912911yescharacteristic
292C22#1457913111yescharacteristic
293C22#1457913411yescharacteristic
294C22SD16×D7911yescharacteristic
295C22#1457918011yescharacteristic
296C22#1457918511yescharacteristic
297C22#1457919011yescharacteristic
298C4—42no—
299C4—3162no—
300C4—3161no—
301C4—3162no—
302C4#1457913111yescharacteristic
303C4#1457913411yescharacteristic
304C4#1457913511yescharacteristic
305C4#1457915711yescharacteristic
306C2—82no—
307C2—3162no—
308C2#1909847211yescharacteristic
309C2#1909870011yescharacteristic
310C2#1909870511yescharacteristic
311C2#1909871511yescharacteristic
312C2#1909872611yescharacteristic
313C2#1909879111yescharacteristic
314C2#1909880811yescharacteristic
subgroupG/H
centerC23D4×D79
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
FittingC2×#102×C79C2
socleC23×C79C2×D4
prime radicalC2×#14579132C2
hypercenterC2×#102D79
hypocenterC79#2000
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#11929612C2semidirect
2. C2×#14579141C2semidirect
4. C2×#14579086C2semidirect
5. C2×(C2×D79)⋊C8C2semidirect
6. #19098325C2semidirect
7. C2×#102×C79C2semidirect
35. C2×Dic158D4semidirect
51. C2×C79⋊C8D4semidirect
70. C4⋊C4×C79D4semidirect
85. C22×D79SD16semidirect
158. C79#2000semidirect
163. C2×#102D79semidirect
226. C4⋊C4C22⋊D79semidirect