Finite Group Databasebeta

← #26225744

Subgroups — #26225744

Order 12032.

966 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689678C211yesmaximal, characteristic
2#20252020C211yesmaximal, characteristic
3#20252019C211yesmaximal, characteristic
4#20244379C214yesmaximal, complemented
5#20244378C211yesmaximal, characteristic, complemented
6#20244377C211yesmaximal, characteristic, complemented
7#20244376C211yesmaximal, characteristic, complemented
8#20243470C214yesmaximal
9C47×#1997C211yesmaximal, characteristic, complemented
10#15689678—21no—
11#15689678—21no—
12#15689678—21no—
13#15689678—21no—
14#15689678—21no—
15#15689678—21no—
16#15689678—21no—
17#15689678—21no—
18C2×#13094024C2211yescharacteristic
19C2×#13094015C2212yes—
20C2×#13094004C412yes—
21C2×#13094000C412yes—
22C2×Q8×Dic47C412yes—
23C2×#13093989C412yes—
24C2×#13093982C2212yes—
25C2×C42×D47C2211yescharacteristic
26#15689179—21no—
27#15689179—21no—
28#15689178—21no—
29#15689178—21no—
30#15689175—21no—
31#15689175—21no—
32#15689174—21no—
33#15689174—21no—
34#15689147C2211yescharacteristic
35#15689146C2212yes—
36#15689086C2212yes—
37#15689086C2212yes—
38C4×#10625329C2211yescharacteristic
39M16×Dic47C2212yes—
40#15688892C2214yes—
41#15688891C2214yes—
42#15688891C2214yes—
43C2×C4⋊Q8×C47C2211yescharacteristic
44C47×#423C2211yescharacteristic
45C4×M16×C47C2211yescharacteristic
46C47×#343C2214yes—
47C22×Dic94C2×C412yes—
48C22×C4×D47C2×C411yescharacteristic
49C22×C4×D47C2×C411yescharacteristic
50C22×C4×D47C2311yescharacteristic
51C2×#10625329C2312yes—
52C2×#10625329C2312yes—
53#13094024—21no—
54#13094024—21no—
55#13094024—21no—
56#13094024—21no—
57#13094015—22no—
58#13094015—22no—
59#13094015—22no—
60#13094015—22no—
61#13094004—22no—
62#13094004—22no—
63#13094004—22no—
64#13094004—22no—
65#13094000—22no—
66#13094000—22no—
67#13094000—22no—
68#13094000—22no—
69Q8×Dic47—22no—
70Q8×Dic47—22no—
71Q8×Dic47—22no—
72Q8×Dic47—22no—
73#13093989—22no—
74#13093989—22no—
75#13093989—22no—
76#13093989—22no—
77#13093982—22no—
78#13093982—22no—
79#13093982—22no—
80#13093982—22no—
81C2×C4⋊Dic47C2×C412yes—
82C2×C4⋊Dic47C2×C414yes—
83C2×C4⋊Dic47C2312yes—
84C2×Dic47⋊C4C2×C414yes—
85C2×(C2×D47)⋊C4C2×C414yes—
86C2×C4×Dic47C2×C414yes—
87C2×C4×Dic47C2×C411yescharacteristic
88C2×C4×Dic47C2×C411yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90C42×D47D411yescharacteristic
91C42×D47D411yescharacteristic
92C42×D47D411yescharacteristic
93C42×D47D411yescharacteristic
94C42×D47D411yescharacteristic
95C42×D47D411yescharacteristic
96C42×D47D411yescharacteristic
97C42×D47D411yescharacteristic
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)—21no—
100Dic47⋊C8—22no—
101Dic47⋊C8—22no—
102(C2×D47)⋊C8—22no—
103(C2×D47)⋊C8—22no—
104(C2×D47)⋊C8—22no—
105(C2×D47)⋊C8—22no—
106#13093935—21no—
107#13093934—22no—
108C4×C47⋊C8—21no—
109C8×Dic47—22no—
110C22×Q8×C47C2×C412yes—
111C2×M16×C47C2312yes—
112C2×M16×C47C2312yes—
113C4⋊Q8×C47—21no—
114C4⋊Q8×C47—21no—
115C4⋊Q8×C47—21no—
116C4⋊Q8×C47—21no—
117C2×C4⋊C4×C47C2×C412yes—
118C2×C4⋊C4×C47C2312yes—
119C2×C42×C47C2311yescharacteristic
120C4⋊C8×C47—21no—
121C4⋊C8×C47—21no—
122#97×C47—21no—
123C4×C8×C47—21no—
124C23×D47C22×C411yescharacteristic
125C2×Q8×C47—22no—
126C2×Q8×C47—22no—
127C2×Q8×C47—44no—
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C22×C414yes—
131C22×C4×C47C2411yescharacteristic
132C22×Dic47C22×C411yescharacteristic
133C22×Dic47C22×C414yes—
134C22×Dic47C22×C411yescharacteristic
135C22×Dic47C22×C411yescharacteristic
136C2×C4×D47—22no—
137C2×C4×D47—22no—
138C2×C4×D47—42no—
139C2×C4×D47—42no—
140C2×C4×D47C22⋊C411yescharacteristic
141C2×C4×D47C22⋊C411yescharacteristic
142C2×C4×D47C22⋊C411yescharacteristic
143C2×C4×D47C22⋊C411yescharacteristic
144C2×C4×D47C22⋊C411yescharacteristic
145C2×C4×D47C22⋊C411yescharacteristic
146C2×C4×D47C22⋊C411yescharacteristic
147C2×C4×D47C22⋊C411yescharacteristic
148C2×C4×D47C2×D411yescharacteristic
149C2×C4×D47C2×D411yescharacteristic
150C2×C4×D47C2×D411yescharacteristic
151C2×C4×D47C2×D411yescharacteristic
152C2×Dic94—22no—
153C2×Dic94—22no—
154C2×Dic94—44no—
155M16×C47—24no—
156M16×C47—22no—
157M16×C47—22no—
158C2×C8×C47—22no—
159C2×C8×C47—22no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—22no—
164C42×C47C2×D411yescharacteristic
165C42×C47C2×D411yescharacteristic
166C42×C47C2×D411yescharacteristic
167C42×C47C2×D411yescharacteristic
168(C2×D47)⋊C4—24no—
169(C2×D47)⋊C4—24no—
170C4⋊Dic47—22no—
171C4⋊Dic47—22no—
172C4⋊Dic47—22no—
173C4⋊Dic47—22no—
174C4⋊Dic47—24no—
175C4⋊Dic47—24no—
176Dic47⋊C4—24no—
177Dic47⋊C4—24no—
178C4×Dic47—24no—
179C4×Dic47—24no—
180C4×Dic47C22⋊C411yescharacteristic
181C4×Dic47C22⋊C411yescharacteristic
182C4×Dic47C22⋊C411yescharacteristic
183C4×Dic47C22⋊C411yescharacteristic
184C4×Dic47C22⋊C411yescharacteristic
185C4×Dic47C22⋊C411yescharacteristic
186C4×Dic47C22⋊C411yescharacteristic
187C4×Dic47C22⋊C411yescharacteristic
188C4×Dic47C2×D411yescharacteristic
189C4×Dic47C2×D411yescharacteristic
190C4×Dic47C2×D411yescharacteristic
191C4×Dic47C2×D411yescharacteristic
192#10625329—22no—
193#10625329—24no—
194#10625329—22no—
195C2×C47⋊C8—22no—
196C2×C47⋊C8—22no—
197C23×C47C23×C411yescharacteristic
198C22×D47—22no—
199C22×D47—41no—
200C22×D47—41no—
201C22×D47C2×C22⋊C411yescharacteristic
202C22×D47C2×C22⋊C411yescharacteristic
203Q8×C47—44no—
204Q8×C47—44no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—24no—
208C2×C4×C47—44no—
209C2×C4×C47C2×C22⋊C411yescharacteristic
210C2×C4×C47C2×C22⋊C411yescharacteristic
211C2×C4×C47C2×C22⋊C411yescharacteristic
212C2×C4×C47C2×C22⋊C411yescharacteristic
213C2×C4×C47C22×D411yescharacteristic
214C2×C4×C47C22×D411yescharacteristic
215C2×C4×C472−1+412yes—
216C2×C4×C472−1+412yes—
217C2×Dic47—22no—
218C2×Dic47—24no—
219C2×Dic47—41no—
220C2×Dic47—41no—
221C2×Dic47—44no—
222C2×Dic47C2×C22⋊C411yescharacteristic
223C2×Dic47C2×C22⋊C411yescharacteristic
224C2×Dic47C2×C22⋊C411yescharacteristic
225C2×Dic47C2×C22⋊C411yescharacteristic
226C2×Dic47C2×C22⋊C411yescharacteristic
227C2×Dic47C2×C22⋊C411yescharacteristic
228C4×D47—21no—
229C4×D47—21no—
230C4×D47—22no—
231C4×D47—22no—
232C4×D47—21no—
233C4×D47—21no—
234C4×D47—22no—
235C4×D47—22no—
236C4×D47—22no—
237C4×D47—22no—
238C4×D47—41no—
239C4×D47—41no—
240C4×D47—41no—
241C4×D47—41no—
242Dic94—44no—
243Dic94—44no—
244C8×C47—42no—
245C8×C47—42no—
246C47⋊C8—42no—
247C47⋊C8—42no—
248#21831—471nomaximal, Sylow
249C22×C47—21no—
250C22×C47—21no—
251C22×C47C22×C22⋊C411yescharacteristic
252C22×C47#51912yes—
253C2×D47—21no—
254C2×D47—21no—
255C2×D47—21no—
256C2×D47—21no—
257C2×D47—21no—
258C2×D47—21no—
259C2×D47—44no—
260C4×C47—21no—
261C4×C47—21no—
262C4×C47—44no—
263C4×C47#41312yes—
264C4×C47#41312yes—
265C4×C47#53611yescharacteristic
266C4×C47#53612yes—
267C4×C47#53611yescharacteristic
268Dic47—21no—
269Dic47—21no—
270Dic47—21no—
271Dic47—21no—
272Dic47—21no—
273Dic47—21no—
274Dic47—44no—
275C2×#533—471no—
276#2920—471no—
277#2920—471no—
278#1998—474no—
279#1997—471no—
280#1997—471no—
281#1997—471no—
282#1997D4711yescharacteristic, complemented
283#1822—474no—
284C2×C47—22no—
285C2×C47#231011yescharacteristic
286C2×C47C2×#41311yescharacteristic
287C2×C47C2×#41311yescharacteristic
288D47—41no—
289D47—41no—
290#533—941no—
291#533—941no—
292#533—941no—
293#533—941no—
294#533—941no—
295#533—941no—
296#533—941no—
297#533—941no—
298C2×C4⋊Q8—471no—
299C2×C4⋊Q8C2×D4711yescharacteristic
300C2×#125—472no—
301C2×C22⋊Q8—472no—
302C2×C22⋊Q8—472no—
303C2×C4×Q8—472no—
304C2×C4×Q8—472no—
305C2×#117—472no—
306C22×C42—471no—
307#432—941no—
308#432—941no—
309#432—941no—
310#432—941no—
311#431—941no—
312#431—941no—
313#431—941no—
314#431—941no—
315#423—472no—
316#423—471no—
317#423C2×D4711yescharacteristic
318#407—472no—
319#407—472no—
320C4×M16—472no—
321C4×M16—471no—
322C4×M16C2×D4711yescharacteristic
323#343—474no—
324#343—474no—
325#343—474no—
326#343C2×D4714yes—
327C47#2183111yescharacteristic, complemented, Sylow
328C22×Q8—472no—
329C22×Q8C4×D4712yes—
330C23×C4—471no—
331C23×C4—471no—
332C23×C4—471no—
333C2×M16—472no—
334C2×M16—472no—
335C2×M16C22×D4712yes—
336C2×M16C22×D4712yes—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—941no—
342C4⋊Q8—941no—
343C4⋊Q8—941no—
344C4⋊Q8—941no—
345#125—942no—
346#125—942no—
347#125—942no—
348#125—942no—
349C22⋊Q8—942no—
350C22⋊Q8—942no—
351C22⋊Q8—942no—
352C22⋊Q8—942no—
353C22⋊Q8—942no—
354C22⋊Q8—942no—
355C22⋊Q8—942no—
356C22⋊Q8—942no—
357C4×Q8—942no—
358C4×Q8—942no—
359C4×Q8—942no—
360C4×Q8—942no—
361C4×Q8—942no—
362C4×Q8—942no—
363C4×Q8—942no—
364C4×Q8—942no—
365#117—942no—
366#117—942no—
367#117—942no—
368#117—942no—
369C2×C4⋊C4—474no—
370C2×C4⋊C4—474no—
371C2×C4⋊C4—472no—
372C2×C4⋊C4—472no—
373C2×C4⋊C4C4×D4712yes—
374C2×C4⋊C4C22×D4712yes—
375C2×C22⋊C4—474no—
376C2×C42—471no—
377C2×C42—471no—
378C2×C42—471no—
379C2×C42—471no—
380C2×C42—471no—
381C2×C42—471no—
382C2×C42—471no—
383C2×C42—471no—
384C2×C42—471no—
385C2×C42—471no—
386C2×C42—471no—
387C2×C42—474no—
388C2×C42C22×D4711yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—942no—
392C4⋊C8—942no—
393C4⋊C8—941no—
394C4⋊C8—941no—
395C22⋊C8—942no—
396C22⋊C8—942no—
397C22⋊C8—942no—
398C22⋊C8—942no—
399#97—21no—
400#97—942no—
401#97—941no—
402C4×C8—21no—
403C4×C8—942no—
404C4×C8—941no—
405C24—471no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—44no—
409C2×Q8—942no—
410C2×Q8—942no—
411C2×Q8—1884no—
412C22×C4—471no—
413C22×C4—471no—
414C22×C4—471no—
415C22×C4—471no—
416C22×C4—471no—
417C22×C4—471no—
418C22×C4—471no—
419C22×C4—471no—
420C22×C4—471no—
421C22×C4—471no—
422C22×C4—471no—
423C22×C4—471no—
424C22×C4—471no—
425C22×C4—471no—
426C22×C4—471no—
427C22×C4—474no—
428C22×C4—942no—
429C22×C4—942no—
430C22×C4—1882no—
431C22×C4—1882no—
432C22×C4C2×C4×D4711yescharacteristic
433C22×C4C2×C4×D4711yescharacteristic
434C22×C4C2×C4×D4714yes—
435C22×C4C23×D4711yescharacteristic
436M16—24no—
437M16—22no—
438M16—22no—
439M16—942no—
440M16—942no—
441M16—944no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—942no—
445C2×C8—942no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—944no—
451C4⋊C4—944no—
452C4⋊C4—944no—
453C4⋊C4—944no—
454C4⋊C4—942no—
455C4⋊C4—942no—
456C4⋊C4—942no—
457C4⋊C4—942no—
458C22⋊C4—944no—
459C22⋊C4—944no—
460C42—471no—
461C42—471no—
462C42—471no—
463C42—471no—
464C42—471no—
465C42—471no—
466C42—471no—
467C42—471no—
468C42—471no—
469C42—471no—
470C42—471no—
471C42—471no—
472C42—944no—
473C42—944no—
474C42D4×D4711yescharacteristic
475C42D4×D4711yescharacteristic
476C42D4×D4711yescharacteristic
477C42D4×D4711yescharacteristic
478C23—471no—
479C23—471no—
480C23—942no—
481C23—1881no—
482C23—1881no—
483C23C22×C4×D4711yescharacteristic
484Q8—44no—
485Q8—44no—
486Q8—1884no—
487Q8—1884no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—44no—
492C2×C4—471no—
493C2×C4—471no—
494C2×C4—471no—
495C2×C4—471no—
496C2×C4—471no—
497C2×C4—471no—
498C2×C4—942no—
499C2×C4—942no—
500C2×C4—942no—
501C2×C4—942no—
502C2×C4—942no—
503C2×C4—941no—
504C2×C4—941no—
505C2×C4—942no—
506C2×C4—942no—
507C2×C4—941no—
508C2×C4—941no—
509C2×C4—944no—
510C2×C4—1881no—
511C2×C4—1881no—
512C2×C4—1881no—
513C2×C4—1881no—
514C2×C4—1881no—
515C2×C4—1881no—
516C2×C4—1884no—
517C2×C4C22⋊C4×D4711yescharacteristic
518C2×C4C22⋊C4×D4711yescharacteristic
519C2×C4C22⋊C4×D4711yescharacteristic
520C2×C4C22⋊C4×D4711yescharacteristic
521C2×C4C2×D4×D4711yescharacteristic
522C2×C4C2×D4×D4711yescharacteristic
523C2×C4#1309407112yes—
524C2×C4#1309407212yes—
525C8—42no—
526C8—42no—
527C8—1882no—
528C8—1882no—
529C22—21no—
530C22—21no—
531C22—941no—
532C22—941no—
533C22—941no—
534C22—941no—
535C22—941no—
536C22—941no—
537C22—1884no—
538C22C2×C22⋊C4×D4711yescharacteristic
539C22#1568959912yes—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—941no—
544C4—941no—
545C4—941no—
546C4—941no—
547C4—941no—
548C4—941no—
549C4—1884no—
550C4#1568910412yes—
551C4#1568910612yes—
552C4#1568969311yescharacteristic
553C4#1568969612yes—
554C4#1568969811yescharacteristic
555C2—22no—
556C2—1881no—
557C2—1881no—
558C2#2024597111yescharacteristic
559C2C2×#1568910411yescharacteristic
560C2C2×#1568910611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1997C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1997D47
hypocenterC47#21831
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
4. #20244379C2semidirect
5. #20244378C2semidirect
6. #20244377C2semidirect
7. #20244376C2semidirect
9. C47×#1997C2semidirect
282. #1997D47semidirect
327. C47#21831semidirect

Maximal subgroups

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

subgroupindex
C2×#156896782
#202520202
#202520192
#202443792
#202443782
#202443772
#202443762
#202434702
C47×#19972
#2183147