Finite Group Databasebeta

← #26106799

Subgroups — #26106799

Order 12032.

602 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689007C211yesmaximal, characteristic
2C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic
3C2×#15688848C212yesmaximal
4#20241230C212yesmaximal
5C47×#1749C211yesmaximal, characteristic
6C22×Dic47⋊C4C411yescharacteristic
7C22×Dic47⋊C4C2211yescharacteristic
8C2×C22⋊(C47⋊C8)C2212yes—
9C2×C4×C47⋊C8—21no—
10#15689007—21no—
11#15689007—21no—
12#15689007—21no—
13#15689007—21no—
14C2×C47⋊#95C411yescharacteristic
15C2×C47⋊#95C411yescharacteristic
16C2×C47⋊#95C411yescharacteristic
17C2×C47⋊#95C2211yescharacteristic
18#15688878—21no—
19#15688848C418yescomplemented
20C22×C42×C47C2211yescharacteristic
21C2×C22⋊C8×C47C2212yes—
22C2×#97×C47—21no—
23C47×#336—21no—
24C23×Dic47C2×C411yescharacteristic
25C23×Dic47C2×C411yescharacteristic
26C23×Dic47C2×C411yescharacteristic
27C23×Dic47C2×C411yescharacteristic
28C22×C47⋊C8—22no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—22no—
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—42no—
35C2×Dic47⋊C4C2×C414yes—
36C22⋊(C47⋊C8)—22no—
37C22⋊(C47⋊C8)C2×C414yes—
38C4×C47⋊C8—42no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C23×C4×C47C2×C411yescharacteristic
48C23×C4×C47C2×C411yescharacteristic
49C23×C4×C47C2311yescharacteristic
50C22×C8×C47—22no—
51C2×C42×C47—42no—
52C2×C42×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54C2×C42×C47D411yescharacteristic
55C2×C42×C47D411yescharacteristic
56C22⋊C8×C47—22no—
57C22⋊C8×C47C2×C414yes—
58#97×C47—42no—
59C24×C47C22×C411yescharacteristic
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—22no—
63C22×C4×C47—22no—
64C22×C4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47—41no—
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C22×C412yes—
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47#4112yes—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47—21no—
80C22×Dic47—22no—
81C22×Dic47—22no—
82C22×Dic47—21no—
83C22×Dic47—21no—
84C22×Dic47—22no—
85C22×Dic47—22no—
86C22×Dic47—41no—
87C22×Dic47—41no—
88C22×Dic47—41no—
89C22×Dic47—41no—
90C22×Dic47—41no—
91C22×Dic47—41no—
92C22×Dic47C4212yes—
93C22×Dic47C4212yes—
94C2×C8×C47—24no—
95C2×C8×C47—42no—
96C2×C8×C47—42no—
97C42×C47—22no—
98C42×C47—22no—
99C42×C47—41no—
100C42×C47—41no—
101Dic47⋊C4—24no—
102Dic47⋊C4—24no—
103Dic47⋊C4—42no—
104Dic47⋊C4—42no—
105C2×C47⋊C8—24no—
106C2×C47⋊C8—42no—
107C2×C47⋊C8—42no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47C2×C4211yescharacteristic
113C23×C47C2×C22⋊C411yescharacteristic
114C23×C47#11711yescharacteristic
115C23×C47#13112yes—
116C23×C47#13112yes—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—42no—
132C2×C4×C47—42no—
133C2×C4×C47—44no—
134C2×C4×C47—44no—
135C2×C4×C47#9912yes—
136C2×C4×C47#10112yes—
137C2×C4×C47C4×D412yes—
138C2×C4×C47C4×D412yes—
139C2×Dic47—22no—
140C2×Dic47—22no—
141C2×Dic47—24no—
142C2×Dic47—42no—
143C2×Dic47—41no—
144C2×Dic47—41no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147C2×Dic47—42no—
148C2×Dic47—42no—
149C2×Dic47—41no—
150C2×Dic47—41no—
151C2×Dic47—41no—
152C2×Dic47—41no—
153C2×Dic47—41no—
154C2×Dic47—41no—
155C2×Dic47—82no—
156C2×Dic47—82no—
157C8×C47—44no—
158C47⋊C8—44no—
159#8154—471nomaximal, Sylow
160C22×C47—22no—
161C22×C47—22no—
162C22×C47—22no—
163C22×C47—22no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47C4×C22⋊C411yescharacteristic
169C22×C47#40512yes—
170C22×C47#40811yescharacteristic
171C22×C47#40811yescharacteristic
172C22×C47C2×#9911yescharacteristic
173C22×C47#41011yescharacteristic
174C22×C47C2×#10111yescharacteristic
175C22×C47#41311yescharacteristic
176C22×C47#43312yes—
177C4×C47—22no—
178C4×C47—22no—
179C4×C47—22no—
180C4×C47—22no—
181C4×C47—41no—
182C4×C47—41no—
183Dic47—42no—
184Dic47—42no—
185Dic47—81no—
186Dic47—81no—
187C2×#387—471no—
188#1749D4711yescharacteristic
189C4×C22⋊C8—471no—
190C2×#324—472no—
191#1280—472no—
192C2×C47—22no—
193C2×C47—22no—
194C2×C47#146811yescharacteristic
195C2×C47#147011yescharacteristic
196C2×C47#147211yescharacteristic
197C2×C47#147311yescharacteristic
198C2×C47#175011yescharacteristic
199C2×C47C4×#9911yescharacteristic
200C2×C47C4×#10111yescharacteristic
201C22×C4⋊C4—471no—
202C22×C4⋊C4—471no—
203C22×C42C2×D4711yescharacteristic
204C2×C22⋊C8—472no—
205C2×C22⋊C8C2×D4712yes—
206C2×#97—21no—
207C2×C4×C8—941no—
208#387—941no—
209#387—941no—
210#387—941no—
211#387—941no—
212C2×#95—471no—
213C2×#95—471no—
214C2×#95—471no—
215C2×#95—471no—
216#336—21no—
217#336—941no—
218#324—478no—
219C47#815411yescharacteristic, complemented, Sylow
220C23×C4—471no—
221C23×C4—471no—
222C23×C4—471no—
223C23×C4—471no—
224C23×C4C4×D4711yescharacteristic
225C23×C4C4×D4711yescharacteristic
226C23×C4C22×D4711yescharacteristic
227C22×C8—22no—
228C22×C8—942no—
229C2×C4⋊C4—474no—
230C2×C4⋊C4—941no—
231C2×C4⋊C4—942no—
232C2×C4⋊C4—941no—
233C2×C4⋊C4—941no—
234C2×C4⋊C4—941no—
235C2×C4⋊C4—1882no—
236C2×C42—42no—
237C2×C42D18811yescharacteristic
238C2×C42D18811yescharacteristic
239C2×C42C22⋊D4711yescharacteristic
240C2×C42C22⋊D4711yescharacteristic
241C22⋊C8—22no—
242C22⋊C8—474no—
243C22⋊C8—942no—
244C22⋊C8C4×D4714yes—
245#97—42no—
246C4×C8—1882no—
247#95—941no—
248#95—941no—
249#95—941no—
250#95—941no—
251#95—941no—
252#95—941no—
253#95—941no—
254#95—941no—
255C24C2×C4×D4711yescharacteristic
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—472no—
265C22×C4—472no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4—942no—
271C22×C4—942no—
272C22×C4—942no—
273C22×C4—942no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4—1881no—
277C22×C4—1881no—
278C22×C4—1881no—
279C22×C4—1881no—
280C22×C4—1881no—
281C22×C4—1881no—
282C22×C4(C2×D47)⋊C411yescharacteristic
283C22×C4(C2×D47)⋊C411yescharacteristic
284C22×C4(C2×D47)⋊C411yescharacteristic
285C22×C4(C2×D47)⋊C411yescharacteristic
286C22×C4C2×C4×D4712yes—
287C22×C4C2×D18811yescharacteristic
288C22×C4#1062535012yes—
289C22×C4C2×C22⋊D4711yescharacteristic
290C2×C8—24no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—944no—
294C2×C8—1882no—
295C2×C8—1882no—
296C4⋊C4—944no—
297C4⋊C4—944no—
298C4⋊C4—1882no—
299C4⋊C4—1882no—
300C42—22no—
301C42—22no—
302C42—41no—
303C42—41no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23C42×D4711yescharacteristic
309C23C2×(C2×D47)⋊C411yescharacteristic
310C23#1309398111yescharacteristic
311C23#1309403212yes—
312C23#1309403212yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—942no—
332C2×C4—942no—
333C2×C4—944no—
334C2×C4—3762no—
335C2×C4—3762no—
336C2×C4—1881no—
337C2×C4—1881no—
338C2×C4—1881no—
339C2×C4—1881no—
340C2×C4—1881no—
341C2×C4—1881no—
342C2×C4—1882no—
343C2×C4—1881no—
344C2×C4—1881no—
345C2×C4—1881no—
346C2×C4—1881no—
347C2×C4—1882no—
348C2×C4—1882no—
349C2×C4#1309393812yes—
350C2×C4#1309394212yes—
351C2×C4C4×C22⋊D4712yes—
352C2×C4C4×D18812yes—
353C8—44no—
354C8—1884no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22C4×(C2×D47)⋊C411yescharacteristic
364C22#1568908012yes—
365C22#1568909111yescharacteristic
366C22#1568909111yescharacteristic
367C22C2×#1309393811yescharacteristic
368C22#1568909611yescharacteristic
369C22C2×#1309394211yescharacteristic
370C22#1568910511yescharacteristic
371C22#1568918512yes—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—3761no—
379C4—3761no—
380C4—1882no—
381C4—1882no—
382C2—22no—
383C2—22no—
384C2#2024173711yescharacteristic
385C2#2024174511yescharacteristic
386C2#2024175311yescharacteristic
387C2#2024175811yescharacteristic
388C2#2024315711yescharacteristic
389C2C4×#1309393811yescharacteristic
390C2C4×#1309394211yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC23×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1749C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenter#1749D47
hypocenterC47#8154
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
19. #15688848C4semidirect
219. C47#8154semidirect

Maximal subgroups

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

subgroupindex
C2×#156890072
C4×C22⋊(C47⋊C8)2
C2×#156888482
#202412302
C47×#17492
#815447