Finite Group Databasebeta

← #11857958

Subgroups — #11857958

Order 1152.

1709 conjugacy classes of subgroups.

The subgroup lattice has 667 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C3⋊D3×#117C211yesmaximal, characteristic, complemented
3C2×#63818C211yesmaximal, characteristic, complemented
4C3×#5004C211yesmaximal, characteristic, complemented
5C3×#5001C211yesmaximal, characteristic, complemented
6#10591100C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic, complemented
8#10590612C214yesmaximal, complemented
9#10590611C214yesmaximal, complemented
10#78956—31nomaximal
11#78924—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×D3×Dic3—21no—
17C2×#3796—21no—
18C2×#3796—21no—
19C2×#3796—24no—
20C2×#3796C418yescomplemented
21C2×#3796C2212yes—
22C2×#3796C2212yes—
23C32×#117C2211yescharacteristic
24#64135C2211yescharacteristic
25#64101C2212yescomplemented
26C4⋊C4×C3⋊D3C2212yescomplemented
27C22⋊C4×C3⋊D3—21no—
28#64086—21no—
29#64081—21no—
30C42×C3⋊D3—21no—
31C2×C3×#208C2211yescharacteristic
32C2×C3×#208C2211yescharacteristic
33C2×#3712C2212yescomplemented
34#63818—24no—
35C2×#3710C2212yescomplemented
36C3×#810C2214yescomplemented
37C3×#809C2214yescomplemented
38#63566C2214yescomplemented
39#63563C2214yescomplemented
40C22×#239—31no—
41C22×#237—31no—
42C2×D3×M16—31no—
43C2×D3×M16—31no—
44D3×#117—31no—
45D3×#117—31no—
46D3×#117—61no—
47C3×#419—31no—
48C3×#418—31no—
49#5225—31no—
50#5215—31no—
51#5131—31no—
52#5120—31no—
53#5004D311yescharacteristic, complemented
54#5001D311yescharacteristic, complemented
55#4804—34no—
56#4803—34no—
57#4772—34no—
58#4771—34no—
59C23×C3⋊D3D411yescharacteristic
60C23×C3×D3—21no—
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3D411yescharacteristic
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3C2×C414yes—
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3D414yes—
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C4×C3⋊D3C2311yescharacteristic
70C22×C3×Dic3—21no—
71C2×C3×D12—21no—
72C2×C3×D12—22no—
73C2×C3×D12C2×C414yescomplemented
74C2×C3×D12C2312yes—
75C2×C3×Dic6—21no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6C2×C414yescomplemented
78C2×C3×Dic6C2312yes—
79C2×#626—28no—
80C2×#626—22no—
81C2×#626—22no—
82C2×D3×Dic3—28no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3—22no—
85#3796—28no—
86#3796—28no—
87#3796—24no—
88#3796—24no—
89#3796C2×C418yes—
90#3796C2×C418yescomplemented
91C32×C4⋊C4C2312yes—
92C32×C22⋊C4—21no—
93C32×C42—21no—
94#3757—21no—
95#3752—22no—
96C4⋊(C3⋊Dic3)C2312yes—
97#3750—22no—
98C4×C3⋊Dic3—21no—
99C4×C3⋊Dic3—22no—
100C3×#208—22no—
101C3×#208—22no—
102C2×C3×C3⋊C8C2312yes—
103C2×C3×C3⋊C8C2312yes—
104#3712—24no—
105#3710—24no—
106#2896—91noSylow
107C22×C3×Q8—31no—
108C22×C3×D4—31no—
109C22×#67—61no—
110C23×Dic3—61no—
111C2×#239—38no—
112C2×#239—32no—
113C2×#239—32no—
114C2×#239—61no—
115C2×#239—61no—
116C2×#239—64no—
117C2×#237—38no—
118C2×#237—32no—
119C2×#237—32no—
120C2×#237—61no—
121C2×#237—61no—
122C2×#237—64no—
123C22×D12—61no—
124C22×D12C2×D311yescharacteristic
125C22×C4×D3—31no—
126C22×C4×D3—31no—
127C22×C4×D3—61no—
128C22×C4×D3—61no—
129C22×Dic6C2×D311yescharacteristic
130C2×C3×M16—31no—
131C2×C3×M16—31no—
132C3×#117—21no—
133C3×#117C2×D311yescharacteristic
134C3×#117C2×D311yescharacteristic
135#926—31no—
136#926—31no—
137#926—61no—
138C2×#208C2×D311yescharacteristic
139C2×#208C2×D311yescharacteristic
140D3×M16—64no—
141D3×M16—64no—
142C2×ΓL(1,𝔽25)—32no—
143C2×ΓL(1,𝔽25)—32no—
144C2×D3×C8—32no—
145C2×D3×C8—32no—
146#892—32no—
147#892—32no—
148#892—62no—
149D3×C4⋊C4—32no—
150D3×C4⋊C4—32no—
151D3×C4⋊C4—62no—
152D3×C22⋊C4—61no—
153D3×C22⋊C4—61no—
154D3×C22⋊C4—62no—
155#877—61no—
156#877—61no—
157#877—62no—
158#872—61no—
159#872—61no—
160#872—62no—
161C42×D3—61no—
162C42×D3—61no—
163C42×D3—62no—
164C3×#103—34no—
165C3×#102—34no—
166#835—34no—
167#832—34no—
168#821—34no—
169#816—34no—
170#810C2×D314yescomplemented
171#809C2×D314yescomplemented
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—42no—
174C22×C3⋊D3C22⋊C414yes—
175C22×C3⋊D3C2×D411yescharacteristic
176C22×C3⋊D3C2×D411yescharacteristic
177C22×C3×D3—24no—
178C22×C3×D3—22no—
179C22×C3×D3—44no—
180C2×C32×C4—22no—
181C2×C32×C4C22×C412yes—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3C22⋊C414yes—
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C4×C3⋊D3—44no—
190C4×C3⋊D3C22⋊C414yes—
191C4×C3⋊D3C22⋊C414yes—
192C4×C3⋊D3C22×C412yes—
193C4×C3⋊D3C22×C412yes—
194C4×C3⋊D3C2×D412yes—
195C4×C3⋊D3C2×D412yes—
196C2×C3×Dic3—24no—
197C2×C3×Dic3—22no—
198C3×D12—24no—
199C3×D12—22no—
200C3×D12C22×C414yes—
201C3×Dic6—24no—
202C3×Dic6—22no—
203C3×Dic6C22×C414yes—
204#626—28no—
205#626—28no—
206D3×Dic3—28no—
207D3×Dic3—28no—
208C3×C3⋊C8—22no—
209C3×C3⋊C8—22no—
210C22×#41—91no—
211C22×M16—91no—
212C2×#117—91no—
213#419—31no—
214#419—91no—
215#418—31no—
216#418—91no—
217#417—94no—
218#416—94no—
219C24×C3—61no—
220C23×D3—21no—
221C23×D3—31no—
222C23×D3—31no—
223C23×D3—61no—
224C2×C3×Q8—34no—
225C2×C3×Q8—32no—
226C2×C3×Q8—62no—
227C2×C3×Q8—61no—
228C2×C3×D4—34no—
229C2×C3×D4—32no—
230C2×C3×D4—62no—
231C2×C3×D4—61no—
232C22×C3×C4—21no—
233C22×C3×C4—61no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—68no—
237C2×#67—62no—
238C2×#67—62no—
239C22×Dic3—21no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—61no—
243C22×Dic3—68no—
244C22×Dic3—62no—
245C22×Dic3—62no—
246#239—38no—
247#239—38no—
248#239—68no—
249#239—68no—
250#239—64no—
251#239—64no—
252#237—38no—
253#237—38no—
254#237—68no—
255#237—68no—
256#237—64no—
257#237—64no—
258C2×D12—22no—
259C2×D12—21no—
260C2×D12—68no—
261C2×D12—62no—
262C2×D12—62no—
263C2×D12C4×D314yescomplemented
264C2×D12C22×D312yes—
265C2×C4×D3—34no—
266C2×C4×D3—34no—
267C2×C4×D3—31no—
268C2×C4×D3—31no—
269C2×C4×D3—31no—
270C2×C4×D3—31no—
271C2×C4×D3—34no—
272C2×C4×D3—34no—
273C2×C4×D3—31no—
274C2×C4×D3—31no—
275C2×C4×D3—31no—
276C2×C4×D3—31no—
277C2×C4×D3—61no—
278C2×C4×D3—61no—
279C2×C4×D3—61no—
280C2×C4×D3—61no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—68no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—62no—
288C2×C4×D3—64no—
289C2×Dic6—22no—
290C2×Dic6—21no—
291C2×Dic6C4×D314yescomplemented
292C2×Dic6C22×D312yes—
293C3×M16—62no—
294C3×M16—62no—
295C2×C3×C8—32no—
296C2×C3×C8—32no—
297C3×C4⋊C4—22no—
298C3×C4⋊C4C22×D312yes—
299C3×C4⋊C4C22×D312yes—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—21no—
303C3×C42—22no—
304C3×C42—21no—
305C3×C42—21no—
306#217—62no—
307#217—61no—
308#217—61no—
309(C2×D3)⋊C4—62no—
310(C2×D3)⋊C4—62no—
311(C2×D3)⋊C4—64no—
312C4⋊Dic3—32no—
313C4⋊Dic3—32no—
314C4⋊Dic3—62no—
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317Dic3⋊C4—64no—
318C4×Dic3—62no—
319C4×Dic3—62no—
320C4×Dic3—62no—
321C4×Dic3—64no—
322C4×Dic3—61no—
323C4×Dic3—61no—
324#208—22no—
325#208—22no—
326C2×C3⋊C8C22×D312yes—
327C2×C3⋊C8C22×D312yes—
328ΓL(1,𝔽25)—64no—
329ΓL(1,𝔽25)—64no—
330D3×C8—64no—
331D3×C8—64no—
332C22×C32—22no—
333C22×C32C2×C22⋊C412yes—
334C22×C32C22×D411yescharacteristic
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—44no—
338C2×C3⋊D3C2×C22⋊C412yes—
339C2×C3⋊D3C2×C22⋊C412yes—
340C2×C3×D3—24no—
341C2×C3×D3—48no—
342C2×C3×D3—44no—
343C32×C4—42no—
344C32×C4C2×C22⋊C412yes—
345C32×C4C23×C411yescharacteristic
346C32×C4C22×D411yescharacteristic
347C3⋊Dic3—42no—
348C3⋊Dic3C2×C22⋊C412yes—
349C3⋊Dic3C2×C22⋊C412yes—
350C3×Dic3—24no—
351C2×#41—92no—
352C2×#41—92no—
353C2×#41—98no—
354C2×#41—184no—
355C2×#41—181no—
356C2×#41—181no—
357C22×Q8—31no—
358C22×D4—31no—
359C22×D4—181no—
360C23×C4—91no—
361C23×C4—181no—
362C2×M16—31no—
363C2×M16—31no—
364C2×M16—92no—
365C2×M16—184no—
366C22×C8—92no—
367#117—91no—
368#117—92no—
369#117—181no—
370#117—181no—
371#117D3211yescharacteristic
372C2×C4⋊C4—92no—
373C2×C22⋊C4—181no—
374C2×C42—181no—
375#103—34no—
376#103—94no—
377#102—34no—
378#102—94no—
379C23×C3—21no—
380C23×C3—64no—
381C23×C3—62no—
382C23×C3—124no—
383C23×C3D3×D411yescharacteristic
384C23×C3D3×D411yescharacteristic
385C22×D3—24no—
386C22×D3—22no—
387C22×D3—31no—
388C22×D3—31no—
389C22×D3—31no—
390C22×D3—31no—
391C22×D3—34no—
392C22×D3—34no—
393C22×D3—44no—
394C22×D3—61no—
395C22×D3—64no—
396C22×D3—61no—
397C22×D3—122no—
398C22×D3—122no—
399C22×D3—124no—
400C3×Q8—34no—
401C3×Q8—64no—
402C3×Q8—62no—
403C3×D4—34no—
404C3×D4—64no—
405C3×D4—62no—
406C2×C3×C4—24no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—64no—
414C2×C3×C4—62no—
415C2×C3×C4C2×C4×D312yes—
416C2×C3×C4C2×C4×D312yes—
417C2×C3×C4D3×D412yes—
418C2×C3×C4D3×D412yes—
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4C23×D311yescharacteristic
422C2×C3×C4C23×D311yescharacteristic
423#67—68no—
424#67—68no—
425C2×Dic3—24no—
426C2×Dic3—22no—
427C2×Dic3—34no—
428C2×Dic3—34no—
429C2×Dic3—31no—
430C2×Dic3—31no—
431C2×Dic3—31no—
432C2×Dic3—31no—
433C2×Dic3—64no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—68no—
437C2×Dic3—68no—
438C2×Dic3—64no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441D12—24no—
442D12—22no—
443D12—68no—
444D12—68no—
445D12C2×C4×D314yes—
446C4×D3—34no—
447C4×D3—34no—
448C4×D3—34no—
449C4×D3—34no—
450C4×D3—32no—
451C4×D3—32no—
452C4×D3—32no—
453C4×D3—32no—
454C4×D3—32no—
455C4×D3—32no—
456C4×D3—32no—
457C4×D3—32no—
458C4×D3—64no—
459C4×D3—64no—
460C4×D3—62no—
461C4×D3—62no—
462C4×D3—62no—
463C4×D3—62no—
464C4×D3—68no—
465C4×D3—68no—
466C4×D3—128no—
467C4×D3—124no—
468C4×D3—124no—
469Dic6—24no—
470Dic6—22no—
471Dic6C2×C4×D314yes—
472C3×C8—62no—
473C3×C8—62no—
474C3⋊C8—22no—
475C3⋊C8—22no—
476C2×C32—22no—
477C2×C32C22×C22⋊C411yescharacteristic
478C2×C32#57512yes—
479C3⋊D3—22no—
480C3⋊D3—22no—
481C3×D3—44no—
482C24—61no—
483C24—91no—
484#41—98no—
485#41—98no—
486#41—184no—
487#41—184no—
488#41—188no—
489#41—188no—
490C2×Q8—32no—
491C2×Q8—34no—
492C2×Q8—62no—
493C2×Q8—61no—
494C2×D4—32no—
495C2×D4—34no—
496C2×D4—62no—
497C2×D4—61no—
498C2×D4—182no—
499C2×D4—182no—
500C2×D4—188no—
501C22×C4—61no—
502C22×C4—91no—
503C22×C4—91no—
504C22×C4—91no—
505C22×C4—94no—
506C22×C4—94no—
507C22×C4—91no—
508C22×C4—91no—
509C22×C4—182no—
510C22×C4—182no—
511C22×C4—182no—
512C22×C4—188no—
513C22×C4C2×D3211yescharacteristic
514M16—62no—
515M16—62no—
516M16—184no—
517C2×C8—32no—
518C2×C8—32no—
519C2×C8—184no—
520C4⋊C4—92no—
521C4⋊C4—182no—
522C4⋊C4C2×D3212yes—
523C22⋊C4—21no—
524C22⋊C4—182no—
525C22⋊C4—181no—
526C42—21no—
527C42—182no—
528C42—181no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—21no—
532C22×C3—22no—
533C22×C3—42no—
534C22×C3—64no—
535C22×C3—128no—
536C22×C3—124no—
537C22×C3D3×C22⋊C412yes—
538C22×C3D3×C22⋊C412yes—
539C22×C3C2×D3×D411yescharacteristic
540C22×C3C2×D3×D411yescharacteristic
541C2×D3—24no—
542C2×D3—32no—
543C2×D3—32no—
544C2×D3—32no—
545C2×D3—32no—
546C2×D3—48no—
547C2×D3—44no—
548C2×D3—62no—
549C2×D3—62no—
550C2×D3—64no—
551C2×D3—62no—
552C2×D3—62no—
553C2×D3—62no—
554C2×D3—62no—
555C2×D3—122no—
556C2×D3—124no—
557C2×D3—124no—
558C2×D3—128no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—22no—
562C3×C4—44no—
563C3×C4—42no—
564C3×C4—42no—
565C3×C4—64no—
566C3×C4D3×C22⋊C412yes—
567C3×C4D3×C22⋊C412yes—
568C3×C4C22×C4×D311yescharacteristic
569C3×C4C22×C4×D311yescharacteristic
570C3×C4C2×D3×D411yescharacteristic
571C3×C4C2×D3×D411yescharacteristic
572Dic3—24no—
573Dic3—32no—
574Dic3—32no—
575Dic3—32no—
576Dic3—32no—
577Dic3—62no—
578Dic3—62no—
579Dic3—124no—
580Dic3—122no—
581Dic3—122no—
582C32#289611yescharacteristic, complemented, Sylow
583C23—62no—
584C23—64no—
585C23—91no—
586C23—91no—
587C23—94no—
588C23—124no—
589C23—362no—
590C23#381111yescharacteristic
591Q8—34no—
592Q8—62no—
593Q8—64no—
594D4—34no—
595D4—62no—
596D4—64no—
597D4—188no—
598D4—188no—
599C2×C4—22no—
600C2×C4—62no—
601C2×C4—64no—
602C2×C4—91no—
603C2×C4—91no—
604C2×C4—94no—
605C2×C4—92no—
606C2×C4—92no—
607C2×C4—92no—
608C2×C4—92no—
609C2×C4—94no—
610C2×C4—94no—
611C2×C4—188no—
612C2×C4—188no—
613C2×C4—182no—
614C2×C4—364no—
615C2×C4C4×D3212yes—
616C2×C4#380212yes—
617C2×C4#381111yescharacteristic
618C2×C4C22×D3211yescharacteristic
619C8—62no—
620C8—62no—
621C2×C3—22no—
622C2×C3—22no—
623C2×C3—22no—
624C2×C3—21no—
625C2×C3—42no—
626C2×C3—124no—
627C2×C3C2×D3×C22⋊C411yescharacteristic
628C2×C3C2×D3×C22⋊C411yescharacteristic
629C2×C3#577312yes—
630C2×C3#577712yes—
631D3—44no—
632D3—64no—
633D3—62no—
634D3—62no—
635D3—62no—
636D3—62no—
637D3—122no—
638C22—22no—
639C22—64no—
640C22—92no—
641C22—92no—
642C22—128no—
643C22—124no—
644C22—182no—
645C22—182no—
646C22—364no—
647C22#6392112yes—
648C22C2×#381111yescharacteristic
649C4—42no—
650C4—64no—
651C4—92no—
652C4—92no—
653C4—362no—
654C4#6392112yes—
655C4C2×C4×D3211yescharacteristic
656C4C2×#380211yescharacteristic
657C3—21no—
658C3#7892411yescharacteristic, complemented
659C3#7895611yescharacteristic, complemented
660C2—22no—
661C2—124no—
662C2—182no—
663C2—182no—
664C2C2×#6392111yescharacteristic
665C2#1059547112yes—
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×#3796C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#117C2semidirect
3. C2×#63818C2semidirect
4. C3×#5004C2semidirect
5. C3×#5001C2semidirect
6. #10591100C2semidirect
7. #10591086C2semidirect
8. #10590612C2semidirect
9. #10590611C2semidirect
20. C2×#3796C4semidirect
25. #64101C22semidirect
26. C4⋊C4×C3⋊D3C22semidirect
33. C2×#3712C22semidirect
35. C2×#3710C22semidirect
36. C3×#810C22semidirect
37. C3×#809C22semidirect
38. #63566C22semidirect
39. #63563C22semidirect
53. #5004D3semidirect
54. #5001D3semidirect
73. C2×C3×D12C2×C4semidirect
77. C2×C3×Dic6C2×C4semidirect
90. #3796C2×C4semidirect
170. #810C2×D3semidirect
171. #809C2×D3semidirect
263. C2×D12C4×D3semidirect
291. C2×Dic6C4×D3semidirect
582. C32#2896semidirect
658. C3#78924semidirect
659. C3#78956semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C3⋊D3×#1172
C2×#638182
C3×#50042
C3×#50012
#105911002
#105910862
#105906122
#105906112
#789563
#789243