Finite Group Databasebeta

← #26107964

Subgroups — #26107964

Order 12032.

818 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689830C211yesmaximal, characteristic
2#20243479C212yesmaximal, complemented
3#20243376C211yesmaximal, characteristic
4#20241961C212yesmaximal, complemented
5C47×#1459C211yesmaximal, characteristic
6#15689830—24no—
7#15689830—24no—
8C2×#13094024C411yescharacteristic, complemented
9C2×#13094015—21no—
10C2×#13094003C411yescharacteristic, complemented
11C2×#13094003C2211yescharacteristic
12C2×#13094001—21no—
13C2×#13094001—21no—
14C2×C4×Dic94C411yescharacteristic, complemented
15C2×D4×Dic47—21no—
16C22×C4⋊Dic47C411yescharacteristic, complemented
17C22×C4⋊Dic47C2211yescharacteristic
18C2×#13093939—21no—
19#15688983C2212yes—
20#15688890—21no—
21#15688886—24no—
22#15688861—24no—
23C2×C4×D4×C47C2211yescharacteristic
24C2×C22⋊C8×C47C2212yes—
25C47×#324—21no—
26C47×#323—21no—
27C22×Dic94—21no—
28C22×Dic94C2×C411yescharacteristic
29C23×Dic47—21no—
30C23×Dic47—21no—
31#13094024—22no—
32#13094024—22no—
33#13094015—28no—
34#13094003—22no—
35#13094003—22no—
36#13094003—22no—
37#13094003D414yes—
38#13094001—28no—
39#13094001—28no—
40C4×Dic94—22no—
41C4×Dic94—22no—
42D4×Dic47—28no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47C2×C411yescharacteristic
51C2×C4⋊Dic47C2×C411yescharacteristic
52C2×C4⋊Dic47C2×C411yescharacteristic
53C2×C4⋊Dic47D414yes—
54C2×Dic47⋊C4—21no—
55C2×Dic47⋊C4—21no—
56C2×Dic47⋊C4—21no—
57C2×C22⋊Dic47—21no—
58C2×C22⋊Dic47—21no—
59C2×C22⋊Dic47—22no—
60C2×C4×Dic47—21no—
61#13093939—42no—
62C47⋊#95—22no—
63C22×D4×C47D411yescharacteristic
64C23×C4×C47C2×C411yescharacteristic
65C23×C4×C47C2311yescharacteristic
66C22×C8×C47—22no—
67C4×D4×C47—22no—
68C4×D4×C47—22no—
69C2×C4⋊C4×C47D411yescharacteristic
70C2×C22⋊C4×C47D411yescharacteristic
71C2×C22⋊C4×C47D411yescharacteristic
72C2×C42×C47C2×C411yescharacteristic
73C22⋊C8×C47—22no—
74C22⋊C8×C47—22no—
75C24×C47C22⋊C411yescharacteristic
76C24×C47C2×D411yescharacteristic
77C2×D4×C47—22no—
78C2×D4×C47—22no—
79C2×D4×C47SD1612yes—
80C2×D4×C47Q1612yes—
81C22×C4×C47—21no—
82C22×C4×C47—21no—
83C22×C4×C47—42no—
84C22×C4×C47—42no—
85C22×C4×C47C22⋊C411yescharacteristic
86C22×C4×C47C22⋊C411yescharacteristic
87C22×C4×C47C22⋊C411yescharacteristic
88C22×C4×C47C22×C411yescharacteristic
89C22×C4×C47C2×D412yes—
90C22×C4×C47C2×D412yes—
91C22×C4×C47C2×D411yescharacteristic
92C22×Dic47—21no—
93C22×Dic47—21no—
94C22×Dic47—21no—
95C22×Dic47—21no—
96C22×Dic47—24no—
97C22×Dic47—24no—
98C22×Dic47—42no—
99C22×Dic47—82no—
100C22×Dic47—82no—
101C2×Dic94—21no—
102C2×Dic94—24no—
103C2×Dic94—42no—
104C2×Dic94—82no—
105C2×Dic94C22⋊C412yes—
106C2×C8×C47—44no—
107C2×C8×C47—42no—
108C4⋊C4×C47—22no—
109C22⋊C4×C47—22no—
110C22⋊C4×C47—22no—
111C42×C47—21no—
112C42×C47—21no—
113C22⋊Dic47—24no—
114C22⋊Dic47—24no—
115C22⋊Dic47—42no—
116C22⋊Dic47—42no—
117C4⋊Dic47—24no—
118C4⋊Dic47—24no—
119C4⋊Dic47—21no—
120C4⋊Dic47—21no—
121C4⋊Dic47—21no—
122C4⋊Dic47—24no—
123C4⋊Dic47—44no—
124C4⋊Dic47C22⋊C412yes—
125C4⋊Dic47C22⋊C412yes—
126C4⋊Dic47C22⋊C412yes—
127Dic47⋊C4—24no—
128Dic47⋊C4—24no—
129Dic47⋊C4—24no—
130C4×Dic47—24no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—41no—
134C23×C47—41no—
135C23×C47—41no—
136C23×C47—41no—
137C23×C47#10312yes—
138C23×C47C2×C22⋊C411yescharacteristic
139C23×C47#12012yes—
140C23×C47C2×SD1611yescharacteristic
141C23×C47C2×Q1611yescharacteristic
142C23×C47#13712yes—
143D4×C47—24no—
144D4×C47—24no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—24no—
148C2×C4×C47—22no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—42no—
152C2×C4×C47—41no—
153C2×C4×C47—42no—
154C2×C4×C47—42no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47#10312yes—
158C2×C4×C47C2×C22⋊C411yescharacteristic
159C2×C4×C47C2×C22⋊C411yescharacteristic
160C2×C4×C47#12012yes—
161C2×Dic47—22no—
162C2×Dic47—22no—
163C2×Dic47—22no—
164C2×Dic47—22no—
165C2×Dic47—42no—
166C2×Dic47—42no—
167C2×Dic47—42no—
168C2×Dic47—42no—
169C2×Dic47—84no—
170C2×Dic47—84no—
171C2×Dic47—82no—
172C2×Dic47—82no—
173C2×Dic47—82no—
174Dic94—42no—
175Dic94—42no—
176Dic94—84no—
177C8×C47—82no—
178#8380—471nomaximal, Sylow
179C22×C47—21no—
180C22×C47—22no—
181C22×C47—21no—
182C22×C47—22no—
183C22×C47—22no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—42no—
187C22×C47—42no—
188C22×C47—42no—
189C22×C47—41no—
190C22×C47—41no—
191C22×C47#37911yescharacteristic
192C22×C47C2×#10311yescharacteristic
193C22×C47#41911yescharacteristic
194C22×C47#44812yes—
195C22×C47#45112yes—
196C4×C47—22no—
197C4×C47—21no—
198C4×C47—22no—
199C4×C47—41no—
200C4×C47—41no—
201C4×C47#41012yes—
202Dic47—42no—
203Dic47—42no—
204Dic47—42no—
205Dic47—42no—
206Dic47—162no—
207C2×#554—471no—
208#1824—472no—
209#1799—471no—
210#1520—472no—
211#1459D4711yescharacteristic
212C2×C47—22no—
213C2×C47—21no—
214C2×C47—21no—
215C2×C47—22no—
216C2×C47—42no—
217C2×C47#178211yescharacteristic
218C2×C47#178711yescharacteristic
219C2×C47#179511yescharacteristic
220#554—944no—
221#554—944no—
222C2×C4⋊Q8—471no—
223C2×#125—941no—
224C2×C22⋊Q8—471no—
225C2×C22⋊Q8—471no—
226C2×C22⋊Q8—941no—
227C2×C22⋊Q8—941no—
228C2×C4×Q8—471no—
229C2×C4×D4—941no—
230C2×C4×D4C2×D4711yescharacteristic
231C22×C4⋊C4—471no—
232C22×C4⋊C4—471no—
233C2×#99—941no—
234C2×C22⋊C8C2×D4712yes—
235#380—472no—
236#342—941no—
237#340—944no—
238#328—944no—
239#324—21no—
240#323—21no—
241C47#838011yescharacteristic, complemented, Sylow
242C22×Q8—471no—
243C22×Q8—941no—
244C22×D4D18811yescharacteristic
245C23×C4—941no—
246C23×C4—941no—
247C23×C4C4×D4711yescharacteristic
248C23×C4C22×D4711yescharacteristic
249C22×C8—22no—
250C4⋊Q8—942no—
251C4⋊Q8—942no—
252#125—948no—
253C22⋊Q8—474no—
254C22⋊Q8—948no—
255C22⋊Q8—948no—
256C22⋊Q8—942no—
257C22⋊Q8—942no—
258C22⋊Q8—942no—
259C4×Q8—942no—
260C4×Q8—942no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—948no—
264C2×C4⋊C4—471no—
265C2×C4⋊C4—471no—
266C2×C4⋊C4—471no—
267C2×C4⋊C4—474no—
268C2×C4⋊C4—942no—
269C2×C4⋊C4—942no—
270C2×C4⋊C4—941no—
271C2×C4⋊C4—941no—
272C2×C4⋊C4—941no—
273C2×C4⋊C4—941no—
274C2×C4⋊C4—942no—
275C2×C4⋊C4—941no—
276C2×C4⋊C4—941no—
277C2×C4⋊C4—942no—
278C2×C4⋊C4C22⋊D4711yescharacteristic
279C2×C22⋊C4—941no—
280C2×C22⋊C4—941no—
281C2×C22⋊C4—942no—
282C2×C22⋊C4D18811yescharacteristic
283C2×C22⋊C4C22⋊D4711yescharacteristic
284C2×C42—941no—
285C2×C42C4×D4711yescharacteristic
286#99—1882no—
287C22⋊C8—22no—
288C22⋊C8—22no—
289#95—942no—
290C24(C2×D47)⋊C411yescharacteristic
291C24C2×D18811yescharacteristic
292C2×Q8—472no—
293C2×Q8—944no—
294C2×Q8—941no—
295C2×Q8—3762no—
296C2×Q8—1882no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4#1062532512yes—
300C2×D4Dic18812yes—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—944no—
306C22×C4—944no—
307C22×C4—941no—
308C22×C4—941no—
309C22×C4—941no—
310C22×C4—941no—
311C22×C4—3762no—
312C22×C4—3762no—
313C22×C4—1882no—
314C22×C4(C2×D47)⋊C411yescharacteristic
315C22×C4(C2×D47)⋊C411yescharacteristic
316C22×C4(C2×D47)⋊C411yescharacteristic
317C22×C4C2×C4×D4711yescharacteristic
318C22×C4D4×D4712yes—
319C22×C4D4×D4712yes—
320C22×C4C2×C22⋊D4711yescharacteristic
321C2×C8—44no—
322C2×C8—42no—
323C4⋊C4—22no—
324C4⋊C4—472no—
325C4⋊C4—472no—
326C4⋊C4—472no—
327C4⋊C4—944no—
328C4⋊C4—944no—
329C4⋊C4—944no—
330C4⋊C4—944no—
331C4⋊C4—941no—
332C4⋊C4—941no—
333C4⋊C4—941no—
334C4⋊C4—944no—
335C4⋊C4—944no—
336C4⋊C4—1884no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—944no—
340C22⋊C4—944no—
341C22⋊C4—1882no—
342C22⋊C4—1882no—
343C42—21no—
344C42—21no—
345C42—944no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23#1309394912yes—
353C23C2×(C2×D47)⋊C411yescharacteristic
354C23#1309399412yes—
355C23C2×#1062532511yescharacteristic
356C23C2×Dic18811yescharacteristic
357C23#1309405712yes—
358Q8—3764no—
359Q8—1882no—
360Q8—1882no—
361D4—24no—
362D4—24no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—942no—
376C2×C4—942no—
377C2×C4—942no—
378C2×C4—942no—
379C2×C4—3764no—
380C2×C4—3764no—
381C2×C4—3762no—
382C2×C4—3762no—
383C2×C4—3762no—
384C2×C4—1882no—
385C2×C4—1882no—
386C2×C4—1882no—
387C2×C4—1882no—
388C2×C4#1309394912yes—
389C2×C4C22⋊C4×D4711yescharacteristic
390C2×C4C22⋊C4×D4711yescharacteristic
391C2×C4#1309399212yes—
392C8—82no—
393C22—21no—
394C22—22no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—42no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22#1568897811yescharacteristic
406C22C2×#1309394911yescharacteristic
407C22#1568913311yescharacteristic
408C22#1568926412yes—
409C22#1568928112yes—
410C4—22no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—1882no—
416C4—1882no—
417C4—1882no—
418C4—1882no—
419C4—7522no—
420C4#1568909512yes—
421C2—22no—
422C2—21no—
423C2—21no—
424C2—22no—
425C2—42no—
426C2#2024330411yescharacteristic
427C2#2024332411yescharacteristic
428C2#2024335911yescharacteristic
subgroupG/H
centerC22#15688978
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1459C2
socleC22×C47#379
prime radicalC22×D4×C47D4
cosocleC23×C4×C47C23
hypercenter#1459D47
hypocenterC47#8380
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #20243479C2semidirect
4. #20241961C2semidirect
8. C2×#13094024C4semidirect
10. C2×#13094003C4semidirect
14. C2×C4×Dic94C4semidirect
16. C22×C4⋊Dic47C4semidirect
241. C47#8380semidirect

Maximal subgroups

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

subgroupindex
C2×#156898302
#202434792
#202433762
#202419612
C47×#14592
#838047