Finite Group Databasebeta

← #26233927

Subgroups — #26233927

Order 12032.

822 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D47C211yesmaximal, characteristic
2#20246264C211yesmaximal, characteristic
3#20246261C211yesmaximal, characteristic
4#20244120C211yesmaximal, characteristic, complemented
5#20244118C211yesmaximal, characteristic, complemented
6#20243982C211yesmaximal, characteristic, complemented
7#20243981C211yesmaximal, characteristic, complemented
8#20243979C211yesmaximal, characteristic, complemented
9#20243477C211yesmaximal, characteristic
10#20243477C211yesmaximal, characteristic
11#20243416C211yesmaximal, characteristic
12C4×#13093957C211yesmaximal, characteristic, complemented
13#20243280C211yesmaximal, characteristic, complemented
14#20243158C211yesmaximal, characteristic
15C47×#1921C211yesmaximal, characteristic, complemented
16C22×C8×D47C2211yescharacteristic
17C2×C4⋊C4×D47C2211yescharacteristic
18C2×C4⋊C4×D47C2211yescharacteristic
19C2×#13093958C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24#107×D47C418yescomplemented
25C2×(C2×D47)⋊C8C2211yescharacteristic
26C2×C4×C47⋊C8C2211yescharacteristic
27C2×C8×Dic47C2211yescharacteristic
28#15689022C2211yescharacteristic
29#15689021C2211yescharacteristic
30#15689019C2211yescharacteristic
31#15689010—21no—
32#15689007—21no—
33#15689005—21no—
34#15689004—21no—
35#15688982—21no—
36#15688980—21no—
37#15688980C2211yescharacteristic
38#15688980C2211yescharacteristic
39C4⋊C4×Dic47C2211yescharacteristic
40C4⋊C4×Dic47C2211yescharacteristic
41C4×C4⋊Dic47C2211yescharacteristic
42C4×(C2×D47)⋊C4—21no—
43C4×(C2×D47)⋊C4C2211yescharacteristic
44#15688970—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688877C2211yescharacteristic
53C2×#107×C47C2211yescharacteristic
54C47×#389C2211yescharacteristic
55C4×C4⋊C4×C47C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×C4×D47—21no—
61C22×C4×D47—21no—
62C22×C4×D47C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C2×C8×D47—22no—
66C2×C8×D47—22no—
67C2×C8×D47C2×C414yes—
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—
77C4⋊C4×D47—22no—
78C4⋊C4×D47—22no—
79C4⋊C4×D47C2×C414yes—
80C4⋊C4×D47C2×C414yes—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×(C2×D47)⋊C4D411yescharacteristic
84C2×(C2×D47)⋊C4D411yescharacteristic
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47C2311yescharacteristic
89#13093958C2×C414yes—
90#13093957—22no—
91#13093957—22no—
92#13093957C2×C414yes—
93#13093957C2×C414yes—
94(C2×D47)⋊C8—22no—
95C4×C47⋊C8—22no—
96C8×Dic47—22no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95D411yescharacteristic
106C47⋊#95D411yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C22×C8×C47C2311yescharacteristic
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C42×C47—21no—
115C2×C42×C47C2311yescharacteristic
116#107×C47C2×C414yes—
117#95×C47—21no—
118#95×C47—21no—
119C23×D47C2×D411yescharacteristic
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2411yescharacteristic
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47C2×D411yescharacteristic
132C22×Dic47C2×D411yescharacteristic
133C22×Dic47C2×D411yescharacteristic
134C2×C4×D47—21no—
135C2×C4×D47—21no—
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×C4×D47—24no—
139C2×C4×D47—24no—
140C2×C4×D47—81no—
141C2×C4×D47—81no—
142C2×C4×D47—81no—
143C2×C4×D47—81no—
144C2×C4×D47C22×C412yes—
145C2×C4×D47#4112yes—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47C22×C412yes—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—81no—
159C4⋊C4×C47C22×C412yes—
160C4⋊C4×C47C22×C412yes—
161C42×C47—21no—
162C42×C47—21no—
163C42×C47—81no—
164(C2×D47)⋊C4—22no—
165(C2×D47)⋊C4—42no—
166(C2×D47)⋊C4—42no—
167(C2×D47)⋊C4Q1614yes—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—21no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—81no—
175C4⋊Dic47C22×C412yes—
176C4⋊Dic47C22×C412yes—
177Dic47⋊C4—24no—
178Dic47⋊C4—24no—
179Dic47⋊C4—81no—
180Dic47⋊C4—81no—
181C4×Dic47—21no—
182C4×Dic47—21no—
183C4×Dic47—81no—
184C4×Dic47—81no—
185C4×Dic47—81no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8C22×C412yes—
190C2×C47⋊C8#4112yes—
191C2×C47⋊C8#4112yes—
192C8×D47—28no—
193C23×C47C22×D411yescharacteristic
194C22×D47—21no—
195C22×D47—21no—
196C22×D47—21no—
197C22×D47—21no—
198C22×D47C4×D412yes—
199C22×D47C2×Q1612yes—
200C22×D47#13512yes—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47C2×Q1612yes—
219C2×C4×C47C23×C411yescharacteristic
220C2×C4×C47C2×#4111yescharacteristic
221C2×C4×C47C2×#4111yescharacteristic
222C2×C4×C47C2×#4111yescharacteristic
223C2×C4×C472−1+411yescharacteristic
224C2×C4×C472−1+411yescharacteristic
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—22no—
230C2×Dic47—22no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—41no—
235C2×Dic47—41no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47C4×D412yes—
245C2×Dic47C2×Q1612yes—
246C4×D47—22no—
247C4×D47—22no—
248C4×D47—22no—
249C4×D47—22no—
250C4×D47—84no—
251C4×D47—84no—
252C8×C47—22no—
253C8×C47—41no—
254C47⋊C8—41no—
255C47⋊C8#11714yes—
256#22612—471nomaximal, Sylow
257C22×C47C2×C4×D411yescharacteristic
258C22×C47#54711yescharacteristic
259C22×C47#54711yescharacteristic
260C22×C47C22×Q1611yescharacteristic
261C22×C47C2×#13511yescharacteristic
262C22×C47#57611yescharacteristic
263C22×C47#57611yescharacteristic
264C2×D47—22no—
265C2×D47—22no—
266C2×D47—22no—
267C2×D47—22no—
268C2×D47—22no—
269C2×D47—22no—
270C2×D47C4×Q1614yes—
271C4×C47—22no—
272C4×C47—41no—
273C4×C47—42no—
274C4×C47—42no—
275C4×C47—81no—
276C4×C47—81no—
277C4×C47C2×#11711yescharacteristic
278C4×C47#51911yescharacteristic
279C4×C47#55211yescharacteristic
280C4×C47#55211yescharacteristic
281Dic47—22no—
282Dic47—22no—
283Dic47—41no—
284Dic47—42no—
285Dic47—42no—
286Dic47—81no—
287Dic47—81no—
288C22×#107—471no—
289#2345—471no—
290#2345—471no—
291#1942—471no—
292#1942—471no—
293#1921—471no—
294#1921—471no—
295#1921—471no—
296#1921D4711yescharacteristic, complemented
297#1824—471no—
298#1824—471no—
299#1808—471no—
300C4×#107—471no—
301C4×#107—471no—
302C8×C22⋊C4—471no—
303C2×C47#234411yescharacteristic
304C2×C47C2×C4×Q1611yescharacteristic
305C2×C47#294811yescharacteristic
306C2×C47#333811yescharacteristic
307C2×C47#333811yescharacteristic
308C2×C47#333911yescharacteristic
309C2×C47#333911yescharacteristic
310D47—24no—
311C23×C8—471no—
312C22×C4⋊C4—471no—
313C22×C4⋊C4—471no—
314C2×#107—471no—
315C2×#107—471no—
316C2×#107—471no—
317C2×#107—478no—
318C2×#107—471no—
319C2×#107—471no—
320C2×#107C2×D4711yescharacteristic
321C2×C22⋊C8—471no—
322C2×C4×C8—471no—
323C2×C4×C8—471no—
324#389—471no—
325#389—471no—
326#389—471no—
327#389C2×D4711yescharacteristic
328#387—941no—
329#387—941no—
330#387—941no—
331#387—941no—
332#380—471no—
333#380—471no—
334#380—941no—
335#380—941no—
336C4×C4⋊C4—471no—
337C4×C4⋊C4—471no—
338C4×C4⋊C4—471no—
339C4×C4⋊C4C2×D4711yescharacteristic
340C4×C22⋊C4—471no—
341C4×C22⋊C4—941no—
342C4×C22⋊C4—941no—
343#340—471no—
344#340—471no—
345#340—471no—
346#340—471no—
347#340—471no—
348#340—471no—
349#340—471no—
350#340C2×D4711yescharacteristic
351#340C2×D4711yescharacteristic
352#340C2×D4711yescharacteristic
353#336—471no—
354#336C2×D4711yescharacteristic
355C47#2261211yescharacteristic, complemented, Sylow
356C23×C4—471no—
357C23×C4—941no—
358C23×C4—941no—
359C22×C8—471no—
360C22×C8—474no—
361C22×C8—471no—
362C22×C8—942no—
363C22×C8—942no—
364C22×C8C22×D4711yescharacteristic
365C22×C8C22×D4711yescharacteristic
366C2×C4⋊C4—21no—
367C2×C4⋊C4—471no—
368C2×C4⋊C4—471no—
369C2×C4⋊C4—474no—
370C2×C4⋊C4—474no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—942no—
374C2×C4⋊C4—942no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4—941no—
378C2×C4⋊C4—941no—
379C2×C4⋊C4—941no—
380C2×C4⋊C4C22×D4711yescharacteristic
381C2×C4⋊C4C22×D4711yescharacteristic
382C2×C4⋊C4C22×D4711yescharacteristic
383C2×C4⋊C4C22×D4711yescharacteristic
384C2×C22⋊C4—471no—
385C2×C22⋊C4—471no—
386C2×C22⋊C4—941no—
387C2×C22⋊C4—941no—
388C2×C42—21no—
389C2×C42—471no—
390C2×C42—941no—
391C2×C42—941no—
392C2×C42—941no—
393C2×C42C22×D4711yescharacteristic
394#107—474no—
395#107—474no—
396#107—474no—
397#107—942no—
398#107—942no—
399#107C4×D4714yes—
400C22⋊C8—942no—
401C4×C8—942no—
402C4×C8—942no—
403#95—21no—
404#95—21no—
405#95—471no—
406#95—471no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95—941no—
411#95—941no—
412#95—941no—
413#95—941no—
414#95—941no—
415C24—471no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—471no—
421C22×C4—471no—
422C22×C4—472no—
423C22×C4—472no—
424C22×C4—471no—
425C22×C4—944no—
426C22×C4—944no—
427C22×C4—941no—
428C22×C4—941no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—941no—
432C22×C4—941no—
433C22×C4—941no—
434C22×C4—941no—
435C22×C4—3761no—
436C22×C4—3761no—
437C22×C4—3761no—
438C22×C4—3761no—
439C22×C4D4×D4711yescharacteristic
440C22×C4D4×D4711yescharacteristic
441C22×C4C23×D4711yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—472no—
448C2×C8—472no—
449C2×C8—472no—
450C2×C8—948no—
451C2×C8—941no—
452C2×C8—941no—
453C2×C8—941no—
454C2×C8C2×C4×D4712yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—472no—
463C4⋊C4—472no—
464C4⋊C4—944no—
465C4⋊C4—944no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—3761no—
473C4⋊C4—3761no—
474C4⋊C4—3761no—
475C4⋊C4C2×C4×D4712yes—
476C4⋊C4C2×C4×D4712yes—
477C22⋊C4—474no—
478C22⋊C4—942no—
479C22⋊C4—1882no—
480C22⋊C4—1882no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—941no—
485C42—941no—
486C42—3761no—
487C42—3761no—
488C42—3761no—
489C23—472no—
490C23—472no—
491C23—472no—
492C23—941no—
493C23—941no—
494C23—941no—
495C23—941no—
496C23C2×D4×D4711yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—472no—
515C2×C4—472no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4—942no—
521C2×C4—942no—
522C2×C4—942no—
523C2×C4—942no—
524C2×C4—941no—
525C2×C4—942no—
526C2×C4—942no—
527C2×C4—941no—
528C2×C4—941no—
529C2×C4—3764no—
530C2×C4—3764no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4—1881no—
538C2×C4—1881no—
539C2×C4—1881no—
540C2×C4—1881no—
541C2×C4Q16×D4712yes—
542C2×C4C22×C4×D4711yescharacteristic
543C2×C4#41×D4711yescharacteristic
544C2×C4#41×D4711yescharacteristic
545C2×C4#41×D4711yescharacteristic
546C2×C4#1309407111yescharacteristic
547C2×C4#1309407211yescharacteristic
548C8—22no—
549C8—41no—
550C8—474no—
551C8—1881no—
552C22—474no—
553C22—942no—
554C22—942no—
555C22—942no—
556C22—942no—
557C22—942no—
558C22—942no—
559C22C4×D4×D4711yescharacteristic
560C22#1568977111yescharacteristic
561C22#1568977511yescharacteristic
562C22C2×Q16×D4711yescharacteristic
563C22#135×D4711yescharacteristic
564C22#1568992711yescharacteristic
565C22#1568992711yescharacteristic
566C4—22no—
567C4—41no—
568C4—42no—
569C4—42no—
570C4—81no—
571C4—81no—
572C4—942no—
573C4—942no—
574C4—3761no—
575C4—3761no—
576C4—1881no—
577C4—1882no—
578C4—1882no—
579C4#117×D4711yescharacteristic
580C4#1568959911yescharacteristic
581C4#1568980511yescharacteristic
582C4#1568980911yescharacteristic
583C2—944no—
584C2#2024625411yescharacteristic
585C2C4×Q16×D4711yescharacteristic
586C2#2025223711yescharacteristic
587C2#2025577511yescharacteristic
588C2#2025577911yescharacteristic
589C2#2025578311yescharacteristic
590C2#2025578711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1921C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1921D47
hypocenterC47#22612
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. #20244120C2semidirect
5. #20244118C2semidirect
6. #20243982C2semidirect
7. #20243981C2semidirect
8. #20243979C2semidirect
12. C4×#13093957C2semidirect
13. #20243280C2semidirect
15. C47×#1921C2semidirect
24. #107×D47C4semidirect
296. #1921D47semidirect
355. C47#22612semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D472
#202462642
#202462612
#202441202
#202441182
#202439822
#202439812
#202439792
#202434772
#202434162
C4×#130939572
#202432802
#202431582
C47×#19212
#2261247