Finite Group Databasebeta

← #26224132

Subgroups — #26224132

Order 12032.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253178C211yesmaximal, characteristic
2#20252328C211yesmaximal, characteristic, complemented
3#20251813C211yesmaximal, characteristic
4#20244331C211yesmaximal, characteristic, complemented
5#20244164C211yesmaximal, characteristic, complemented
6#20243988C211yesmaximal, characteristic, complemented
7#20243988C211yesmaximal, characteristic, complemented
8#20243666C211yesmaximal, characteristic
9#20243666C211yesmaximal, characteristic
10#20243409C211yesmaximal, characteristic
11#20243272C211yesmaximal, characteristic, complemented
12#20243267C211yesmaximal, characteristic, complemented
13#20243232C211yesmaximal, characteristic
14#20243225C211yesmaximal, characteristic
15C47×#1771C211yesmaximal, characteristic, complemented
16C2×#13094030C2211yescharacteristic
17C2×#13094030C2211yescharacteristic
18#15689680C2211yescharacteristic
19C4×#10625350C2211yescharacteristic
20#15689431C411yescharacteristic, complemented
21#15689431C411yescharacteristic, complemented
22#15689424C411yescharacteristic, complemented
23#15689424C411yescharacteristic, complemented
24#15689419C411yescharacteristic, complemented
25#15689414C411yescharacteristic, complemented
26#15689409C411yescharacteristic, complemented
27#15689404C411yescharacteristic, complemented
28#15689251—21no—
29#15689251—21no—
30#15689251—21no—
31#15689251—21no—
32C2×#13093960C2211yescharacteristic
33C2×#13093960C2211yescharacteristic
34#15689161C2211yescharacteristic
35#15689161C2211yescharacteristic
36#15689149C2211yescharacteristic
37#15689149C2211yescharacteristic
38#15689147C2211yescharacteristic
39C2×#13093952C2211yescharacteristic
40C2×#13093952C2211yescharacteristic
41#15689120C2211yescharacteristic
42#15689120C2211yescharacteristic
43#15689080—21no—
44#15689080—21no—
45#15689078C2211yescharacteristic
46#15689078C2211yescharacteristic
47#15689078C2211yescharacteristic
48#15689078C2211yescharacteristic
49C4×#10625329C2211yescharacteristic
50#15689075—21no—
51#97×D47—21no—
52#15688888C2211yescharacteristic
53#15688888C2211yescharacteristic
54#15688883C2211yescharacteristic
55#15688883C2211yescharacteristic
56#15688883C2211yescharacteristic
57#15688883C2211yescharacteristic
58#15688883C2211yescharacteristic
59#15688883C2211yescharacteristic
60C2×C4⋊C8×C47C2211yescharacteristic
61C2×#97×C47C2211yescharacteristic
62C2×#97×C47C2211yescharacteristic
63C2×C4×C8×C47C2211yescharacteristic
64C4×C4⋊C4×C47C2211yescharacteristic
65C47×#336C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68#13094030—22no—
69#13094030—22no—
70#13094030—22no—
71#13094030Q814yescomplemented
72C2×#10625329C2311yescharacteristic
73C2×#10625329C2311yescharacteristic
74C2×#10625329C2311yescharacteristic
75C2×#10625329C2311yescharacteristic
76C2×#10625324—21no—
77C2×#10625324—21no—
78C2×C8×D47—21no—
79C2×C8×D47—21no—
80#13094024C2×C411yescharacteristic
81#13094024C2×C411yescharacteristic
82#13094016C2×C411yescharacteristic
83#13094016C2×C411yescharacteristic
84#13094003—21no—
85#13094003—21no—
86C4×Dic94—21no—
87C4×Dic94—21no—
88C4×Dic94C2×C411yescharacteristic
89C4×Dic94C2×C411yescharacteristic
90C4×D188C2×C411yescharacteristic
91C4×D188C2×C411yescharacteristic
92C4×C22⋊D47—21no—
93C4×C22⋊D47—21no—
94#13093983C2311yescharacteristic
95#13093983C2311yescharacteristic
96#13093983C2311yescharacteristic
97#13093981—21no—
98C42×D47—21no—
99#13093960—22no—
100#13093960—22no—
101#13093958C2×C411yescharacteristic
102#13093958C2×C411yescharacteristic
103#13093958C2×C411yescharacteristic
104#13093958C2×C411yescharacteristic
105#13093956C2×C411yescharacteristic
106#13093956C2×C411yescharacteristic
107#13093956C2×C411yescharacteristic
108#13093956C2×C411yescharacteristic
109C4⋊(C47⋊C8)—21no—
110C4⋊(C47⋊C8)—21no—
111Dic47⋊C8—21no—
112Dic47⋊C8—21no—
113Dic47⋊C8—21no—
114Dic47⋊C8—21no—
115#13093952—22no—
116#13093952—22no—
117#13093949C2×C411yescharacteristic
118#13093949C2×C411yescharacteristic
119#13093949C2×C411yescharacteristic
120#13093949C2×C411yescharacteristic
121#13093946C2×C411yescharacteristic
122#13093946C2×C411yescharacteristic
123#13093946C2×C411yescharacteristic
124#13093946C2×C411yescharacteristic
125#13093935—21no—
126#13093934—21no—
127#13093934—21no—
128#13093934—21no—
129#13093934—21no—
130C4×C47⋊C8—21no—
131C8×Dic47—21no—
132C8×Dic47—21no—
133C8×Dic47—21no—
134C8×Dic47—21no—
135C22×C8×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C2×C4⋊C4×C47—21no—
140C2×C42×C47C2311yescharacteristic
141C2×C42×C47C2311yescharacteristic
142C2×C42×C47C2311yescharacteristic
143C4⋊C8×C47C2×C411yescharacteristic
144C4⋊C8×C47C2×C411yescharacteristic
145C4⋊C8×C47C2×C411yescharacteristic
146C4⋊C8×C47C2×C411yescharacteristic
147#97×C47—22no—
148#97×C47D411yescharacteristic
149#97×C47D411yescharacteristic
150#97×C47D411yescharacteristic
151#97×C47D411yescharacteristic
152C4×C8×C47—22no—
153#95×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47#4111yescharacteristic
157C22×C4×C47#4111yescharacteristic
158C22×C4×C47C2411yescharacteristic
159C2×C22⋊D47—21no—
160#10625350—21no—
161#10625350—21no—
162#10625350C2×Q812yes—
163#10625350#4112yes—
164C2×D188C22×C411yescharacteristic
165C2×C4×D47—21no—
166C2×C4×D47—21no—
167C2×C4×D47—21no—
168C2×Dic94—21no—
169C2×Dic94—21no—
170C2×Dic94C22×C411yescharacteristic
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47C22×C411yescharacteristic
178C2×C8×C47C22×C411yescharacteristic
179C2×C8×C47C22×C411yescharacteristic
180C2×C8×C47C22×C411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
183C2×C8×C47C2×D411yescharacteristic
184C2×C8×C47C2×D411yescharacteristic
185C2×C8×C47C2×Q812yes—
186C2×C8×C47#4112yes—
187C4⋊C4×C47—42no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47C22×C411yescharacteristic
193C42×C47C22×C411yescharacteristic
194C42×C47C2×D411yescharacteristic
195C42×C47C2×D411yescharacteristic
196C22⋊Dic47—21no—
197C22⋊Dic47—21no—
198C22⋊Dic47—21no—
199(C2×D47)⋊C4—21no—
200(C2×D47)⋊C4—21no—
201C4⋊Dic47—21no—
202C4⋊Dic47—21no—
203C4⋊Dic47C22×C411yescharacteristic
204C4⋊Dic47C22×C411yescharacteristic
205C4⋊Dic47C22×C411yescharacteristic
206C4⋊Dic47C22×C411yescharacteristic
207C4⋊Dic47C22×C411yescharacteristic
208C4⋊Dic47C22×C411yescharacteristic
209Dic47⋊C4—21no—
210Dic47⋊C4—21no—
211Dic47⋊C4—21no—
212Dic47⋊C4—21no—
213Dic47⋊C4—21no—
214Dic47⋊C4—21no—
215C4×Dic47—21no—
216C4×Dic47—21no—
217C4×Dic47—21no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220#10625329—21no—
221#10625329—21no—
222#10625329—21no—
223#10625329—21no—
224#10625329—21no—
225#10625329—21no—
226#10625329C2×Q812yes—
227#10625329#4112yes—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232#10625324—24no—
233#10625324—24no—
234C8×D47—24no—
235C8×D47—24no—
236C23×C47C2×#4111yescharacteristic
237C22×D47—21no—
238C2×C4×C47—22no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47C4×D411yescharacteristic
247C2×C4×C47C4×D411yescharacteristic
248C2×C4×C47C4×D411yescharacteristic
249C2×C4×C47C4×D411yescharacteristic
250C2×C4×C47C23×C411yescharacteristic
251C2×C4×C47C22×D411yescharacteristic
252C2×C4×C47C22×Q811yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47C2×#4111yescharacteristic
256C22⋊D47—22no—
257C22⋊D47—22no—
258C2×Dic47—21no—
259C2×Dic47—21no—
260C2×Dic47—21no—
261C2×Dic47—21no—
262C2×Dic47—21no—
263C2×Dic47—21no—
264C2×Dic47—21no—
265D188—21no—
266D188C4×Q812yes—
267C4×D47—22no—
268C4×D47—22no—
269C4×D47—81no—
270C4×D47—81no—
271Dic94—21no—
272Dic94—81no—
273Dic94—81no—
274Dic94C4×Q812yes—
275C8×C47—21no—
276C8×C47—21no—
277C8×C47—21no—
278C8×C47—21no—
279C8×C47—21no—
280C8×C47—21no—
281C8×C47C22⋊Q812yes—
282C8×C47C22⋊Q812yes—
283C47⋊C8—22no—
284C47⋊C8—22no—
285C47⋊C8—41no—
286C47⋊C8—41no—
287#21629—471nomaximal, Sylow
288C22×C47—21no—
289C22×C47—21no—
290C22×C47C2×C4×D411yescharacteristic
291C22×C47#52911yescharacteristic
292C22×C47#53311yescharacteristic
293C2×D47—22no—
294C2×D47—41no—
295C2×D47—41no—
296C4×C47—21no—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—21no—
300C4×C47—42no—
301C4×C47—81no—
302C4×C47C2×C4×Q811yescharacteristic
303C4×C47C4×#4111yescharacteristic
304C4×C47C2×C22⋊Q811yescharacteristic
305C4×C47#52511yescharacteristic
306Dic47—22no—
307Dic47—41no—
308Dic47—41no—
309Dic47—41no—
310Dic47—41no—
311Dic47—41no—
312Dic47—41no—
313#3076—471no—
314#2961—471no—
315#2875—471no—
316#1986—471no—
317#1950—471no—
318#1922—471no—
319#1922—471no—
320#1866—471no—
321#1866—471no—
322#1806—471no—
323#1773—471no—
324#1772—471no—
325#1771D4711yescharacteristic, complemented
326#1765—471no—
327#1764—471no—
328C2×C47—21no—
329C2×C47—21no—
330C2×C47C4×C22⋊Q811yescharacteristic
331C2×C47#295611yescharacteristic
332C2×C47#295711yescharacteristic
333D47—42no—
334C2×#131—471no—
335C2×#131—471no—
336#533—471no—
337C4×#41—471no—
338#479—471no—
339#479—471no—
340#478—471no—
341#478—471no—
342#477—471no—
343#476—471no—
344#475—471no—
345#474—471no—
346#446—941no—
347#446—941no—
348#446—941no—
349#446—941no—
350C2×#108—471no—
351C2×#108—471no—
352#427—471no—
353#427—471no—
354#424—471no—
355#424—471no—
356#423—471no—
357C2×C4⋊C8C2×D4711yescharacteristic
358C2×#104—471no—
359C2×#104—471no—
360#416—471no—
361#416—471no—
362#405—471no—
363#405—471no—
364#405—471no—
365#405—471no—
366#405—941no—
367#405—941no—
368C4×M16—471no—
369C4×M16—941no—
370C2×#97—941no—
371C2×#97C2×D4711yescharacteristic
372C2×#97C2×D4711yescharacteristic
373C2×C4×C8C2×D4711yescharacteristic
374C4×C4⋊C4C2×D4711yescharacteristic
375#341—471no—
376#341—471no—
377#339—471no—
378#339—471no—
379#339—471no—
380#339—471no—
381#339—471no—
382#339—471no—
383#336C2×D4711yescharacteristic
384#336C2×D4711yescharacteristic
385C47#2162911yescharacteristic, complemented, Sylow
386C2×#41—471no—
387#131—474no—
388#131—942no—
389#131—942no—
390#131—942no—
391C2×M16—471no—
392C2×M16—471no—
393C2×M16—471no—
394C2×M16—471no—
395C2×M16—941no—
396C2×M16—941no—
397C22×C8—941no—
398C22×C8—941no—
399C22×C8C22×D4711yescharacteristic
400C22×C8C22×D4711yescharacteristic
401C22×C8C22×D4711yescharacteristic
402C22×C8C22×D4711yescharacteristic
403C4⋊Q8—471no—
404C4⋊Q8—471no—
405#125—471no—
406#125—471no—
407C22⋊Q8—941no—
408C22⋊Q8—941no—
409C4×Q8—471no—
410C4×Q8—471no—
411C4×Q8—941no—
412C4×Q8—941no—
413C4×D4—471no—
414C4×D4—471no—
415C4×D4—941no—
416C4×D4—941no—
417#117—471no—
418#117—471no—
419#117—471no—
420#117—941no—
421C2×C4⋊C4—21no—
422C2×C42—941no—
423C2×C42C22×D4711yescharacteristic
424C2×C42C22×D4711yescharacteristic
425C2×C42C22×D4711yescharacteristic
426#108—942no—
427#108—942no—
428#107—471no—
429#107—471no—
430#107—471no—
431#107—471no—
432#106—471no—
433#106—471no—
434#106—471no—
435#106—471no—
436C4⋊C8—941no—
437C4⋊C8—941no—
438C4⋊C8—941no—
439C4⋊C8—941no—
440C4⋊C8—941no—
441C4⋊C8—941no—
442C4⋊C8C4×D4711yescharacteristic
443C4⋊C8C4×D4711yescharacteristic
444C4⋊C8C4×D4711yescharacteristic
445C4⋊C8C4×D4711yescharacteristic
446#104—942no—
447#104—942no—
448#103—471no—
449#103—471no—
450#103—471no—
451#103—471no—
452#102—471no—
453#102—471no—
454#102—471no—
455#102—471no—
456#97—22no—
457#97—941no—
458#97—941no—
459#97—941no—
460#97—941no—
461#97—941no—
462#97D18811yescharacteristic
463#97D18811yescharacteristic
464#97D18811yescharacteristic
465#97D18811yescharacteristic
466C4×C8—22no—
467C4×C8—941no—
468C4×C8—941no—
469C4×C8—941no—
470C4×C8—941no—
471C4×C8—941no—
472#95—21no—
473#41—472no—
474#41—472no—
475#41—941no—
476#41—941no—
477C2×Q8—471no—
478C2×Q8—941no—
479C2×Q8—941no—
480C2×D4—471no—
481C2×D4—941no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4#1062535011yescharacteristic
488C22×C4#1062535011yescharacteristic
489C22×C4C23×D4711yescharacteristic
490M16—472no—
491M16—472no—
492M16—944no—
493M16—941no—
494M16—941no—
495M16—944no—
496M16—941no—
497M16—941no—
498M16—941no—
499M16—941no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—944no—
507C2×C8—941no—
508C2×C8—941no—
509C2×C8—944no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8C2×C4×D4711yescharacteristic
513C2×C8C2×C4×D4711yescharacteristic
514C2×C8C2×C4×D4711yescharacteristic
515C2×C8C2×C4×D4711yescharacteristic
516C2×C8C2×D18811yescharacteristic
517C2×C8C2×D18811yescharacteristic
518C2×C8C2×D18811yescharacteristic
519C2×C8C2×D18811yescharacteristic
520C2×C8#1062535212yes—
521C2×C8Q8×D4712yes—
522C4⋊C4—42no—
523C4⋊C4—471no—
524C4⋊C4—471no—
525C4⋊C4—471no—
526C4⋊C4—471no—
527C4⋊C4—471no—
528C4⋊C4—471no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C4⋊C4—941no—
532C4⋊C4—941no—
533C4⋊C4—941no—
534C4⋊C4—941no—
535C4⋊C4—941no—
536C4⋊C4—941no—
537C22⋊C4—941no—
538C22⋊C4—941no—
539C22⋊C4—941no—
540C22⋊C4—941no—
541C22⋊C4—941no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—941no—
547C42—941no—
548C42—941no—
549C42—941no—
550C42—941no—
551C42C2×C4×D4711yescharacteristic
552C42C2×C4×D4711yescharacteristic
553C42C2×D18811yescharacteristic
554C42C2×D18811yescharacteristic
555C23—941no—
556C23C2×#1062535011yescharacteristic
557Q8—472no—
558Q8—941no—
559Q8—3761no—
560Q8—3761no—
561D4—472no—
562D4—942no—
563D4—942no—
564D4—941no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—941no—
574C2×C4—942no—
575C2×C4—942no—
576C2×C4—941no—
577C2×C4—941no—
578C2×C4—941no—
579C2×C4—941no—
580C2×C4—941no—
581C2×C4—941no—
582C2×C4—3761no—
583C2×C4—3761no—
584C2×C4C4×D18811yescharacteristic
585C2×C4C4×D18811yescharacteristic
586C2×C4C4×D18811yescharacteristic
587C2×C4C4×D18811yescharacteristic
588C2×C4C22×C4×D4711yescharacteristic
589C2×C4C22×D18811yescharacteristic
590C2×C4C2×Q8×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C2×C4C2×#1062535211yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—21no—
600C8—942no—
601C8—942no—
602C8—1881no—
603C8—1881no—
604C8#1309400412yes—
605C8#1309400412yes—
606C22—21no—
607C22—21no—
608C22—942no—
609C22—1881no—
610C22—1881no—
611C22C2×C4×D18811yescharacteristic
612C22#1568965511yescharacteristic
613C22#1568967711yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—81no—
620C4—942no—
621C4—1881no—
622C4—1881no—
623C4—1881no—
624C4—1881no—
625C4—1881no—
626C4—1881no—
627C4C4×Q8×D4711yescharacteristic
628C4C4×#1062535211yescharacteristic
629C4C2×#1309400411yescharacteristic
630C4#1568963511yescharacteristic
631C2—21no—
632C2—21no—
633C2—1882no—
634C2C4×#1309400411yescharacteristic
635C2#2025229911yescharacteristic
636C2#2025230611yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1771C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C23
cosocleC22×C4×C47C24
hypercenter#1771D47
hypocenterC47#21629
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #20252328C2semidirect
4. #20244331C2semidirect
5. #20244164C2semidirect
6. #20243988C2semidirect
7. #20243988C2semidirect
11. #20243272C2semidirect
12. #20243267C2semidirect
15. C47×#1771C2semidirect
20. #15689431C4semidirect
21. #15689431C4semidirect
22. #15689424C4semidirect
23. #15689424C4semidirect
24. #15689419C4semidirect
25. #15689414C4semidirect
26. #15689409C4semidirect
27. #15689404C4semidirect
71. #13094030Q8semidirect
325. #1771D47semidirect
385. C47#21629semidirect

Maximal subgroups

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

subgroupindex
#202531782
#202523282
#202518132
#202443312
#202441642
#202439882
#202436662
#202434092
#202432722
#202432672
#202432322
#202432252
C47×#17712
#2162947