Finite Group Databasebeta

← #26274342

Subgroups — #26274342

Order 12032.

696 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246271C211yesmaximal, characteristic
2#20244955C211yesmaximal, characteristic, complemented
3#20244890C211yesmaximal, characteristic, complemented
4#20244890C211yesmaximal, characteristic, complemented
5#20244723C211yesmaximal, characteristic, complemented
6#20244346C211yesmaximal, characteristic, complemented
7#20244154C211yesmaximal, characteristic, complemented
8#20243963C211yesmaximal, characteristic, complemented
9#20243963C211yesmaximal, characteristic, complemented
10#20243581C211yesmaximal, characteristic
11#20243573C211yesmaximal, characteristic
12#20243480C211yesmaximal, characteristic
13#20243419C211yesmaximal, characteristic
14#20243107C211yesmaximal, characteristic
15C47×#2442C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×#13093983C2211yescharacteristic
18C2×#13093957C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25#15689021C2211yescharacteristic
26#15689021C2211yescharacteristic
27#15689011—21no—
28#15689011—21no—
29#15688987—21no—
30#15688983C2211yescharacteristic
31C4×C4⋊Dic47C2211yescharacteristic
32C4×C4⋊Dic47C2211yescharacteristic
33#15688968—21no—
34#15688885C2211yescharacteristic
35#15688885C2211yescharacteristic
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×#125×C47C2211yescharacteristic
49C22×C4⋊C4×C47C2211yescharacteristic
50C47×#400—21no—
51C47×#398—21no—
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#385—21no—
55C47×#382C2211yescharacteristic
56C47×#380—21no—
57C47×#380C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C2×#10625329—22no—
60C2×#10625329—22no—
61C2×#10625329—41no—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13093983—22no—
67#13093983Q814yes—
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×C22⋊Dic47—21no—
75C2×C22⋊Dic47—21no—
76C2×C4×Dic47—21no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47—21no—
79#13093957—41no—
80#13093955—22no—
81#13093955—22no—
82#13093955—41no—
83C4⋊(C47⋊C8)—22no—
84C4⋊(C47⋊C8)—41no—
85C22⋊(C47⋊C8)—22no—
86C47⋊#95—21no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C23×C4×C47—21no—
92C23×C4×C47C2311yescharacteristic
93#125×C47—22no—
94#125×C47—41no—
95C2×C4⋊C4×C47—22no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—41no—
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47D411yescharacteristic
108C2×C22⋊C4×C47D411yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47D411yescharacteristic
117#95×C47D411yescharacteristic
118C24×C47C2×D411yescharacteristic
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—42no—
128C22×C4×C47—42no—
129C22×C4×C47—81no—
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×Q812yes—
136C22×C4×C47#4112yes—
137C22×C4×C47C2411yescharacteristic
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C4⋊C4×C47—21no—
143C4⋊C4×C47—21no—
144C4⋊C4×C47—21no—
145C4⋊C4×C47—21no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—42no—
150C4⋊C4×C47—42no—
151C4⋊C4×C47—42no—
152C4⋊C4×C47—81no—
153C4⋊C4×C47—81no—
154C4⋊C4×C47#4112yes—
155C22⋊C4×C47—41no—
156C22⋊C4×C47—41no—
157C22⋊C4×C47—42no—
158C42×C47—21no—
159C42×C47—21no—
160C42×C47—21no—
161C42×C47—21no—
162C22⋊Dic47—24no—
163C22⋊Dic47—81no—
164C4⋊Dic47—21no—
165C4⋊Dic47—21no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47C2×Q812yes—
171C4⋊Dic47C2×Q812yes—
172Dic47⋊C4—81no—
173Dic47⋊C4—81no—
174C4×Dic47—24no—
175C4×Dic47—42no—
176C4×Dic47—42no—
177#10625329—44no—
178C2×C47⋊C8—21no—
179C2×C47⋊C8—21no—
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#4112yes—
190C23×C47—21no—
191C23×C47—21no—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47C22⋊Q812yes—
197C23×C47C22×D411yescharacteristic
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—22no—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—22no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
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—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
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×Q811yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47H(5,𝔽2)11yescharacteristic
235C2×C4×C472−1+411yescharacteristic
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C47⋊C8—22no—
249C47⋊C8—41no—
250C47⋊C8—41no—
251C47⋊C8—41no—
252#26019—471nomaximal, Sylow
253C22×C47—22no—
254C22×C47—22no—
255C22×C47—22no—
256C22×C47—41no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47C2×C22⋊Q811yescharacteristic
261C22×C47#54611yescharacteristic
262C22×C47#54711yescharacteristic
263C22×C47#57511yescharacteristic
264C22×C47#57511yescharacteristic
265C22×C47#57711yescharacteristic
266C22×C47#57711yescharacteristic
267C4×C47—22no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—42no—
273C4×C47—81no—
274C4×C47—81no—
275C4×C47—81no—
276C4×C47#53311yescharacteristic
277C4×C47#54411yescharacteristic
278C4×C47#55111yescharacteristic
279C4×C47#55211yescharacteristic
280Dic47—42no—
281Dic47—42no—
282Dic47—81no—
283Dic47—81no—
284#2442D4711yescharacteristic
285#2346—471no—
286#2101—471no—
287#2088—471no—
288#2088—471no—
289#2059—471no—
290#1989—471no—
291#1949—471no—
292#1919—471no—
293#1919—471no—
294#1853—471no—
295#1851—471no—
296#1825—471no—
297#1809—471no—
298#1736—471no—
299C2×C47—42no—
300C2×C47#243811yescharacteristic
301C2×C47#308011yescharacteristic
302C2×C47#308411yescharacteristic
303C2×C47#332111yescharacteristic
304C2×C47#332311yescharacteristic
305C2×C47#334811yescharacteristic
306C2×C47#335111yescharacteristic
307C22×M16—471no—
308C2×#125C2×D4711yescharacteristic
309C2×#117—471no—
310C22×C4⋊C4C2×D4711yescharacteristic
311C2×#107—471no—
312C2×#106—471no—
313C2×#106—471no—
314C2×#106—471no—
315C2×C4⋊C8—471no—
316C2×C4⋊C8—471no—
317C2×C22⋊C8—471no—
318#400—21no—
319#398—21no—
320#389—471no—
321#389—471no—
322#389C2×D4711yescharacteristic
323#389C2×D4711yescharacteristic
324#388—941no—
325#388—941no—
326#385—21no—
327#382—941no—
328#382C2×D4711yescharacteristic
329#380—21no—
330#380—471no—
331#380C2×D4711yescharacteristic
332C4×C4⋊C4—471no—
333C4×C4⋊C4—471no—
334C4×C22⋊C4C2×D4711yescharacteristic
335#376—941no—
336#340—471no—
337#340—471no—
338#340—471no—
339#340—471no—
340#340—471no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340—471no—
346#340—471no—
347#340—471no—
348#336—471no—
349#336—471no—
350C47#2601911yescharacteristic, complemented, Sylow
351C23×C4—21no—
352C23×C4C22×D4711yescharacteristic
353C2×M16—942no—
354C2×M16—942no—
355C2×M16—1881no—
356C22×C8—471no—
357C22×C8—471no—
358C22×C8—471no—
359C22×C8—471no—
360#125—22no—
361#125—41no—
362#117—474no—
363#117—942no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—471no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4C22×D4711yescharacteristic
378C2×C4⋊C4C22×D4711yescharacteristic
379C2×C4⋊C4C22×D4711yescharacteristic
380C2×C4⋊C4C22×D4711yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C22⋊C4C22⋊D4711yescharacteristic
385C2×C22⋊C4C22⋊D4711yescharacteristic
386C2×C42—941no—
387C2×C42—941no—
388C2×C42—941no—
389C2×C42C22×D4711yescharacteristic
390C2×C42C22×D4711yescharacteristic
391#107—1881no—
392#106—942no—
393#106—942no—
394#106—1881no—
395C4⋊C8—942no—
396C4⋊C8—1881no—
397C22⋊C8—942no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—941no—
404#95—941no—
405#95—941no—
406#95—941no—
407#95—941no—
408#95C22⋊D4711yescharacteristic
409#95C22⋊D4711yescharacteristic
410C24C2×C22⋊D4711yescharacteristic
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—81no—
422C22×C4—941no—
423C22×C4—941no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4Q8×D4712yes—
427C22×C4#1062535412yes—
428C22×C4C2×C22⋊D4711yescharacteristic
429C22×C4C2×C22⋊D4711yescharacteristic
430C22×C4C2×C22⋊D4711yescharacteristic
431C22×C4C2×C22⋊D4711yescharacteristic
432C22×C4C2×C22⋊D4711yescharacteristic
433C22×C4C23×D4711yescharacteristic
434M16—1884no—
435C2×C8—472no—
436C2×C8—941no—
437C2×C8—941no—
438C2×C8—941no—
439C2×C8—941no—
440C2×C8—941no—
441C2×C8—941no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—81no—
458C4⋊C4—81no—
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—3761no—
469C4⋊C4#1062535212yes—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—944no—
474C22⋊C4—3761no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—944no—
480C42—1882no—
481C42—1882no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23#1309400012yes—
489C23C22×C22⋊D4711yescharacteristic
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
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—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—84no—
521C2×C4—942no—
522C2×C4—942no—
523C2×C4—1881no—
524C2×C4—1881no—
525C2×C4—1881no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4#1309400012yes—
534C2×C4C2×Q8×D4711yescharacteristic
535C2×C4#41×D4711yescharacteristic
536C2×C4C2×#1062535211yescharacteristic
537C2×C4C2×#1062535411yescharacteristic
538C2×C4#1309406911yescharacteristic
539C2×C4#1309407111yescharacteristic
540C8—942no—
541C8—1881no—
542C8—1881no—
543C8—1881no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×#1309400011yescharacteristic
552C22#1568976711yescharacteristic
553C22#1568977211yescharacteristic
554C22#1568992111yescharacteristic
555C22#1568992111yescharacteristic
556C22#1568993111yescharacteristic
557C22#1568993411yescharacteristic
558C4—22no—
559C4—41no—
560C4—41no—
561C4—42no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—3761no—
568C4—3761no—
569C4—1882no—
570C4—1882no—
571C4#1568967511yescharacteristic
572C4#1568975211yescharacteristic
573C4#1568980011yescharacteristic
574C4#1568981511yescharacteristic
575C2—42no—
576C2#2024706011yescharacteristic
577C2#2025320611yescharacteristic
578C2#2025324611yescharacteristic
579C2#2025557411yescharacteristic
580C2#2025560411yescharacteristic
581C2#2025589711yescharacteristic
582C2#2025594211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2442C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#2442D47
hypocenterC47#26019
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
2. #20244955C2semidirect
3. #20244890C2semidirect
4. #20244890C2semidirect
5. #20244723C2semidirect
6. #20244346C2semidirect
7. #20244154C2semidirect
8. #20243963C2semidirect
9. #20243963C2semidirect
350. C47#26019semidirect

Maximal subgroups

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

subgroupindex
#202462712
#202449552
#202448902
#202447232
#202443462
#202441542
#202439632
#202435812
#202435732
#202434802
#202434192
#202431072
C47×#24422
#2601947