Finite Group Databasebeta

← #11857963

Subgroups — #11857963

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10594969C211yesmaximal, characteristic, complemented
4C3×#5131C211yesmaximal, characteristic, complemented
5C3×#5120C211yesmaximal, characteristic, complemented
6#10591099C211yesmaximal, characteristic, complemented
7#10591085C211yesmaximal, characteristic, complemented
8#10590957C214yesmaximal, complemented
9#10590956C214yesmaximal, 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—
23C2×C32×M16C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25M16×C3⋊D3—24no—
26C2×#3743C2212yescomplemented
27C2×C8×C3⋊D3C2212yescomplemented
28C3×#926C2211yescharacteristic
29C3×#926C2211yescharacteristic
30#63974—21no—
31#63957—21no—
32#63900C2212yescomplemented
33C4×#624—21no—
34#63874—21no—
35#63849C2212yescomplemented
36C3×#821C2214yescomplemented
37C3×#816C2214yescomplemented
38#63565C2214yescomplemented
39#63562C2214yescomplemented
40C22×#239—31no—
41C22×#237—31no—
42C2×D3×M16—31no—
43C2×D3×M16—31no—
44C2×D3×M16—61no—
45D3×#117—31no—
46D3×#117—31no—
47C3×#419—31no—
48C3×#418—31no—
49#5225—31no—
50#5215—31no—
51#5131D311yescharacteristic, complemented
52#5120D311yescharacteristic, complemented
53#5004—31no—
54#5001—31no—
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⋊D3C2×C414yes—
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D414yes—
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C22×C3×Dic3—21no—
70C2×C3×D12—21no—
71C2×C3×D12—22no—
72C2×C3×D12C2×C414yescomplemented
73C2×C3×D12C2312yes—
74C2×C3×Dic6—21no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6C2×C414yescomplemented
77C2×C3×Dic6C2312yes—
78C2×#626—28no—
79C2×#626—22no—
80C2×#626—22no—
81C2×#624—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×M16—22no—
92C2×C32×C8C2312yes—
93#3748—22no—
94C2×C3⋊(C3⋊C8)C2312yes—
95#3743—24no—
96C8×C3⋊D3—24no—
97C3×#217—21no—
98C3×#217—21no—
99C3×C4⋊Dic3C2312yes—
100C3×C4⋊Dic3C2312yes—
101C3×C4×Dic3—21no—
102C3×C4×Dic3—21no—
103#3724—22no—
104#3722—22no—
105Dic32—22no—
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—21no—
131C2×C3×M16C2×D311yescharacteristic
132C2×C3×M16C2×D311yescharacteristic
133C3×#117—31no—
134C3×#117—31no—
135#926C2×D311yescharacteristic
136#926C2×D311yescharacteristic
137C2×#208—31no—
138C2×#208—31no—
139C2×#208—61no—
140D3×M16—64no—
141D3×M16—64no—
142D3×M16—68no—
143C2×ΓL(1,𝔽25)—32no—
144C2×ΓL(1,𝔽25)—32no—
145C2×ΓL(1,𝔽25)—62no—
146C2×D3×C8—32no—
147C2×D3×C8—32no—
148C2×D3×C8—62no—
149#892—32no—
150#892—32no—
151D3×C4⋊C4—32no—
152D3×C4⋊C4—32no—
153D3×C22⋊C4—61no—
154D3×C22⋊C4—61no—
155#877—61no—
156#877—61no—
157#872—61no—
158#872—61no—
159C42×D3—61no—
160C42×D3—61no—
161C3×#103—34no—
162C3×#102—34no—
163#835—34no—
164#832—34no—
165#821C2×D314yescomplemented
166#816C2×D314yescomplemented
167#810—34no—
168#809—34no—
169C23×C32C2×D411yescharacteristic
170C22×C3⋊D3—42no—
171C22×C3⋊D3C22⋊C414yes—
172C22×C3⋊D3C2×D411yescharacteristic
173C22×C3⋊D3C2×D411yescharacteristic
174C22×C3×D3—24no—
175C22×C3×D3—22no—
176C22×C3×D3—44no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3C22⋊C414yes—
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C4×C3⋊D3C22⋊C414yes—
185C4×C3⋊D3C22⋊C414yes—
186C4×C3⋊D3C22×C412yes—
187C4×C3⋊D3C22×C412yes—
188C4×C3⋊D3C2×D412yes—
189C4×C3⋊D3C2×D412yes—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C3×D12—24no—
195C3×D12—22no—
196C3×D12C22×C414yes—
197C3×Dic6—24no—
198C3×Dic6—22no—
199C3×Dic6C22×C414yes—
200#626—28no—
201#626—28no—
202#624—44no—
203D3×Dic3—28no—
204D3×Dic3—28no—
205C32×C8—22no—
206C3⋊(C3⋊C8)—22no—
207C22×#41—91no—
208C22×M16—91no—
209C2×#117—91no—
210#419—31no—
211#419—91no—
212#418—31no—
213#418—91no—
214#417—94no—
215#416—94no—
216C24×C3—61no—
217C23×D3—21no—
218C23×D3—31no—
219C23×D3—31no—
220C23×D3—61no—
221C2×C3×Q8—34no—
222C2×C3×Q8—32no—
223C2×C3×Q8—61no—
224C2×C3×Q8—62no—
225C2×C3×D4—34no—
226C2×C3×D4—32no—
227C2×C3×D4—61no—
228C2×C3×D4—62no—
229C22×C3×C4—21no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—68no—
234C2×#67—62no—
235C2×#67—62no—
236C22×Dic3—21no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—61no—
240C22×Dic3—68no—
241C22×Dic3—62no—
242C22×Dic3—62no—
243#239—38no—
244#239—38no—
245#239—68no—
246#239—68no—
247#239—64no—
248#239—64no—
249#237—38no—
250#237—38no—
251#237—68no—
252#237—68no—
253#237—64no—
254#237—64no—
255C2×D12—21no—
256C2×D12—22no—
257C2×D12—68no—
258C2×D12—62no—
259C2×D12—62no—
260C2×D12C4×D314yescomplemented
261C2×D12C22×D312yes—
262C2×C4×D3—34no—
263C2×C4×D3—34no—
264C2×C4×D3—31no—
265C2×C4×D3—31no—
266C2×C4×D3—31no—
267C2×C4×D3—31no—
268C2×C4×D3—34no—
269C2×C4×D3—34no—
270C2×C4×D3—31no—
271C2×C4×D3—31no—
272C2×C4×D3—31no—
273C2×C4×D3—31no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—64no—
277C2×C4×D3—64no—
278C2×C4×D3—61no—
279C2×C4×D3—61no—
280C2×C4×D3—68no—
281C2×C4×D3—62no—
282C2×C4×D3—62no—
283C2×C4×D3—62no—
284C2×C4×D3—62no—
285C2×Dic6—21no—
286C2×Dic6—22no—
287C2×Dic6C4×D314yescomplemented
288C2×Dic6C22×D312yes—
289C3×M16—24no—
290C3×M16—22no—
291C3×M16—22no—
292C2×C3×C8—22no—
293C2×C3×C8C22×D312yes—
294C2×C3×C8C22×D312yes—
295C3×C4⋊C4—32no—
296C3×C4⋊C4—32no—
297C3×C22⋊C4—61no—
298C3×C22⋊C4—61no—
299C3×C42—61no—
300C3×C42—61no—
301#217—21no—
302#217—21no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—62no—
305C4⋊Dic3C22×D312yes—
306C4⋊Dic3C22×D312yes—
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309C4×Dic3—21no—
310C4×Dic3—21no—
311C4×Dic3—62no—
312C4×Dic3—62no—
313#208—64no—
314#208—62no—
315#208—62no—
316C2×C3⋊C8—32no—
317C2×C3⋊C8—32no—
318C2×C3⋊C8—62no—
319ΓL(1,𝔽25)—64no—
320ΓL(1,𝔽25)—64no—
321ΓL(1,𝔽25)—68no—
322D3×C8—64no—
323D3×C8—64no—
324D3×C8—68no—
325C22×C32—22no—
326C22×C32C2×C22⋊C412yes—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—22no—
329C2×C3⋊D3—22no—
330C2×C3⋊D3—44no—
331C2×C3⋊D3C2×C22⋊C412yes—
332C2×C3⋊D3C2×C22⋊C412yes—
333C2×C3×D3—24no—
334C2×C3×D3—48no—
335C2×C3×D3—44no—
336C32×C4C2×C22⋊C412yes—
337C32×C4C23×C411yescharacteristic
338C32×C4C22×D411yescharacteristic
339C3⋊Dic3C2×C22⋊C412yes—
340C3⋊Dic3C2×C22⋊C412yes—
341C3×Dic3—24no—
342C3×Dic3—42no—
343C3×Dic3—42no—
344C2×#41—92no—
345C2×#41—92no—
346C2×#41—98no—
347C2×#41—181no—
348C2×#41—181no—
349C2×#41—184no—
350C22×Q8—31no—
351C22×D4—31no—
352C22×D4—181no—
353C23×C4—91no—
354C23×C4—181no—
355C2×M16—91no—
356C2×M16—92no—
357C2×M16—184no—
358C2×M16D3211yescharacteristic
359C22×C8—92no—
360#117—31no—
361#117—31no—
362#117—92no—
363#117—181no—
364#117—181no—
365C2×C4⋊C4—92no—
366C2×C22⋊C4—181no—
367C2×C42—181no—
368#103—34no—
369#103—94no—
370#102—34no—
371#102—94no—
372C23×C3—21no—
373C23×C3—64no—
374C23×C3—62no—
375C23×C3—124no—
376C23×C3D3×D411yescharacteristic
377C23×C3D3×D411yescharacteristic
378C22×D3—24no—
379C22×D3—22no—
380C22×D3—31no—
381C22×D3—31no—
382C22×D3—31no—
383C22×D3—31no—
384C22×D3—34no—
385C22×D3—34no—
386C22×D3—44no—
387C22×D3—61no—
388C22×D3—64no—
389C22×D3—61no—
390C22×D3—122no—
391C22×D3—122no—
392C22×D3—124no—
393C3×Q8—34no—
394C3×Q8—64no—
395C3×Q8—62no—
396C3×D4—34no—
397C3×D4—64no—
398C3×D4—62no—
399C2×C3×C4—21no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—64no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4C2×C4×D312yes—
408C2×C3×C4C2×C4×D312yes—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D412yes—
412C2×C3×C4D3×D412yes—
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415#67—68no—
416#67—68no—
417C2×Dic3—24no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—34no—
422C2×Dic3—34no—
423C2×Dic3—31no—
424C2×Dic3—31no—
425C2×Dic3—31no—
426C2×Dic3—31no—
427C2×Dic3—64no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—68no—
431C2×Dic3—68no—
432D12—24no—
433D12—22no—
434D12—68no—
435D12—68no—
436D12C2×C4×D314yes—
437C4×D3—34no—
438C4×D3—34no—
439C4×D3—34no—
440C4×D3—34no—
441C4×D3—32no—
442C4×D3—32no—
443C4×D3—32no—
444C4×D3—32no—
445C4×D3—32no—
446C4×D3—32no—
447C4×D3—32no—
448C4×D3—32no—
449C4×D3—64no—
450C4×D3—64no—
451C4×D3—62no—
452C4×D3—62no—
453C4×D3—62no—
454C4×D3—62no—
455C4×D3—68no—
456C4×D3—68no—
457C4×D3—124no—
458C4×D3—124no—
459Dic6—24no—
460Dic6—22no—
461Dic6C2×C4×D314yes—
462C3×C8—24no—
463C3×C8—22no—
464C3×C8—22no—
465C3⋊C8—64no—
466C3⋊C8—62no—
467C3⋊C8—62no—
468C2×C32—22no—
469C2×C32C22×C22⋊C411yescharacteristic
470C2×C32#57512yes—
471C3⋊D3—22no—
472C3⋊D3—22no—
473C3×D3—44no—
474C24—61no—
475C24—91no—
476#41—98no—
477#41—98no—
478#41—184no—
479#41—184no—
480#41—188no—
481#41—188no—
482C2×Q8—32no—
483C2×Q8—34no—
484C2×Q8—61no—
485C2×Q8—62no—
486C2×D4—32no—
487C2×D4—34no—
488C2×D4—61no—
489C2×D4—62no—
490C2×D4—182no—
491C2×D4—182no—
492C2×D4—188no—
493C22×C4—61no—
494C22×C4—91no—
495C22×C4—91no—
496C22×C4—91no—
497C22×C4—94no—
498C22×C4—91no—
499C22×C4—91no—
500C22×C4—94no—
501C22×C4—182no—
502C22×C4—182no—
503C22×C4—182no—
504C22×C4—188no—
505C22×C4C2×D3211yescharacteristic
506M16—22no—
507M16—184no—
508M16—182no—
509C2×C8—92no—
510C2×C8—184no—
511C2×C8C2×D3212yes—
512C4⋊C4—32no—
513C4⋊C4—32no—
514C4⋊C4—182no—
515C22⋊C4—61no—
516C22⋊C4—61no—
517C22⋊C4—182no—
518C42—61no—
519C42—61no—
520C42—182no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—21no—
524C22×C3—22no—
525C22×C3—42no—
526C22×C3—64no—
527C22×C3—128no—
528C22×C3—124no—
529C22×C3D3×C22⋊C412yes—
530C22×C3D3×C22⋊C412yes—
531C22×C3C2×D3×D411yescharacteristic
532C22×C3C2×D3×D411yescharacteristic
533C2×D3—24no—
534C2×D3—32no—
535C2×D3—32no—
536C2×D3—32no—
537C2×D3—32no—
538C2×D3—48no—
539C2×D3—44no—
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—64no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—122no—
548C2×D3—124no—
549C2×D3—124no—
550C2×D3—128no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—22no—
554C3×C4—64no—
555C3×C4—122no—
556C3×C4—122no—
557C3×C4D3×C22⋊C412yes—
558C3×C4D3×C22⋊C412yes—
559C3×C4C22×C4×D311yescharacteristic
560C3×C4C22×C4×D311yescharacteristic
561C3×C4C2×D3×D411yescharacteristic
562C3×C4C2×D3×D411yescharacteristic
563Dic3—24no—
564Dic3—32no—
565Dic3—32no—
566Dic3—32no—
567Dic3—32no—
568Dic3—42no—
569Dic3—42no—
570Dic3—62no—
571Dic3—62no—
572C32#289611yescharacteristic, complemented, Sylow
573C23—62no—
574C23—64no—
575C23—91no—
576C23—91no—
577C23—94no—
578C23—124no—
579C23—362no—
580C23#380211yescharacteristic
581Q8—34no—
582Q8—62no—
583Q8—64no—
584D4—34no—
585D4—62no—
586D4—64no—
587D4—188no—
588D4—188no—
589C2×C4—62no—
590C2×C4—64no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—91no—
594C2×C4—91no—
595C2×C4—94no—
596C2×C4—92no—
597C2×C4—92no—
598C2×C4—92no—
599C2×C4—92no—
600C2×C4—94no—
601C2×C4—94no—
602C2×C4—188no—
603C2×C4—188no—
604C2×C4—364no—
605C2×C4C4×D3212yes—
606C2×C4#380211yescharacteristic
607C2×C4#381112yes—
608C2×C4C22×D3211yescharacteristic
609C8—22no—
610C8—182no—
611C2×C3—22no—
612C2×C3—22no—
613C2×C3—22no—
614C2×C3—21no—
615C2×C3—42no—
616C2×C3—124no—
617C2×C3C2×D3×C22⋊C411yescharacteristic
618C2×C3C2×D3×C22⋊C411yescharacteristic
619C2×C3#577312yes—
620C2×C3#577712yes—
621D3—44no—
622D3—64no—
623D3—62no—
624D3—62no—
625D3—62no—
626D3—62no—
627D3—122no—
628C22—22no—
629C22—64no—
630C22—92no—
631C22—92no—
632C22—128no—
633C22—124no—
634C22—182no—
635C22—182no—
636C22—364no—
637C22#6392112yes—
638C22C2×#380211yescharacteristic
639C4—64no—
640C4—92no—
641C4—92no—
642C4—122no—
643C4—122no—
644C4#6392112yes—
645C4C2×C4×D3211yescharacteristic
646C4C2×#381111yescharacteristic
647C3—21no—
648C3#7892411yescharacteristic, complemented
649C3#7895611yescharacteristic, complemented
650C2—22no—
651C2—124no—
652C2—182no—
653C2—182no—
654C2#1059471812yes—
655C2C2×#6392111yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×#3796C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×M16×C3⋊D3C2semidirect
3. #10594969C2semidirect
4. C3×#5131C2semidirect
5. C3×#5120C2semidirect
6. #10591099C2semidirect
7. #10591085C2semidirect
8. #10590957C2semidirect
9. #10590956C2semidirect
20. C2×#3796C4semidirect
26. C2×#3743C22semidirect
27. C2×C8×C3⋊D3C22semidirect
32. #63900C22semidirect
35. #63849C22semidirect
36. C3×#821C22semidirect
37. C3×#816C22semidirect
38. #63565C22semidirect
39. #63562C22semidirect
51. #5131D3semidirect
52. #5120D3semidirect
72. C2×C3×D12C2×C4semidirect
76. C2×C3×Dic6C2×C4semidirect
90. #3796C2×C4semidirect
165. #821C2×D3semidirect
166. #816C2×D3semidirect
260. C2×D12C4×D3semidirect
287. C2×Dic6C4×D3semidirect
572. C32#2896semidirect
648. C3#78924semidirect
649. C3#78956semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C2×M16×C3⋊D32
#105949692
C3×#51312
C3×#51202
#105910992
#105910852
#105909572
#105909562
#789563
#789243