Finite Group Databasebeta

← #26123779

Subgroups — #26123779

Order 12032.

854 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×#15689172C211yesmaximal, characteristic, complemented
2C2×#15689105C211yesmaximal, characteristic
3#20251832C211yesmaximal, characteristic
4C2×#15689089C211yesmaximal, characteristic
5#20243114C211yesmaximal, characteristic, complemented
6C2×#15688888C211yesmaximal, characteristic, complemented
7C2×C47×#341C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12#15689172—22no—
13#15689172—22no—
14C2×#13093960—22no—
15#15689105—22no—
16#15689105—22no—
17C2×#13093942C412yes—
18C2×#13093940C412yes—
19#15689091—22no—
20#15689089—22no—
21#15689089—22no—
22#15689089—22no—
23#15689086—22no—
24C2×(C2×D47)⋊C8—22no—
25#15688888—22no—
26#15688887—22no—
27C22×M16×C47C2211yescharacteristic
28C22×M16×C47C2211yescharacteristic
29C23×C8×C47C2211yescharacteristic
30C47×#341—22no—
31C2×#10625350—21no—
32C2×#10625350—21no—
33C2×#10625350—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C22×Dic94C2×C411yescharacteristic
44C22×D188C2×C411yescharacteristic
45C22×C22⋊D47Q812yes—
46C22×C4×D47D412yes—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329C2×C412yes—
63C2×#10625329D412yes—
64C2×#10625329D412yes—
65C22×C47⋊C8—21no—
66C22×C47⋊C8—21no—
67C22×C47⋊C8—21no—
68#13093960—28no—
69#13093942—24no—
70#13093940—24no—
71(C2×D47)⋊C8—28no—
72(C2×D47)⋊C8—28no—
73C23×C4×C47C2311yescharacteristic
74C2×M16×C47—21no—
75C2×M16×C47—21no—
76C2×M16×C47—21no—
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C2×M16×C47—21no—
82C2×M16×C47C2×C412yes—
83C2×M16×C47D412yes—
84C2×M16×C47D412yes—
85C2×M16×C47D412yes—
86C22×C8×C47—21no—
87C22×C8×C47—21no—
88C22×C8×C47—21no—
89C22×C8×C47—21no—
90C22×C8×C47—21no—
91C22×C8×C47—21no—
92C22×C8×C47—21no—
93C22×C8×C47—21no—
94C22×C8×C47D412yes—
95C24×C47C2×Q811yescharacteristic
96C23×D47C4⋊C412yes—
97C22×C4×C47C22×C411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47#4111yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C2×C22⋊D47—22no—
112C2×C22⋊D47—22no—
113C2×C22⋊D47—22no—
114C2×C22⋊D47—22no—
115C2×C22⋊D47—22no—
116C2×C22⋊D47—22no—
117C22×Dic47C4⋊C412yes—
118#10625350—41no—
119#10625350—41no—
120#10625350—41no—
121#10625350—41no—
122#10625350—41no—
123#10625350—41no—
124#10625350—41no—
125#10625350—41no—
126#10625350—41no—
127#10625350—41no—
128#10625350—41no—
129#10625350—41no—
130#10625350—41no—
131#10625350—41no—
132#10625350—41no—
133#10625350—41no—
134C2×D188—21no—
135C2×D188—21no—
136C2×D188—21no—
137C2×D188—21no—
138C2×D188—21no—
139C2×D188—21no—
140C2×C4×D47—22no—
141C2×C4×D47—22no—
142C2×C4×D47—22no—
143C2×C4×D47—22no—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×Dic94—21no—
147C2×Dic94—21no—
148C2×Dic94—21no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152M16×C47—22no—
153M16×C47—22no—
154M16×C47—22no—
155M16×C47—22no—
156M16×C47—22no—
157M16×C47—41no—
158M16×C47—41no—
159M16×C47C22⋊C414yes—
160C2×C8×C47—22no—
161C2×C8×C47—22no—
162C2×C8×C47—22no—
163C2×C8×C47—22no—
164C2×C8×C47—22no—
165C2×C8×C47—22no—
166C2×C8×C47—22no—
167C2×C8×C47—41no—
168C2×C8×C47—41no—
169C2×C8×C47—41no—
170C2×C8×C47—41no—
171C2×C8×C47—41no—
172C2×C8×C47—41no—
173#10625329—22no—
174#10625329—22no—
175#10625329—22no—
176#10625329—22no—
177#10625329—22no—
178#10625329—22no—
179#10625329—41no—
180#10625329—41no—
181#10625329—41no—
182#10625329—41no—
183#10625329—41no—
184#10625329—41no—
185C2×C47⋊C8—22no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—41no—
189C2×C47⋊C8—41no—
190C2×C47⋊C8—41no—
191C2×C47⋊C8—41no—
192C2×C47⋊C8—41no—
193C2×C47⋊C8—41no—
194C23×C47—42no—
195C23×C47C2×C4⋊C411yescharacteristic
196C23×C47C22⋊Q811yescharacteristic
197C23×C47C22⋊Q811yescharacteristic
198C23×C47C22⋊Q811yescharacteristic
199C23×C47C22⋊Q811yescharacteristic
200C23×C47C22⋊Q811yescharacteristic
201C23×C47C22⋊Q811yescharacteristic
202C22×D47—22no—
203C22×D47—22no—
204C22×D47—22no—
205C22×D47—44no—
206C2×C4×C47C2×C22⋊C411yescharacteristic
207C2×C4×C47#11711yescharacteristic
208C2×C4×C47C4×D411yescharacteristic
209C2×C4×C47C4×D411yescharacteristic
210C2×C4×C47C4×D411yescharacteristic
211C2×C4×C47C4×D411yescharacteristic
212C2×C4×C47#12011yescharacteristic
213C2×C4×C47#12011yescharacteristic
214C2×C4×C47#12011yescharacteristic
215C2×C4×C47#12111yescharacteristic
216C2×C4×C47#12111yescharacteristic
217C2×C4×C47#12111yescharacteristic
218C2×C4×C47#12111yescharacteristic
219C2×C4×C47#12111yescharacteristic
220C2×C4×C47#12111yescharacteristic
221C2×C4×C47#12111yescharacteristic
222C2×C4×C47#12111yescharacteristic
223C2×C4×C47#12311yescharacteristic
224C2×C4×C47#12311yescharacteristic
225C2×C4×C47#12311yescharacteristic
226C2×C4×C47#12311yescharacteristic
227C2×C4×C47#12311yescharacteristic
228C2×C4×C47#12411yescharacteristic
229C2×C4×C47#12411yescharacteristic
230C2×C4×C47#12411yescharacteristic
231C2×C4×C47#12611yescharacteristic
232C2×C4×C47#12611yescharacteristic
233C2×C4×C47#12711yescharacteristic
234C22⋊D47—42no—
235C22⋊D47—42no—
236C22⋊D47—42no—
237C22⋊D47—42no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241D188—41no—
242D188—41no—
243D188—41no—
244D188—41no—
245C4×D47—42no—
246C4×D47—42no—
247C4×D47—42no—
248C4×D47—42no—
249Dic94—41no—
250Dic94—41no—
251Dic94—41no—
252Dic94—41no—
253C8×C47—24no—
254C8×C47—42no—
255C8×C47—42no—
256C47⋊C8—42no—
257C47⋊C8—42no—
258C47⋊C8—42no—
259#11137—471nomaximal, Sylow
260C22×C47—22no—
261C22×C47—22no—
262C22×C47—22no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47#38011yescharacteristic
268C22×C47#38511yescharacteristic
269C22×C47#38511yescharacteristic
270C22×C47#39311yescharacteristic
271C22×C47#39611yescharacteristic
272C22×C47#39611yescharacteristic
273C22×C47#39911yescharacteristic
274C2×D47—44no—
275C2×D47—44no—
276C2×D47—42no—
277C2×D47—82no—
278C4×C47#38611yescharacteristic
279C4×C47#38811yescharacteristic
280C4×C47#38811yescharacteristic
281C4×C47#39011yescharacteristic
282C4×C47#39211yescharacteristic
283C4×C47#39411yescharacteristic
284C4×C47#39411yescharacteristic
285C4×C47#39711yescharacteristic
286Dic47—42no—
287C2×#430—471no—
288C2×#413—471no—
289#2879—471no—
290C2×#408—471no—
291#1738—471no—
292C2×#341—471no—
293C2×#341D4711yescharacteristic, complemented
294C2×C47—21no—
295C2×C47—21no—
296C2×C47—21no—
297C2×C47—21no—
298C2×C47—21no—
299C2×C47—21no—
300C2×C47#143911yescharacteristic
301C2×C47#185812yes—
302D47—82no—
303C22×#41—471no—
304C22×M16—471no—
305C22×M16—471no—
306C22×M16—471no—
307C22×M16C2×D4711yescharacteristic
308C22×M16C2×D4711yescharacteristic
309C23×C8C2×D4711yescharacteristic
310#430—942no—
311#430—942no—
312C2×#108—942no—
313#413—942no—
314#413—942no—
315C2×#101—472no—
316C2×#100—472no—
317#408—942no—
318#408—942no—
319#408—942no—
320#408—942no—
321#407—942no—
322C2×C22⋊C8—942no—
323#341—22no—
324#341—942no—
325#341—942no—
326C47#1113711yescharacteristic, complemented, Sylow
327C2×#41—941no—
328C2×#41—941no—
329C2×#41—941no—
330C2×#41—941no—
331C2×#41—941no—
332C2×#41—941no—
333C2×#41—941no—
334C2×#41—941no—
335C2×#41—941no—
336C2×#41—941no—
337C2×#41—941no—
338C2×#41—941no—
339C22×Q8—471no—
340C22×D4—472no—
341C22×D4—471no—
342C23×C4—472no—
343C23×C4C22×D4711yescharacteristic
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—472no—
353C2×M16—472no—
354C2×M16—472no—
355C2×M16—941no—
356C2×M16—941no—
357C2×M16—941no—
358C2×M16—941no—
359C2×M16—941no—
360C2×M16—941no—
361C2×M16—941no—
362C2×M16—941no—
363C2×M16—941no—
364C2×M16—941no—
365C2×M16—941no—
366C2×M16—941no—
367C2×M16—941no—
368C2×M16—941no—
369C2×M16—941no—
370C2×M16C4×D4712yes—
371C2×M16D18812yes—
372C2×M16D18812yes—
373C2×M16C22⋊D4712yes—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—941no—
383C22×C8—941no—
384C22×C8—941no—
385C22×C8D18812yes—
386#108—948no—
387#101—944no—
388#100—944no—
389C22⋊C8—948no—
390C22⋊C8—948no—
391C24—472no—
392C24Q8×D4711yescharacteristic
393#41—1881no—
394#41—1881no—
395#41—1881no—
396#41—1881no—
397#41—1881no—
398#41—1881no—
399#41—1881no—
400#41—1881no—
401#41—1881no—
402#41—1881no—
403#41—1881no—
404#41—1881no—
405#41—1881no—
406#41—1881no—
407#41—1881no—
408#41—1881no—
409C2×Q8—941no—
410C2×Q8—941no—
411C2×Q8—941no—
412C2×Q8—941no—
413C2×Q8—941no—
414C2×Q8—941no—
415C2×D4—942no—
416C2×D4—942no—
417C2×D4—942no—
418C2×D4—942no—
419C2×D4—942no—
420C2×D4—942no—
421C2×D4—941no—
422C2×D4—941no—
423C2×D4—941no—
424C2×D4—941no—
425C2×D4—941no—
426C2×D4—941no—
427C22×C4—472no—
428C22×C4—942no—
429C22×C4—942no—
430C22×C4—942no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4C2×C4×D4711yescharacteristic
435C22×C4C2×D18811yescharacteristic
436C22×C4C2×D18811yescharacteristic
437C22×C4C2×D18811yescharacteristic
438C22×C4#1062535011yescharacteristic
439C22×C4#1062535011yescharacteristic
440C22×C4D4×D4711yescharacteristic
441C22×C4D4×D4711yescharacteristic
442C22×C4D4×D4711yescharacteristic
443C22×C4#1062535211yescharacteristic
444C22×C4#1062535211yescharacteristic
445C22×C4#1062535211yescharacteristic
446C22×C4#1062535411yescharacteristic
447C22×C4C2×C22⋊D4711yescharacteristic
448M16—22no—
449M16—22no—
450M16—22no—
451M16—22no—
452M16—22no—
453M16—41no—
454M16—41no—
455M16—942no—
456M16—942no—
457M16—942no—
458M16—942no—
459M16—942no—
460M16—942no—
461M16—1881no—
462M16—1881no—
463M16—1881no—
464M16—1881no—
465M16—1881no—
466M16—1881no—
467M16(C2×D47)⋊C414yes—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—942no—
482C2×C8—942no—
483C2×C8—942no—
484C2×C8—1881no—
485C2×C8—1881no—
486C2×C8—1881no—
487C2×C8—1881no—
488C2×C8—1881no—
489C2×C8—1881no—
490C23—42no—
491C23—942no—
492C23—942no—
493C23—942no—
494C23—1884no—
495C23C4⋊C4×D4711yescharacteristic
496C23#1309400011yescharacteristic
497C23#1309400211yescharacteristic
498C23#1309400211yescharacteristic
499C23#1309400411yescharacteristic
500C23#1309400411yescharacteristic
501C23#1309400411yescharacteristic
502Q8—1881no—
503Q8—1881no—
504Q8—1881no—
505Q8—1881no—
506D4—1882no—
507D4—1882no—
508D4—1882no—
509D4—1882no—
510D4—1881no—
511D4—1881no—
512D4—1881no—
513D4—1881no—
514C2×C4—942no—
515C2×C4—942no—
516C2×C4—942no—
517C2×C4—1882no—
518C2×C4—1882no—
519C2×C4—1882no—
520C2×C4—1882no—
521C2×C4C2×(C2×D47)⋊C411yescharacteristic
522C2×C4#1309398211yescharacteristic
523C2×C4(C22⋊D47)⋊C411yescharacteristic
524C2×C4(C22⋊D47)⋊C411yescharacteristic
525C2×C4C4×D18811yescharacteristic
526C2×C4C4×D18811yescharacteristic
527C2×C4#1309399411yescharacteristic
528C2×C4#1309399411yescharacteristic
529C2×C4#1309399411yescharacteristic
530C2×C4#1309399511yescharacteristic
531C2×C4#1309399611yescharacteristic
532C2×C4#1309399611yescharacteristic
533C2×C4#1309399811yescharacteristic
534C2×C4#1309399811yescharacteristic
535C2×C4#1309399911yescharacteristic
536C2×C4#1309399911yescharacteristic
537C2×C4#1309399911yescharacteristic
538C2×C4#1309400611yescharacteristic
539C2×C4#1309400611yescharacteristic
540C2×C4#1309400811yescharacteristic
541C2×C4#1309400811yescharacteristic
542C2×C4#1309400811yescharacteristic
543C2×C4#1309401011yescharacteristic
544C2×C4#1309401011yescharacteristic
545C2×C4#1309401211yescharacteristic
546C2×C4#1309401911yescharacteristic
547C2×C4#1309401911yescharacteristic
548C2×C4#1309402111yescharacteristic
549C8—24no—
550C8—42no—
551C8—42no—
552C8—1882no—
553C8—1882no—
554C8—1882no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—3762no—
563C22—1884no—
564C22—1884no—
565C22—1882no—
566C22#1568898011yescharacteristic
567C22#1568899711yescharacteristic
568C22#1568899711yescharacteristic
569C22#1568903611yescharacteristic
570C22#1568904511yescharacteristic
571C22#1568904511yescharacteristic
572C22#1568906011yescharacteristic
573C4—1882no—
574C4#1568900011yescharacteristic
575C4#1568901511yescharacteristic
576C4#1568901511yescharacteristic
577C4#1568902511yescharacteristic
578C4#1568903311yescharacteristic
579C4#1568903911yescharacteristic
580C4#1568903911yescharacteristic
581C4#1568905011yescharacteristic
582C2—21no—
583C2—21no—
584C2—21no—
585C2—21no—
586C2—21no—
587C2—21no—
588C2—3762no—
589C2#2024163411yescharacteristic
590C2#2024360912yes—
subgroupG/H
centerC2×C4#13093994
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#341C2
socleC22×C47#385
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#341D47
hypocenterC47#11137
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
1. C2×#15689172C2semidirect
5. #20243114C2semidirect
6. C2×#15688888C2semidirect
7. C2×C47×#341C2semidirect
293. C2×#341D47semidirect
326. C47#11137semidirect

Maximal subgroups

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

subgroupindex
C2×#156891722
C2×#156891052
#202518322
C2×#156890892
#202431142
C2×#156888882
C2×C47×#3412
#1113747