Finite Group Databasebeta

← #26112615

Subgroups — #26112615

Order 12032.

514 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252423C211yesmaximal, characteristic, complemented
2#20241986C211yesmaximal, characteristic, complemented
3#20241831C211yesmaximal, characteristic, complemented
4#20241740C211yesmaximal, characteristic, complemented
5#20241258C211yesmaximal, characteristic, complemented
6#20241238C211yesmaximal, characteristic, complemented
7C2×C47×#463C211yesmaximal, characteristic
8#15689201—21no—
9#15689195—22no—
10D4×C47⋊C8—21no—
11#15689180C2211yescharacteristic
12#15689180C2211yescharacteristic
13#15689176C2211yescharacteristic
14#15689087—21no—
15C2×C22⋊(C47⋊C8)—21no—
16C4×#10625329C2211yescharacteristic
17#15688863—22no—
18D4⋊(C47⋊C8)—21no—
19D4⋊(C47⋊C8)—21no—
20#15688847—21no—
21#15688847—21no—
22C22×SD16×C47C411yescharacteristic
23C22×D8×C47C411yescharacteristic
24C2×#124×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic
26C47×#463—21no—
27C47×#463—21no—
28C47×#463—21no—
29C47×#463—21no—
30C2×C4⋊C8×C47C2211yescharacteristic
31C2×#103×C47C411yescharacteristic
32C2×#102×C47C411yescharacteristic
33C2×#10625329—22no—
34C2×#10625329—21no—
35C22×C47⋊C8—22no—
36C4⋊(C47⋊C8)—21no—
37C4⋊(C47⋊C8)—21no—
38C4⋊(C47⋊C8)—21no—
39C22⋊(C47⋊C8)—22no—
40C22⋊(C47⋊C8)—22no—
41C22⋊(C47⋊C8)—21no—
42C22⋊(C47⋊C8)—21no—
43C22⋊(C47⋊C8)D411yescharacteristic
44C22⋊(C47⋊C8)D411yescharacteristic
45#13093935—21no—
46#13093935—21no—
47#13093935D412yes—
48C4×C47⋊C8—21no—
49C4×C47⋊C8—21no—
50C22×Q8×C47C2×C411yescharacteristic
51C22×D4×C47C2×C411yescharacteristic
52C22×D4×C47C2×C411yescharacteristic
53C23×C4×C47—21no—
54C2×SD16×C47—21no—
55C2×SD16×C47—21no—
56C2×SD16×C47—42no—
57C2×D8×C47—21no—
58C2×D8×C47—21no—
59C2×D8×C47—42no—
60C22×C8×C47C2×C411yescharacteristic
61C22×C8×C47C2×C411yescharacteristic
62#124×C47—21no—
63#124×C47—21no—
64#124×C47—21no—
65#124×C47—21no—
66C4×D4×C47—21no—
67C4×D4×C47—21no—
68C4×D4×C47D411yescharacteristic
69C4×D4×C47D411yescharacteristic
70C4×D4×C47D411yescharacteristic
71C4×D4×C47D411yescharacteristic
72C2×C4⋊C4×C47C2×C411yescharacteristic
73C2×C22⋊C4×C47—21no—
74C2×C22⋊C4×C47—21no—
75C2×C22⋊C4×C47—21no—
76C2×C42×C47C2311yescharacteristic
77C4⋊C8×C47—21no—
78C4⋊C8×C47—21no—
79#103×C47—21no—
80#103×C47—21no—
81#102×C47—21no—
82#102×C47—21no—
83C24×C47—21no—
84C24×C47—21no—
85C2×Q8×C47—21no—
86C2×Q8×C47—21no—
87C2×Q8×C47—41no—
88C2×Q8×C47—41no—
89C2×D4×C47—22no—
90C2×D4×C47—21no—
91C2×D4×C47—21no—
92C2×D4×C47—21no—
93C2×D4×C47—41no—
94C2×D4×C47—41no—
95C2×D4×C47—41no—
96C2×D4×C47C22⋊C411yescharacteristic
97C2×D4×C47C22⋊C411yescharacteristic
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—82no—
105C22×C4×C47C22×C411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47#4111yescharacteristic
108SD16×C47—42no—
109SD16×C47—42no—
110D8×C47—42no—
111D8×C47—42no—
112C2×C8×C47—21no—
113C2×C8×C47—21no—
114C2×C8×C47—41no—
115C2×C8×C47—41no—
116C4⋊C4×C47—21no—
117C4⋊C4×C47C22⋊C411yescharacteristic
118C4⋊C4×C47C22⋊C411yescharacteristic
119C22⋊C4×C47—21no—
120C22⋊C4×C47—21no—
121C22⋊C4×C47—21no—
122C22⋊C4×C47—21no—
123C22⋊C4×C47—41no—
124C22⋊C4×C47—41no—
125C22⋊C4×C47—41no—
126C22⋊C4×C47—41no—
127C42×C47C2×D411yescharacteristic
128C42×C47C2×D411yescharacteristic
129C42×C47C2×D411yescharacteristic
130C42×C47#4111yescharacteristic
131#10625329—22no—
132#10625329—41no—
133#10625329—82no—
134C2×C47⋊C8—21no—
135C2×C47⋊C8—21no—
136C2×C47⋊C8—22no—
137C2×C47⋊C8—41no—
138C2×C47⋊C8—41no—
139C2×C47⋊C8—82no—
140C23×C47—21no—
141C23×C47—21no—
142C23×C47—42no—
143C23×C47—41no—
144C23×C47—41no—
145C23×C47—41no—
146C23×C47—41no—
147C23×C47—41no—
148C23×C47—81no—
149C23×C47—81no—
150C23×C47—81no—
151C23×C47C4×D411yescharacteristic
152Q8×C47—41no—
153Q8×C47—41no—
154Q8×C47—81no—
155D4×C47—21no—
156D4×C47—21no—
157D4×C47—21no—
158D4×C47—42no—
159D4×C47—41no—
160D4×C47—41no—
161D4×C47—81no—
162D4×C47#10012yes—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—21no—
169C2×C4×C47—41no—
170C2×C4×C47—42no—
171C2×C4×C47—42no—
172C2×C4×C47—41no—
173C2×C4×C47—81no—
174C2×C4×C47—81no—
175C2×C4×C47—81no—
176C2×C4×C47—81no—
177C2×C4×C47C2×C22⋊C411yescharacteristic
178C2×C4×C47C4×D411yescharacteristic
179C2×C4×C47#12011yescharacteristic
180C2×C4×C47#12111yescharacteristic
181C2×C4×C47#12111yescharacteristic
182C2×C4×C47#12311yescharacteristic
183C8×C47—41no—
184C8×C47—41no—
185C47⋊C8—41no—
186C47⋊C8—42no—
187C47⋊C8—41no—
188C47⋊C8—42no—
189C47⋊C8—81no—
190#9243—471nomaximal, Sylow
191C22×C47—21no—
192C22×C47—21no—
193C22×C47—22no—
194C22×C47—41no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47—82no—
200C22×C47—82no—
201C22×C47—81no—
202C22×C47—81no—
203C22×C47—81no—
204C22×C47—161no—
205C22×C47—161no—
206C22×C47#38611yescharacteristic
207C22×C47#44311yescharacteristic
208C22×C47#44411yescharacteristic
209C4×C47—21no—
210C4×C47—21no—
211C4×C47—21no—
212C4×C47—21no—
213C4×C47—21no—
214C4×C47—41no—
215C4×C47—41no—
216C4×C47—81no—
217C4×C47C2×#10011yescharacteristic
218C4×C47#41311yescharacteristic
219C2×#463D4711yescharacteristic
220#2974—471no—
221#1527—471no—
222#1490—471no—
223#1469—471no—
224#1290—471no—
225#1283—471no—
226C2×C47—21no—
227C2×C47—21no—
228C2×C47—42no—
229C2×C47—81no—
230C2×C47—161no—
231C2×C47#187611yescharacteristic
232C2×C47#190011yescharacteristic
233C2×C47#190411yescharacteristic
234C22×SD16Dic4711yescharacteristic
235C22×D8Dic4711yescharacteristic
236C2×#124C2×D4711yescharacteristic
237C2×C4×D4C2×D4711yescharacteristic
238#463—21no—
239#463—21no—
240#463—21no—
241#463—21no—
242#436—941no—
243#435—942no—
244C8×D4—941no—
245#432—471no—
246#432—471no—
247#431—471no—
248C2×C4⋊C8C2×D4711yescharacteristic
249C2×#103Dic4711yescharacteristic
250C2×#102Dic4711yescharacteristic
251#407—941no—
252C2×C22⋊C8—941no—
253C4×M16—471no—
254#329—942no—
255D4⋊C8—941no—
256D4⋊C8—941no—
257#323—941no—
258#323—941no—
259C47#924311yescharacteristic, complemented, Sylow
260C22×Q8C2×Dic4711yescharacteristic
261C22×D4C2×Dic4711yescharacteristic
262C22×D4C2×Dic4711yescharacteristic
263C23×C4—21no—
264C2×SD16—21no—
265C2×SD16—21no—
266C2×SD16—42no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—42no—
270C2×M16—942no—
271C2×M16—941no—
272C22×C8—942no—
273C22×C8C2×Dic4711yescharacteristic
274C22×C8C2×Dic4711yescharacteristic
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4C22⋊D4711yescharacteristic
282C4×D4C22⋊D4711yescharacteristic
283C4×D4C22⋊D4711yescharacteristic
284C4×D4C22⋊D4711yescharacteristic
285C2×C4⋊C4C2×Dic4711yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C42C22×D4711yescharacteristic
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—941no—
293C4⋊C8—941no—
294C4⋊C8—941no—
295#103—21no—
296#103—21no—
297#102—21no—
298#102—21no—
299C22⋊C8—471no—
300C22⋊C8—471no—
301C22⋊C8—942no—
302C22⋊C8—942no—
303C22⋊C8—941no—
304C22⋊C8—941no—
305#97—472no—
306#97—941no—
307#97—941no—
308C4×C8—941no—
309C4×C8—941no—
310C24—21no—
311C24—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4C22⋊Dic4711yescharacteristic
324C2×D4C22⋊Dic4711yescharacteristic
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—82no—
332C22×C4D4×D4711yescharacteristic
333C22×C4#1062535211yescharacteristic
334C22×C4C22×Dic4711yescharacteristic
335SD16—42no—
336SD16—42no—
337D8—42no—
338D8—42no—
339M16—942no—
340M16—3762no—
341M16—1881no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—941no—
347C2×C8—941no—
348C2×C8—942no—
349C2×C8—3762no—
350C2×C8—1881no—
351C2×C8—1881no—
352C4⋊C4—21no—
353C4⋊C4C22⋊Dic4711yescharacteristic
354C4⋊C4C22⋊Dic4711yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42D4×D4711yescharacteristic
364C42#1062535211yescharacteristic
365C42C2×C22⋊D4711yescharacteristic
366C42C2×C22⋊D4711yescharacteristic
367C23—21no—
368C23—21no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23D4×Dic4711yescharacteristic
379Q8—41no—
380Q8—41no—
381Q8—81no—
382D4—21no—
383D4—21no—
384D4—21no—
385D4—42no—
386D4—41no—
387D4—41no—
388D4—81no—
389D4#1309394112yes—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4C2×C22⋊Dic4711yescharacteristic
405C2×C4D4×Dic4711yescharacteristic
406C2×C4#1309399211yescharacteristic
407C2×C4#1309399611yescharacteristic
408C2×C4#1309399611yescharacteristic
409C2×C4#1309400511yescharacteristic
410C8—41no—
411C8—41no—
412C8—3761no—
413C8—1881no—
414C8—1882no—
415C8—1881no—
416C8—1882no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—82no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—161no—
431C22—161no—
432C22#1568900311yescharacteristic
433C22#1568924011yescharacteristic
434C22#1568924511yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—81no—
443C4C2×#1309394111yescharacteristic
444C4#1568910711yescharacteristic
445C2—21no—
446C2—21no—
447C2—42no—
448C2—81no—
449C2—161no—
450C2#2024371711yescharacteristic
451C2#2024385211yescharacteristic
452C2#2024387711yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#463C2
socleC22×C47#386
prime radicalC22×D8×C47C4
cosocleC2×C42×C47C23
hypercenterC2×#463D47
hypocenterC47#9243
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. #20252423C2semidirect
2. #20241986C2semidirect
3. #20241831C2semidirect
4. #20241740C2semidirect
5. #20241258C2semidirect
6. #20241238C2semidirect
259. C47#9243semidirect

Maximal subgroups

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

subgroupindex
#202524232
#202419862
#202418312
#202417402
#202412582
#202412382
C2×C47×#4632
#924347