Finite Group Databasebeta

← #23767712

Subgroups — #23767712

Order 10112.

584 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14579123C211yesmaximal, characteristic
2C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
3#19098502C211yesmaximal, characteristic, complemented
4#19098500C211yesmaximal, characteristic, complemented
5#19098498C211yesmaximal, characteristic, complemented
6#19098460C212yesmaximal, complemented
7#19098441C212yesmaximal
8#19098437C212yesmaximal, complemented
9#19098422C212yesmaximal, complemented
10#19098422C211yesmaximal, characteristic, complemented
11#400×C79C211yesmaximal, characteristic, complemented
12C22×D316C2211yescharacteristic
13C22×C4×D79C2211yescharacteristic
14C22×C4×D79C2211yescharacteristic
15C22×C4×D79C2212yes—
16#14579123—24no—
17C2×C4⋊Dic79C2211yescharacteristic
18C2×C4⋊Dic79C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2212yes—
21C2×Dic79⋊C4C2212yes—
22C4⋊C4×D79—24no—
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2211yescharacteristic
26C2×(C2×D79)⋊C4C2212yes—
27C2×(C2×D79)⋊C4C2212yes—
28C2×C4×Dic79C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2211yescharacteristic
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34#95×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C23×D79C2311yescharacteristic
38C23×D79C2311yescharacteristic
39C2×D316—22no—
40C2×D316—22no—
41C2×D316Q814yes—
42C22×Dic79C2312yes—
43C22×Dic79C2312yes—
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2311yescharacteristic
46C2×C4×D79—24no—
47C2×C4×D79—22no—
48C2×C4×D79—24no—
49C2×C4×D79—24no—
50C2×C4×D79—42no—
51C2×C4×D79—42no—
52C2×C4×D79D414yes—
53C4⋊Dic79—22no—
54C4⋊Dic79—42no—
55Dic79⋊C4—24no—
56Dic79⋊C4—24no—
57Dic79⋊C4—42no—
58(C2×D79)⋊C4—22no—
59(C2×D79)⋊C4—24no—
60(C2×D79)⋊C4—22no—
61(C2×D79)⋊C4—42no—
62(C2×D79)⋊C4—42no—
63C4×Dic79—22no—
64C22×C4×C79C2312yes—
65C22×C4×C79C2311yescharacteristic
66C22×C4×C79C2312yes—
67C22×C4×C79C2311yescharacteristic
68C22×C4×C79C2311yescharacteristic
69C4⋊C4×C79—22no—
70C4⋊C4×C79—22no—
71C23×C79C2411yescharacteristic
72C22×D79—22no—
73C22×D79—22no—
74C22×D79—21no—
75C22×D79—22no—
76C22×D79—21no—
77C22×D79—22no—
78C22×D79C2×D412yes—
79C22×D79C2×Q812yes—
80C22×D79C2×Q812yes—
81C22×D79#4112yes—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79—21no—
85C2×C4×C79—21no—
86C2×C4×C79—22no—
87C2×C4×C79—22no—
88C2×C4×C79—22no—
89C2×C4×C79—22no—
90C2×C4×C79—22no—
91C2×C4×C79—22no—
92C2×C4×C79—22no—
93C2×C4×C79C2×D412yes—
94C2×C4×C79C2×Q812yes—
95C2×Dic79—21no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—22no—
100C2×Dic79—22no—
101C2×Dic79—22no—
102C2×Dic79—22no—
103C2×Dic79C2×D412yes—
104C2×Dic79#4114yes—
105D316—28no—
106C4×D79—28no—
107C4×D79—48no—
108C4×D79—44no—
109C22×C79C22×D411yescharacteristic
110C22×C79C22×Q811yescharacteristic
111C22×C79C2×#4111yescharacteristic
112C22×C79C2×#4112yes—
113C22×C79H(5,𝔽2)12yes—
114C2×D79—22no—
115C2×D79—22no—
116C2×D79—24no—
117C2×D79—24no—
118C2×D79—22no—
119C2×D79—24no—
120C2×D79—41no—
121C2×D79—41no—
122C2×D79—42no—
123C2×D79C22⋊Q814yes—
124C4×C79—22no—
125C4×C79—22no—
126C4×C79—41no—
127C4×C79—42no—
128C4×C79—42no—
129Dic79—42no—
130Dic79—41no—
131Dic79—42no—
132Dic79#12314yes—
133C2×C79C2×C22⋊Q811yescharacteristic
134C2×C79C2×#12311yescharacteristic
135C2×C79#53511yescharacteristic
136C2×C79#55312yes—
137C2×C79#55412yes—
138D79—24no—
139D79—42no—
140#2487—791nomaximal, Sylow
141C79#248711yescharacteristic, complemented, Sylow
142C2×C4×D4—791no—
143C22×C4⋊C4—791no—
144#400—791no—
145#400D7911yescharacteristic, complemented
146#399—791no—
147#399—791no—
148#389—792no—
149#386—792no—
150#385—792no—
151#380—792no—
152#380—791no—
153C22×D4—791no—
154C23×C4—792no—
155C23×C4—791no—
156C23×C4—791no—
157C4×D4—1584no—
158C2×C4⋊C4—792no—
159C2×C4⋊C4—792no—
160C2×C4⋊C4—792no—
161C2×C4⋊C4—791no—
162C2×C4⋊C4—792no—
163C2×C4⋊C4—1584no—
164C2×C4⋊C4C2×D7911yescharacteristic
165C2×C4⋊C4C2×D7911yescharacteristic
166C2×C22⋊C4—792no—
167C2×C22⋊C4—792no—
168C2×C22⋊C4—791no—
169C2×C22⋊C4—791no—
170C2×C22⋊C4—792no—
171C2×C42—791no—
172#95—792no—
173#95—791no—
174#95—792no—
175#95C2×D7912yes—
176#95C2×D7911yescharacteristic
177#95C2×D7912yes—
178C24—791no—
179C24—791no—
180C2×D4—794no—
181C2×D4—1582no—
182C2×D4—1582no—
183C22×C4—3162no—
184C22×C4—3162no—
185C22×C4—791no—
186C22×C4—794no—
187C22×C4—792no—
188C22×C4—792no—
189C22×C4—791no—
190C22×C4—1582no—
191C22×C4—1584no—
192C22×C4—1584no—
193C22×C4—1584no—
194C22×C4C22×D7911yescharacteristic
195C22×C4C22×D7912yes—
196C22×C4C22×D7912yes—
197C22×C4C22×D7911yescharacteristic
198C22×C4C22×D7911yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—3162no—
202C4⋊C4—3162no—
203C4⋊C4—1584no—
204C4⋊C4—1584no—
205C4⋊C4—1582no—
206C22⋊C4—3162no—
207C22⋊C4—3162no—
208C22⋊C4—1584no—
209C22⋊C4—1582no—
210C22⋊C4—1582no—
211C42—1582no—
212C23—792no—
213C23—792no—
214C23—792no—
215C23—792no—
216C23—1582no—
217C23—1581no—
218C23—1582no—
219C23—1581no—
220C23—1582no—
221C23—1582no—
222C23C23×D7911yescharacteristic
223D4—1588no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—3168no—
236C2×C4—3164no—
237C2×C4—794no—
238C2×C4—792no—
239C2×C4—1588no—
240C2×C4—1582no—
241C2×C4—1582no—
242C2×C4—1582no—
243C2×C4—1582no—
244C2×C4—1582no—
245C2×C4—1582no—
246C2×C4—1581no—
247C2×C4—1582no—
248C2×C4D4×D7912yes—
249C2×C4Q8×D7912yes—
250C22—3162no—
251C22—3161no—
252C22—3161no—
253C22—794no—
254C22—1584no—
255C22—1582no—
256C22—1584no—
257C22—1584no—
258C22—1582no—
259C22—1582no—
260C22C2×D4×D7911yescharacteristic
261C22C2×Q8×D7911yescharacteristic
262C22#41×D7911yescharacteristic
263C22#41×D7912yes—
264C22#1457920712yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—41no—
269C4—42no—
270C4—3162no—
271C4—3162no—
272C4—3161no—
273C4—794no—
274C2—3162no—
275C2—1584no—
276C2C22⋊Q8×D7911yescharacteristic
277C2#123×D7911yescharacteristic
278C2#1909913111yescharacteristic
279C2#1909926412yes—
280C2#1909926912yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#400×C79C2
prime radicalC22×D316C22
hypercenter#400D79
hypocenterC79#2487
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D79C2semidirect
3. #19098502C2semidirect
4. #19098500C2semidirect
5. #19098498C2semidirect
6. #19098460C2semidirect
8. #19098437C2semidirect
9. #19098422C2semidirect
10. #19098422C2semidirect
11. #400×C79C2semidirect
141. C79#2487semidirect
145. #400D79semidirect