Finite Group Databasebeta

← #23768874

Subgroups — #23768874

Order 10112.

596 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14579132C211yesmaximal, characteristic
2C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
3#19098503C211yesmaximal, characteristic, complemented
4#19098502C211yesmaximal, characteristic, complemented
5#19098477C211yesmaximal, characteristic, complemented
6#19098456C212yesmaximal, complemented
7#19098451C212yesmaximal, complemented
8#19098439C212yesmaximal, complemented
9#19098439C212yesmaximal, complemented
10#19098410C211yesmaximal, characteristic, complemented
11#394×C79C211yesmaximal, characteristic, complemented
12C22×C22⋊D79C2212yes—
13C22×C4×D79C2211yescharacteristic
14C22×C4×D79C2211yescharacteristic
15C22×C4×D79C2211yescharacteristic
16#14579132—24no—
17C2×C4⋊Dic79C2211yescharacteristic
18C2×C4⋊Dic79C2211yescharacteristic
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C4⋊C4×D79—24no—
22C2×C22⋊Dic79C2212yes—
23C2×C22⋊Dic79C2212yes—
24C2×C22⋊Dic79C2212yes—
25C2×(C2×D79)⋊C4C2212yes—
26C2×C4×Dic79C2212yes—
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C22×D4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C22⋊C4×C79C2212yes—
35C2×C22⋊C4×C79C2212yes—
36#95×C79C2211yescharacteristic
37C23×D79C2311yescharacteristic
38C2×C22⋊D79—24no—
39C2×C22⋊D79—24no—
40C2×C22⋊D79—24no—
41C22×Dic79C2312yes—
42C22×Dic79C2312yes—
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2311yescharacteristic
46C2×C4×D79—22no—
47C2×C4×D79—22no—
48C2×C4×D79—22no—
49C2×C4×D79—22no—
50C2×C4×D79—42no—
51C2×C4×D79—42no—
52C2×C4×D79D414yes—
53C4⋊Dic79—22no—
54C4⋊Dic79—22no—
55Dic79⋊C4—22no—
56Dic79⋊C4—22no—
57C22⋊Dic79—24no—
58C22⋊Dic79—24no—
59C22⋊Dic79—42no—
60(C2×D79)⋊C4—24no—
61C4×Dic79—42no—
62C24×C79C2312yes—
63C2×D4×C79—22no—
64C2×D4×C79—42no—
65C22×C4×C79C2312yes—
66C22×C4×C79C2311yescharacteristic
67C22×C4×C79C2311yescharacteristic
68C22×C4×C79C2311yescharacteristic
69C4⋊C4×C79—22no—
70C22⋊C4×C79—24no—
71C22⋊C4×C79—42no—
72C23×C79—22no—
73C23×C79—22no—
74C23×C79—22no—
75C23×C79—22no—
76C23×C79—22no—
77C23×C79—22no—
78C23×C79—22no—
79C23×C79C2411yescharacteristic
80C22×D79—21no—
81C22×D79—21no—
82C22×D79—22no—
83C22×D79C2×D412yes—
84C22×D79#4114yes—
85D4×C79—44no—
86C2×C4×C79—21no—
87C2×C4×C79—21no—
88C2×C4×C79—22no—
89C2×C4×C79—21no—
90C2×C4×C79—22no—
91C2×C4×C79—22no—
92C2×C4×C79—22no—
93C2×C4×C79—22no—
94C2×C4×C79C2×D412yes—
95C2×C4×C79#4112yes—
96C22⋊D79—48no—
97C2×Dic79—21no—
98C2×Dic79—21no—
99C2×Dic79—22no—
100C2×Dic79—22no—
101C2×Dic79—21no—
102C2×Dic79—22no—
103C2×Dic79—22no—
104C2×Dic79—22no—
105C2×Dic79—22no—
106C2×Dic79—22no—
107C2×Dic79—22no—
108C2×Dic79C2×D412yes—
109C2×Dic79#4112yes—
110C4×D79—28no—
111C4×D79—44no—
112C4×D79—44no—
113C22×C79—42no—
114C22×C79—42no—
115C22×C79—42no—
116C22×C79—42no—
117C22×C79—42no—
118C22×C79—42no—
119C22×C79—42no—
120C22×C79C22×D411yescharacteristic
121C22×C79C2×#4111yescharacteristic
122C22×C79C2×#4112yes—
123C22×C79C2×#4111yescharacteristic
124C22×C79H(5,𝔽2)12yes—
125C2×D79—22no—
126C2×D79—22no—
127C2×D79—24no—
128C2×D79—24no—
129C2×D79#12414yes—
130C4×C79—22no—
131C4×C79—22no—
132C4×C79—41no—
133C4×C79—42no—
134Dic79—22no—
135Dic79—22no—
136Dic79—42no—
137Dic79—41no—
138Dic79—42no—
139C2×C79—82no—
140C2×C79#52511yescharacteristic
141C2×C79C2×#12411yescharacteristic
142C2×C79#53411yescharacteristic
143C2×C79#55312yes—
144C2×C79#55312yes—
145D79—24no—
146#2591—791nomaximal, Sylow
147C79#259111yescharacteristic, complemented, Sylow
148C2×#121—791no—
149C22×C4⋊C4—791no—
150#400—791no—
151#400—791no—
152#394—791no—
153#394D7911yescharacteristic, complemented
154#388—792no—
155#388—792no—
156#386—792no—
157#386—792no—
158C4×C22⋊C4—791no—
159C22×D4—792no—
160C22×D4C2×D7911yescharacteristic
161C23×C4—791no—
162C23×C4—791no—
163C23×C4—791no—
164#121—1584no—
165C2×C4⋊C4—791no—
166C2×C4⋊C4—791no—
167C2×C4⋊C4—791no—
168C2×C4⋊C4—791no—
169C2×C4⋊C4—1584no—
170C2×C4⋊C4C2×D7911yescharacteristic
171C2×C22⋊C4—792no—
172C2×C22⋊C4—792no—
173C2×C22⋊C4—792no—
174C2×C22⋊C4—792no—
175C2×C22⋊C4C2×D7912yes—
176C2×C22⋊C4C2×D7912yes—
177C2×C42—792no—
178#95—791no—
179#95—792no—
180#95—792no—
181#95—792no—
182#95—792no—
183#95C2×D7911yescharacteristic
184C24—791no—
185C24C22×D7912yes—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—1584no—
189C2×D4—1584no—
190C2×D4—1584no—
191C22×C4—3162no—
192C22×C4—3162no—
193C22×C4—794no—
194C22×C4—791no—
195C22×C4—791no—
196C22×C4—792no—
197C22×C4—792no—
198C22×C4—791no—
199C22×C4—1582no—
200C22×C4—1582no—
201C22×C4—1582no—
202C22×C4—1582no—
203C22×C4C22×D7912yes—
204C22×C4C22×D7911yescharacteristic
205C22×C4C22×D7911yescharacteristic
206C22×C4C22×D7911yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—1582no—
209C4⋊C4—1582no—
210C4⋊C4—1582no—
211C4⋊C4—1582no—
212C22⋊C4—24no—
213C22⋊C4—42no—
214C22⋊C4—3162no—
215C22⋊C4—1584no—
216C22⋊C4—1584no—
217C22⋊C4—1584no—
218C42—3162no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—794no—
227C23—792no—
228C23—1581no—
229C23—1581no—
230C23—1582no—
231C23C23×D7911yescharacteristic
232D4—44no—
233D4—3168no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—3164no—
243C2×C4—3164no—
244C2×C4—792no—
245C2×C4—792no—
246C2×C4—1588no—
247C2×C4—1582no—
248C2×C4—1582no—
249C2×C4—1582no—
250C2×C4—1582no—
251C2×C4—1582no—
252C2×C4—1582no—
253C2×C4—1582no—
254C2×C4—1581no—
255C2×C4—1581no—
256C2×C4—1582no—
257C2×C4—1581no—
258C2×C4D4×D7912yes—
259C2×C4#1192962312yes—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—794no—
268C22—1584no—
269C22—1584no—
270C22—1582no—
271C22—1582no—
272C22C2×D4×D7911yescharacteristic
273C22#41×D7911yescharacteristic
274C22#41×D7912yes—
275C22C2×#1192962311yescharacteristic
276C22#1457920612yes—
277C4—22no—
278C4—22no—
279C4—42no—
280C4—41no—
281C4—3162no—
282C4—3162no—
283C4—3161no—
284C4—1582no—
285C4—1582no—
286C2—82no—
287C2—1584no—
288C2#1909907311yescharacteristic
289C2#124×D7911yescharacteristic
290C2#1909912311yescharacteristic
291C2#1909925812yes—
292C2#1909926012yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radicalC2×#14579132C2
hypercenter#394D79
hypocenterC79#2591
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D79C2semidirect
3. #19098503C2semidirect
4. #19098502C2semidirect
5. #19098477C2semidirect
6. #19098456C2semidirect
7. #19098451C2semidirect
8. #19098439C2semidirect
9. #19098439C2semidirect
10. #19098410C2semidirect
11. #394×C79C2semidirect
147. C79#2591semidirect
153. #394D79semidirect