Finite Group Databasebeta

← #27180973

Subgroups — #27180973

Order 12928.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265807C211yesmaximal, characteristic
2#20265653C211yesmaximal, characteristic
3#20265486C211yesmaximal, characteristic, complemented
4#20265483C211yesmaximal, characteristic, complemented
5#20265481C211yesmaximal, characteristic, complemented
6#20265473C211yesmaximal, characteristic, complemented
7#20265470C211yesmaximal, characteristic, complemented
8#20265462C211yesmaximal, characteristic, complemented
9#20265461C211yesmaximal, characteristic, complemented
10#20265216C211yesmaximal, characteristic
11#20265214C211yesmaximal, characteristic
12#20265202C211yesmaximal, characteristic
13#20265184C211yesmaximal, characteristic
14#103×D101C211yesmaximal, characteristic
15#479×C101C211yesmaximal, characteristic, complemented
16C2×Q8×D101C2211yescharacteristic
17C2×#13108057C2211yescharacteristic
18C2×C8×D101C2211yescharacteristic
19#15692255C2211yescharacteristic
20#15692254—21no—
21#15692254C2211yescharacteristic
22#15692246C2211yescharacteristic
23#15692245—21no—
24#15692235—21no—
25#15692233—21no—
26Q8×Dic101C2211yescharacteristic
27C4×Dic202—21no—
28C4×Dic202C2211yescharacteristic
29#15692220—21no—
30#15692220C2211yescharacteristic
31#15692213—21no—
32#15692213C2211yescharacteristic
33#15692213C2211yescharacteristic
34#15692212—21no—
35#15692212C2211yescharacteristic
36C4⋊C4×D101C2211yescharacteristic
37#15692189C2211yescharacteristic
38#15692189C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692186C2211yescharacteristic
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×Dic202—21no—
61C2×Dic202—21no—
62C2×Dic202C2311yescharacteristic
63Q8×D101—22no—
64Q8×D101Q814yescomplemented
65C2×C4×D101—21no—
66C2×C4×D101—21no—
67C2×C4×D101C2311yescharacteristic
68#13108057—22no—
69C2×#11717579C2311yescharacteristic
70C2×#11717579C2311yescharacteristic
71C8×D101—22no—
72C4⋊Dic101—21no—
73C4⋊Dic101—21no—
74C4⋊Dic101—21no—
75C4⋊Dic101C2311yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77C4⋊Dic101C2311yescharacteristic
78#13108053—21no—
79#13108053—21no—
80#13108053—21no—
81#13108053—21no—
82#13108053—21no—
83#13108053D411yescharacteristic
84#13108053D411yescharacteristic
85#13108051—21no—
86#13108051—21no—
87#13108051D411yescharacteristic
88#13108051D411yescharacteristic
89C4×Dic101—21no—
90C4×Dic101—21no—
91C4×Dic101—21no—
92C4×Dic101—21no—
93C4×Dic101—21no—
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—81no—
125C4×D101C2×Q812yes—
126C4×D101#4112yes—
127Dic202—21no—
128Dic202—24no—
129Dic202—81no—
130Dic202—81no—
131Dic202C2×Q812yes—
132C8×C101—21no—
133C8×C101—21no—
134#11717579—21no—
135#11717579—21no—
136C22×C101C22×D411yescharacteristic
137C2×D101—21no—
138C2×D101—21no—
139C2×D101C22⋊Q812yes—
140C4×C101—22no—
141C4×C101—21no—
142C4×C101—21no—
143C4×C101—41no—
144C4×C101—41no—
145C4×C101—41no—
146C4×C101C22×Q811yescharacteristic
147C4×C101C2×#4111yescharacteristic
148Dic101—22no—
149Dic101—21no—
150Dic101—21no—
151Dic101—41no—
152Dic101—41no—
153Dic101—41no—
154Dic101C22⋊Q812yes—
155C2×C101C2×C22⋊Q811yescharacteristic
156C2×C101#57711yescharacteristic
157C2×C101#57811yescharacteristic
158D101—22no—
159#3082—1011nomaximal, Sylow
160C101#308211yescharacteristic, complemented, Sylow
161#544—1011no—
162#519—1011no—
163#479—1011no—
164#479—1011no—
165#479—1011no—
166#479D10111yescharacteristic, complemented
167#477—1011no—
168#477—1011no—
169#475—1011no—
170#475—1011no—
171#428—1011no—
172#427—1011no—
173#424—1011no—
174#419—1011no—
175C2×#103—1011no—
176C22×Q8—1011no—
177C2×M16—1011no—
178C22×C8—1011no—
179C4⋊Q8—1011no—
180C4⋊Q8—1011no—
181C4⋊Q8—2021no—
182#125—1011no—
183#125—2021no—
184#125C2×D10111yescharacteristic
185C22⋊Q8—2021no—
186C22⋊Q8—2021no—
187C4×Q8—1011no—
188C4×Q8—1011no—
189C4×Q8—1011no—
190C4×Q8—2021no—
191C4×Q8—2021no—
192C4×Q8C2×D10111yescharacteristic
193#117—1011no—
194#117—1011no—
195#117—1011no—
196#117—2021no—
197#117—2021no—
198C2×C4⋊C4—1011no—
199#107—1011no—
200#107—1011no—
201#107—1011no—
202#107C2×D10111yescharacteristic
203#106—1011no—
204#106—1011no—
205#106—1011no—
206#106C2×D10111yescharacteristic
207C4⋊C8—1011no—
208C4⋊C8—1011no—
209C4⋊C8—1011no—
210C4⋊C8C2×D10111yescharacteristic
211#103—1011no—
212#103—1011no—
213#103—1011no—
214#103—1011no—
215#103—1011no—
216#103—1011no—
217#103C2×D10111yescharacteristic
218#103C2×D10111yescharacteristic
219C2×Q8—1014no—
220C2×Q8—1011no—
221C2×Q8—2021no—
222C2×Q8—2021no—
223C2×Q8—2022no—
224C2×Q8—2021no—
225C2×Q8C22×D10111yescharacteristic
226C22×C4—1011no—
227C22×C4—2021no—
228C22×C4—2021no—
229M16—2022no—
230C2×C8—1011no—
231C2×C8—1011no—
232C2×C8—2022no—
233C2×C8C22×D10111yescharacteristic
234C2×C8C22×D10111yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—1011no—
239C4⋊C4—1011no—
240C4⋊C4—1011no—
241C4⋊C4—1011no—
242C4⋊C4—1011no—
243C4⋊C4—2021no—
244C4⋊C4—2021no—
245C4⋊C4—2021no—
246C4⋊C4—2021no—
247C4⋊C4—2021no—
248C4⋊C4—2021no—
249C4⋊C4—2021no—
250C4⋊C4—2021no—
251C4⋊C4C22×D10111yescharacteristic
252C4⋊C4C22×D10111yescharacteristic
253C4⋊C4C22×D10111yescharacteristic
254C22⋊C4—1011no—
255C22⋊C4—1011no—
256C22⋊C4—2021no—
257C22⋊C4—2021no—
258C42—21no—
259C42—1011no—
260C42—2021no—
261C42—2021no—
262C42—2021no—
263C42—2021no—
264C42—2021no—
265C42C22×D10111yescharacteristic
266C23—1011no—
267Q8—21no—
268Q8—8081no—
269Q8—8081no—
270Q8—1012no—
271Q8—2024no—
272Q8—2021no—
273Q8Q8×D10112yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—8081no—
279C2×C4—1011no—
280C2×C4—1012no—
281C2×C4—1012no—
282C2×C4—1011no—
283C2×C4—1011no—
284C2×C4—2024no—
285C2×C4—2021no—
286C2×C4—2021no—
287C2×C4—2021no—
288C2×C4—2021no—
289C2×C4D4×D10111yescharacteristic
290C2×C4D4×D10111yescharacteristic
291C2×C4C23×D10111yescharacteristic
292C8—21no—
293C8—21no—
294C8—2021no—
295C8—2021no—
296C22—1012no—
297C22—2021no—
298C22—2021no—
299C22C2×D4×D10111yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—1012no—
307C4—4041no—
308C4—4041no—
309C4—4041no—
310C4—2021no—
311C4—2021no—
312C4—2022no—
313C4C2×Q8×D10111yescharacteristic
314C4#41×D10111yescharacteristic
315C2—2022no—
316C2C22⋊Q8×D10111yescharacteristic
317C2#2026598611yescharacteristic
318C2#2026599111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#479×C101C2
socleC22×C101C22×D4
prime radicalC22×D101C2×D4
hypercenter#479D101
hypocenterC101#3082
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. #20265486C2semidirect
4. #20265483C2semidirect
5. #20265481C2semidirect
6. #20265473C2semidirect
7. #20265470C2semidirect
8. #20265462C2semidirect
9. #20265461C2semidirect
15. #479×C101C2semidirect
64. Q8×D101Q8semidirect
160. C101#3082semidirect
166. #479D101semidirect

Maximal subgroups

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

subgroupindex
#202658072
#202656532
#202654862
#202654832
#202654812
#202654732
#202654702
#202654622
#202654612
#202652162
#202652142
#202652022
#202651842
#103×D1012
#479×C1012
#3082101