Finite Group Databasebeta

← #26111665

Subgroups — #26111665

Order 12032.

628 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689176C211yesmaximal, characteristic
2#20243456C211yesmaximal, characteristic
3C2×#15688849C212yesmaximal
4#20241231C212yesmaximal
5C2×C47×#387C211yesmaximal, characteristic
6#15689176—24no—
7C2×C4⋊(C47⋊C8)—21no—
8C2×C22⋊(C47⋊C8)C2212yes—
9C2×C22⋊(C47⋊C8)C2212yes—
10C2×C4×C47⋊C8—21no—
11#15688878—21no—
12#15688878—21no—
13#15688849—24no—
14C22×C4⋊C4×C47C411yescharacteristic
15C22×C4⋊C4×C47C2211yescharacteristic
16C22×C42×C47C2211yescharacteristic
17C47×#387—21no—
18C47×#387—21no—
19C47×#387—21no—
20C47×#387—21no—
21C2×#95×C47C411yescharacteristic
22C2×#95×C47C411yescharacteristic
23C2×#95×C47C411yescharacteristic
24C2×#95×C47C2211yescharacteristic
25C22×C47⋊C8—22no—
26C22×C47⋊C8—22no—
27C4⋊(C47⋊C8)—24no—
28C22⋊(C47⋊C8)—22no—
29C22⋊(C47⋊C8)—22no—
30C22⋊(C47⋊C8)—22no—
31C22⋊(C47⋊C8)D414yes—
32C4×C47⋊C8—24no—
33C23×C4×C47C2×C411yescharacteristic
34C23×C4×C47C2×C411yescharacteristic
35C23×C4×C47C2×C411yescharacteristic
36C23×C4×C47C2×C411yescharacteristic
37C23×C4×C47C2×C411yescharacteristic
38C23×C4×C47C2×C411yescharacteristic
39C23×C4×C47C2311yescharacteristic
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47—22no—
43C2×C4⋊C4×C47—22no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47—21no—
46C2×C4⋊C4×C47—22no—
47C2×C4⋊C4×C47C814yescomplemented
48C2×C42×C47—22no—
49C2×C42×C47—22no—
50C2×C42×C47D411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54#95×C47—21no—
55#95×C47—21no—
56#95×C47—21no—
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—21no—
60#95×C47—21no—
61#95×C47—21no—
62C24×C47C22×C411yescharacteristic
63C22×C4×C47—22no—
64C22×C4×C47—22no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—22no—
72C22×C4×C47—22no—
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47—22no—
76C22×C4×C47—22no—
77C22×C4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47—41no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47—41no—
86C22×C4×C47C22⋊C411yescharacteristic
87C22×C4×C47C22⋊C411yescharacteristic
88C22×C4×C47C22⋊C411yescharacteristic
89C22×C4×C47C22⋊C411yescharacteristic
90C22×C4×C47C2×C812yes—
91C22×C4×C47C2×C812yes—
92C22×C4×C47C2×C812yes—
93C22×C4×C47M1612yes—
94C22×C4×C47C2×D411yescharacteristic
95C22×C4×C47C2×D411yescharacteristic
96C22×C4×C47C2×D412yes—
97C22×C4×C47#4112yes—
98C4⋊C4×C47—24no—
99C4⋊C4×C47—24no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—42no—
102C4⋊C4×C47—41no—
103C42×C47—21no—
104C42×C47—21no—
105C42×C47—22no—
106C42×C47—22no—
107C42×C47—21no—
108C42×C47—21no—
109C2×C47⋊C8—24no—
110C2×C47⋊C8—42no—
111C2×C47⋊C8—42no—
112C2×C47⋊C8—42no—
113C2×C47⋊C8—42no—
114C2×C47⋊C8—42no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47C2×C22⋊C411yescharacteristic
120C23×C47C4×D412yes—
121C23×C47C22×C811yescharacteristic
122C23×C47C2×M1611yescharacteristic
123C23×C47#13112yes—
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—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—24no—
135C2×C4×C47—24no—
136C2×C4×C47—21no—
137C2×C4×C47—22no—
138C2×C4×C47—22no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—24no—
142C2×C4×C47—42no—
143C2×C4×C47—42no—
144C2×C4×C47—44no—
145C2×C4×C47—42no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—42no—
151C2×C4×C47—42no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—82no—
159C2×C4×C47—82no—
160C2×C4×C47C22⋊C812yes—
161C2×C4×C47C22⋊C812yes—
162C2×C4×C47#10112yes—
163C2×C4×C47#12011yescharacteristic
164C2×C4×C47#12112yes—
165C2×C4×C47#12311yescharacteristic
166C47⋊C8—44no—
167C47⋊C8—82no—
168#9082—471nomaximal, Sylow
169C22×C47—22no—
170C22×C47—22no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—22no—
176C22×C47—22no—
177C22×C47#38611yescharacteristic
178C22×C47C2×C22⋊C811yescharacteristic
179C22×C47#40811yescharacteristic
180C22×C47#41011yescharacteristic
181C22×C47#41011yescharacteristic
182C22×C47C2×#10111yescharacteristic
183C22×C47#41311yescharacteristic
184C22×C47C8×D412yes—
185C22×C47#43512yes—
186C4×C47—22no—
187C4×C47—22no—
188C4×C47—21no—
189C4×C47—22no—
190C4×C47—21no—
191C4×C47—22no—
192C4×C47—42no—
193C4×C47—41no—
194C4×C47—42no—
195C4×C47—81no—
196C4×C47—81no—
197C2×#431—471no—
198C2×#387D4711yescharacteristic
199#1817—471no—
200C2×#324—472no—
201#1280—472no—
202C2×C47—22no—
203C2×C47—22no—
204C2×C47#145811yescharacteristic
205C2×C47#146111yescharacteristic
206C2×C47#147011yescharacteristic
207C2×C47#147311yescharacteristic
208C2×C47#186911yescharacteristic
209C2×C47#189911yescharacteristic
210C2×C47#190111yescharacteristic
211C22×C4⋊C4Dic4711yescharacteristic
212C22×C4⋊C4C2×D4711yescharacteristic
213C22×C42C2×D4711yescharacteristic
214#431—944no—
215C2×C4⋊C8—941no—
216C2×C22⋊C8—472no—
217C2×C22⋊C8—472no—
218C2×C4×C8—941no—
219#387—21no—
220#387—21no—
221#387—21no—
222#387—21no—
223C2×#95Dic4711yescharacteristic
224C2×#95Dic4711yescharacteristic
225C2×#95Dic4711yescharacteristic
226C2×#95C2×D4711yescharacteristic
227#336—941no—
228#336—941no—
229#324—944no—
230C47#908211yescharacteristic, complemented, Sylow
231C23×C4C2×Dic4711yescharacteristic
232C23×C4C2×Dic4711yescharacteristic
233C23×C4C2×Dic4711yescharacteristic
234C23×C4C2×Dic4711yescharacteristic
235C23×C4C2×Dic4711yescharacteristic
236C23×C4C2×Dic4711yescharacteristic
237C23×C4C22×D4711yescharacteristic
238C22×C8—942no—
239C22×C8—942no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4C47⋊C814yescomplemented
248C2×C42—22no—
249C2×C42—22no—
250C2×C42C22⋊D4711yescharacteristic
251C2×C42C22⋊D4711yescharacteristic
252C2×C42C22⋊D4711yescharacteristic
253C2×C42C22⋊D4711yescharacteristic
254C4⋊C8—944no—
255C22⋊C8—474no—
256C22⋊C8—942no—
257C22⋊C8—942no—
258C22⋊C8—942no—
259C4×C8—944no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268C24C22×Dic4711yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4C2×C47⋊C812yes—
293C22×C4C2×C47⋊C812yes—
294C22×C4C2×C47⋊C812yes—
295C22×C4#1062532912yes—
296C22×C4C22⋊Dic4711yescharacteristic
297C22×C4C22⋊Dic4711yescharacteristic
298C22×C4C22⋊Dic4711yescharacteristic
299C22×C4C22⋊Dic4711yescharacteristic
300C22×C4D4×D4712yes—
301C22×C4#1062535212yes—
302C22×C4C2×C22⋊D4711yescharacteristic
303C22×C4C2×C22⋊D4711yescharacteristic
304C2×C8—944no—
305C2×C8—1882no—
306C2×C8—1882no—
307C2×C8—1882no—
308C2×C8—1882no—
309C2×C8—1882no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C42—21no—
316C42—21no—
317C42—22no—
318C42—22no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×C22⋊Dic4711yescharacteristic
326C23D4×Dic4712yes—
327C23C22×C47⋊C811yescharacteristic
328C23C2×#1062532911yescharacteristic
329C23#1309403112yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—24no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4C22⋊(C47⋊C8)12yes—
367C2×C4C22⋊(C47⋊C8)12yes—
368C2×C4#1309394312yes—
369C2×C4#1309399211yescharacteristic
370C2×C4#1309399612yes—
371C2×C4#1309400511yescharacteristic
372C8—3762no—
373C8—1884no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22#1568900311yescharacteristic
383C22C2×C22⋊(C47⋊C8)11yescharacteristic
384C22#1568909011yescharacteristic
385C22#1568909711yescharacteristic
386C22#1568909711yescharacteristic
387C22C2×#1309394311yescharacteristic
388C22#1568910711yescharacteristic
389C22D4×C47⋊C812yes—
390C22#1568919512yes—
391C4—22no—
392C4—21no—
393C4—21no—
394C4—22no—
395C4—22no—
396C4—22no—
397C4—42no—
398C4—41no—
399C4—42no—
400C4—81no—
401C4—81no—
402C2—22no—
403C2—22no—
404C2#2024170211yescharacteristic
405C2#2024171211yescharacteristic
406C2#2024174411yescharacteristic
407C2#2024175711yescharacteristic
408C2#2024368111yescharacteristic
409C2#2024384711yescharacteristic
410C2#2024385711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC23×C47C22×C8
FrattiniC23×C4C22×D47
FittingC2×C47×#387C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenterC2×#387D47
hypocenterC47#9082
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
47. C2×C4⋊C4×C47C8semidirect
230. C47#9082semidirect
247. C2×C4⋊C4C47⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#156891762
#202434562
C2×#156888492
#202412312
C2×C47×#3872
#908247