Finite Group Databasebeta

← #26111977

Subgroups — #26111977

Order 12032.

568 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689179C211yesmaximal, characteristic
2#20251741C211yesmaximal, characteristic
3#20243365C211yesmaximal, characteristic
4C2×#15688870C211yesmaximal, characteristic, complemented
5C2×#15688868C211yesmaximal, characteristic, complemented
6#20241271C211yesmaximal, characteristic, complemented
7C47×#1296C211yesmaximal, characteristic, complemented
8C2×#13094024C2211yescharacteristic
9C2×#13094004—21no—
10C2×C42×D47C2211yescharacteristic
11#15689179—22no—
12#15689179—22no—
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14C2×C4⋊(C47⋊C8)C2211yescharacteristic
15C2×(C2×D47)⋊C8—21no—
16C2×(C2×D47)⋊C8—21no—
17C2×#13093934—21no—
18#15689028—21no—
19#15689022—21no—
20#15689022C412yes—
21#15688980—21no—
22#15688980C412yes—
23#15688877—21no—
24#15688870—22no—
25#15688868—22no—
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C47×#384C2211yescharacteristic
29C22×Dic94—21no—
30C22×C4×D47C2×C411yescharacteristic
31C22×C4×D47D411yescharacteristic
32C22×C4×D47D411yescharacteristic
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35#13094024—21no—
36#13094024—21no—
37#13094024—21no—
38#13094024—21no—
39#13094004—42no—
40#13094004—42no—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47—22no—
43C2×C4⋊Dic47C2×C412yes—
44C2×(C2×D47)⋊C4—22no—
45C2×C4×Dic47C2×C411yescharacteristic
46C2×C4×Dic47D411yescharacteristic
47C2×C4×Dic47D411yescharacteristic
48C42×D47—21no—
49C42×D47—21no—
50C42×D47—21no—
51C42×D47—21no—
52C4⋊(C47⋊C8)—21no—
53C4⋊(C47⋊C8)—21no—
54C4⋊(C47⋊C8)—21no—
55C4⋊(C47⋊C8)D412yes—
56(C2×D47)⋊C8—24no—
57(C2×D47)⋊C8—42no—
58#13093934—24no—
59C47⋊#95—22no—
60C47⋊#95—22no—
61C22×C8×C47—21no—
62C22×C8×C47—21no—
63C2×C4⋊C4×C47—21no—
64C2×C4⋊C4×C47—21no—
65C2×C4⋊C4×C47C2×C412yes—
66C2×C42×C47C2311yescharacteristic
67C4⋊C8×C47—21no—
68C4⋊C8×C47—21no—
69C4⋊C8×C47—21no—
70C4⋊C8×C47D412yes—
71C23×D47C22⋊C411yescharacteristic
72C22×C4×C47—22no—
73C22×C4×C47C22×C411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×Dic47—22no—
77C22×Dic47C22⋊C411yescharacteristic
78C22×Dic47C22⋊C411yescharacteristic
79C22×Dic47C22⋊C411yescharacteristic
80C2×C4×D47—22no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47—21no—
90C2×C4×D47—21no—
91C2×C4×D47—21no—
92C2×C4×D47—21no—
93C2×C4×D47—21no—
94C2×C4×D47—21no—
95C2×C4×D47—41no—
96C2×Dic94—41no—
97C2×Dic94—41no—
98C2×Dic94—41no—
99C2×Dic94—41no—
100C2×Dic94—41no—
101C2×Dic94—41no—
102C2×C8×C47—22no—
103C2×C8×C47—41no—
104C2×C8×C47—41no—
105C2×C8×C47—41no—
106C2×C8×C47—41no—
107C2×C8×C47—41no—
108C4⋊C4×C47—42no—
109C4⋊C4×C47—41no—
110C4⋊C4×C47—41no—
111C4⋊C4×C47—41no—
112C4⋊C4×C47—41no—
113C42×C47C2×D411yescharacteristic
114C42×C47C2×D411yescharacteristic
115C42×C47#4111yescharacteristic
116C42×C47#4111yescharacteristic
117(C2×D47)⋊C4—44no—
118C4⋊Dic47—22no—
119C4⋊Dic47—22no—
120C4⋊Dic47—44no—
121C4⋊Dic47—41no—
122C4⋊Dic47—41no—
123C4×Dic47—21no—
124C4×Dic47—21no—
125C4×Dic47—21no—
126C4×Dic47—21no—
127C4×Dic47—21no—
128C4×Dic47—21no—
129C2×C47⋊C8—22no—
130C2×C47⋊C8—41no—
131C2×C47⋊C8—41no—
132C2×C47⋊C8—41no—
133C2×C47⋊C8—41no—
134C2×C47⋊C8—41no—
135C23×C47C2×C22⋊C411yescharacteristic
136C22×D47—21no—
137C22×D47—21no—
138C22×D47—21no—
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47#10112yes—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47—42no—
148C2×C4×C47C4×D411yescharacteristic
149C2×C4×C47C4×D411yescharacteristic
150C2×C4×C47#12011yescharacteristic
151C2×C4×C47#12111yescharacteristic
152C2×C4×C47#12111yescharacteristic
153C2×C4×C47#12311yescharacteristic
154C2×C4×C47#13511yescharacteristic
155C2×C4×C47#13511yescharacteristic
156C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C47#13711yescharacteristic
160C2×C4×C47#13711yescharacteristic
161C2×C4×C47#13711yescharacteristic
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—42no—
172C2×Dic47—42no—
173C2×Dic47—42no—
174C4×D47—42no—
175C4×D47—42no—
176C4×D47—41no—
177C4×D47—41no—
178C4×D47—41no—
179C4×D47—41no—
180C4×D47—41no—
181C4×D47—41no—
182C4×D47—41no—
183C4×D47—41no—
184Dic94—81no—
185Dic94—81no—
186Dic94—81no—
187Dic94—81no—
188C8×C47—42no—
189C8×C47—81no—
190C47⋊C8—42no—
191C47⋊C8—81no—
192#9140—471nomaximal, Sylow
193C22×C47#38611yescharacteristic
194C22×C47C2×#10111yescharacteristic
195C22×C47#41311yescharacteristic
196C22×C47#41611yescharacteristic
197C22×C47#41711yescharacteristic
198C22×C47#41811yescharacteristic
199C22×C47#41911yescharacteristic
200C2×D47—22no—
201C2×D47—22no—
202C2×D47—22no—
203C2×D47—41no—
204C2×D47—41no—
205C2×D47—41no—
206C2×D47—41no—
207C4×C47—21no—
208C4×C47—21no—
209C4×C47—82no—
210C4×C47#44911yescharacteristic
211C4×C47#44911yescharacteristic
212C4×C47#46811yescharacteristic
213C4×C47#46811yescharacteristic
214C4×C47#47011yescharacteristic
215C4×C47#47011yescharacteristic
216C4×C47#48211yescharacteristic
217C4×C47#48211yescharacteristic
218Dic47—41no—
219Dic47—41no—
220Dic47—41no—
221Dic47—82no—
222C2×#432—471no—
223#2857—471no—
224#1797—471no—
225C2×#332—471no—
226C2×#332—471no—
227#1296—471no—
228#1296D4711yescharacteristic, complemented
229C2×C47#155211yescharacteristic
230C2×C47#155411yescharacteristic
231C2×C47#155611yescharacteristic
232C2×C47#155711yescharacteristic
233C2×C47#187511yescharacteristic
234C2×C47#189411yescharacteristic
235C2×C47#190111yescharacteristic
236D47—42no—
237C2×C4⋊Q8—471no—
238C2×C22⋊Q8—941no—
239C22×C42—471no—
240#432—942no—
241#432—942no—
242C2×C4⋊C8—471no—
243C2×C4⋊C8—471no—
244C2×C4⋊C8C2×D4711yescharacteristic
245C2×C4⋊C8C2×D4711yescharacteristic
246C2×C22⋊C8—941no—
247C2×C22⋊C8—941no—
248C2×#97—941no—
249#391—941no—
250#389—472no—
251#389—941no—
252#384C2×D4711yescharacteristic
253#380—472no—
254#380—941no—
255#336—941no—
256#332—942no—
257#332—942no—
258C47#914011yescharacteristic, complemented, Sylow
259C22×Q8—941no—
260C23×C4—471no—
261C23×C4—471no—
262C23×C4—471no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—941no—
266C22×C8—941no—
267C4⋊Q8—941no—
268C4⋊Q8—941no—
269C4⋊Q8—941no—
270C4⋊Q8—941no—
271C22⋊Q8—1882no—
272C22⋊Q8—1882no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—472no—
276C2×C4⋊C4—942no—
277C2×C4⋊C4—941no—
278C2×C4⋊C4C4×D4712yes—
279C2×C22⋊C4—942no—
280C2×C42—471no—
281C2×C42—471no—
282C2×C42—471no—
283C2×C42—941no—
284C2×C42—941no—
285C2×C42—941no—
286C2×C42—941no—
287C2×C42C22×D4711yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—472no—
292C4⋊C8—941no—
293C4⋊C8—941no—
294C4⋊C8—941no—
295C4⋊C8D18812yes—
296C22⋊C8—944no—
297C22⋊C8—1882no—
298#97—944no—
299#95—942no—
300#95—942no—
301C24—471no—
302C2×Q8—1881no—
303C2×Q8—1881no—
304C2×Q8—1881no—
305C2×Q8—1881no—
306C2×Q8—1881no—
307C2×Q8—1881no—
308C22×C4—22no—
309C22×C4—471no—
310C22×C4—471no—
311C22×C4—471no—
312C22×C4—942no—
313C22×C4—941no—
314C22×C4—941no—
315C22×C4—941no—
316C22×C4—941no—
317C22×C4—941no—
318C22×C4—941no—
319C22×C4—941no—
320C22×C4—941no—
321C22×C4—941no—
322C22×C4—941no—
323C22×C4—941no—
324C22×C4—941no—
325C22×C4—941no—
326C22×C4—941no—
327C22×C4—942no—
328C22×C4—1881no—
329C22×C4C2×C4×D4711yescharacteristic
330C22×C4D4×D4711yescharacteristic
331C22×C4D4×D4711yescharacteristic
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—942no—
339C2×C8—1881no—
340C2×C8—1881no—
341C2×C8—1881no—
342C2×C8—1881no—
343C2×C8—1881no—
344C4⋊C4—42no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—942no—
350C4⋊C4—942no—
351C4⋊C4—1884no—
352C4⋊C4—1881no—
353C4⋊C4—1881no—
354C22⋊C4—1884no—
355C42—941no—
356C42—941no—
357C42—941no—
358C42—941no—
359C42—941no—
360C42—941no—
361C42C2×D18811yescharacteristic
362C42#1062535011yescharacteristic
363C42D4×D4711yescharacteristic
364C42#1062535411yescharacteristic
365C23—472no—
366C23—941no—
367C23—941no—
368C23—941no—
369C23—941no—
370C23—941no—
371C23—941no—
372C23C22⋊C4×D4711yescharacteristic
373Q8—3761no—
374Q8—3761no—
375Q8—3761no—
376Q8—3761no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—941no—
389C2×C4—941no—
390C2×C4—941no—
391C2×C4—1882no—
392C2×C4—1882no—
393C2×C4—1882no—
394C2×C4—1882no—
395C2×C4—1882no—
396C2×C4—1881no—
397C2×C4—1881no—
398C2×C4—1881no—
399C2×C4—1881no—
400C2×C4—1881no—
401C2×C4—1881no—
402C2×C4—1881no—
403C2×C4—1881no—
404C2×C4#1309398611yescharacteristic
405C2×C4C4×D18811yescharacteristic
406C2×C4#1309399411yescharacteristic
407C2×C4#1309399711yescharacteristic
408C2×C4#1309399911yescharacteristic
409C2×C4#1309400911yescharacteristic
410C2×C4#1309404511yescharacteristic
411C2×C4#1309404711yescharacteristic
412C2×C4#1309404811yescharacteristic
413C2×C4#1309404811yescharacteristic
414C2×C4#1309405111yescharacteristic
415C2×C4#1309405311yescharacteristic
416C2×C4#1309405311yescharacteristic
417C2×C4#1309405611yescharacteristic
418C8—42no—
419C8—81no—
420C8—3761no—
421C8—1882no—
422C22—942no—
423C22—942no—
424C22—942no—
425C22—1881no—
426C22—1881no—
427C22—1881no—
428C22—1881no—
429C22#1568900111yescharacteristic
430C22#101×D4711yescharacteristic
431C22#1568910411yescharacteristic
432C22#1568911811yescharacteristic
433C22#1568912111yescharacteristic
434C22#1568912611yescharacteristic
435C22#1568913011yescharacteristic
436C4—21no—
437C4—21no—
438C4—82no—
439C4—3762no—
440C4—1881no—
441C4—1881no—
442C4—1881no—
443C4#1568926911yescharacteristic
444C4#1568927111yescharacteristic
445C4#1568936811yescharacteristic
446C4#1568937011yescharacteristic
447C4#1568938011yescharacteristic
448C4#1568938211yescharacteristic
449C4#1568944911yescharacteristic
450C4#1568945011yescharacteristic
451C2—1882no—
452C2#2024208711yescharacteristic
453C2#2024209711yescharacteristic
454C2#2024210311yescharacteristic
455C2#2024210711yescharacteristic
456C2#2024370911yescharacteristic
457C2#2024382011yescharacteristic
458C2#2024385511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1296C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1296D47
hypocenterC47#9140
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. C2×#15688870C2semidirect
5. C2×#15688868C2semidirect
6. #20241271C2semidirect
7. C47×#1296C2semidirect
228. #1296D47semidirect
258. C47#9140semidirect

Maximal subgroups

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

subgroupindex
C2×#156891792
#202517412
#202433652
C2×#156888702
C2×#156888682
#202412712
C47×#12962
#914047