Finite Group Databasebeta

← #26268172

Subgroups — #26268172

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689420C211yesmaximal, characteristic
2C2×Q8×C47⋊C8C211yesmaximal, characteristic, complemented
3#20248746C211yesmaximal, characteristic
4#20244889C211yesmaximal, characteristic, complemented
5#20244884C211yesmaximal, characteristic, complemented
6#20244773C211yesmaximal, characteristic
7#20244759C211yesmaximal, characteristic
8#20244354C211yesmaximal, characteristic, complemented
9#20244156C211yesmaximal, characteristic, complemented
10#20244118C211yesmaximal, characteristic, complemented
11#20244113C211yesmaximal, characteristic, complemented
12#20244070C211yesmaximal, characteristic
13#20244070C211yesmaximal, characteristic
14C4×#13093944C211yesmaximal, characteristic
15C47×#2584C211yesmaximal, characteristic, complemented
16C2×C4×D188C2211yescharacteristic
17#15689420—24no—
18Q8×C47⋊C8—24no—
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×#13093944C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31C2×C4×C47⋊C8C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33#15689058—21no—
34#15689034—21no—
35#15689025C2211yescharacteristic
36#15689025C2211yescharacteristic
37#15689021C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15688994—21no—
40#15688994—21no—
41#15688989C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50C2×#125×C47C2211yescharacteristic
51C2×C4×Q8×C47C2211yescharacteristic
52C47×#398—21no—
53C47×#395—21no—
54C47×#389—21no—
55C47×#389—21no—
56C47×#389C2211yescharacteristic
57C47×#389C2211yescharacteristic
58C47×#389C2211yescharacteristic
59C47×#389C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C22×D188C2311yescharacteristic
62C22×C4×D47—21no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C4×D188—22no—
68C4×D188—22no—
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×(C2×D47)⋊C4—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79#13093957—22no—
80#13093957—22no—
81#13093955—22no—
82#13093955—22no—
83C4⋊(C47⋊C8)—22no—
84C4⋊(C47⋊C8)—22no—
85C4⋊(C47⋊C8)D414yes—
86#13093944—22no—
87#13093944—22no—
88#13093944—22no—
89#13093944Q814yescomplemented
90C4×C47⋊C8—22no—
91C4×C47⋊C8—22no—
92C4×C47⋊C8—22no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C22×Q8×C47D411yescharacteristic
98#125×C47—22no—
99#125×C47—22no—
100C4×Q8×C47—22no—
101C4×Q8×C47—22no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47D411yescharacteristic
109C2×C4⋊C4×C47D411yescharacteristic
110C2×C4⋊C4×C47D411yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C42×C47—21no—
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119#95×C47—21no—
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124C23×D47—21no—
125C2×Q8×C47—22no—
126C2×Q8×C47—22no—
127C2×Q8×C47—22no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2411yescharacteristic
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188C2×Q812yes—
148C2×C4×D47—42no—
149C2×C4×D47—81no—
150C2×C4×D47—81no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—42no—
161C4⋊C4×C47—42no—
162C4⋊C4×C47—42no—
163C4⋊C4×C47—42no—
164C4⋊C4×C47—81no—
165C4⋊C4×C47—81no—
166C4⋊C4×C47C2×Q812yes—
167C4⋊C4×C47#4112yes—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—21no—
172C42×C47—81no—
173C42×C47C2×D412yes—
174C42×C47#4112yes—
175(C2×D47)⋊C4—42no—
176(C2×D47)⋊C4—42no—
177(C2×D47)⋊C4—42no—
178(C2×D47)⋊C4—81no—
179(C2×D47)⋊C4—81no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186Dic47⋊C4—81no—
187Dic47⋊C4—81no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8C2×D412yes—
198C2×C47⋊C8C2×D412yes—
199C2×C47⋊C8C2×Q812yes—
200C23×C47C22×D411yescharacteristic
201C22×D47—22no—
202C22×D47—41no—
203C22×D47—41no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—41no—
207C22×D47—41no—
208Q8×C47—28no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47#12112yes—
236C2×C4×C47#12112yes—
237C2×C4×C47#13512yes—
238C2×C4×C47#13512yes—
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C22×Q811yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C472−1+411yescharacteristic
244C2×C4×C472−1+411yescharacteristic
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254D188—22no—
255D188—22no—
256D188—41no—
257D188—41no—
258C4×D47—84no—
259C47⋊C8—22no—
260C47⋊C8—22no—
261C47⋊C8—22no—
262C47⋊C8—41no—
263#25473—471nomaximal, Sylow
264C22×C47C2×#12111yescharacteristic
265C22×C47#54811yescharacteristic
266C22×C47D4×Q811yescharacteristic
267C22×C47C2×#13511yescharacteristic
268C22×C47C2×#13511yescharacteristic
269C22×C47#57611yescharacteristic
270C22×C47#57711yescharacteristic
271C2×D47—42no—
272C2×D47—42no—
273C2×D47—42no—
274C2×D47—81no—
275C2×D47—81no—
276C2×D47—81no—
277C2×D47—81no—
278C4×C47—22no—
279C4×C47—22no—
280C4×C47—22no—
281C4×C47—22no—
282C4×C47—42no—
283C4×C47—42no—
284C4×C47—41no—
285C4×C47—41no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47#53311yescharacteristic
289C4×C47#54111yescharacteristic
290C4×C47#54711yescharacteristic
291C4×C47D4×Q811yescharacteristic
292Dic47—81no—
293Dic47—81no—
294Dic47—81no—
295C2×#478—471no—
296C2×C8×Q8—471no—
297#2584D4711yescharacteristic, complemented
298#2580—471no—
299#2088—471no—
300#2087—471no—
301#2067—471no—
302#2065—471no—
303#1991—471no—
304#1949—471no—
305#1942—471no—
306#1941—471no—
307#1934—471no—
308#1934—471no—
309C4×#102—471no—
310C2×C47#242911yescharacteristic
311C2×C47#305011yescharacteristic
312C2×C47#306211yescharacteristic
313C2×C47#336111yescharacteristic
314C2×C47#336511yescharacteristic
315C2×C47#338011yescharacteristic
316C2×C47#338111yescharacteristic
317D47—82no—
318C2×#125C2×D4711yescharacteristic
319C2×C4×Q8C2×D4711yescharacteristic
320C2×C4×D4—471no—
321#478—944no—
322C8×Q8—944no—
323C2×#107—471no—
324C2×#107—471no—
325C2×#106—471no—
326C2×#106—471no—
327C2×C4⋊C8—471no—
328C2×C4⋊C8—471no—
329C2×C4⋊C8—471no—
330C2×#102—471no—
331C2×#102—471no—
332C2×#102—471no—
333C2×#102—471no—
334C2×C4×C8—471no—
335C2×C4×C8—471no—
336C2×C4×C8—471no—
337#399—941no—
338#398—21no—
339#395—21no—
340#393—941no—
341#390—471no—
342#390—471no—
343#389—21no—
344#389—21no—
345#389—471no—
346#389—471no—
347#389C2×D4711yescharacteristic
348#389C2×D4711yescharacteristic
349#389C2×D4711yescharacteristic
350#389C2×D4711yescharacteristic
351#385—941no—
352#385—941no—
353#382—471no—
354C4×C4⋊C4C2×D4711yescharacteristic
355#340—471no—
356#340—471no—
357#340—471no—
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363C47#2547311yescharacteristic, complemented, Sylow
364C22×Q8C22⋊D4711yescharacteristic
365C22×D4—471no—
366C23×C4—941no—
367C22×C8—471no—
368C22×C8—471no—
369C22×C8—471no—
370C22×C8—471no—
371#125—22no—
372#125—22no—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×D4—942no—
376C4×D4—942no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4C22⋊D4711yescharacteristic
389C2×C4⋊C4C22⋊D4711yescharacteristic
390C2×C4⋊C4C22⋊D4711yescharacteristic
391C2×C4⋊C4C22×D4711yescharacteristic
392C2×C4⋊C4C22×D4711yescharacteristic
393C2×C4⋊C4C22×D4711yescharacteristic
394C2×C4⋊C4C22×D4711yescharacteristic
395C2×C22⋊C4—941no—
396C2×C22⋊C4—941no—
397C2×C22⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C22⋊C4—941no—
400C2×C42—21no—
401C2×C42C22×D4711yescharacteristic
402C2×C42C22×D4711yescharacteristic
403C2×C42C22×D4711yescharacteristic
404#107—942no—
405#107—942no—
406#106—942no—
407#106—942no—
408C4⋊C8—474no—
409C4⋊C8—942no—
410C4⋊C8—942no—
411#102—474no—
412#102—942no—
413#102—942no—
414#102—942no—
415C4×C8—942no—
416C4×C8—942no—
417C4×C8—942no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—941no—
424#95—941no—
425#95—941no—
426#95—941no—
427C24—941no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×D4—472no—
432C2×D4—941no—
433C2×D4—941no—
434C2×D4—941no—
435C2×D4—941no—
436C2×D4—941no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—941no—
444C22×C4—3761no—
445C22×C4—3761no—
446C22×C4—1882no—
447C22×C4C2×C22⋊D4711yescharacteristic
448C22×C4C2×C22⋊D4711yescharacteristic
449C22×C4C2×C22⋊D4711yescharacteristic
450C22×C4C2×C22⋊D4711yescharacteristic
451C22×C4C2×C22⋊D4711yescharacteristic
452C22×C4C2×C22⋊D4711yescharacteristic
453C22×C4C23×D4711yescharacteristic
454C2×C8—472no—
455C2×C8—472no—
456C2×C8—472no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8—941no—
460C2×C8—941no—
461C2×C8—941no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—3761no—
488C4⋊C4—3761no—
489C4⋊C4Q8×D4712yes—
490C4⋊C4#1062535412yes—
491C22⋊C4—3761no—
492C22⋊C4—3761no—
493C22⋊C4—1882no—
494C22⋊C4—1882no—
495C22⋊C4—1882no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—81no—
501C42D4×D4712yes—
502C42#1062535212yes—
503C23—942no—
504C23—1881no—
505C23—1881no—
506C23—1881no—
507C23—1881no—
508C23—1881no—
509C23—1881no—
510C23C22×C22⋊D4711yescharacteristic
511Q8—28no—
512D4—942no—
513D4—942no—
514D4—1881no—
515D4—1881no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—3764no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4#1309399612yes—
553C2×C4#1309399612yes—
554C2×C4#1309404412yes—
555C2×C4#1309404412yes—
556C2×C4C2×D4×D4711yescharacteristic
557C2×C4C2×Q8×D4711yescharacteristic
558C2×C4C2×#1062535211yescharacteristic
559C2×C4C2×#1062535411yescharacteristic
560C2×C4#1309407211yescharacteristic
561C2×C4#1309407211yescharacteristic
562C8—942no—
563C8—942no—
564C8—942no—
565C8—1881no—
566C22—3761no—
567C22—3761no—
568C22—3761no—
569C22—3761no—
570C22—1882no—
571C22—1882no—
572C22—1882no—
573C22C2×#1309399611yescharacteristic
574C22#1568978411yescharacteristic
575C22Q8×C22⋊D4711yescharacteristic
576C22C2×#1309404411yescharacteristic
577C22C2×#1309404411yescharacteristic
578C22#1568992611yescharacteristic
579C22#1568993111yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—42no—
585C4—41no—
586C4—41no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—3761no—
591C4—3761no—
592C4—3761no—
593C4#1568967811yescharacteristic
594C4#1568973411yescharacteristic
595C4#1568977611yescharacteristic
596C4#1568978811yescharacteristic
597C2—3762no—
598C2#2024699011yescharacteristic
599C2#2025296611yescharacteristic
600C2#2025307011yescharacteristic
601C2#2025604811yescharacteristic
602C2#2025608411yescharacteristic
603C2#2025625111yescharacteristic
604C2#2025625911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2584C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenter#2584D47
hypocenterC47#25473
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2584

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C47⋊C8C2semidirect
4. #20244889C2semidirect
5. #20244884C2semidirect
8. #20244354C2semidirect
9. #20244156C2semidirect
10. #20244118C2semidirect
11. #20244113C2semidirect
15. C47×#2584C2semidirect
89. #13093944Q8semidirect
297. #2584D47semidirect
363. C47#25473semidirect

Maximal subgroups

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

subgroupindex
C2×#156894202
C2×Q8×C47⋊C82
#202487462
#202448892
#202448842
#202447732
#202447592
#202443542
#202441562
#202441182
#202441132
#202440702
C4×#130939442
C47×#25842
#2547347