Finite Group Databasebeta

← #23769141

Subgroups — #23769141

Order 10112.

632 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#14579143C212yesmaximal, complemented
2C2×#14579132C211yesmaximal, characteristic
3C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
4#19098495C211yesmaximal, characteristic, complemented
5#19098493C211yesmaximal, characteristic, complemented
6#19098486C212yesmaximal, complemented
7#19098486C212yesmaximal, complemented
8#19098477C211yesmaximal, characteristic, complemented
9#19098439C212yesmaximal, complemented
10#19098422C211yesmaximal, characteristic, complemented
11#394×C79C211yesmaximal, characteristic, complemented
12C22×C22⋊D79C2212yes—
13C22×C4×D79C2211yescharacteristic
14C22×C4×D79C2211yescharacteristic
15C22×C4×D79C2211yescharacteristic
16#14579143—28no—
17#14579132—24no—
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2212yes—
20C2×C4⋊Dic79C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2212yes—
24C2×Dic79⋊C4C2212yes—
25C4⋊C4×D79—24no—
26C2×C22⋊Dic79C2212yes—
27C2×C22⋊Dic79C2212yes—
28C2×C22⋊Dic79C2212yes—
29C2×(C2×D79)⋊C4C2212yes—
30C79⋊#95C2211yescharacteristic
31C79⋊#95C2212yes—
32C79⋊#95C2212yes—
33C22×D4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2212yes—
36C2×C22⋊C4×C79C2212yes—
37#95×C79C2211yescharacteristic
38C23×D79C2311yescharacteristic
39C2×C22⋊D79—24no—
40C2×C22⋊D79—24no—
41C2×C22⋊D79—24no—
42C22×Dic79C2312yes—
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2312yes—
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2311yescharacteristic
47C2×C4×D79—22no—
48C2×C4×D79—22no—
49C2×C4×D79—22no—
50C2×C4×D79—42no—
51C2×C4×D79—42no—
52C2×C4×D79D414yes—
53C2×C4×D79D414yescomplemented
54C4⋊Dic79—22no—
55C4⋊Dic79—24no—
56C4⋊Dic79—22no—
57Dic79⋊C4—22no—
58Dic79⋊C4—22no—
59Dic79⋊C4—24no—
60Dic79⋊C4—42no—
61C22⋊Dic79—24no—
62C22⋊Dic79—24no—
63C22⋊Dic79—42no—
64(C2×D79)⋊C4—24no—
65C24×C79C2312yes—
66C2×D4×C79—22no—
67C2×D4×C79—42no—
68C22×C4×C79C2312yes—
69C22×C4×C79C2311yescharacteristic
70C22×C4×C79C2311yescharacteristic
71C22×C4×C79C2311yescharacteristic
72C4⋊C4×C79—22no—
73C22⋊C4×C79—24no—
74C22⋊C4×C79—42no—
75C23×C79—22no—
76C23×C79—22no—
77C23×C79—22no—
78C23×C79—22no—
79C23×C79—22no—
80C23×C79—22no—
81C23×C79—22no—
82C23×C79C2411yescharacteristic
83C22×D79—22no—
84C22×D79—22no—
85C22×D79C2×D412yes—
86C22×D79C2×D412yes—
87C22×D79#4112yes—
88D4×C79—44no—
89C2×C4×C79—21no—
90C2×C4×C79—21no—
91C2×C4×C79—22no—
92C2×C4×C79—22no—
93C2×C4×C79—21no—
94C2×C4×C79—22no—
95C2×C4×C79—22no—
96C2×C4×C79—22no—
97C2×C4×C79C2×D412yes—
98C2×C4×C79C2×D412yes—
99C22⋊D79—48no—
100C2×Dic79—21no—
101C2×Dic79—21no—
102C2×Dic79—22no—
103C2×Dic79—22no—
104C2×Dic79—22no—
105C2×Dic79—21no—
106C2×Dic79—22no—
107C2×Dic79—22no—
108C2×Dic79—22no—
109C2×Dic79—22no—
110C2×Dic79—22no—
111C2×Dic79C2×D412yes—
112C2×Dic79C2×D412yes—
113C4×D79—28no—
114C4×D79—44no—
115C4×D79—44no—
116C22×C79—42no—
117C22×C79—42no—
118C22×C79—42no—
119C22×C79—42no—
120C22×C79—42no—
121C22×C79—42no—
122C22×C79—42no—
123C22×C79C22×D411yescharacteristic
124C22×C79C22×D411yescharacteristic
125C22×C79C2×#4111yescharacteristic
126C22×C79H(5,𝔽2)12yes—
127C22×C792−1+412yes—
128C2×D79—22no—
129C2×D79—22no—
130C2×D79—24no—
131C2×D79—24no—
132C2×D79#12114yes—
133C4×C79—22no—
134C4×C79—22no—
135C4×C79—41no—
136C4×C79—42no—
137Dic79—22no—
138Dic79—22no—
139Dic79—42no—
140Dic79—41no—
141Dic79—42no—
142C2×C79—82no—
143C2×C79C2×#12111yescharacteristic
144C2×C79#53411yescharacteristic
145C2×C79#53611yescharacteristic
146C2×C79#53712yes—
147C2×C79#53912yes—
148D79—24no—
149#2618—791nomaximal, Sylow
150C79#261811yescharacteristic, complemented, Sylow
151C2×#123—792no—
152C2×#121—791no—
153C22×C4⋊C4—791no—
154#398—791no—
155#398—791no—
156#396—792no—
157#396—792no—
158#394—791no—
159#394D7911yescharacteristic, complemented
160#386—792no—
161#380—791no—
162C22×D4—792no—
163C22×D4C2×D7911yescharacteristic
164C23×C4—791no—
165C23×C4—791no—
166C23×C4—791no—
167#123—1588no—
168#121—1584no—
169C2×C4⋊C4—792no—
170C2×C4⋊C4—791no—
171C2×C4⋊C4—791no—
172C2×C4⋊C4—791no—
173C2×C4⋊C4—791no—
174C2×C4⋊C4—792no—
175C2×C4⋊C4—792no—
176C2×C4⋊C4—1584no—
177C2×C4⋊C4C2×D7911yescharacteristic
178C2×C22⋊C4—792no—
179C2×C22⋊C4—792no—
180C2×C22⋊C4—792no—
181C2×C22⋊C4—792no—
182C2×C22⋊C4C2×D7912yes—
183C2×C22⋊C4C2×D7912yes—
184#95—791no—
185#95—792no—
186#95—792no—
187#95C2×D7911yescharacteristic
188C24—791no—
189C24C22×D7912yes—
190C2×D4—22no—
191C2×D4—42no—
192C2×D4—1584no—
193C2×D4—1584no—
194C2×D4—1584no—
195C22×C4—3162no—
196C22×C4—3162no—
197C22×C4—794no—
198C22×C4—791no—
199C22×C4—791no—
200C22×C4—794no—
201C22×C4—792no—
202C22×C4—791no—
203C22×C4—792no—
204C22×C4—1582no—
205C22×C4—1582no—
206C22×C4—1582no—
207C22×C4C22×D7911yescharacteristic
208C22×C4C22×D7912yes—
209C22×C4C22×D7911yescharacteristic
210C22×C4C22×D7911yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—3162no—
213C4⋊C4—1582no—
214C4⋊C4—1582no—
215C4⋊C4—1584no—
216C4⋊C4—1582no—
217C4⋊C4—1584no—
218C4⋊C4—1582no—
219C22⋊C4—24no—
220C22⋊C4—42no—
221C22⋊C4—3162no—
222C22⋊C4—1584no—
223C22⋊C4—1584no—
224C22⋊C4—1584no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—792no—
233C23—792no—
234C23—792no—
235C23—1582no—
236C23—1582no—
237C23C23×D7911yescharacteristic
238D4—44no—
239D4—3168no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—3164no—
249C2×C4—3164no—
250C2×C4—792no—
251C2×C4—792no—
252C2×C4—1588no—
253C2×C4—1582no—
254C2×C4—1582no—
255C2×C4—1582no—
256C2×C4—1582no—
257C2×C4—1582no—
258C2×C4—1582no—
259C2×C4—1581no—
260C2×C4—1582no—
261C2×C4—1581no—
262C2×C4—1582no—
263C2×C4—1581no—
264C2×C4D4×D7912yes—
265C2×C4D4×D7912yes—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—794no—
274C22—1584no—
275C22—1584no—
276C22—1582no—
277C22—1582no—
278C22C2×D4×D7911yescharacteristic
279C22C2×D4×D7911yescharacteristic
280C22#41×D7911yescharacteristic
281C22#1457920612yes—
282C22#1457920812yes—
283C4—22no—
284C4—22no—
285C4—42no—
286C4—41no—
287C4—3162no—
288C4—3162no—
289C4—3161no—
290C4—1582no—
291C4—1582no—
292C2—82no—
293C2—1584no—
294C2#121×D7911yescharacteristic
295C2#1909912311yescharacteristic
296C2#1909913311yescharacteristic
297C2#1909914212yes—
298C2#1909915612yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radicalC2×#14579132C2
hypercenter#394D79
hypocenterC79#2618
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14579143C2semidirect
3. C2×C4⋊C4×D79C2semidirect
4. #19098495C2semidirect
5. #19098493C2semidirect
6. #19098486C2semidirect
7. #19098486C2semidirect
8. #19098477C2semidirect
9. #19098439C2semidirect
10. #19098422C2semidirect
11. #394×C79C2semidirect
53. C2×C4×D79D4semidirect
150. C79#2618semidirect
159. #394D79semidirect