Finite Group Databasebeta

← #26274443

Subgroups — #26274443

Order 12032.

706 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248409C211yesmaximal, characteristic, complemented
2#20244776C211yesmaximal, characteristic
3#20244762C211yesmaximal, characteristic
4#20244534C211yesmaximal, characteristic
5#20244524C211yesmaximal, characteristic
6#20244345C211yesmaximal, characteristic, complemented
7#20244340C211yesmaximal, characteristic, complemented
8#20244154C211yesmaximal, characteristic, complemented
9#20244107C211yesmaximal, characteristic, complemented
10#20243980C211yesmaximal, characteristic, complemented
11#20243973C211yesmaximal, characteristic, complemented
12#20243518C211yesmaximal, characteristic, complemented
13#20243398C211yesmaximal, characteristic
14C4×#13093945C211yesmaximal, characteristic
15C47×#2357C211yesmaximal, characteristic
16C2×#13094024C2211yescharacteristic
17C2×#13094016C2211yescharacteristic
18C2×#13093957C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×C4×C47⋊C8C2211yescharacteristic
28#15689056—21no—
29#15689043—21no—
30#15689027—21no—
31#15689021C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689020—21no—
34#15688989C2211yescharacteristic
35C4×C4⋊Dic47C2211yescharacteristic
36#15688885C2211yescharacteristic
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×C4×D4×C47C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#388—21no—
52C47×#388—21no—
53C47×#382C2211yescharacteristic
54C47×#381—21no—
55C4×C4⋊C4×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47—21no—
59C22×Dic94—21no—
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64#13094024—22no—
65#13094024—41no—
66#13094016—22no—
67#13094016—41no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
76C2×Dic47⋊C4—21no—
77C2×C4×Dic47—21no—
78#13093957—22no—
79#13093955—22no—
80C4⋊(C47⋊C8)—22no—
81C4⋊(C47⋊C8)—41no—
82C4⋊(C47⋊C8)—41no—
83#13093945—22no—
84#13093945—22no—
85#13093945—41no—
86#13093945—41no—
87C4×C47⋊C8—22no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C22×D4×C47C2311yescharacteristic
94C23×C4×C47—21no—
95C4×D4×C47—22no—
96C4×D4×C47Q814yescomplemented
97C2×C4⋊C4×C47D411yescharacteristic
98C2×C4⋊C4×C47D411yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C42×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111C2×C42×C47C2311yescharacteristic
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47D411yescharacteristic
117#95×C47D411yescharacteristic
118C24×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47—21no—
121C2×D4×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47C2×Q812yes—
125C22×C4×C47—21no—
126C22×C4×C47—24no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—81no—
130C22×C4×C47—81no—
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2411yescharacteristic
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C2×Dic94—42no—
143C2×Dic94—42no—
144C2×Dic94—81no—
145C4⋊C4×C47—22no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—41no—
152C4⋊C4×C47C2×Q812yes—
153C22⋊C4×C47—24no—
154C22⋊C4×C47—42no—
155C22⋊C4×C47—42no—
156C22⋊C4×C47—81no—
157C22⋊C4×C47—81no—
158C42×C47—21no—
159C42×C47—21no—
160C42×C47—21no—
161C42×C47—21no—
162C42×C47—81no—
163C42×C47—81no—
164C42×C47C2×Q812yes—
165C42×C47#4112yes—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—21no—
172C4⋊Dic47—42no—
173C4⋊Dic47#4112yes—
174C4⋊Dic47#4112yes—
175Dic47⋊C4—42no—
176Dic47⋊C4—42no—
177Dic47⋊C4—42no—
178Dic47⋊C4—81no—
179C4×Dic47—81no—
180C2×C47⋊C8—21no—
181C2×C47⋊C8—21no—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—21no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C23×C47—22no—
193C23×C47—41no—
194C23×C47—41no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47—41no—
199C23×C47C22×D411yescharacteristic
200D4×C47—22no—
201D4×C47—22no—
202D4×C47—41no—
203D4×C47—41no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—22no—
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—21no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—84no—
229C2×C4×C47C22⋊Q812yes—
230C2×C4×C47C22⋊Q812yes—
231C2×C4×C47#13512yes—
232C2×C4×C47C22×Q811yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47H(5,𝔽2)11yescharacteristic
237C2×C4×C472−1+411yescharacteristic
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250Dic94—84no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255#26028—471nomaximal, Sylow
256C22×C47—42no—
257C22×C47—42no—
258C22×C47—42no—
259C22×C47—81no—
260C22×C47—81no—
261C22×C47—81no—
262C22×C47—81no—
263C22×C47C2×C22⋊Q811yescharacteristic
264C22×C47#54611yescharacteristic
265C22×C47#54811yescharacteristic
266C22×C47C2×#13511yescharacteristic
267C22×C47#57511yescharacteristic
268C22×C47#57611yescharacteristic
269C22×C47#57711yescharacteristic
270C4×C47—22no—
271C4×C47—22no—
272C4×C47—22no—
273C4×C47—42no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—81no—
278C4×C47—81no—
279C4×C47#53311yescharacteristic
280C4×C47#54411yescharacteristic
281C4×C47#55511yescharacteristic
282C4×C47#55611yescharacteristic
283Dic47—42no—
284Dic47—42no—
285Dic47—81no—
286Dic47—81no—
287#2550—471no—
288#2357D4711yescharacteristic
289#2067—471no—
290#2065—471no—
291#2025—471no—
292#2023—471no—
293#1989—471no—
294#1988—471no—
295#1949—471no—
296#1939—471no—
297#1921—471no—
298#1920—471no—
299#1835—471no—
300#1804—471no—
301C4×#102—471no—
302C2×C47—82no—
303C2×C47#243911yescharacteristic
304C2×C47#307611yescharacteristic
305C2×C47#308111yescharacteristic
306C2×C47#329711yescharacteristic
307C2×C47#332611yescharacteristic
308C2×C47#336511yescharacteristic
309C2×C47#337011yescharacteristic
310C2×C4⋊Q8—471no—
311C2×#125—471no—
312C2×C4×D4C2×D4711yescharacteristic
313C2×#107—471no—
314C2×#106—471no—
315C2×C4⋊C8—471no—
316C2×C4⋊C8—471no—
317C2×C4⋊C8—471no—
318C2×#102—471no—
319C2×#102—471no—
320C2×#102—471no—
321C2×#102—471no—
322C2×C4×C8—471no—
323#398—941no—
324#395—941no—
325#391—941no—
326#390C2×D4711yescharacteristic
327#390C2×D4711yescharacteristic
328#389—471no—
329#389—471no—
330#389—941no—
331#388—21no—
332#388—21no—
333#382—471no—
334#382C2×D4711yescharacteristic
335#381—21no—
336C4×C4⋊C4—471no—
337C4×C4⋊C4C2×D4711yescharacteristic
338C4×C4⋊C4C2×D4711yescharacteristic
339C4×C4⋊C4C2×D4711yescharacteristic
340C4×C22⋊C4—21no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340—471no—
346#340—471no—
347#340—471no—
348#340—471no—
349#340—471no—
350#340—471no—
351#336—471no—
352#336—471no—
353C47#2602811yescharacteristic, complemented, Sylow
354C22×Q8—941no—
355C22×D4C22×D4711yescharacteristic
356C23×C4—21no—
357C22×C8—471no—
358C22×C8—471no—
359C22×C8—471no—
360C22×C8—471no—
361C4⋊Q8—942no—
362C4⋊Q8—1881no—
363#125—942no—
364#125—1881no—
365C4×D4—22no—
366C4×D4Dic9414yescomplemented
367C2×C4⋊C4—471no—
368C2×C4⋊C4—471no—
369C2×C4⋊C4—471no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—941no—
372C2×C4⋊C4—941no—
373C2×C4⋊C4—941no—
374C2×C4⋊C4—941no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4C22⋊D4711yescharacteristic
377C2×C4⋊C4C22⋊D4711yescharacteristic
378C2×C4⋊C4C22×D4711yescharacteristic
379C2×C4⋊C4C22×D4711yescharacteristic
380C2×C4⋊C4C22×D4711yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—941no—
389C2×C42C22×D4711yescharacteristic
390C2×C42C22×D4711yescharacteristic
391C2×C42C22×D4711yescharacteristic
392#107—942no—
393#106—942no—
394C4⋊C8—942no—
395C4⋊C8—1881no—
396C4⋊C8—1881no—
397#102—942no—
398#102—942no—
399#102—1881no—
400#102—1881no—
401C4×C8—942no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—941no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95—941no—
411#95C22⋊D4711yescharacteristic
412#95C22⋊D4711yescharacteristic
413C24—21no—
414C2×Q8—3761no—
415C2×Q8—1882no—
416C2×Q8—1882no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×Dic9412yes—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—941no—
432C22×C4—941no—
433C22×C4C2×C22⋊D4711yescharacteristic
434C22×C4C2×C22⋊D4711yescharacteristic
435C22×C4C2×C22⋊D4711yescharacteristic
436C22×C4C2×C22⋊D4711yescharacteristic
437C22×C4C2×C22⋊D4711yescharacteristic
438C22×C4C2×C22⋊D4711yescharacteristic
439C22×C4C23×D4711yescharacteristic
440C2×C8—941no—
441C2×C8—941no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8—941no—
449C2×C8—941no—
450C2×C8—941no—
451C2×C8—941no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—472no—
460C4⋊C4—472no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—941no—
466C4⋊C4—941no—
467C4⋊C4—3761no—
468C4⋊C4—1882no—
469C4⋊C4—1882no—
470C4⋊C4—1882no—
471C4⋊C4—1882no—
472C4⋊C4C2×Dic9412yes—
473C22⋊C4—24no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—81no—
483C42—81no—
484C42—3761no—
485C42C2×Dic9412yes—
486C42#1062535012yes—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C22×C22⋊D4711yescharacteristic
495Q8—3764no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—84no—
525C2×C4—942no—
526C2×C4—942no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4#1309400312yes—
538C2×C4#1309400312yes—
539C2×C4#1309404412yes—
540C2×C4C22×Dic9411yescharacteristic
541C2×C4#41×D4711yescharacteristic
542C2×C4#41×D4711yescharacteristic
543C2×C4C2×#1062535011yescharacteristic
544C2×C4#1309407011yescharacteristic
545C2×C4#1309407111yescharacteristic
546C8—1881no—
547C8—1881no—
548C8—1881no—
549C8—1881no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#1309400311yescharacteristic
558C22#1568976111yescharacteristic
559C22#1568978011yescharacteristic
560C22C2×#1309404411yescharacteristic
561C22#1568992111yescharacteristic
562C22#1568992611yescharacteristic
563C22#1568993411yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—3761no—
574C4—3761no—
575C4—1882no—
576C4—1882no—
577C4#1568967611yescharacteristic
578C4#1568975111yescharacteristic
579C4#1568983611yescharacteristic
580C4#1568984111yescharacteristic
581C2—82no—
582C2#2024707311yescharacteristic
583C2#2025317611yescharacteristic
584C2#2025321911yescharacteristic
585C2#2025523211yescharacteristic
586C2#2025563511yescharacteristic
587C2#2025608011yescharacteristic
588C2#2025613511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2357C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#2357D47
hypocenterC47#26028
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
1. #20248409C2semidirect
6. #20244345C2semidirect
7. #20244340C2semidirect
8. #20244154C2semidirect
9. #20244107C2semidirect
10. #20243980C2semidirect
11. #20243973C2semidirect
12. #20243518C2semidirect
96. C4×D4×C47Q8semidirect
353. C47#26028semidirect
366. C4×D4Dic94semidirect

Maximal subgroups

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

subgroupindex
#202484092
#202447762
#202447622
#202445342
#202445242
#202443452
#202443402
#202441542
#202441072
#202439802
#202439732
#202435182
#202433982
C4×#130939452
C47×#23572
#2602847