Finite Group Databasebeta

← #26275131

Subgroups — #26275131

Order 12032.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689164C211yesmaximal, characteristic
2#20247097C211yesmaximal, characteristic
3#20247086C211yesmaximal, characteristic
4#20244867C211yesmaximal, characteristic, complemented
5#20244862C211yesmaximal, characteristic, complemented
6#20244723C211yesmaximal, characteristic, complemented
7#20244718C211yesmaximal, characteristic, complemented
8#20244126C211yesmaximal, characteristic, complemented
9#20244122C211yesmaximal, characteristic, complemented
10#20243584C211yesmaximal, characteristic
11#20243579C211yesmaximal, characteristic
12#20243543C211yesmaximal, characteristic, complemented
13#20243418C211yesmaximal, characteristic
14#20243173C211yesmaximal, characteristic
15C2×C47×#501C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C2×#13094000—21no—
18C2×#13093982C2211yescharacteristic
19C2×C4⋊C4×D47C2211yescharacteristic
20#15689164—24no—
21C2×#13093958C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093956C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093955C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×C8×Dic47C2211yescharacteristic
29#15689058—21no—
30#15689056—21no—
31#15689045—21no—
32#15689042—21no—
33#15689022C2211yescharacteristic
34#15689022C2211yescharacteristic
35#15689021C2211yescharacteristic
36#15689021C2211yescharacteristic
37#15689019—21no—
38#15689004—21no—
39#15688994—21no—
40#15688992C2211yescharacteristic
41#15688992C2211yescharacteristic
42#15688980C2211yescharacteristic
43#15688980C2211yescharacteristic
44C4×(C2×D47)⋊C4C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688877C2211yescharacteristic
53C2×C4⋊Q8×C47C2211yescharacteristic
54C2×#125×C47C2211yescharacteristic
55C47×#501—24no—
56C2×#107×C47C2211yescharacteristic
57C2×#107×C47C2211yescharacteristic
58C2×#106×C47C2211yescharacteristic
59C2×#106×C47C2211yescharacteristic
60C2×#97×C47C2211yescharacteristic
61C22×C4×D47—21no—
62C22×C4×D47C2311yescharacteristic
63C2×#10625324—22no—
64C2×#10625324—22no—
65C2×#10625324Q814yescomplemented
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13094000—44no—
69#13093982—22no—
70#13093982—41no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—21no—
84C4⋊C4×D47—22no—
85C4⋊C4×D47—41no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4D411yescharacteristic
90C2×(C2×D47)⋊C4D411yescharacteristic
91C2×C4×Dic47—21no—
92C2×C4×Dic47C2311yescharacteristic
93#13093958—22no—
94#13093957—22no—
95#13093956—22no—
96#13093955—22no—
97#13093955—41no—
98#13093955—41no—
99(C2×D47)⋊C8Q814yescomplemented
100C8×Dic47—22no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95D411yescharacteristic
108C47⋊#95D411yescharacteristic
109C22×Q8×C47—21no—
110C22×C8×C47C2311yescharacteristic
111C22×C8×C47C2311yescharacteristic
112C4⋊Q8×C47—22no—
113C4⋊Q8×C47—41no—
114#125×C47—22no—
115#125×C47—41no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124#107×C47—22no—
125#107×C47D414yes—
126#106×C47—22no—
127#106×C47—22no—
128#97×C47—22no—
129C23×D47C2×D411yescharacteristic
130C2×Q8×C47—42no—
131C2×Q8×C47—42no—
132C2×Q8×C47—81no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2411yescharacteristic
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47C2×D411yescharacteristic
145C22×Dic47C2×D411yescharacteristic
146C22×Dic47C2×D411yescharacteristic
147C2×C4×D47—21no—
148C2×C4×D47—21no—
149C2×C4×D47—21no—
150C2×C4×D47—21no—
151C2×C4×D47—42no—
152C2×C4×D47—42no—
153C2×C4×D47—81no—
154C2×C4×D47C2×Q812yes—
155C2×C4×D47C2×Q812yes—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47C2×D412yes—
159C2×C8×C47C2×Q812yes—
160C2×C8×C47C2×Q812yes—
161C2×C8×C47#4112yes—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—42no—
169C4⋊C4×C47—42no—
170C4⋊C4×C47—42no—
171C4⋊C4×C47C2×D412yes—
172C4⋊C4×C47C2×D412yes—
173C42×C47—21no—
174C42×C47—21no—
175(C2×D47)⋊C4—22no—
176(C2×D47)⋊C4—22no—
177(C2×D47)⋊C4—42no—
178(C2×D47)⋊C4—42no—
179(C2×D47)⋊C4—81no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47—42no—
189C4⋊Dic47—42no—
190Dic47⋊C4—42no—
191Dic47⋊C4—42no—
192Dic47⋊C4—42no—
193Dic47⋊C4—42no—
194Dic47⋊C4—81no—
195Dic47⋊C4—81no—
196Dic47⋊C4—81no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47—42no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8C2×Q812yes—
205C2×C47⋊C8C2×Q812yes—
206#10625324—28no—
207C23×C47C22×D411yescharacteristic
208C22×D47—21no—
209C22×D47—21no—
210C22×D47—21no—
211C22×D47—21no—
212C22×D47—21no—
213C22×D47—21no—
214C22×D47C4⋊Q812yes—
215Q8×C47—84no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—41no—
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×C47C22×D411yescharacteristic
235C2×C4×C47C22×Q811yescharacteristic
236C2×C4×C47C22×Q811yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47H(5,𝔽2)11yescharacteristic
239C2×C4×C472−1+411yescharacteristic
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47C4⋊Q812yes—
259C2×Dic47AGL(1,ℤ/8)12yes—
260C2×Dic47#13712yes—
261C4×D47—22no—
262C4×D47—22no—
263C4×D47—22no—
264C4×D47—22no—
265C4×D47—84no—
266C8×C47—22no—
267C8×C47C22⋊Q814yescomplemented
268C47⋊C8—22no—
269C47⋊C8—22no—
270#26078—471nomaximal, Sylow
271C22×C47C2×C4⋊Q811yescharacteristic
272C22×C47D4211yescharacteristic
273C22×C47#54711yescharacteristic
274C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C47C2×#13711yescharacteristic
276C22×C47#57711yescharacteristic
277C22×C47#57711yescharacteristic
278C2×D47—22no—
279C2×D47—22no—
280C2×D47—22no—
281C2×D47—41no—
282C2×D47—41no—
283C2×D47—41no—
284C2×D47—41no—
285C4×C47—42no—
286C4×C47—41no—
287C4×C47—42no—
288C4×C47—41no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47C2×C22⋊Q811yescharacteristic
292C4×C47#54411yescharacteristic
293C4×C47D4×Q811yescharacteristic
294C4×C47#55411yescharacteristic
295Dic47—22no—
296Dic47—22no—
297Dic47—22no—
298Dic47—81no—
299Dic47—81no—
300Dic47—81no—
301Dic47—81no—
302C2×#501D4711yescharacteristic, complemented
303C2×#428—471no—
304#2441—471no—
305#2440—471no—
306#2084—471no—
307#2083—471no—
308#2059—471no—
309#2058—471no—
310#1943—471no—
311#1942—471no—
312#1854—471no—
313#1853—471no—
314#1844—471no—
315#1809—471no—
316#1753—471no—
317C2×C47#244011yescharacteristic
318C2×C47#316311yescharacteristic
319C2×C47#316511yescharacteristic
320C2×C47#327211yescharacteristic
321C2×C47#327811yescharacteristic
322C2×C47#334411yescharacteristic
323C2×C47#334511yescharacteristic
324D47—42no—
325C22×M16—471no—
326C2×C4⋊Q8C2×D4711yescharacteristic
327C2×#125C2×D4711yescharacteristic
328C2×C22⋊Q8—941no—
329C2×#117—471no—
330C22×C4⋊C4—471no—
331#501—24no—
332#428—944no—
333C2×#107—471no—
334C2×#107—471no—
335C2×#107C2×D4711yescharacteristic
336C2×#107C2×D4711yescharacteristic
337C2×#106—471no—
338C2×#106—471no—
339C2×#106—471no—
340C2×#106—471no—
341C2×#106C2×D4711yescharacteristic
342C2×#106C2×D4711yescharacteristic
343C2×C22⋊C8—471no—
344C2×#97C2×D4711yescharacteristic
345C2×C4×C8—471no—
346#399—941no—
347#398—941no—
348#396—941no—
349#395—941no—
350#389—471no—
351#389—471no—
352#389—471no—
353#389—471no—
354#389—941no—
355#387—941no—
356#385—941no—
357#384—471no—
358#384—471no—
359#380—471no—
360#380—471no—
361C4×C22⋊C4—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340—471no—
366#340—471no—
367#340—471no—
368#336—471no—
369#336—471no—
370C47#2607811yescharacteristic, complemented, Sylow
371C22×Q8—21no—
372C23×C4—471no—
373C23×C4—941no—
374C2×M16—474no—
375C2×M16—942no—
376C2×M16—942no—
377C22×C8—471no—
378C22×C8—471no—
379C22×C8C22×D4711yescharacteristic
380C22×C8C22×D4711yescharacteristic
381C4⋊Q8—22no—
382C4⋊Q8—41no—
383#125—22no—
384#125—41no—
385C22⋊Q8—1884no—
386#117—942no—
387#117—1881no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—942no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4—941no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4—1881no—
406C2×C4⋊C4C22×D4711yescharacteristic
407C2×C4⋊C4C22×D4711yescharacteristic
408C2×C4⋊C4C22×D4711yescharacteristic
409C2×C4⋊C4C22×D4711yescharacteristic
410C2×C22⋊C4—471no—
411C2×C22⋊C4—471no—
412C2×C22⋊C4—941no—
413C2×C22⋊C4—941no—
414C2×C22⋊C4—941no—
415C2×C42—471no—
416C2×C42—941no—
417C2×C42C22×D4711yescharacteristic
418#107—22no—
419#107—942no—
420#107—942no—
421#107C22⋊D4714yes—
422#106—22no—
423#106—22no—
424#106—942no—
425#106—942no—
426#106—1881no—
427#106—1881no—
428C22⋊C8—474no—
429#97—22no—
430C4×C8—942no—
431#95—471no—
432#95—471no—
433#95—941no—
434#95—941no—
435#95—941no—
436#95—941no—
437#95—941no—
438#95—941no—
439C24—471no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—81no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—471no—
450C22×C4—472no—
451C22×C4—472no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—3761no—
461C22×C4—1882no—
462C22×C4—1882no—
463C22×C4D4×D4711yescharacteristic
464C22×C4D4×D4711yescharacteristic
465C22×C4C23×D4711yescharacteristic
466M16—948no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—472no—
470C2×C8—472no—
471C2×C8—941no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8Q8×D4712yes—
476C2×C8Q8×D4712yes—
477C2×C8#1062535412yes—
478C2×C8C2×C22⋊D4712yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—3761no—
497C4⋊C4—3761no—
498C4⋊C4—3761no—
499C4⋊C4—1882no—
500C4⋊C4—1882no—
501C4⋊C4—1882no—
502C4⋊C4—1882no—
503C4⋊C4—1882no—
504C4⋊C4—1882no—
505C4⋊C4C2×C22⋊D4712yes—
506C4⋊C4C2×C22⋊D4712yes—
507C22⋊C4—942no—
508C22⋊C4—942no—
509C22⋊C4—3761no—
510C22⋊C4—1882no—
511C22⋊C4—1882no—
512C42—21no—
513C42—21no—
514C42—941no—
515C42—941no—
516C42—1882no—
517C23—472no—
518C23—941no—
519C23—941no—
520C23—941no—
521C23—941no—
522C23—941no—
523C23—941no—
524C23C2×D4×D4711yescharacteristic
525Q8—84no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
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—41no—
543C2×C4—41no—
544C2×C4—472no—
545C2×C4—472no—
546C2×C4—472no—
547C2×C4—941no—
548C2×C4—941no—
549C2×C4—941no—
550C2×C4—941no—
551C2×C4—941no—
552C2×C4—941no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—942no—
556C2×C4—942no—
557C2×C4—3764no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4C22×C22⋊D4711yescharacteristic
571C2×C4C2×Q8×D4711yescharacteristic
572C2×C4C2×Q8×D4711yescharacteristic
573C2×C4C2×#1062535411yescharacteristic
574C2×C4#1309406911yescharacteristic
575C2×C4#1309407211yescharacteristic
576C8—22no—
577C8—942no—
578C8—942no—
579C8#1309400014yescomplemented
580C22—942no—
581C22—942no—
582C22—942no—
583C22—1881no—
584C22—1881no—
585C22—1881no—
586C22—1881no—
587C22C4⋊Q8×D4711yescharacteristic
588C22D4×C22⋊D4711yescharacteristic
589C22#1568977611yescharacteristic
590C22AGL(1,ℤ/8)×D4711yescharacteristic
591C22#137×D4711yescharacteristic
592C22#1568993211yescharacteristic
593C22#1568993311yescharacteristic
594C4—41no—
595C4—42no—
596C4—42no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—942no—
601C4—942no—
602C4—942no—
603C4—3761no—
604C4—3761no—
605C4—3761no—
606C4—3761no—
607C4C2×#1309400011yescharacteristic
608C4#1568975011yescharacteristic
609C4Q8×C22⋊D4711yescharacteristic
610C4#1568983411yescharacteristic
611C2—1882no—
612C2#2024708611yescharacteristic
613C2#2025391511yescharacteristic
614C2#2025393311yescharacteristic
615C2#2025498211yescharacteristic
616C2#2025504811yescharacteristic
617C2#2025584211yescharacteristic
618C2#2025585711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#501C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#501D47
hypocenterC47#26078
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
4. #20244867C2semidirect
5. #20244862C2semidirect
6. #20244723C2semidirect
7. #20244718C2semidirect
8. #20244126C2semidirect
9. #20244122C2semidirect
12. #20243543C2semidirect
15. C2×C47×#501C2semidirect
65. C2×#10625324Q8semidirect
99. (C2×D47)⋊C8Q8semidirect
267. C8×C47C22⋊Q8semidirect
302. C2×#501D47semidirect
370. C47#26078semidirect
579. C8#13094000semidirect

Maximal subgroups

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

subgroupindex
C2×#156891642
#202470972
#202470862
#202448672
#202448622
#202447232
#202447182
#202441262
#202441222
#202435842
#202435792
#202435432
#202434182
#202431732
C2×C47×#5012
#2607847