Finite Group Databasebeta

← #26109122

Subgroups — #26109122

Order 12032.

546 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625324C211yesmaximal, characteristic
2#20243365C212yesmaximal
3C2×#15688874C211yesmaximal, characteristic, complemented
4#20241222C212yesmaximal, complemented
5C2×C47×#335C211yesmaximal, characteristic, complemented
6C22×#10625324C411yescharacteristic
7C22×#10625324C411yescharacteristic
8C2×C42×D47C2211yescharacteristic
9C2×C4⋊(C47⋊C8)C2212yes—
10C2×(C2×D47)⋊C8—22no—
11C4×#10625324—22no—
12C4×#10625324—22no—
13C2×#13093934C411yescharacteristic
14C2×#13093934C411yescharacteristic
15C2×C4×C47⋊C8C2211yescharacteristic
16#15688877—22no—
17#15688874—22no—
18C2×C4⋊C8×C47C2212yes—
19C2×C4×C8×C47C2211yescharacteristic
20C47×#335—22no—
21C22×C4×D47C2×C411yescharacteristic
22C22×C4×D47D411yescharacteristic
23C22×C4×D47Q811yescharacteristic
24C2×#10625324—22no—
25C2×#10625324—22no—
26C2×#10625324—22no—
27C2×#10625324—22no—
28C2×#10625324—22no—
29C2×#10625324C814yescomplemented
30C22×C47⋊C8—22no—
31C22×C47⋊C8C2×C411yescharacteristic
32C22×C47⋊C8C2×C411yescharacteristic
33C2×C4×Dic47C2×C411yescharacteristic
34C2×C4×Dic47D411yescharacteristic
35C2×C4×Dic47Q811yescharacteristic
36C42×D47—21no—
37C42×D47—21no—
38C42×D47—21no—
39C42×D47—21no—
40C4⋊(C47⋊C8)—22no—
41C4⋊(C47⋊C8)—22no—
42(C2×D47)⋊C8—44no—
43#13093934—22no—
44#13093934—22no—
45C4×C47⋊C8—21no—
46C4×C47⋊C8—21no—
47C22×C8×C47—22no—
48C22×C8×C47C2×C411yescharacteristic
49C22×C8×C47C2×C411yescharacteristic
50C2×C42×C47C2311yescharacteristic
51C4⋊C8×C47—22no—
52C4⋊C8×C47—22no—
53C4×C8×C47D412yes—
54C4×C8×C47D412yes—
55C23×D47C4⋊C411yescharacteristic
56C22×C4×C47C22×C411yescharacteristic
57C22×C4×C47C2×D411yescharacteristic
58C22×C4×C47C2×Q811yescharacteristic
59C22×Dic47C4⋊C411yescharacteristic
60C22×Dic47C4⋊C411yescharacteristic
61C22×Dic47C4⋊C411yescharacteristic
62C2×C4×D47—21no—
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—22no—
71C2×C4×D47—22no—
72C2×C4×D47—42no—
73C2×C4×D47C2×C812yes—
74C2×C4×D47M1612yes—
75C2×C8×C47—21no—
76C2×C8×C47—21no—
77C2×C8×C47—42no—
78C2×C8×C47—42no—
79C2×C8×C47—42no—
80C2×C8×C47C22⋊C412yes—
81C2×C8×C47C22⋊C412yes—
82C2×C8×C47C2×C812yes—
83C2×C8×C47M1612yes—
84C42×C47C2×D411yescharacteristic
85C42×C47C2×D411yescharacteristic
86C42×C47#4111yescharacteristic
87C42×C47#4111yescharacteristic
88C4×Dic47—21no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C4×Dic47—21no—
92C4×Dic47—21no—
93C4×Dic47—21no—
94C2×C47⋊C8—21no—
95C2×C47⋊C8—21no—
96C2×C47⋊C8—21no—
97C2×C47⋊C8—21no—
98C2×C47⋊C8—42no—
99C2×C47⋊C8—42no—
100C2×C47⋊C8—42no—
101C2×C47⋊C8C2×C812yes—
102C2×C47⋊C8M1612yes—
103#10625324—28no—
104#10625324—28no—
105C23×C47C2×C4⋊C411yescharacteristic
106C22×D47—21no—
107C22×D47—21no—
108C22×D47—22no—
109C22×D47—22no—
110C22×D47C4⋊C812yes—
111C2×C4×C47—22no—
112C2×C4×C47C2×C22⋊C411yescharacteristic
113C2×C4×C47#11711yescharacteristic
114C2×C4×C47#12111yescharacteristic
115C2×C4×C47#12111yescharacteristic
116C2×C4×C47C22⋊Q811yescharacteristic
117C2×C4×C47C22⋊Q811yescharacteristic
118C2×C4×C47C22×C811yescharacteristic
119C2×C4×C47C2×M1611yescharacteristic
120C2×C4×C47C2×M1611yescharacteristic
121C2×C4×C47C2×M1611yescharacteristic
122C2×C4×C47AGL(1,ℤ/8)12yes—
123C2×C4×C47#13712yes—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47C4⋊C812yes—
131C4×D47—22no—
132C4×D47—22no—
133C4×D47—22no—
134C4×D47—22no—
135C4×D47—42no—
136C4×D47—42no—
137C4×D47—42no—
138C4×D47—41no—
139C4×D47—41no—
140C8×C47—22no—
141C8×C47—82no—
142C8×C47C22⋊C814yescomplemented
143C47⋊C8—22no—
144C47⋊C8—22no—
145C47⋊C8—82no—
146#8597—471nomaximal, Sylow
147C22×C47#38011yescharacteristic
148C22×C47C2×C4⋊C811yescharacteristic
149C22×C47#42311yescharacteristic
150C22×C47#42812yes—
151C22×C47#43012yes—
152C2×D47—22no—
153C2×D47—24no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—42no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47C2×C22⋊C811yescharacteristic
160C4×C47#40711yescharacteristic
161C4×C47#43111yescharacteristic
162C4×C47#43211yescharacteristic
163C4×C47#46812yes—
164C4×C47#46911yescharacteristic
165C4×C47#47011yescharacteristic
166Dic47—22no—
167Dic47—41no—
168Dic47—41no—
169C2×C4×M16—471no—
170#1797—472no—
171C2×#335D4711yescharacteristic, complemented
172C2×#334—471no—
173#1277—472no—
174C2×C47#156512yes—
175C2×C47#156912yes—
176C2×C47#179711yescharacteristic
177C2×C47#180911yescharacteristic
178C2×C47#181111yescharacteristic
179D47—42no—
180C22×M16—471no—
181C22×M16—471no—
182C22×C42—471no—
183C2×C4⋊C8—472no—
184C2×C4⋊C8C2×D4712yes—
185C2×C22⋊C8—942no—
186C4×M16—942no—
187C4×M16—942no—
188C2×#97—471no—
189C2×#97—471no—
190C2×C4×C8—471no—
191C2×C4×C8C2×D4711yescharacteristic
192#336—942no—
193#335—22no—
194#334—942no—
195C47#859711yescharacteristic, complemented, Sylow
196C23×C4—471no—
197C23×C4—471no—
198C23×C4—471no—
199C2×M16—474no—
200C2×M16—942no—
201C2×M16—942no—
202C2×M16—942no—
203C2×M16—942no—
204C2×M16—942no—
205C22×C8—22no—
206C22×C8—471no—
207C22×C8—471no—
208C22×C8—942no—
209C22×C8C4×D4711yescharacteristic
210C22×C8C4×D4711yescharacteristic
211C2×C42—471no—
212C2×C42—471no—
213C2×C42—471no—
214C2×C42—941no—
215C2×C42—941no—
216C2×C42—941no—
217C2×C42—941no—
218C2×C42C22×D4711yescharacteristic
219C4⋊C8—22no—
220C4⋊C8—22no—
221C4⋊C8—942no—
222C4⋊C8—942no—
223C22⋊C8—1884no—
224#97—942no—
225#97—942no—
226C4×C8—941no—
227C4×C8—941no—
228C4×C8D18812yes—
229C4×C8C22⋊D4712yes—
230C24—471no—
231C22×C4—471no—
232C22×C4—472no—
233C22×C4—472no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244C22×C4—942no—
245C22×C4—942no—
246C22×C4—1882no—
247C22×C4C2×C4×D4711yescharacteristic
248C22×C4D4×D4711yescharacteristic
249C22×C4Q8×D4711yescharacteristic
250M16—948no—
251M16—948no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—472no—
258C2×C8—472no—
259C2×C8—941no—
260C2×C8—941no—
261C2×C8—941no—
262C2×C8—941no—
263C2×C8—1882no—
264C2×C8—1882no—
265C2×C8—1882no—
266C2×C8C8×D4712yes—
267C2×C8#1062532412yes—
268C2×C8(C2×D47)⋊C412yes—
269C2×C8(C2×D47)⋊C412yes—
270C42—941no—
271C42—941no—
272C42—941no—
273C42—941no—
274C42—941no—
275C42—941no—
276C42C2×D18811yescharacteristic
277C42#1062535211yescharacteristic
278C42#1062535411yescharacteristic
279C42C2×C22⋊D4711yescharacteristic
280C23—472no—
281C23—941no—
282C23—941no—
283C23—942no—
284C23—942no—
285C23C4⋊C4×D4711yescharacteristic
286C2×C4—22no—
287C2×C4—472no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—942no—
291C2×C4—942no—
292C2×C4—942no—
293C2×C4—942no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—942no—
297C2×C4—942no—
298C2×C4—1882no—
299C2×C4—1882no—
300C2×C4—1882no—
301C2×C4—1881no—
302C2×C4—1881no—
303C2×C4C2×(C2×D47)⋊C411yescharacteristic
304C2×C4#1309398211yescharacteristic
305C2×C4#1309399511yescharacteristic
306C2×C4#1309399911yescharacteristic
307C2×C4#1309400011yescharacteristic
308C2×C4#1309400411yescharacteristic
309C2×C4C2×C8×D4711yescharacteristic
310C2×C4M16×D4711yescharacteristic
311C2×C4M16×D4711yescharacteristic
312C2×C4C2×#1062532411yescharacteristic
313C2×C4#1309404812yes—
314C2×C4#1309405612yes—
315C8—22no—
316C8—82no—
317C8—942no—
318C8—942no—
319C8—3762no—
320C8(C2×D47)⋊C814yescomplemented
321C22—942no—
322C22—944no—
323C22—1881no—
324C22—1881no—
325C22—1882no—
326C22#1568898011yescharacteristic
327C22C4⋊C8×D4711yescharacteristic
328C22#1568914511yescharacteristic
329C22#1568916412yes—
330C22#1568917012yes—
331C4—21no—
332C4—21no—
333C4—942no—
334C4—1881no—
335C4—1881no—
336C4C2×(C2×D47)⋊C811yescharacteristic
337C4#1568908611yescharacteristic
338C4#1568917511yescharacteristic
339C4#1568917911yescharacteristic
340C4#1568937012yes—
341C4#1568937311yescharacteristic
342C4#1568937811yescharacteristic
343C2—1882no—
344C2#2024213912yes—
345C2#2024215412yes—
346C2#2024336511yescharacteristic
347C2#2024342211yescharacteristic
348C2#2024342711yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×#335C2
socleC23×C47C2×C4⋊C4
prime radicalC23×D47C4⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#335D47
hypocenterC47#8597
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
3. C2×#15688874C2semidirect
4. #20241222C2semidirect
5. C2×C47×#335C2semidirect
29. C2×#10625324C8semidirect
142. C8×C47C22⋊C8semidirect
171. C2×#335D47semidirect
195. C47#8597semidirect
320. C8(C2×D47)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253242
#202433652
C2×#156888742
#202412222
C2×C47×#3352
#859747