Finite Group Databasebeta

← #26107784

Subgroups — #26107784

Order 12032.

802 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689678C211yesmaximal, characteristic
2#20243365C211yesmaximal, characteristic
3#20243365C211yesmaximal, characteristic
4C2×#15688870C211yesmaximal, characteristic, complemented
5C2×#15688869C211yesmaximal, characteristic, complemented
6C2×#15688868C211yesmaximal, characteristic, complemented
7C2×C47×#332C211yesmaximal, characteristic, complemented
8#15689678—22no—
9#15689678—22no—
10#15689678—22no—
11#15689678—22no—
12C2×#13094024C2211yescharacteristic
13C2×#13094015C412yes—
14C2×#13094004—21no—
15C2×#13094000—21no—
16C2×Q8×Dic47—21no—
17C2×#13093989—21no—
18C2×#13093982C412yes—
19C2×C42×D47C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×(C2×D47)⋊C8—21no—
23C2×(C2×D47)⋊C8—21no—
24#15688877—21no—
25#15688877—21no—
26#15688870—22no—
27#15688869—22no—
28#15688868—22no—
29C2×C4⋊Q8×C47C2211yescharacteristic
30C2×C4⋊C8×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C47×#332—22no—
33C22×Dic94—21no—
34C22×C4×D47C2×C411yescharacteristic
35C22×C4×D47D411yescharacteristic
36C22×C4×D47D411yescharacteristic
37C22×C47⋊C8—21no—
38C22×C47⋊C8—21no—
39#13094024—21no—
40#13094024—21no—
41#13094024D412yes—
42#13094024D412yes—
43#13094015—24no—
44#13094015—24no—
45#13094004—24no—
46#13094004—24no—
47#13094000—24no—
48#13094000—24no—
49Q8×Dic47—24no—
50Q8×Dic47—24no—
51#13093989—24no—
52#13093989—24no—
53#13093982—24no—
54#13093982—24no—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47C2×C412yes—
58C2×Dic47⋊C4—22no—
59C2×(C2×D47)⋊C4—22no—
60C2×C4×Dic47—22no—
61C2×C4×Dic47C2×C411yescharacteristic
62C2×C4×Dic47D411yescharacteristic
63C2×C4×Dic47D411yescharacteristic
64C42×D47—21no—
65C42×D47—21no—
66C42×D47—21no—
67C42×D47—21no—
68C4⋊(C47⋊C8)—21no—
69C4⋊(C47⋊C8)—21no—
70C4⋊(C47⋊C8)—21no—
71C4⋊(C47⋊C8)—21no—
72(C2×D47)⋊C8—42no—
73(C2×D47)⋊C8—42no—
74C22×Q8×C47—21no—
75C22×C8×C47—21no—
76C22×C8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47—21no—
79C4⋊Q8×C47D412yes—
80C4⋊Q8×C47D412yes—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47C2×C412yes—
83C2×C42×C47C2311yescharacteristic
84C4⋊C8×C47—21no—
85C4⋊C8×C47—21no—
86C4⋊C8×C47—21no—
87C4⋊C8×C47—21no—
88C23×D47C22⋊C411yescharacteristic
89C2×Q8×C47—22no—
90C2×Q8×C47—22no—
91C2×Q8×C47—41no—
92C2×Q8×C47—41no—
93C2×Q8×C47—41no—
94C2×Q8×C47—41no—
95C22×C4×C47—22no—
96C22×C4×C47C22×C411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×Dic47—22no—
100C22×Dic47C22⋊C411yescharacteristic
101C22×Dic47C22⋊C411yescharacteristic
102C22×Dic47C22⋊C411yescharacteristic
103C2×C4×D47—22no—
104C2×C4×D47—21no—
105C2×C4×D47—21no—
106C2×C4×D47—22no—
107C2×C4×D47—21no—
108C2×C4×D47—21no—
109C2×C4×D47—21no—
110C2×C4×D47—21no—
111C2×C4×D47—21no—
112C2×C4×D47—21no—
113C2×C4×D47—21no—
114C2×C4×D47—21no—
115C2×C4×D47—21no—
116C2×C4×D47—21no—
117C2×C4×D47—21no—
118C2×C4×D47—21no—
119C2×Dic94—22no—
120C2×Dic94—22no—
121C2×Dic94—41no—
122C2×Dic94—41no—
123C2×Dic94—41no—
124C2×Dic94—41no—
125C2×C8×C47—41no—
126C2×C8×C47—41no—
127C2×C8×C47—41no—
128C2×C8×C47—41no—
129C2×C8×C47—41no—
130C2×C8×C47—41no—
131C4⋊C4×C47—22no—
132C4⋊C4×C47—22no—
133C4⋊C4×C47—22no—
134C4⋊C4×C47C22⋊C414yes—
135C42×C47C2×D411yescharacteristic
136C42×C47C2×D411yescharacteristic
137C42×C47C2×D411yescharacteristic
138C42×C47C2×D411yescharacteristic
139(C2×D47)⋊C4—28no—
140C4⋊Dic47—28no—
141C4⋊Dic47—22no—
142C4⋊Dic47—22no—
143C4⋊Dic47—22no—
144C4⋊Dic47C22⋊C414yes—
145Dic47⋊C4—28no—
146C4×Dic47—28no—
147C4×Dic47—21no—
148C4×Dic47—21no—
149C4×Dic47—21no—
150C4×Dic47—21no—
151C4×Dic47—21no—
152C4×Dic47—21no—
153C2×C47⋊C8—41no—
154C2×C47⋊C8—41no—
155C2×C47⋊C8—41no—
156C2×C47⋊C8—41no—
157C2×C47⋊C8—41no—
158C2×C47⋊C8—41no—
159C23×C47C2×C22⋊C411yescharacteristic
160C22×D47—21no—
161C22×D47—21no—
162C22×D47—21no—
163C22×D47—21no—
164C22×D47—21no—
165C22×D47—21no—
166C22×D47#10112yes—
167Q8×C47—42no—
168Q8×C47—42no—
169Q8×C47—42no—
170Q8×C47—42no—
171C2×C4×C47—21no—
172C2×C4×C47—21no—
173C2×C4×C47—24no—
174C2×C4×C47—42no—
175C2×C4×C47—42no—
176C2×C4×C47C2×C22⋊C411yescharacteristic
177C2×C4×C47C2×C22⋊C411yescharacteristic
178C2×C4×C47#12011yescharacteristic
179C2×C4×C47#12011yescharacteristic
180C2×C4×C47#12011yescharacteristic
181C2×C4×C47#12011yescharacteristic
182C2×C4×C47#13511yescharacteristic
183C2×C4×C47#13511yescharacteristic
184C2×C4×C47#13511yescharacteristic
185C2×C4×C47#13511yescharacteristic
186C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C47#13711yescharacteristic
189C2×C4×C47#13711yescharacteristic
190C2×Dic47—21no—
191C2×Dic47—21no—
192C2×Dic47—21no—
193C2×Dic47—21no—
194C2×Dic47—24no—
195C2×Dic47—21no—
196C2×Dic47—21no—
197C2×Dic47—21no—
198C2×Dic47—21no—
199C2×Dic47—42no—
200C2×Dic47—42no—
201C2×Dic47#10112yes—
202C4×D47—24no—
203C4×D47—24no—
204C4×D47—41no—
205C4×D47—41no—
206C4×D47—41no—
207C4×D47—41no—
208C4×D47—41no—
209C4×D47—41no—
210C4×D47—41no—
211C4×D47—41no—
212Dic94—42no—
213Dic94—42no—
214Dic94—42no—
215Dic94—42no—
216C8×C47—81no—
217C8×C47—81no—
218C47⋊C8—81no—
219C47⋊C8—81no—
220#8345—471nomaximal, Sylow
221C22×C47#37911yescharacteristic
222C22×C47C2×#10111yescharacteristic
223C22×C47C2×#10111yescharacteristic
224C22×C47#41611yescharacteristic
225C22×C47#41611yescharacteristic
226C22×C47#41711yescharacteristic
227C22×C47#41711yescharacteristic
228C2×D47—22no—
229C2×D47—22no—
230C2×D47—22no—
231C2×D47—41no—
232C2×D47—41no—
233C2×D47—41no—
234C2×D47—41no—
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—44no—
238C4×C47#44911yescharacteristic
239C4×C47#44911yescharacteristic
240C4×C47#44911yescharacteristic
241C4×C47#44911yescharacteristic
242C4×C47#45211yescharacteristic
243C4×C47#45211yescharacteristic
244C4×C47#45211yescharacteristic
245C4×C47#45211yescharacteristic
246Dic47—22no—
247Dic47—44no—
248Dic47—41no—
249Dic47—41no—
250C2×#533—471no—
251#1797—471no—
252#1797—471no—
253C2×#332—471no—
254C2×#332—471no—
255C2×#332—471no—
256C2×#332D4711yescharacteristic, complemented
257C2×C47#154411yescharacteristic
258C2×C47#155211yescharacteristic
259C2×C47#155211yescharacteristic
260C2×C47#156111yescharacteristic
261C2×C47#178411yescharacteristic
262C2×C47#178811yescharacteristic
263C2×C47#178811yescharacteristic
264D47—42no—
265#533—942no—
266#533—942no—
267#533—942no—
268#533—942no—
269C2×C4⋊Q8—471no—
270C2×C4⋊Q8C2×D4711yescharacteristic
271C2×#125—472no—
272C2×C22⋊Q8—941no—
273C2×C22⋊Q8—941no—
274C2×C4×Q8—941no—
275C2×C4×Q8—941no—
276C2×#117—472no—
277C22×C42—471no—
278C2×C4⋊C8—471no—
279C2×C4⋊C8—471no—
280C2×C4⋊C8C2×D4711yescharacteristic
281C2×C4⋊C8C2×D4711yescharacteristic
282C2×C22⋊C8—941no—
283C2×C22⋊C8—941no—
284#336—941no—
285#336—941no—
286#332—22no—
287#332—942no—
288#332—942no—
289#332—942no—
290C47#834511yescharacteristic, complemented, Sylow
291C22×Q8—21no—
292C22×Q8—941no—
293C23×C4—471no—
294C23×C4—471no—
295C23×C4—471no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—941no—
299C22×C8—941no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—472no—
303C4⋊Q8—472no—
304C4⋊Q8—941no—
305C4⋊Q8—941no—
306C4⋊Q8D18812yes—
307C4⋊Q8C22⋊D4712yes—
308#125—944no—
309#125—944no—
310C22⋊Q8—944no—
311C22⋊Q8—944no—
312C22⋊Q8—944no—
313C22⋊Q8—944no—
314C4×Q8—944no—
315C4×Q8—944no—
316C4×Q8—944no—
317C4×Q8—944no—
318#117—944no—
319#117—944no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—472no—
322C2×C4⋊C4—942no—
323C2×C4⋊C4—942no—
324C2×C4⋊C4—941no—
325C2×C4⋊C4C4×D4712yes—
326C2×C22⋊C4—942no—
327C2×C42—471no—
328C2×C42—471no—
329C2×C42—471no—
330C2×C42—942no—
331C2×C42—941no—
332C2×C42—941no—
333C2×C42—941no—
334C2×C42—941no—
335C2×C42C22×D4711yescharacteristic
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8—941no—
341C4⋊C8—941no—
342C4⋊C8—941no—
343C4⋊C8—941no—
344C22⋊C8—1882no—
345C22⋊C8—1882no—
346C24—471no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—942no—
354C2×Q8—942no—
355C2×Q8—1881no—
356C2×Q8—1881no—
357C2×Q8—1881no—
358C2×Q8—1881no—
359C22×C4—22no—
360C22×C4—471no—
361C22×C4—471no—
362C22×C4—471no—
363C22×C4—942no—
364C22×C4—942no—
365C22×C4—941no—
366C22×C4—941no—
367C22×C4—942no—
368C22×C4—941no—
369C22×C4—941no—
370C22×C4—941no—
371C22×C4—941no—
372C22×C4—941no—
373C22×C4—941no—
374C22×C4—941no—
375C22×C4—941no—
376C22×C4—941no—
377C22×C4—941no—
378C22×C4—941no—
379C22×C4—941no—
380C22×C4C2×C4×D4711yescharacteristic
381C22×C4D4×D4711yescharacteristic
382C22×C4D4×D4711yescharacteristic
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—1881no—
390C2×C8—1881no—
391C2×C8—1881no—
392C2×C8—1881no—
393C2×C8—1881no—
394C2×C8—1881no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—474no—
399C4⋊C4—948no—
400C4⋊C4—948no—
401C4⋊C4—942no—
402C4⋊C4—942no—
403C4⋊C4—942no—
404C4⋊C4(C2×D47)⋊C414yes—
405C22⋊C4—948no—
406C42—948no—
407C42—941no—
408C42—941no—
409C42—941no—
410C42—941no—
411C42—941no—
412C42—941no—
413C42C2×D18811yescharacteristic
414C42D4×D4711yescharacteristic
415C42D4×D4711yescharacteristic
416C42C2×C22⋊D4711yescharacteristic
417C23—472no—
418C23—941no—
419C23—941no—
420C23—941no—
421C23—941no—
422C23—941no—
423C23—941no—
424C23C22⋊C4×D4711yescharacteristic
425Q8—42no—
426Q8—42no—
427Q8—42no—
428Q8—42no—
429Q8—1882no—
430Q8—1882no—
431Q8—1882no—
432Q8—1882no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—24no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—472no—
439C2×C4—944no—
440C2×C4—944no—
441C2×C4—941no—
442C2×C4—941no—
443C2×C4—941no—
444C2×C4—941no—
445C2×C4—944no—
446C2×C4—941no—
447C2×C4—941no—
448C2×C4—941no—
449C2×C4—941no—
450C2×C4—1882no—
451C2×C4—1882no—
452C2×C4—1881no—
453C2×C4—1881no—
454C2×C4—1881no—
455C2×C4—1881no—
456C2×C4—1881no—
457C2×C4—1881no—
458C2×C4—1881no—
459C2×C4—1881no—
460C2×C4C22⋊C4×D4711yescharacteristic
461C2×C4C2×(C2×D47)⋊C411yescharacteristic
462C2×C4#1309399211yescharacteristic
463C2×C4#1309399211yescharacteristic
464C2×C4#1309399411yescharacteristic
465C2×C4#1309399411yescharacteristic
466C2×C4#1309404311yescharacteristic
467C2×C4#1309404511yescharacteristic
468C2×C4#1309404511yescharacteristic
469C2×C4#1309404711yescharacteristic
470C2×C4#1309404811yescharacteristic
471C2×C4#1309405111yescharacteristic
472C2×C4#1309405311yescharacteristic
473C2×C4#1309405611yescharacteristic
474C8—81no—
475C8—81no—
476C8—3761no—
477C8—3761no—
478C22—942no—
479C22—942no—
480C22—942no—
481C22—1881no—
482C22—1881no—
483C22—1881no—
484C22—1881no—
485C22#1568897811yescharacteristic
486C22#101×D4711yescharacteristic
487C22#101×D4711yescharacteristic
488C22#1568911611yescharacteristic
489C22#1568911811yescharacteristic
490C22#1568912111yescharacteristic
491C22#1568912311yescharacteristic
492C4—21no—
493C4—21no—
494C4—44no—
495C4—942no—
496C4—1881no—
497C4—1881no—
498C4—1884no—
499C4#1568926511yescharacteristic
500C4#1568926711yescharacteristic
501C4#1568926911yescharacteristic
502C4#1568927111yescharacteristic
503C4#1568928211yescharacteristic
504C4#1568928411yescharacteristic
505C4#1568928611yescharacteristic
506C4#1568928811yescharacteristic
507C2—1882no—
508C2#2024205111yescharacteristic
509C2#2024208511yescharacteristic
510C2#2024208711yescharacteristic
511C2#2024212411yescharacteristic
512C2#2024331011yescharacteristic
513C2#2024332511yescharacteristic
514C2#2024332711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#332C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#332D47
hypocenterC47#8345
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
4. C2×#15688870C2semidirect
5. C2×#15688869C2semidirect
6. C2×#15688868C2semidirect
7. C2×C47×#332C2semidirect
256. C2×#332D47semidirect
290. C47#8345semidirect

Maximal subgroups

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

subgroupindex
C2×#156896782
#202433652
C2×#156888702
C2×#156888692
C2×#156888682
C2×C47×#3322
#834547