Finite Group Databasebeta

← #26111620

Subgroups — #26111620

Order 12032.

610 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689176C211yesmaximal, characteristic
2#20243368C211yesmaximal, characteristic
3C2×Q8⋊(C47⋊C8)C212yesmaximal, complemented
4#20241229C212yesmaximal, complemented
5C4×C22⋊Q8×C47C211yesmaximal, characteristic
6#15689176—24no—
7C2×C4⋊(C47⋊C8)—21no—
8C2×C4⋊(C47⋊C8)C2212yes—
9C2×C22⋊(C47⋊C8)—21no—
10C2×C22⋊(C47⋊C8)—21no—
11C2×C4×C47⋊C8C2212yes—
12#15688878—21no—
13Q8⋊(C47⋊C8)—24no—
14C2×C22⋊Q8×C47C411yescharacteristic
15C2×C4×Q8×C47C2211yescharacteristic
16C22×C42×C47C2211yescharacteristic
17C47×#391C411yescharacteristic
18C47×#389C411yescharacteristic
19C47×#387—21no—
20C47×#385—21no—
21C47×#380C411yescharacteristic
22C4×C4⋊C4×C47—21no—
23C4×C4⋊C4×C47C2211yescharacteristic
24C4×C22⋊C4×C47—21no—
25C22×C47⋊C8—22no—
26C22×C47⋊C8—22no—
27C4⋊(C47⋊C8)—24no—
28C4⋊(C47⋊C8)—22no—
29C4⋊(C47⋊C8)—22no—
30C22⋊(C47⋊C8)—24no—
31C22⋊(C47⋊C8)—42no—
32C4×C47⋊C8—22no—
33C4×C47⋊C8D414yes—
34C22×Q8×C47C2×C411yescharacteristic
35C23×C4×C47C2×C411yescharacteristic
36C23×C4×C47D411yescharacteristic
37C23×C4×C47D411yescharacteristic
38C22⋊Q8×C47—22no—
39C22⋊Q8×C47C814yescomplemented
40C4×Q8×C47—22no—
41C4×Q8×C47—22no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47C2×C411yescharacteristic
46C2×C4⋊C4×C47C2×C411yescharacteristic
47C2×C4⋊C4×C47C2×C411yescharacteristic
48C2×C22⋊C4×C47—21no—
49C2×C22⋊C4×C47—21no—
50C2×C42×C47—22no—
51C2×C42×C47—22no—
52C2×C42×C47—21no—
53C2×C42×C47—21no—
54C2×C42×C47C2×C411yescharacteristic
55C2×C42×C47D411yescharacteristic
56C2×C42×C47D411yescharacteristic
57C2×C42×C47C2311yescharacteristic
58#95×C47—21no—
59#95×C47—21no—
60#95×C47—21no—
61#95×C47—21no—
62#95×C47—21no—
63C24×C47C22⋊C411yescharacteristic
64C2×Q8×C47—21no—
65C2×Q8×C47—22no—
66C2×Q8×C47—22no—
67C2×Q8×C47C2×C812yes—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—22no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—22no—
78C22×C4×C47—21no—
79C22×C4×C47—21no—
80C22×C4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47C22⋊C411yescharacteristic
83C22×C4×C47C22⋊C411yescharacteristic
84C22×C4×C47C22⋊C411yescharacteristic
85C22×C4×C47C2×C812yes—
86C22×C4×C47M1612yes—
87C22×C4×C47C22×C411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C4⋊C4×C47—24no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—22no—
93C4⋊C4×C47—22no—
94C4⋊C4×C47—42no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—41no—
97C4⋊C4×C47C2×C812yes—
98C22⋊C4×C47—24no—
99C22⋊C4×C47—42no—
100C42×C47—22no—
101C42×C47—21no—
102C42×C47—22no—
103C42×C47—21no—
104C42×C47—42no—
105C42×C47—41no—
106C42×C47—41no—
107C42×C47C2×D412yes—
108C42×C47#4112yes—
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×C47—21no—
120C23×C47—21no—
121C23×C47C22⋊C812yes—
122C23×C47C2×C22⋊C411yescharacteristic
123Q8×C47—24no—
124Q8×C47—42no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—24no—
130C2×C4×C47—24no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—22no—
134C2×C4×C47—22no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—42no—
140C2×C4×C47—42no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47C22⋊C812yes—
154C2×C4×C47C4×D412yes—
155C2×C4×C47#12011yescharacteristic
156C2×C4×C47#12112yes—
157C2×C4×C47#12311yescharacteristic
158C2×C4×C47C22×C811yescharacteristic
159C2×C4×C47C2×M1611yescharacteristic
160C2×C4×C47#13112yes—
161C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C47#13711yescharacteristic
163C2×C4×C47#13712yes—
164C47⋊C8—44no—
165C47⋊C8—82no—
166#9073—471nomaximal, Sylow
167C22×C47—22no—
168C22×C47—22no—
169C22×C47—22no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47#38611yescharacteristic
175C22×C47C2×C22⋊C811yescharacteristic
176C22×C47#40811yescharacteristic
177C22×C47#41711yescharacteristic
178C22×C47#41911yescharacteristic
179C22×C47#42111yescharacteristic
180C22×C47#42111yescharacteristic
181C4×C47—22no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—42no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47—42no—
188C4×C47—81no—
189C4×C47—81no—
190C4×C47C8×D412yes—
191C4×C47#43512yes—
192C4×C47#46812yes—
193C4×C47#47012yes—
194C2×#431—471no—
195C4×C22⋊Q8D4711yescharacteristic
196#1797—471no—
197C2×Q8⋊C8—472no—
198#1279—472no—
199C2×C47—42no—
200C2×C47#147711yescharacteristic
201C2×C47#147911yescharacteristic
202C2×C47#149511yescharacteristic
203C2×C47#149711yescharacteristic
204C2×C47#186911yescharacteristic
205C2×C47#189411yescharacteristic
206C2×C47#189711yescharacteristic
207C2×C22⋊Q8Dic4711yescharacteristic
208C2×C4×Q8C2×D4711yescharacteristic
209C22×C42C2×D4711yescharacteristic
210#431—944no—
211C2×C4⋊C8—472no—
212C2×C4⋊C8—941no—
213C2×C22⋊C8—941no—
214C2×C22⋊C8—941no—
215C2×C4×C8—472no—
216#391Dic4711yescharacteristic
217#389Dic4711yescharacteristic
218#387—21no—
219#385—21no—
220#380Dic4711yescharacteristic
221C4×C4⋊C4—21no—
222C4×C4⋊C4C2×D4711yescharacteristic
223C4×C22⋊C4—21no—
224#336—941no—
225Q8⋊C8—944no—
226C47#907311yescharacteristic, complemented, Sylow
227C22×Q8C2×Dic4711yescharacteristic
228C23×C4C2×Dic4711yescharacteristic
229C23×C4C22⋊D4711yescharacteristic
230C23×C4C22⋊D4711yescharacteristic
231C22×C8—942no—
232C22×C8—942no—
233C22⋊Q8—22no—
234C22⋊Q8C47⋊C814yescomplemented
235C4×Q8—22no—
236C4×Q8—22no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C2×Dic4711yescharacteristic
241C2×C4⋊C4C2×Dic4711yescharacteristic
242C2×C4⋊C4C2×Dic4711yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42C2×Dic4711yescharacteristic
250C2×C42C22⋊D4711yescharacteristic
251C2×C42C22⋊D4711yescharacteristic
252C2×C42C22×D4711yescharacteristic
253C4⋊C8—944no—
254C4⋊C8—942no—
255C4⋊C8—942no—
256C22⋊C8—944no—
257C22⋊C8—1882no—
258C4×C8—474no—
259C4×C8—942no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265C24C22⋊Dic4711yescharacteristic
266C2×Q8—21no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8C2×C47⋊C812yes—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×C47⋊C812yes—
285C22×C4#1062532912yes—
286C22×C4C22⋊Dic4711yescharacteristic
287C22×C4C22⋊Dic4711yescharacteristic
288C22×C4C22⋊Dic4711yescharacteristic
289C22×C4C22×Dic4711yescharacteristic
290C22×C4C2×C22⋊D4711yescharacteristic
291C22×C4C2×C22⋊D4711yescharacteristic
292C2×C8—944no—
293C2×C8—1882no—
294C2×C8—1882no—
295C2×C8—1882no—
296C2×C8—1882no—
297C2×C8—1882no—
298C4⋊C4—24no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—42no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4C2×C47⋊C812yes—
306C22⋊C4—24no—
307C22⋊C4—42no—
308C42—22no—
309C42—21no—
310C42—22no—
311C42—21no—
312C42—42no—
313C42—41no—
314C42—41no—
315C42D4×D4712yes—
316C42#1062535212yes—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23C22⋊(C47⋊C8)12yes—
324C23C2×C22⋊Dic4711yescharacteristic
325Q8—24no—
326Q8—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4C22⋊(C47⋊C8)12yes—
356C2×C4D4×Dic4712yes—
357C2×C4#1309399211yescharacteristic
358C2×C4#1309399612yes—
359C2×C4#1309400511yescharacteristic
360C2×C4C22×C47⋊C811yescharacteristic
361C2×C4C2×#1062532911yescharacteristic
362C2×C4#1309403112yes—
363C2×C4#1309404911yescharacteristic
364C2×C4#1309405411yescharacteristic
365C2×C4#1309405512yes—
366C8—3762no—
367C8—1884no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22#1568900311yescharacteristic
376C22C2×C22⋊(C47⋊C8)11yescharacteristic
377C22#1568909011yescharacteristic
378C22#1568912411yescharacteristic
379C22#1568913211yescharacteristic
380C22#1568914011yescharacteristic
381C22#1568914011yescharacteristic
382C4—21no—
383C4—21no—
384C4—22no—
385C4—41no—
386C4—42no—
387C4—41no—
388C4—42no—
389C4—81no—
390C4—81no—
391C4D4×C47⋊C812yes—
392C4#1568919512yes—
393C4#1568937112yes—
394C4#1568937912yes—
395C2—42no—
396C2#2024177511yescharacteristic
397C2#2024178311yescharacteristic
398C2#2024185311yescharacteristic
399C2#2024186111yescharacteristic
400C2#2024368111yescharacteristic
401C2#2024382211yescharacteristic
402C2#2024383711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC4×C22⋊Q8×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×C22⋊Q8D47
hypocenterC47#9073
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×Q8⋊(C47⋊C8)C2semidirect
4. #20241229C2semidirect
39. C22⋊Q8×C47C8semidirect
226. C47#9073semidirect
234. C22⋊Q8C47⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#156891762
#202433682
C2×Q8⋊(C47⋊C8)2
#202412292
C4×C22⋊Q8×C472
#907347