Finite Group Databasebeta

← #26121892

Subgroups — #26121892

Order 12032.

918 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C47⋊C8C211yesmaximal, characteristic
2C2×#15688878C212yesmaximal
3C2×#15688878C212yesmaximal
4C2×#15688878C211yesmaximal, characteristic
5C4×#95×C47C211yesmaximal, characteristic
6C23×C47⋊C8C2212yes—
7C23×C47⋊C8C2211yescharacteristic
8C23×C47⋊C8C2211yescharacteristic
9C2×C4×C47⋊C8—24no—
10C2×C4×C47⋊C8C414yescomplemented
11#15688878—24no—
12#15688878—24no—
13#15688878C414yescomplemented
14C22×C42×C47C2212yes—
15C22×C42×C47C2211yescharacteristic
16C2×#95×C47C412yes—
17C2×#95×C47C412yes—
18C22×C47⋊C8—22no—
19C22×C47⋊C8—22no—
20C22×C47⋊C8—22no—
21C22×C47⋊C8—21no—
22C22×C47⋊C8—21no—
23C22×C47⋊C8—22no—
24C22×C47⋊C8—22no—
25C22×C47⋊C8—22no—
26C22×C47⋊C8—22no—
27C22×C47⋊C8—22no—
28C22×C47⋊C8—22no—
29C22×C47⋊C8C2×C414yes—
30C22×C47⋊C8C2×C412yes—
31C22×C47⋊C8C2×C412yes—
32C22×C47⋊C8D414yes—
33C22×C47⋊C8D412yes—
34C22×C47⋊C8Q812yes—
35C4×C47⋊C8—28no—
36C23×C4×C47C2×C414yes—
37C23×C4×C47C2×C411yescharacteristic
38C23×C4×C47C2×C411yescharacteristic
39C23×C4×C47C2311yescharacteristic
40C2×C42×C47—22no—
41C2×C42×C47—22no—
42C2×C42×C47—22no—
43C2×C42×C47—22no—
44C2×C42×C47—22no—
45C2×C42×C47—22no—
46C2×C42×C47—22no—
47C2×C42×C47—22no—
48C2×C42×C47C2×C412yes—
49C2×C42×C47C2×C412yes—
50#95×C47—24no—
51#95×C47C818yescomplemented
52C24×C47C22×C411yescharacteristic
53C22×C4×C47—22no—
54C22×C4×C47—22no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
57C22×C4×C47—24no—
58C22×C4×C47—24no—
59C22×C4×C47—24no—
60C22×C4×C47—24no—
61C22×C4×C47—24no—
62C22×C4×C47—24no—
63C22×C4×C47C4212yes—
64C22×C4×C47C4212yes—
65C22×C4×C47C2×C818yes—
66C22×C4×C47C2×C814yes—
67C22×C4×C47M1614yes—
68C22×C4×C47C22×C411yescharacteristic
69C22×C4×C47C22×C411yescharacteristic
70C22×C4×C47C2×D412yes—
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×Q811yescharacteristic
73C22×C4×C47#4112yes—
74C22×C4×C47#4112yes—
75C22×C4×C47#4111yescharacteristic
76C22×C4×C47#4112yes—
77C22×C4×C47#4111yescharacteristic
78C42×C47—22no—
79C42×C47—22no—
80C42×C47—24no—
81C42×C47—42no—
82C42×C47—42no—
83C42×C47—42no—
84C42×C47—42no—
85C2×C47⋊C8—22no—
86C2×C47⋊C8—22no—
87C2×C47⋊C8—22no—
88C2×C47⋊C8—22no—
89C2×C47⋊C8—24no—
90C2×C47⋊C8—24no—
91C2×C47⋊C8—24no—
92C2×C47⋊C8—24no—
93C2×C47⋊C8—24no—
94C2×C47⋊C8—24no—
95C2×C47⋊C8—24no—
96C2×C47⋊C8—42no—
97C2×C47⋊C8—42no—
98C2×C47⋊C8—42no—
99C2×C47⋊C8—42no—
100C2×C47⋊C8C22⋊C414yes—
101C2×C47⋊C8C4⋊C414yes—
102C23×C47C2×C4211yescharacteristic
103C23×C47#11712yes—
104C23×C47C4×D412yes—
105C23×C47C4×D411yescharacteristic
106C23×C47C4×Q811yescharacteristic
107C23×C47C22×C812yes—
108C23×C47C2×M1612yes—
109C23×C47#13112yes—
110C23×C47#13112yes—
111C2×C4×C47—22no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—22no—
115C2×C4×C47—28no—
116C2×C4×C47—28no—
117C2×C4×C47—28no—
118C2×C4×C47—28no—
119C2×C4×C47—28no—
120C2×C4×C47—44no—
121C2×C4×C47—44no—
122C2×C4×C47—44no—
123C2×C4×C47—44no—
124C2×C4×C47C4×C814yes—
125C2×C4×C47#9714yes—
126C2×C4×C47C2×C22⋊C411yescharacteristic
127C2×C4×C47C2×C4⋊C411yescharacteristic
128C2×C4×C47#11711yescharacteristic
129C2×C4×C47#11711yescharacteristic
130C2×C4×C47#11711yescharacteristic
131C2×C4×C47#11712yes—
132C2×C4×C47#11711yescharacteristic
133C2×C4×C47C4×D412yes—
134C2×C4×C47C4×D411yescharacteristic
135C2×C4×C47C4×Q811yescharacteristic
136C2×C4×C47#12112yes—
137C2×C4×C47C22⋊Q812yes—
138C2×C4×C47#12312yes—
139C2×C4×C47#12312yes—
140C2×C4×C47#12412yes—
141C2×C4×C47#12512yes—
142C2×C4×C47#12612yes—
143C2×C4×C47#12612yes—
144C47⋊C8—24no—
145C47⋊C8—24no—
146C47⋊C8—44no—
147#10797—471nomaximal, Sylow
148C22×C47#37611yescharacteristic
149C22×C47C4×C22⋊C411yescharacteristic
150C22×C47C4×C4⋊C411yescharacteristic
151C22×C47#38712yes—
152C22×C47#38812yes—
153C22×C47C2×C4×C811yescharacteristic
154C22×C47C2×#9711yescharacteristic
155C22×C47#40511yescharacteristic
156C22×C47#40511yescharacteristic
157C22×C47#43114yes—
158C22×C47#43314yes—
159C22×C47C8×D414yes—
160C22×C47C8×D412yes—
161C22×C47#43514yes—
162C22×C47#43612yes—
163C22×C47C8×Q812yes—
164C22×C47#44612yes—
165C4×C47—24no—
166C4×C47—24no—
167C4×C47—48no—
168C4×C47#38011yescharacteristic
169C4×C47#38111yescharacteristic
170C4×C47#38211yescharacteristic
171C4×C47#38311yescharacteristic
172C4×C47#38712yes—
173C4×C47#38812yes—
174C22×C4×C8—471no—
175C2×#336—471no—
176C2×#336—472no—
177C2×#336—472no—
178C4×#95D4711yescharacteristic
179C2×C47#143411yescharacteristic
180C2×C47#174411yescharacteristic
181C2×C47#174611yescharacteristic
182C2×C47C8×C22⋊C411yescharacteristic
183C2×C47#175211yescharacteristic
184C2×C47C8×C4⋊C411yescharacteristic
185C2×C47#177011yescharacteristic
186C2×C47#191614yes—
187C2×C47#192314yes—
188C23×C8—471no—
189C23×C8—471no—
190C23×C8—472no—
191C22×C42C2×D4712yes—
192C22×C42C2×D4711yescharacteristic
193C2×C4×C8—474no—
194C2×C4×C8—944no—
195C2×#95Dic4712yes—
196C2×#95Dic4712yes—
197#336—474no—
198#336—944no—
199#336—944no—
200C47#1079711yescharacteristic, complemented, Sylow
201C23×C4C2×Dic4714yes—
202C23×C4C2×Dic4711yescharacteristic
203C23×C4C2×Dic4711yescharacteristic
204C23×C4C22×D4711yescharacteristic
205C22×C8—472no—
206C22×C8—472no—
207C22×C8—472no—
208C22×C8—474no—
209C22×C8—472no—
210C22×C8—474no—
211C22×C8—942no—
212C22×C8—942no—
213C22×C8—942no—
214C22×C8—941no—
215C22×C8—941no—
216C22×C8—942no—
217C22×C8—942no—
218C22×C8—942no—
219C22×C8—942no—
220C22×C8—942no—
221C22×C8—942no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—22no—
230C2×C42C4×D4712yes—
231C2×C42C4×D4712yes—
232C4×C8—948no—
233#95—24no—
234#95C47⋊C818yescomplemented
235C24C22×Dic4711yescharacteristic
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4C2×C47⋊C818yes—
247C22×C4C2×C47⋊C814yes—
248C22×C4#1062532914yes—
249C22×C4C4×Dic4712yes—
250C22×C4C4×Dic4712yes—
251C22×C4C2×C4×D4711yescharacteristic
252C22×C4C2×C4×D4711yescharacteristic
253C22×C4#1062535012yes—
254C22×C4#1062535012yes—
255C22×C4D4×D4712yes—
256C22×C4D4×D4711yescharacteristic
257C22×C4#1062535212yes—
258C22×C4#1062535211yescharacteristic
259C22×C4Q8×D4711yescharacteristic
260C22×C4#1062535411yescharacteristic
261C2×C8—474no—
262C2×C8—474no—
263C2×C8—942no—
264C2×C8—942no—
265C2×C8—942no—
266C2×C8—942no—
267C2×C8—944no—
268C2×C8—944no—
269C2×C8—944no—
270C2×C8—944no—
271C2×C8—944no—
272C2×C8—944no—
273C2×C8—944no—
274C2×C8—1882no—
275C2×C8—1882no—
276C2×C8—1882no—
277C2×C8—1882no—
278C42—22no—
279C42—22no—
280C42—24no—
281C42—42no—
282C42—42no—
283C42—42no—
284C42—42no—
285C23C2×C4×Dic4711yescharacteristic
286C23#1309398312yes—
287C23D4×Dic4712yes—
288C23D4×Dic4711yescharacteristic
289C23Q8×Dic4711yescharacteristic
290C23C22×C47⋊C812yes—
291C23C2×#1062532912yes—
292C23#1309403112yes—
293C23#1309403112yes—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—28no—
299C2×C4—28no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—28no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4C4×C47⋊C814yes—
308C2×C4#1309393514yes—
309C2×C4C22⋊C4×D4711yescharacteristic
310C2×C4C4⋊C4×D4711yescharacteristic
311C2×C4#1309398011yescharacteristic
312C2×C4#1309398111yescharacteristic
313C2×C4#1309398111yescharacteristic
314C2×C4#1309398112yes—
315C2×C4#1309398211yescharacteristic
316C2×C4(C22⋊D47)⋊C412yes—
317C2×C4#1309398611yescharacteristic
318C2×C4#1309398911yescharacteristic
319C2×C4#1309399712yes—
320C2×C4#1309400212yes—
321C2×C4#1309400612yes—
322C2×C4#1309400912yes—
323C2×C4#1309401012yes—
324C2×C4#1309401412yes—
325C2×C4#1309401712yes—
326C2×C4#1309401912yes—
327C8—944no—
328C8—944no—
329C8—1884no—
330C22#1568896911yescharacteristic
331C22C22⋊C4×Dic4711yescharacteristic
332C22C4⋊C4×Dic4711yescharacteristic
333C22#1568900912yes—
334C22#1568901612yes—
335C22C2×C4×C47⋊C811yescharacteristic
336C22C2×#1309393511yescharacteristic
337C22#1568907911yescharacteristic
338C22#1568907911yescharacteristic
339C22#1568917614yes—
340C22#1568918414yes—
341C22D4×C47⋊C812yes—
342C22D4×C47⋊C814yes—
343C22#1568919514yes—
344C22#1568920112yes—
345C22Q8×C47⋊C812yes—
346C22#1568925412yes—
347C4—24no—
348C4—24no—
349C4—48no—
350C4#1568898211yescharacteristic
351C4#1568898511yescharacteristic
352C4#1568898711yescharacteristic
353C4#1568899011yescharacteristic
354C4#1568900512yes—
355C4#1568901212yes—
356C2#2024161311yescharacteristic
357C2#2024313411yescharacteristic
358C2#2024314011yescharacteristic
359C2C22⋊C4×C47⋊C811yescharacteristic
360C2#2024316611yescharacteristic
361C2C4⋊C4×C47⋊C811yescharacteristic
362C2#2024325711yescharacteristic
363C2#2024394714yes—
364C2#2024399614yes—
subgroupG/H
center, FrattiniC23×C4C22×D47
commutatorC22×C47C2×C4×C8
FittingC4×#95×C47C2
socle, prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenterC4×#95D47
hypocenterC47#10797
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
10. C2×C4×C47⋊C8C4semidirect
13. #15688878C4semidirect
51. #95×C47C8semidirect
200. C47#10797semidirect
234. #95C47⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C47⋊C82
C2×#156888782
C4×#95×C472
#1079747