Finite Group Databasebeta

← #26111167

Subgroups — #26111167

Order 12032.

530 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251956C211yesmaximal, characteristic, complemented
2#20241839C211yesmaximal, characteristic, complemented
3#20241787C211yesmaximal, characteristic, complemented
4#20241770C211yesmaximal, characteristic, complemented
5#20241285C211yesmaximal, characteristic, complemented
6#20241222C211yesmaximal, characteristic, complemented
7C47×#3035C211yesmaximal, characteristic
8C2×#13094031—21no—
9#15689176C2211yescharacteristic
10#15689150—22no—
11#15689150—21no—
12#15689147—21no—
13#15689147C2211yescharacteristic
14C2×C4⋊(C47⋊C8)—21no—
15C2×C4⋊(C47⋊C8)C2211yescharacteristic
16C2×C4×C47⋊C8C2211yescharacteristic
17Q8⋊(C47⋊C8)—21no—
18D4⋊(C47⋊C8)—21no—
19D4⋊(C47⋊C8)—21no—
20D4⋊(C47⋊C8)—22no—
21D4⋊(C47⋊C8)—21no—
22C2×#135×C47—21no—
23C47×#532C2211yescharacteristic
24C4×#41×C47C2211yescharacteristic
25C47×#464—21no—
26C47×#463—21no—
27C47×#462C411yescharacteristic
28C47×#461C411yescharacteristic
29C47×#460C411yescharacteristic
30C47×#459C411yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C47×#416—21no—
33#13094031—42no—
34#13094031—42no—
35C2×#10625329—22no—
36C2×#10625329—21no—
37C22×C47⋊C8—22no—
38C22×C47⋊C8—21no—
39C22×C47⋊C8—21no—
40C4⋊(C47⋊C8)—22no—
41C4⋊(C47⋊C8)—22no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)D411yescharacteristic
46C4⋊(C47⋊C8)D411yescharacteristic
47C4⋊(C47⋊C8)D412yes—
48C22⋊(C47⋊C8)—21no—
49C4×C47⋊C8—21no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C2×#41×C47—21no—
53C2×#41×C47D411yescharacteristic
54#135×C47—42no—
55#135×C47—42no—
56C2×Q16×C47—21no—
57C2×SD16×C47—21no—
58C2×SD16×C47—21no—
59C2×D8×C47—21no—
60C22×C8×C47—21no—
61C4⋊Q8×C47C2×C411yescharacteristic
62#127×C47C2×C411yescharacteristic
63#124×C47—21no—
64#121×C47—21no—
65#121×C47—21no—
66C4×Q8×C47C2×C411yescharacteristic
67C4×Q8×C47D411yescharacteristic
68C4×D4×C47—21no—
69C4×D4×C47—21no—
70C4×D4×C47—21no—
71C4×D4×C47—21no—
72C4×D4×C47C2×C411yescharacteristic
73C4×D4×C47D411yescharacteristic
74#117×C47—21no—
75#117×C47D411yescharacteristic
76C2×C42×C47—21no—
77C2×C42×C47C2311yescharacteristic
78C4⋊C8×C47—21no—
79C4⋊C8×C47C2×C411yescharacteristic
80C4⋊C8×C47C2×C411yescharacteristic
81#103×C47—21no—
82#103×C47—21no—
83#102×C47—21no—
84#102×C47—21no—
85#41×C47—21no—
86#41×C47—21no—
87#41×C47—41no—
88#41×C47—41no—
89#41×C47—41no—
90#41×C47—41no—
91#41×C47D812yes—
92#41×C47SD1612yes—
93C2×Q8×C47—21no—
94C2×Q8×C47C22⋊C411yescharacteristic
95C2×D4×C47—21no—
96C2×D4×C47—21no—
97C2×D4×C47—21no—
98C2×D4×C47—21no—
99C2×D4×C47—41no—
100C2×D4×C47C22⋊C411yescharacteristic
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—41no—
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108Q16×C47—42no—
109SD16×C47—42no—
110SD16×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×C47—21no—
118C4⋊C4×C47—21no—
119C4⋊C4×C47—21no—
120C4⋊C4×C47C22⋊C411yescharacteristic
121C4⋊C4×C47C22⋊C411yescharacteristic
122C22⋊C4×C47—21no—
123C22⋊C4×C47—21no—
124C22⋊C4×C47—21no—
125C22⋊C4×C47—41no—
126C22⋊C4×C47—41no—
127C42×C47—21no—
128C42×C47—21no—
129C42×C47—21no—
130C42×C47C22×C411yescharacteristic
131C42×C47C2×D411yescharacteristic
132C42×C47C2×D411yescharacteristic
133C42×C47C2×D411yescharacteristic
134#10625329—44no—
135#10625329—41no—
136#10625329—41no—
137C2×C47⋊C8—22no—
138C2×C47⋊C8—21no—
139C2×C47⋊C8—22no—
140C2×C47⋊C8—21no—
141C2×C47⋊C8—41no—
142C2×C47⋊C8—44no—
143C2×C47⋊C8—41no—
144C2×C47⋊C8—41no—
145C2×C47⋊C8—41no—
146C2×C47⋊C8—41no—
147C23×C47—21no—
148C23×C47—41no—
149C23×C47#12311yescharacteristic
150Q8×C47—21no—
151Q8×C47—41no—
152Q8×C47—41no—
153Q8×C47#10212yes—
154D4×C47—22no—
155D4×C47—22no—
156D4×C47—21no—
157D4×C47—42no—
158D4×C47—41no—
159D4×C47—41no—
160D4×C47—41no—
161D4×C47—41no—
162D4×C47—81no—
163D4×C47—81no—
164D4×C47#10212yes—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—22no—
169C2×C4×C47—22no—
170C2×C4×C47—21no—
171C2×C4×C47—21no—
172C2×C4×C47—41no—
173C2×C4×C47—41no—
174C2×C4×C47—41no—
175C2×C4×C47—41no—
176C2×C4×C47—81no—
177C2×C4×C47—81no—
178C2×C4×C47—81no—
179C2×C4×C47C2×C22⋊C411yescharacteristic
180C2×C4×C47C4×D411yescharacteristic
181C2×C4×C47C4×D411yescharacteristic
182C2×C4×C47#12011yescharacteristic
183C2×C4×C47#12111yescharacteristic
184C2×C4×C47#12111yescharacteristic
185C2×C4×C47C2×D811yescharacteristic
186C2×C4×C47C2×SD1611yescharacteristic
187C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C47#13711yescharacteristic
189C8×C47—41no—
190C8×C47—41no—
191C47⋊C8—42no—
192C47⋊C8—41no—
193C47⋊C8—42no—
194C47⋊C8—41no—
195C47⋊C8—81no—
196#8995—471nomaximal, Sylow
197C22×C47—21no—
198C22×C47—21no—
199C22×C47—22no—
200C22×C47—41no—
201C22×C47—41no—
202C22×C47—81no—
203C22×C47—81no—
204C22×C47—81no—
205C22×C47#38611yescharacteristic
206C22×C47#48011yescharacteristic
207C22×C47#48111yescharacteristic
208C4×C47—22no—
209C4×C47—21no—
210C4×C47—21no—
211C4×C47—21no—
212C4×C47—41no—
213C4×C47—41no—
214C4×C47—81no—
215C4×C47C2×#10211yescharacteristic
216C4×C47#41711yescharacteristic
217C4×C47#44311yescharacteristic
218C4×C47#44411yescharacteristic
219C4×C47#44711yescharacteristic
220C4×C47#44811yescharacteristic
221#3035D4711yescharacteristic
222#2906—471no—
223#1492—471no—
224#1480—471no—
225#1476—471no—
226#1301—471no—
227#1277—471no—
228C2×C47—21no—
229C2×C47—21no—
230C2×C47—42no—
231C2×C47—161no—
232C2×C47#187411yescharacteristic
233C2×C47#187611yescharacteristic
234C2×C47#188111yescharacteristic
235C2×#135—21no—
236C2×#131—941no—
237#532C2×D4711yescharacteristic
238C4×#41C2×D4711yescharacteristic
239#464—21no—
240#463—21no—
241#462Dic4711yescharacteristic
242#461Dic4711yescharacteristic
243#460Dic4711yescharacteristic
244#459Dic4711yescharacteristic
245#431—471no—
246#424—942no—
247#424—941no—
248#423—471no—
249#423—941no—
250C2×C4⋊C8—471no—
251C2×C4⋊C8—941no—
252C2×C4⋊C8C2×D4711yescharacteristic
253#416—21no—
254C2×C4×C8—471no—
255Q8⋊C8—941no—
256D4⋊C8—941no—
257D4⋊C8—941no—
258D4⋊C8—942no—
259D4⋊C8—941no—
260C47#899511yescharacteristic, complemented, Sylow
261C2×#41—21no—
262C2×#41C22⋊D4711yescharacteristic
263#135—42no—
264#135—42no—
265C2×Q16—21no—
266C2×SD16—21no—
267C2×SD16—21no—
268C2×D8—21no—
269#131—1882no—
270#131—1882no—
271C2×M16—942no—
272C2×M16—941no—
273C22×C8—21no—
274C22×C8—942no—
275C22×C8—941no—
276C22×C8—941no—
277C4⋊Q8C2×Dic4711yescharacteristic
278#127C2×Dic4711yescharacteristic
279#124—21no—
280#121—21no—
281#121—21no—
282C4×Q8C2×Dic4711yescharacteristic
283C4×Q8C22⋊D4711yescharacteristic
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4C2×Dic4711yescharacteristic
289C4×D4C22⋊D4711yescharacteristic
290#117—21no—
291#117C22⋊D4711yescharacteristic
292C2×C42—21no—
293C2×C42C22×D4711yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—471no—
296C4⋊C8—471no—
297C4⋊C8—472no—
298C4⋊C8—942no—
299C4⋊C8—942no—
300C4⋊C8—941no—
301C4⋊C8—941no—
302C4⋊C8—941no—
303C4⋊C8C2×Dic4711yescharacteristic
304C4⋊C8C2×Dic4711yescharacteristic
305#103—21no—
306#103—21no—
307#102—21no—
308#102—21no—
309C22⋊C8—941no—
310C4×C8—941no—
311C4×C8—941no—
312C4×C8—941no—
313#41—21no—
314#41—21no—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—41no—
319#41#1062533412yes—
320#41#1062533512yes—
321C2×Q8—21no—
322C2×Q8C22⋊Dic4711yescharacteristic
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—41no—
328C2×D4C22⋊Dic4711yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—41no—
333C22×C4#1062535211yescharacteristic
334C22×C4#1062535211yescharacteristic
335C22×C4C2×C22⋊D4711yescharacteristic
336Q16—42no—
337SD16—42no—
338SD16—42no—
339D8—42no—
340M16—1884no—
341M16—1881no—
342M16—1881no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—942no—
348C2×C8—941no—
349C2×C8—941no—
350C2×C8—942no—
351C2×C8—1881no—
352C2×C8—1881no—
353C2×C8—1884no—
354C2×C8—1881no—
355C2×C8—1881no—
356C2×C8—1881no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4C22⋊Dic4711yescharacteristic
362C4⋊C4C22⋊Dic4711yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42D4×D4711yescharacteristic
372C42D4×D4711yescharacteristic
373C42C22×Dic4711yescharacteristic
374C42C2×C22⋊D4711yescharacteristic
375C23—21no—
376C23—41no—
377C23#1309400511yescharacteristic
378Q8—21no—
379Q8—41no—
380Q8—41no—
381Q8#1309394512yes—
382D4—22no—
383D4—22no—
384D4—21no—
385D4—42no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—81no—
391D4—81no—
392D4#1309394512yes—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4C2×C22⋊Dic4711yescharacteristic
408C2×C4D4×Dic4711yescharacteristic
409C2×C4D4×Dic4711yescharacteristic
410C2×C4#1309399211yescharacteristic
411C2×C4#1309399611yescharacteristic
412C2×C4#1309399611yescharacteristic
413C2×C4C2×#1062533411yescharacteristic
414C2×C4C2×#1062533511yescharacteristic
415C2×C4#1309404911yescharacteristic
416C2×C4#1309405411yescharacteristic
417C8—41no—
418C8—41no—
419C8—3761no—
420C8—1882no—
421C8—1881no—
422C8—1882no—
423C8—1881no—
424C22—21no—
425C22—21no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22#1568900311yescharacteristic
433C22#1568943411yescharacteristic
434C22#1568943911yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—22no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4C2×#1309394511yescharacteristic
443C4#1568912411yescharacteristic
444C4#1568924011yescharacteristic
445C4#1568924511yescharacteristic
446C4#1568925611yescharacteristic
447C4#1568926111yescharacteristic
448C2—21no—
449C2—21no—
450C2—42no—
451C2—161no—
452C2#2024370611yescharacteristic
453C2#2024371711yescharacteristic
454C2#2024375211yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#3035C2
socleC22×C47#386
cosocleC2×C42×C47C23
hypercenter#3035D47
hypocenterC47#8995
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #20251956C2semidirect
2. #20241839C2semidirect
3. #20241787C2semidirect
4. #20241770C2semidirect
5. #20241285C2semidirect
6. #20241222C2semidirect
260. C47#8995semidirect

Maximal subgroups

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

subgroupindex
#202519562
#202418392
#202417872
#202417702
#202412852
#202412222
C47×#30352
#899547