Finite Group Databasebeta

← #11858081

Subgroups — #11858081

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C211yesmaximal, characteristic
2C2×C3×#901C211yesmaximal, characteristic, complemented
3#10594992C211yesmaximal, characteristic, complemented
4C2×#63643C211yesmaximal, characteristic, complemented
5C3×#5113C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591088C211yesmaximal, characteristic, complemented
8#10590954C212yesmaximal, complemented
9#10590948C212yesmaximal, complemented
10#10590670C212yesmaximal, complemented
11D3×#816C212yesmaximal, complemented
12#83806—31nomaximal
13#78832—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C2×#3805—22no—
18#64298—24no—
19#64298C418yescomplemented
20C2×#3795—21no—
21C2×#3795C2212yes—
22C2×D3×Dic6—21no—
23C2×D3×Dic6C2212yes—
24C22×C32×C8C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C3×#901—24no—
29C2×C3×ΓL(1,𝔽25)C2212yes—
30C2×C3×D3×C8C2212yes—
31#67⋊Dic3—22no—
32Dic3×D12—21no—
33D3×C4⋊Dic3C2212yes—
34Dic3×Dic6—21no—
35#63841C2212yes—
36#63643C2212yes—
37#63643C2212yes—
38C3×#821C2211yescharacteristic
39C3×#821C2211yescharacteristic
40C3×#816C2211yescharacteristic
41C3×#816C2211yescharacteristic
42#63567C2212yes—
43#63567C2212yes—
44#63566C2212yes—
45#63563C2212yes—
46C2×#1010—31no—
47C2×#1010—31no—
48C2×C3×#131—31no—
49#5827—31no—
50C2×#901D311yescharacteristic, complemented
51#5523—31no—
52C3×#416—31no—
53#5232—31no—
54#5133—31no—
55#5133—32no—
56#5120—31no—
57#5120—32no—
58#5113—32no—
59#5113D311yescharacteristic, complemented
60C2×#816—31no—
61C2×#816—31no—
62C2×#816—32no—
63C2×#816—61no—
64#5004—31no—
65#4802—32no—
66D3×#103—32no—
67#4772—32no—
68#4771—32no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C22×C3⋊Dic3—21no—
72C2×#634—21no—
73C2×#634—22no—
74C2×#634C2×C414yescomplemented
75C2×#634C2312yes—
76C2×C3×#67—21no—
77C2×C3×#67D412yes—
78C3×#235—22no—
79C3×#235C2×C414yes—
80C3×#235C2×C414yescomplemented
81C3×#235D414yes—
82C2×C3×D12D411yescharacteristic
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3C2312yes—
86C2×C3×Dic6D411yescharacteristic
87C2×C3×Dic6C2311yescharacteristic
88C2×#627—22no—
89C2×#625—22no—
90#3805—216no—
91C2×D3×Dic3—22no—
92C2×D3×Dic3—22no—
93C2×D3×Dic3—22no—
94#3795—28no—
95#3795—24no—
96#3795C2×C418yescomplemented
97D3×Dic6—24no—
98D3×Dic6—28no—
99D3×Dic6C2×C418yescomplemented
100C2×C32×C8—22no—
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)C2312yes—
105C3×#217—21no—
106C3×C4⋊Dic3C2311yescharacteristic
107C3×C4⋊Dic3C2311yescharacteristic
108C3×C4×Dic3—21no—
109C3×#208—22no—
110C2×C3×C3⋊C8C2312yes—
111C3×ΓL(1,𝔽25)—24no—
112C3×D3×C8—24no—
113Dic3⋊Dic3—22no—
114(C2×D3)⋊Dic3—22no—
115Dic32—22no—
116#2898—91noSylow
117C2×C3×#41—31no—
118C2×C3×#41—31no—
119#1010—38no—
120#1010—38no—
121#1010—64no—
122#1010—64no—
123C2×D3×Q8—32no—
124C2×D3×Q8—61no—
125C2×#237—32no—
126C2×#237—61no—
127C2×#237—62no—
128C2×#237—62no—
129C2×#235—32no—
130C2×#235—61no—
131C2×#235C2×D311yescharacteristic
132C2×#235C2×D311yescharacteristic
133C22×Dic6—31no—
134C22×Dic6—31no—
135C22×Dic6—32no—
136C22×Dic6—61no—
137C22×Dic6—61no—
138C3×#131—64no—
139C2×C3×M16—31no—
140C2×C3×M16—32no—
141C22×C3×C8—21no—
142C22×C3×C8—32no—
143C22×C3×C8C2×D311yescharacteristic
144C22×C3×C8C2×D311yescharacteristic
145C3×#117—31no—
146Q8×Dic3—61no—
147D4×Dic3—61no—
148D4×Dic3—62no—
149#926—32no—
150#926C2×D311yescharacteristic
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—61no—
155C2×#208C2×D311yescharacteristic
156#901—24no—
157C2×ΓL(1,𝔽25)C2×D312yes—
158C2×D3×C8C2×D312yes—
159#892—32no—
160D3×C4⋊C4—32no—
161#67⋊C4—62no—
162C4×D12—61no—
163C4×Dic6—61no—
164C3×#103—31no—
165C3×#103—31no—
166C3×#102—31no—
167C3×#102—31no—
168#835—32no—
169#832—32no—
170#821—32no—
171#821C2×D311yescharacteristic
172#821C2×D311yescharacteristic
173#816—32no—
174#816—32no—
175#816—32no—
176#816—32no—
177#816—32no—
178#816—32no—
179#816—32no—
180#816—62no—
181#816—62no—
182#816C2×D311yescharacteristic
183#816C2×D311yescharacteristic
184#810—32no—
185#810—32no—
186C23×C32C2×D411yescharacteristic
187C22×C3×D3—21no—
188C22×C3×D3C2×D412yes—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D412yes—
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—24no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—81no—
197#634—24no—
198#634—22no—
199#634C22×C414yes—
200C3×#67—24no—
201C3×#67C22⋊C418yes—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3C2×D412yes—
206C3×D12—21no—
207C3×D12C22⋊C414yes—
208C3×D12C22×C412yes—
209C3×C4×D3—24no—
210C3×C4×D3C22×C414yes—
211C3×C4×D3C2×D414yes—
212C3×Dic6—21no—
213C3×Dic6C22⋊C414yes—
214C3×Dic6C22×C412yes—
215#627—28no—
216#625—28no—
217D3×Dic3—28no—
218D3×Dic3—28no—
219D3×Dic3—82no—
220C32×C8—21no—
221C32×C8—21no—
222C3×C3⋊C8—22no—
223C2×2−1+4—91no—
224C2×#131—31no—
225#520—91no—
226#419—92no—
227#419—91no—
228#417—92no—
229#417—91no—
230#416—31no—
231#416—92no—
232C2×#103—92no—
233C2×#103—91no—
234C3×#41—34no—
235C3×#41—34no—
236C3×#41—34no—
237C3×#41—62no—
238C2×C3×Q8—31no—
239C2×C3×Q8—31no—
240C2×C3×D4—32no—
241C2×C3×D4—31no—
242C2×C3×D4—31no—
243C2×C3×D4—61no—
244C22×C3×C4—21no—
245C22×C3×C4—32no—
246C22×C3×C4—61no—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—21no—
250C2×#67—62no—
251C2×#67—62no—
252C2×#67D1212yes—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3—61no—
256C22×Dic3—61no—
257C22×Dic3—62no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—121no—
261C22×Dic3—121no—
262D3×Q8—38no—
263D3×Q8—68no—
264D3×Q8—64no—
265#237—38no—
266#237—68no—
267#237—616no—
268#237—616no—
269#237—64no—
270#235—22no—
271#235—38no—
272#235—64no—
273#235—68no—
274#235C4×D314yes—
275#235C4×D314yescomplemented
276#235#6714yes—
277C2×D12D1211yescharacteristic
278C2×D12C22×D311yescharacteristic
279C2×C4×D3—21no—
280C2×C4×D3—62no—
281C2×C4×D3—62no—
282C2×C4×D3—62no—
283C2×C4×D3C22×D312yes—
284C2×Dic6—34no—
285C2×Dic6—34no—
286C2×Dic6—32no—
287C2×Dic6—32no—
288C2×Dic6—38no—
289C2×Dic6—62no—
290C2×Dic6—64no—
291C2×Dic6—64no—
292C2×Dic6—62no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—62no—
296C2×Dic6—62no—
297C2×Dic6—62no—
298C2×Dic6—68no—
299C2×Dic6—121no—
300C2×Dic6—122no—
301C2×Dic6D1211yescharacteristic
302C2×Dic6C22×D311yescharacteristic
303C3×M16—64no—
304C3×M16—62no—
305C2×C3×C8—22no—
306C2×C3×C8—22no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—32no—
310C2×C3×C8—42no—
311C2×C3×C8—64no—
312C2×C3×C8C22×D311yescharacteristic
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C22⋊C4—61no—
319C3×C42—61no—
320#217—21no—
321#217—62no—
322(C2×D3)⋊C4—62no—
323C4⋊Dic3—32no—
324C4⋊Dic3—32no—
325C4⋊Dic3—62no—
326C4⋊Dic3—62no—
327C4⋊Dic3—61no—
328C4⋊Dic3—61no—
329C4⋊Dic3—121no—
330C4⋊Dic3C22×D311yescharacteristic
331C4⋊Dic3C22×D311yescharacteristic
332Dic3⋊C4—62no—
333C4×Dic3—21no—
334C4×Dic3—62no—
335C4×Dic3—62no—
336#208—22no—
337C2×C3⋊C8C22×D312yes—
338ΓL(1,𝔽25)—24no—
339D3×C8—24no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32C2×C22⋊C412yes—
343C22×C32C22×D411yescharacteristic
344C2×C3×D3—22no—
345C2×C3×D3—22no—
346C2×C3×D3—22no—
347C2×C3×D3—41no—
348C2×C3×D3—41no—
349C2×C3×D3C2×C22⋊C414yes—
350C32×C4C2×C22⋊C412yes—
351C32×C4C23×C411yescharacteristic
352C32×C4C22×D411yescharacteristic
353C3⋊Dic3—24no—
354C3⋊Dic3—42no—
355C3×Dic3—22no—
356C3×Dic3—41no—
357C3×Dic3—41no—
358C3×Dic3C2×C22⋊C414yes—
3592−1+4—98no—
3602−1+4—184no—
361C2×#41—31no—
362C2×#41—31no—
363C2×#41—92no—
364C2×#41—181no—
365C2×#41—182no—
366C22×Q8—92no—
367C22×Q8—91no—
368C22×Q8—181no—
369#131—64no—
370C2×M16—31no—
371C2×M16—32no—
372C22×C8—32no—
373C22×C8D3211yescharacteristic
374C4×Q8—181no—
375C4×D4—181no—
376C4×D4—182no—
377#117—31no—
378#117—92no—
379C2×C4⋊C4—92no—
380C2×C4⋊C4—91no—
381#103—31no—
382#103—31no—
383#103—92no—
384#103—92no—
385#103—92no—
386#103—92no—
387#103—92no—
388#102—31no—
389#102—31no—
390#102—92no—
391C23×C3—21no—
392C23×C3—32no—
393C23×C3—61no—
394C23×C3C2×D1211yescharacteristic
395C23×C3D3×D411yescharacteristic
396C22×D3—21no—
397C22×D3C2×D1212yes—
398C3×Q8—34no—
399C3×Q8—32no—
400C3×Q8—61no—
401C3×D4—38no—
402C3×D4—34no—
403C3×D4—32no—
404C3×D4—64no—
405C3×D4—61no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—32no—
411C2×C3×C4—34no—
412C2×C3×C4—34no—
413C2×C3×C4—61no—
414C2×C3×C4—64no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4C2×C4×D312yes—
418C2×C3×C4C2×C4×D312yes—
419C2×C3×C4C2×D1211yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D412yes—
422C2×C3×C4C2×#6712yes—
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425#67—24no—
426#67—68no—
427#67—68no—
428#67(C2×D3)⋊C418yes—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3—68no—
433C2×Dic3—64no—
434C2×Dic3—64no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—68no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3—122no—
441C2×Dic3—124no—
442C2×Dic3—122no—
443C2×Dic3—242no—
444C2×Dic3—241no—
445C2×Dic3—241no—
446C2×Dic3—242no—
447C2×Dic3C2×D1212yes—
448D12—21no—
449D12(C2×D3)⋊C414yes—
450D12C2×C4×D312yes—
451C4×D3—24no—
452C4×D3—68no—
453C4×D3—68no—
454C4×D3—242no—
455C4×D3C2×C4×D314yes—
456C4×D3C2×#6714yes—
457Dic6—21no—
458Dic6—34no—
459Dic6—34no—
460Dic6—64no—
461Dic6—68no—
462Dic6—64no—
463Dic6—64no—
464Dic6—62no—
465Dic6—62no—
466Dic6—68no—
467Dic6—122no—
468Dic6—124no—
469Dic6(C2×D3)⋊C414yes—
470Dic6C2×C4×D312yes—
471C3×C8—21no—
472C3×C8—21no—
473C3×C8—21no—
474C3×C8—21no—
475C3×C8—41no—
476C3×C8—41no—
477C3×C8—62no—
478C3⋊C8—22no—
479C2×C32—22no—
480C2×C32C22×C22⋊C411yescharacteristic
481C2×C32#57711yescharacteristic
482C2×C32#57811yescharacteristic
483C3×D3—24no—
484C3×D3—42no—
485#41—34no—
486#41—34no—
487#41—34no—
488#41—62no—
489#41—98no—
490#41—184no—
491#41—188no—
492#41—1816no—
493C2×Q8—31no—
494C2×Q8—31no—
495C2×Q8—98no—
496C2×Q8—92no—
497C2×Q8—94no—
498C2×Q8—182no—
499C2×Q8—184no—
500C2×Q8—188no—
501C2×Q8—181no—
502C2×Q8—182no—
503C2×D4—32no—
504C2×D4—31no—
505C2×D4—31no—
506C2×D4—61no—
507C2×D4—182no—
508C22×C4—32no—
509C22×C4—61no—
510C22×C4—182no—
511C22×C4—182no—
512C22×C4—182no—
513C22×C4—181no—
514C22×C4—181no—
515C22×C4C2×D3211yescharacteristic
516M16—64no—
517M16—62no—
518C2×C8—22no—
519C2×C8—32no—
520C2×C8—64no—
521C2×C8C2×D3211yescharacteristic
522C2×C8C2×D3211yescharacteristic
523C4⋊C4—31no—
524C4⋊C4—31no—
525C4⋊C4—92no—
526C4⋊C4—182no—
527C4⋊C4—181no—
528C22⋊C4—61no—
529C22⋊C4—182no—
530C42—61no—
531C42—182no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—22no—
540C22×C3—34no—
541C22×C3—62no—
542C22×C3—62no—
543C22×C3—62no—
544C22×C3—121no—
545C22×C3—121no—
546C22×C3D3×C22⋊C412yes—
547C22×C3C2×(C2×D3)⋊C412yes—
548C22×C3C22×D1211yescharacteristic
549C22×C3C2×D3×D411yescharacteristic
550C2×D3—22no—
551C2×D3—22no—
552C2×D3—22no—
553C2×D3—41no—
554C2×D3—41no—
555C2×D3C2×(C2×D3)⋊C414yes—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—22no—
559C3×C4—34no—
560C3×C4—62no—
561C3×C4—121no—
562C3×C4—121no—
563C3×C4D3×C22⋊C412yes—
564C3×C4C2×(C2×D3)⋊C412yes—
565C3×C4C22×C4×D311yescharacteristic
566C3×C4C22×C4×D311yescharacteristic
567C3×C4C2×D3×D411yescharacteristic
568C3×C4C22×#6711yescharacteristic
569Dic3—22no—
570Dic3—41no—
571Dic3—41no—
572Dic3—64no—
573Dic3—64no—
574Dic3—124no—
575Dic3—122no—
576Dic3—122no—
577Dic3—242no—
578Dic3C2×(C2×D3)⋊C414yes—
579C32#289811yescharacteristic, complemented, Sylow
580C23—32no—
581C23—61no—
582C23D3×D1211yescharacteristic
583Q8—34no—
584Q8—32no—
585Q8—61no—
586Q8—94no—
587Q8—188no—
588Q8—182no—
589Q8—184no—
590D4—38no—
591D4—32no—
592D4—34no—
593D4—64no—
594D4—61no—
595D4—188no—
596C2×C4—32no—
597C2×C4—34no—
598C2×C4—34no—
599C2×C4—61no—
600C2×C4—64no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—188no—
604C2×C4—188no—
605C2×C4—182no—
606C2×C4—184no—
607C2×C4—182no—
608C2×C4—722no—
609C2×C4—721no—
610C2×C4C4×D3212yes—
611C2×C4D3×D1211yescharacteristic
612C2×C4D3×#6712yes—
613C2×C4C22×D3211yescharacteristic
614C8—21no—
615C8—21no—
616C8—62no—
617C2×C3—24no—
618C2×C3—22no—
619C2×C3—22no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—64no—
624C2×C3—122no—
625C2×C3C2×D3×C22⋊C411yescharacteristic
626C2×C3#575111yescharacteristic
627C2×C3#575311yescharacteristic
628C2×C3#577011yescharacteristic
629C2×C3#577111yescharacteristic
630C2×C3C22×(C2×D3)⋊C411yescharacteristic
631D3—24no—
632D3—42no—
633C22—21no—
634C22—21no—
635C22—34no—
636C22—62no—
637C22—62no—
638C22—62no—
639C22—121no—
640C22—121no—
641C22D3×(C2×D3)⋊C412yes—
642C22C2×D3×D1211yescharacteristic
643C4—34no—
644C4—62no—
645C4—121no—
646C4—121no—
647C4—184no—
648C4—362no—
649C4D3×(C2×D3)⋊C412yes—
650C4C2×C4×D3211yescharacteristic
651C4C2×D3×#6711yescharacteristic
652C3—21no—
653C3#7883211yescharacteristic, complemented
654C3#8380611yescharacteristic, complemented
655C2—22no—
656C2—64no—
657C2—122no—
658C2#1059467911yescharacteristic
659C2#1059469211yescharacteristic
660C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#64298C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2898
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#901C2semidirect
3. #10594992C2semidirect
4. C2×#63643C2semidirect
5. C3×#5113C2semidirect
6. #10591107C2semidirect
7. #10591088C2semidirect
8. #10590954C2semidirect
9. #10590948C2semidirect
10. #10590670C2semidirect
11. D3×#816C2semidirect
19. #64298C4semidirect
50. C2×#901D3semidirect
59. #5113D3semidirect
74. C2×#634C2×C4semidirect
80. C3×#235C2×C4semidirect
96. #3795C2×C4semidirect
99. D3×Dic6C2×C4semidirect
275. #235C4×D3semidirect
579. C32#2898semidirect
653. C3#78832semidirect
654. C3#83806semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C2×C3×#9012
#105949922
C2×#636432
C3×#51132
#105911072
#105910882
#105909542
#105909482
#105906702
D3×#8162
#838063
#788323