Finite Group Databasebeta

← #479×D101 #27180905

Subgroups — #479×D101 #27180905

Order 12928.

384 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×D101C211yesmaximal, characteristic
2C4×Q8×D101C211yesmaximal, characteristic
3#20265487C211yesmaximal, characteristic, complemented
4#20265486C211yesmaximal, characteristic, complemented
5#20265485C211yesmaximal, characteristic, complemented
6#20265484C211yesmaximal, characteristic, complemented
7#20265483C211yesmaximal, characteristic, complemented
8#20265482C211yesmaximal, characteristic, complemented
9#20265481C211yesmaximal, characteristic, complemented
10#107×D101C211yesmaximal, characteristic
11#106×D101C211yesmaximal, characteristic
12C4⋊C8×D101C211yesmaximal, characteristic
13#103×D101C211yesmaximal, characteristic
14#103×D101C211yesmaximal, characteristic
15#479×C101C211yesmaximal, characteristic, complemented
16C2×Q8×D101C2211yescharacteristic
17C2×C8×D101C2211yescharacteristic
18C2×C8×D101C2211yescharacteristic
19#15692247C2211yescharacteristic
20#15692246C2211yescharacteristic
21#15692246C2211yescharacteristic
22#15692245—21no—
23#15692245—21no—
24Q8×Dic101C2211yescharacteristic
25C4×Dic202—21no—
26C4×Dic202C2211yescharacteristic
27#15692220—21no—
28#15692220C2211yescharacteristic
29C4⋊C4×D101—21no—
30C4⋊C4×D101—21no—
31C4⋊C4×D101—21no—
32C4⋊C4×D101C2211yescharacteristic
33C4⋊C4×D101C2211yescharacteristic
34C4⋊C4×D101C2211yescharacteristic
35C42×D101—21no—
36C42×D101C2211yescharacteristic
37#15692189C2211yescharacteristic
38#15692188C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692187C2211yescharacteristic
41#15692186C2211yescharacteristic
42#15692186C2211yescharacteristic
43C4⋊#11717579C2211yescharacteristic
44#15692184C2211yescharacteristic
45#15692184C2211yescharacteristic
46#15692180C2211yescharacteristic
47#15692180C2211yescharacteristic
48#15692179C2211yescharacteristic
49#15692179C2211yescharacteristic
50#15692178C2211yescharacteristic
51#15692178C2211yescharacteristic
52#125×C101C2211yescharacteristic
53C4×Q8×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic
55#106×C101C2211yescharacteristic
56C4⋊C8×C101C2211yescharacteristic
57#103×C101C2211yescharacteristic
58#103×C101C2211yescharacteristic
59C2×Dic202—21no—
60C2×Dic202C2311yescharacteristic
61Q8×D101—22no—
62Q8×D101Q814yes—
63C2×C4×D101—21no—
64C2×C4×D101—21no—
65C2×C4×D101—21no—
66C2×C4×D101—21no—
67C2×C4×D101D411yescharacteristic
68C2×C4×D101D411yescharacteristic
69C2×C4×D101C2311yescharacteristic
70C2×#11717579C2311yescharacteristic
71C2×#11717579C2311yescharacteristic
72C8×D101—22no—
73C8×D101—22no—
74C4⋊Dic101—21no—
75C4⋊Dic101—21no—
76C4⋊Dic101—21no—
77C4⋊Dic101C2311yescharacteristic
78C4⋊Dic101C2311yescharacteristic
79C4⋊Dic101C2311yescharacteristic
80#13108053—21no—
81#13108053—21no—
82#13108053—21no—
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88#13108053—21no—
89C4×Dic101—21no—
90C4×Dic101—21no—
91C4×Dic101—21no—
92C4×Dic101D411yescharacteristic
93C4×Dic101D411yescharacteristic
94C4×Dic101C2311yescharacteristic
95C2×Q8×C101C2311yescharacteristic
96C2×C8×C101C2311yescharacteristic
97C2×C8×C101C2311yescharacteristic
98C4⋊C4×C101—21no—
99C4⋊C4×C101—21no—
100C4⋊C4×C101—21no—
101C4⋊C4×C101C2311yescharacteristic
102C4⋊C4×C101C2311yescharacteristic
103C4⋊C4×C101C2311yescharacteristic
104C42×C101—21no—
105C42×C101C2311yescharacteristic
106C22×D101C2×D411yescharacteristic
107Q8×C101—21no—
108Q8×C101C2×Q812yes—
109C2×C4×C101—21no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101C2×D411yescharacteristic
114C2×C4×C101C2×D411yescharacteristic
115C2×C4×C101C2411yescharacteristic
116C2×Dic101—21no—
117C2×Dic101—21no—
118C2×Dic101—21no—
119C2×Dic101—21no—
120C2×Dic101C2×D411yescharacteristic
121C2×Dic101C2×D411yescharacteristic
122C2×Dic101C2×D411yescharacteristic
123C4×D101—24no—
124C4×D101—22no—
125C4×D101—22no—
126C4×D101—42no—
127C4×D101—42no—
128C4×D101—42no—
129C4×D101C2×Q812yes—
130C4×D101#4112yes—
131Dic202—21no—
132Dic202—24no—
133Dic202C2×Q812yes—
134C8×C101—21no—
135C8×C101—21no—
136#11717579—21no—
137#11717579—21no—
138C22×C101C22×D411yescharacteristic
139C2×D101C22⋊Q812yes—
140C2×D101#13512yes—
141C2×D101#13712yes—
142C4×C101—22no—
143C4×C101—21no—
144C4×C101—21no—
145C4×C101—41no—
146C4×C101—41no—
147C4×C101—41no—
148C4×C101C22×Q811yescharacteristic
149C4×C101C2×#4111yescharacteristic
150Dic101—22no—
151Dic101—21no—
152Dic101—21no—
153Dic101—41no—
154Dic101—41no—
155Dic101—41no—
156Dic101C22⋊Q812yes—
157C2×C101C2×C22⋊Q811yescharacteristic
158C2×C101C2×#13511yescharacteristic
159C2×C101C2×#13711yescharacteristic
160D101#47914yesdirect product factor
161C2×#479—1011nomaximal, Sylow
162C101C2×#47911yescharacteristic, complemented, Sylow
163C2×#125—1011no—
164C2×C4×Q8—1011no—
165#479—1011no—
166#479—1011no—
167#479—1011no—
168#479—1011no—
169#479—1011no—
170#479—1011no—
171#479—1011no—
172#479D10111yescharacteristic, direct product factor
173C2×#107—1011no—
174C2×#106—1011no—
175C2×C4⋊C8—1011no—
176C2×#103—1011no—
177C2×#103—1011no—
178C22×Q8—1011no—
179C22×C8—1011no—
180C22×C8—1011no—
181#125—1011no—
182#125—1011no—
183#125—1011no—
184#125—2021no—
185#125—2021no—
186#125C2×D10111yescharacteristic
187C4×Q8—1011no—
188C4×Q8—1011no—
189C4×Q8—1011no—
190C4×Q8—2021no—
191C4×Q8—2021no—
192C4×Q8C2×D10111yescharacteristic
193C2×C4⋊C4—1011no—
194C2×C4⋊C4—1011no—
195C2×C4⋊C4—1011no—
196C2×C4⋊C4—2021no—
197C2×C4⋊C4—2021no—
198C2×C4⋊C4—2021no—
199C2×C42—1011no—
200C2×C42—2021no—
201#107—1011no—
202#107—1011no—
203#107—1011no—
204#107C2×D10111yescharacteristic
205#106—1011no—
206#106—1011no—
207#106—1011no—
208#106C2×D10111yescharacteristic
209C4⋊C8—1011no—
210C4⋊C8—1011no—
211C4⋊C8—1011no—
212C4⋊C8C2×D10111yescharacteristic
213#103—1011no—
214#103—1011no—
215#103—1011no—
216#103—1011no—
217#103—1011no—
218#103—1011no—
219#103C2×D10111yescharacteristic
220#103C2×D10111yescharacteristic
221C2×Q8—1014no—
222C2×Q8—1011no—
223C2×Q8—2021no—
224C2×Q8—2022no—
225C2×Q8C22×D10111yescharacteristic
226C22×C4—1011no—
227C22×C4—1011no—
228C22×C4—1011no—
229C22×C4—2021no—
230C22×C4—2021no—
231C22×C4—2021no—
232C22×C4—2021no—
233C2×C8—1011no—
234C2×C8—1011no—
235C2×C8—2022no—
236C2×C8—2022no—
237C2×C8C22×D10111yescharacteristic
238C2×C8C22×D10111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—1011no—
243C4⋊C4—1011no—
244C4⋊C4—1011no—
245C4⋊C4—2021no—
246C4⋊C4—2021no—
247C4⋊C4—2021no—
248C4⋊C4—2021no—
249C4⋊C4—2021no—
250C4⋊C4—2021no—
251C4⋊C4—2021no—
252C4⋊C4—2021no—
253C4⋊C4—2021no—
254C4⋊C4—2021no—
255C4⋊C4—2021no—
256C4⋊C4—2021no—
257C4⋊C4C22×D10111yescharacteristic
258C4⋊C4C22×D10111yescharacteristic
259C4⋊C4C22×D10111yescharacteristic
260C42—21no—
261C42—1011no—
262C42—1011no—
263C42—1011no—
264C42—2021no—
265C42—2021no—
266C42—2021no—
267C42C22×D10111yescharacteristic
268C23—1011no—
269Q8—21no—
270Q8—1012no—
271Q8—2024no—
272Q8—2021no—
273Q8Q8×D10112yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—1011no—
279C2×C4—1012no—
280C2×C4—1012no—
281C2×C4—1011no—
282C2×C4—1011no—
283C2×C4—4042no—
284C2×C4—4042no—
285C2×C4—4042no—
286C2×C4—2022no—
287C2×C4—2022no—
288C2×C4—2024no—
289C2×C4—2021no—
290C2×C4—2021no—
291C2×C4—2021no—
292C2×C4—2021no—
293C2×C4D4×D10111yescharacteristic
294C2×C4D4×D10111yescharacteristic
295C2×C4C23×D10111yescharacteristic
296C8—21no—
297C8—21no—
298C8—2021no—
299C8—2021no—
300C22—1012no—
301C22—1012no—
302C22—1012no—
303C22C2×D4×D10111yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—1012no—
311C4—4041no—
312C4—4041no—
313C4—4041no—
314C4—2022no—
315C4—2021no—
316C4—2021no—
317C4C2×Q8×D10111yescharacteristic
318C4#41×D10111yescharacteristic
319C2—1014no—
320C2C22⋊Q8×D10111yescharacteristic
321C2#135×D10111yescharacteristic
322C2#137×D10111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#479×C101C2
socleC22×C101C22×D4
prime radicalC22×D101C2×D4
hypercenter#479D101
hypocenterC101C2×#479
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #20265487C2semidirect
4. #20265486C2semidirect
5. #20265485C2semidirect
6. #20265484C2semidirect
7. #20265483C2semidirect
8. #20265482C2semidirect
9. #20265481C2semidirect
15. #479×C101C2semidirect
160. D101#479direct (N × H)
162. C101C2×#479semidirect
172. #479D101direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#125×D1012
C4×Q8×D1012
#202654872
#202654862
#202654852
#202654842
#202654832
#202654822
#202654812
#107×D1012
#106×D1012
C4⋊C8×D1012
#103×D1012
#479×C1012
C2×#479101