Finite Group Databasebeta

← #26107777

Subgroups — #26107777

Order 12032.

802 conjugacy classes of subgroups.

The subgroup lattice has 508 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×#15688871C211yesmaximal, characteristic, complemented
5C2×#15688871C211yesmaximal, characteristic, complemented
6C2×#15688869C211yesmaximal, characteristic, complemented
7C2×C47×#332C211yesmaximal, characteristic, complemented
8#15689678—22no—
9#15689678—22no—
10#15689678—22no—
11#15689678—22no—
12C2×#13094024C2211yescharacteristic
13C2×#13094015—21no—
14C2×#13094004C412yes—
15C2×#13094000—21no—
16C2×Q8×Dic47—21no—
17C2×#13093989C412yes—
18C2×#13093982—21no—
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#15688871—22no—
27#15688871—22no—
28#15688869—22no—
29C2×C4⋊Q8×C47C2211yescharacteristic
30C2×C4⋊C8×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C47×#332—22no—
33C22×Dic94C2×C412yes—
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—21no—
57C2×C4⋊Dic47—22no—
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—21no—
104C2×C4×D47—21no—
105C2×C4×D47—21no—
106C2×C4×D47—21no—
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—41no—
116C2×C4×D47—41no—
117C2×C4×D47SD1612yes—
118C2×C4×D47Q1612yes—
119C2×Dic94—22no—
120C2×Dic94—42no—
121C2×Dic94—42no—
122C2×Dic94C22⋊C414yes—
123C2×C8×C47—41no—
124C2×C8×C47—41no—
125C2×C8×C47—41no—
126C2×C8×C47—41no—
127C2×C8×C47—41no—
128C2×C8×C47—41no—
129C4⋊C4×C47—22no—
130C4⋊C4×C47—22no—
131C4⋊C4×C47—22no—
132C4⋊C4×C47C22⋊C414yes—
133C42×C47C2×D411yescharacteristic
134C42×C47C2×D411yescharacteristic
135C42×C47C2×D411yescharacteristic
136C42×C47C2×D411yescharacteristic
137(C2×D47)⋊C4—28no—
138C4⋊Dic47—28no—
139C4⋊Dic47—22no—
140C4⋊Dic47—22no—
141C4⋊Dic47—22no—
142C4⋊Dic47—22no—
143Dic47⋊C4—28no—
144C4×Dic47—28no—
145C4×Dic47—21no—
146C4×Dic47—21no—
147C4×Dic47—21no—
148C4×Dic47—21no—
149C4×Dic47—21no—
150C4×Dic47—21no—
151C2×C47⋊C8—41no—
152C2×C47⋊C8—41no—
153C2×C47⋊C8—41no—
154C2×C47⋊C8—41no—
155C2×C47⋊C8—41no—
156C2×C47⋊C8—41no—
157C23×C47C2×C22⋊C411yescharacteristic
158C22×D47—21no—
159C22×D47—21no—
160C22×D47—21no—
161C22×D47—21no—
162C22×D47—21no—
163C22×D47—21no—
164C22×D47#10312yes—
165Q8×C47—42no—
166Q8×C47—42no—
167Q8×C47—42no—
168Q8×C47—42no—
169C2×C4×C47—21no—
170C2×C4×C47—21no—
171C2×C4×C47—24no—
172C2×C4×C47—42no—
173C2×C4×C47—42no—
174C2×C4×C47C2×C22⋊C411yescharacteristic
175C2×C4×C47C2×C22⋊C411yescharacteristic
176C2×C4×C47#12011yescharacteristic
177C2×C4×C47#12011yescharacteristic
178C2×C4×C47#12011yescharacteristic
179C2×C4×C47#12011yescharacteristic
180C2×C4×C47C2×SD1611yescharacteristic
181C2×C4×C47C2×Q1611yescharacteristic
182C2×C4×C47#13511yescharacteristic
183C2×C4×C47#13511yescharacteristic
184C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C47#13711yescharacteristic
186C2×C4×C47#13711yescharacteristic
187C2×C4×C47#13711yescharacteristic
188C2×Dic47—21no—
189C2×Dic47—21no—
190C2×Dic47—21no—
191C2×Dic47—21no—
192C2×Dic47—24no—
193C2×Dic47—21no—
194C2×Dic47—21no—
195C2×Dic47—21no—
196C2×Dic47—21no—
197C2×Dic47—42no—
198C2×Dic47—42no—
199C2×Dic47#10312yes—
200C4×D47—22no—
201C4×D47—22no—
202C4×D47—22no—
203C4×D47—22no—
204C4×D47—42no—
205C4×D47—42no—
206C4×D47—41no—
207C4×D47—41no—
208C4×D47—41no—
209C4×D47—41no—
210Dic94—44no—
211Dic94—44no—
212C8×C47—81no—
213C8×C47—81no—
214C47⋊C8—81no—
215C47⋊C8—81no—
216#8343—471nomaximal, Sylow
217C22×C47#37911yescharacteristic
218C22×C47#41311yescharacteristic
219C22×C47#41311yescharacteristic
220C22×C47C2×#10311yescharacteristic
221C22×C47#41611yescharacteristic
222C22×C47#41711yescharacteristic
223C22×C47#41911yescharacteristic
224C2×D47—22no—
225C2×D47—22no—
226C2×D47—22no—
227C2×D47—41no—
228C2×D47—41no—
229C2×D47—41no—
230C2×D47—41no—
231C4×C47—21no—
232C4×C47—21no—
233C4×C47—44no—
234C4×C47#44811yescharacteristic
235C4×C47#44811yescharacteristic
236C4×C47#44911yescharacteristic
237C4×C47#44911yescharacteristic
238C4×C47#45111yescharacteristic
239C4×C47#45111yescharacteristic
240C4×C47#45211yescharacteristic
241C4×C47#45211yescharacteristic
242Dic47—22no—
243Dic47—44no—
244Dic47—41no—
245Dic47—41no—
246C2×#533—471no—
247#1797—471no—
248#1797—471no—
249C2×#333—471no—
250C2×#333—471no—
251C2×#332—471no—
252C2×#332D4711yescharacteristic, complemented
253C2×C47#154211yescharacteristic
254C2×C47#155011yescharacteristic
255C2×C47#155411yescharacteristic
256C2×C47#155911yescharacteristic
257C2×C47#178511yescharacteristic
258C2×C47#178711yescharacteristic
259C2×C47#178811yescharacteristic
260D47—42no—
261#533—942no—
262#533—942no—
263#533—942no—
264#533—942no—
265C2×C4⋊Q8—471no—
266C2×C4⋊Q8C2×D4711yescharacteristic
267C2×#125—941no—
268C2×C22⋊Q8—472no—
269C2×C22⋊Q8—941no—
270C2×C4×Q8—472no—
271C2×C4×Q8—941no—
272C2×#117—941no—
273C22×C42—471no—
274C2×C4⋊C8—471no—
275C2×C4⋊C8—471no—
276C2×C4⋊C8C2×D4711yescharacteristic
277C2×C4⋊C8C2×D4711yescharacteristic
278C2×C22⋊C8—941no—
279C2×C22⋊C8—941no—
280#336—941no—
281#336—941no—
282#333—942no—
283#333—942no—
284#332—22no—
285#332—942no—
286C47#834311yescharacteristic, complemented, Sylow
287C22×Q8—21no—
288C22×Q8—472no—
289C23×C4—471no—
290C23×C4—471no—
291C23×C4—471no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—941no—
295C22×C8—941no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—472no—
299C4⋊Q8—472no—
300C4⋊Q8—941no—
301C4⋊Q8—941no—
302C4⋊Q8D18812yes—
303C4⋊Q8C22⋊D4712yes—
304#125—944no—
305#125—944no—
306C22⋊Q8—944no—
307C22⋊Q8—944no—
308C22⋊Q8—944no—
309C22⋊Q8—944no—
310C4×Q8—944no—
311C4×Q8—944no—
312C4×Q8—944no—
313C4×Q8—944no—
314#117—944no—
315#117—944no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—942no—
318C2×C4⋊C4—942no—
319C2×C4⋊C4—941no—
320C2×C4⋊C4—941no—
321C2×C4⋊C4C4×D4712yes—
322C2×C22⋊C4—942no—
323C2×C42—471no—
324C2×C42—471no—
325C2×C42—471no—
326C2×C42—942no—
327C2×C42—941no—
328C2×C42—941no—
329C2×C42—941no—
330C2×C42—941no—
331C2×C42C22×D4711yescharacteristic
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8—941no—
337C4⋊C8—941no—
338C4⋊C8—941no—
339C4⋊C8—941no—
340C22⋊C8—1882no—
341C22⋊C8—1882no—
342C24—471no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8—474no—
350C2×Q8—942no—
351C2×Q8—1882no—
352C2×Q8—1882no—
353C22×C4—22no—
354C22×C4—471no—
355C22×C4—472no—
356C22×C4—472no—
357C22×C4—471no—
358C22×C4—471no—
359C22×C4—941no—
360C22×C4—941no—
361C22×C4—941no—
362C22×C4—941no—
363C22×C4—942no—
364C22×C4—941no—
365C22×C4—941no—
366C22×C4—941no—
367C22×C4—941no—
368C22×C4—941no—
369C22×C4—941no—
370C22×C4—941no—
371C22×C4—941no—
372C22×C4—1881no—
373C22×C4—1881no—
374C22×C4C2×C4×D4711yescharacteristic
375C22×C4D4×D4711yescharacteristic
376C22×C4D4×D4711yescharacteristic
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—41no—
381C2×C8—41no—
382C2×C8—41no—
383C2×C8—1881no—
384C2×C8—1881no—
385C2×C8—1881no—
386C2×C8—1881no—
387C2×C8—1881no—
388C2×C8—1881no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—948no—
393C4⋊C4—948no—
394C4⋊C4—942no—
395C4⋊C4—942no—
396C4⋊C4—942no—
397C4⋊C4—942no—
398C4⋊C4(C2×D47)⋊C414yes—
399C22⋊C4—948no—
400C42—948no—
401C42—941no—
402C42—941no—
403C42—941no—
404C42—941no—
405C42—941no—
406C42—941no—
407C42C2×D18811yescharacteristic
408C42D4×D4711yescharacteristic
409C42D4×D4711yescharacteristic
410C42C2×C22⋊D4711yescharacteristic
411C23—472no—
412C23—941no—
413C23—941no—
414C23—941no—
415C23—941no—
416C23—941no—
417C23—941no—
418C23C22⋊C4×D4711yescharacteristic
419Q8—42no—
420Q8—42no—
421Q8—42no—
422Q8—42no—
423Q8—1884no—
424Q8—1884no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—24no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—472no—
431C2×C4—941no—
432C2×C4—941no—
433C2×C4—942no—
434C2×C4—942no—
435C2×C4—942no—
436C2×C4—942no—
437C2×C4—941no—
438C2×C4—941no—
439C2×C4—944no—
440C2×C4—941no—
441C2×C4—941no—
442C2×C4—941no—
443C2×C4—941no—
444C2×C4—1882no—
445C2×C4—1882no—
446C2×C4—1882no—
447C2×C4—1882no—
448C2×C4—1881no—
449C2×C4—1881no—
450C2×C4—1881no—
451C2×C4—1881no—
452C2×C4C22⋊C4×D4711yescharacteristic
453C2×C4C2×(C2×D47)⋊C411yescharacteristic
454C2×C4#1309399211yescharacteristic
455C2×C4#1309399211yescharacteristic
456C2×C4#1309399411yescharacteristic
457C2×C4#1309399411yescharacteristic
458C2×C4SD16×D4711yescharacteristic
459C2×C4Q16×D4711yescharacteristic
460C2×C4#1309404311yescharacteristic
461C2×C4#1309404511yescharacteristic
462C2×C4#1309404811yescharacteristic
463C2×C4#1309405311yescharacteristic
464C2×C4#1309405311yescharacteristic
465C2×C4#1309405611yescharacteristic
466C8—81no—
467C8—81no—
468C8—3761no—
469C8—3761no—
470C22—942no—
471C22—942no—
472C22—942no—
473C22—1881no—
474C22—1881no—
475C22—1881no—
476C22—1881no—
477C22#1568897811yescharacteristic
478C22#1568910611yescharacteristic
479C22#1568910611yescharacteristic
480C22#103×D4711yescharacteristic
481C22#1568911611yescharacteristic
482C22#1568912111yescharacteristic
483C22#1568913011yescharacteristic
484C4—21no—
485C4—21no—
486C4—44no—
487C4—942no—
488C4—1881no—
489C4—1884no—
490C4—1881no—
491C4#1568926011yescharacteristic
492C4#1568926311yescharacteristic
493C4#1568926511yescharacteristic
494C4#1568926911yescharacteristic
495C4#1568927711yescharacteristic
496C4#1568928011yescharacteristic
497C4#1568928211yescharacteristic
498C4#1568928611yescharacteristic
499C2—1882no—
500C2#2024204411yescharacteristic
501C2#2024207711yescharacteristic
502C2#2024209511yescharacteristic
503C2#2024211711yescharacteristic
504C2#2024331511yescharacteristic
505C2#2024332111yescharacteristic
506C2#2024332511yescharacteristic
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#8343
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×#15688871C2semidirect
5. C2×#15688871C2semidirect
6. C2×#15688869C2semidirect
7. C2×C47×#332C2semidirect
252. C2×#332D47semidirect
286. C47#8343semidirect

Maximal subgroups

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

subgroupindex
C2×#156896782
#202433652
C2×#156888712
C2×#156888692
C2×C47×#3322
#834347