Finite Group Databasebeta

← #11792015

Subgroups — #11792015

Order 1152.

945 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C2×C3×#830C211yesmaximal, characteristic
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#71700—31nomaximal
9#69964—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×#3757—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15#64133—22no—
16#64133—22no—
17C2×#3750—21no—
18C2×C3×#217—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C3×#924—22no—
21C3×#924—22no—
22C2×C3×Dic3⋊C4—21no—
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3719—22no—
26C2×#3719—22no—
27C2×#3719—22no—
28C3×#830—22no—
29#63567—22no—
30#63566—22no—
31C2×C3×C22⋊Q8—31no—
32C22×#216—31no—
33C2×#924—31no—
34C2×#924—31no—
35C2×#924—61no—
36C2×#924D311yescharacteristic
37C22×Dic12—31no—
38C2×C3×C22⋊C8—31no—
39C2×#835—31no—
40C2×#830D311yescharacteristic
41C2×#816—31no—
42C2×#816—31no—
43C2×#810—31no—
44#4551—31no—
45#4529—31no—
46C24×C32D411yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634—21no—
62C2×#634D412yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D412yes—
71#3757—24no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)D412yes—
74#3750—24no—
75C3×#217—24no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3D412yes—
78C3×Dic3⋊C4—24no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84C2×C3×C3⋊C8D412yes—
85#3719—28no—
86#2001—91noSylow
87C22×C3×Q8—31no—
88C23×C3×C4—21no—
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C3×C22⋊Q8—62no—
98C3×C22⋊Q8—62no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C22⋊C4—61no—
102C2×#217—21no—
103C2×#217—62no—
104C2×#217—61no—
105C2×#217—61no—
106C2×#216—62no—
107C2×#216—62no—
108C2×#216—62no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3C2×D311yescharacteristic
113#924—22no—
114#924—22no—
115#924—62no—
116#924—62no—
117#924—62no—
118#924—62no—
119#924—64no—
120#924—64no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—62no—
123C2×Dic3⋊C4—61no—
124C2×Dic3⋊C4—61no—
125C22×C3⋊C8C2×D311yescharacteristic
126C22×C3⋊C8C2×D311yescharacteristic
127C2×Dic12—62no—
128C2×Dic12—62no—
129C2×Dic12—62no—
130C3×C22⋊C8—62no—
131#835—62no—
132#830—22no—
133#816—62no—
134#816—62no—
135#810—62no—
136C23×C32—21no—
137C23×C32—21no—
138C23×C32—21no—
139C23×C32—21no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32Q1612yescomplemented
143C23×C32C2×D411yescharacteristic
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4—41no—
148C2×C32×C4—41no—
149C2×C32×C4—41no—
150C2×C32×C4—41no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4#4111yescharacteristic
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—41no—
160C2×C3⋊Dic3—41no—
161C2×C3⋊Dic3—41no—
162C2×C3⋊Dic3—41no—
163#634—22no—
164#634—22no—
165#634—41no—
166#634—41no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—41no—
176C3×Dic6—41no—
177C3×C3⋊C8—22no—
178C3×C3⋊C8—41no—
179C22×Q16—91no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—91no—
182C2×#103—91no—
183C2×#103—91no—
184C2×C22⋊C8—31no—
185#340—91no—
186C24×C3—21no—
187C24×C3D1211yescharacteristic
188C24×C3#6711yescharacteristic
189C2×C3×Q8—32no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×Q8—61no—
193C2×C3×Q8—61no—
194C2×C3×Q8—61no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4—41no—
214C22×C3×C4—41no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4D1211yescharacteristic
218C22×C3×C4#6711yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C2×Dic6—21no—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6—21no—
234C2×Dic6—32no—
235C2×Dic6—32no—
236C2×Dic6—62no—
237C2×Dic6—61no—
238C2×Dic6—61no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—62no—
246C2×Dic6—61no—
247C2×Dic6—61no—
248C2×Dic6—121no—
249C2×Dic6—121no—
250C2×Dic6—121no—
251C2×Dic6—121no—
252C2×Dic6#6712yes—
253C2×C3×C8—32no—
254C2×C3×C8—61no—
255C2×C3×C8—61no—
256C2×C3×C8—61no—
257C2×C3×C8—61no—
258C2×C3×C8—61no—
259C3×C4⋊C4—32no—
260C3×C4⋊C4—64no—
261C3×C4⋊C4—61no—
262C3×C22⋊C4—64no—
263#217—24no—
264#217—68no—
265#217—64no—
266#217—64no—
267#216—68no—
268C4⋊Dic3—21no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3#6712yes—
276Dic3⋊C4—24no—
277Dic3⋊C4—68no—
278Dic3⋊C4—64no—
279Dic3⋊C4—64no—
280C2×C3⋊C8—21no—
281C2×C3⋊C8—21no—
282C2×C3⋊C8—21no—
283C2×C3⋊C8—21no—
284C2×C3⋊C8—21no—
285C2×C3⋊C8#6712yes—
286Dic12—68no—
287C22×C32—22no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32#12011yescharacteristic
295C22×C32#12011yescharacteristic
296C22×C32#12111yescharacteristic
297C22×C32C2×Q1611yescharacteristic
298C22×C32#13511yescharacteristic
299C22×C32#13711yescharacteristic
300C22×C32#13711yescharacteristic
301C32×C4—41no—
302C32×C4#12011yescharacteristic
303C32×C4#12111yescharacteristic
304C32×C4#12111yescharacteristic
305C32×C4#12711yescharacteristic
306C3⋊Dic3—42no—
307C3⋊Dic3—42no—
308C3×Dic3—42no—
309C3×Dic3—42no—
310C22×Q8—31no—
311C22×Q8—91no—
312C23×C4D3211yescharacteristic
313C2×Q16—182no—
314C2×Q16—182no—
315C2×Q16—182no—
316C22×C8—31no—
317C22×C8—31no—
318C22⋊Q8—62no—
319C22⋊Q8—62no—
320C22⋊Q8—182no—
321C22⋊Q8—182no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—61no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—181no—
326C2×C22⋊C4—61no—
327C2×C22⋊C4—181no—
328#103—182no—
329#103—182no—
330C22⋊C8—62no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—22no—
346C23×C3—21no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3Dic1212yescomplemented
352C23×C3#21612yescomplemented
353C23×C3C2×D1211yescharacteristic
354C23×C3C2×#6711yescharacteristic
355C3×Q8—62no—
356C3×Q8—62no—
357C3×Q8—121no—
358C3×Q8—121no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—121no—
389C2×C3×C4—121no—
390C2×C3×C4—121no—
391C2×C3×C4—121no—
392C2×C3×C4#23511yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4#23711yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—41no—
407C2×Dic3—41no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—64no—
411C2×Dic3—64no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3—121no—
425C2×Dic3—121no—
426C2×Dic3—121no—
427C2×Dic3—121no—
428Dic6—22no—
429Dic6—22no—
430Dic6—41no—
431Dic6—41no—
432Dic6—62no—
433Dic6—62no—
434Dic6—62no—
435Dic6—62no—
436Dic6—122no—
437Dic6—122no—
438Dic6—122no—
439Dic6—122no—
440Dic6—121no—
441Dic6—121no—
442Dic6—121no—
443Dic6—121no—
444C3×C8—62no—
445C3×C8—121no—
446C3⋊C8—22no—
447C3⋊C8—41no—
448C2×C32—42no—
449C2×C32#39211yescharacteristic
450C2×C32#45111yescharacteristic
451C2×C32#45111yescharacteristic
452C2×C32#45211yescharacteristic
453C2×C32#45211yescharacteristic
454C2×C32#46711yescharacteristic
455C2×C32#47011yescharacteristic
456C24#62611yescharacteristic
457C2×Q8—32no—
458C2×Q8—61no—
459C2×Q8—61no—
460C2×Q8—61no—
461C2×Q8—61no—
462C2×Q8—61no—
463C2×Q8—92no—
464C2×Q8—181no—
465C2×Q8—181no—
466C2×Q8—181no—
467C2×Q8—181no—
468C2×Q8—181no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—61no—
476C22×C4—61no—
477C22×C4—181no—
478C22×C4—181no—
479C22×C4#62611yescharacteristic
480C22×C4C2×D3211yescharacteristic
481Q16—188no—
482C2×C8—32no—
483C2×C8—61no—
484C2×C8—61no—
485C2×C8—61no—
486C2×C8—61no—
487C2×C8—61no—
488C4⋊C4—32no—
489C4⋊C4—64no—
490C4⋊C4—61no—
491C4⋊C4—92no—
492C4⋊C4—184no—
493C4⋊C4—181no—
494C22⋊C4—64no—
495C22⋊C4—184no—
496C22×C3—24no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3#88211yescharacteristic
525C22×C3#88211yescharacteristic
526C22×C3#90411yescharacteristic
527C22×C3C2×Dic1211yescharacteristic
528C22×C3#90911yescharacteristic
529C22×C3#90911yescharacteristic
530C22×C3#93011yescharacteristic
531C22×C3#93711yescharacteristic
532C22×C3#93911yescharacteristic
533C22×C3#94211yescharacteristic
534C22×C3C2×#21611yescharacteristic
535C22×C3#95011yescharacteristic
536C22×C3#95111yescharacteristic
537C22×C3#95311yescharacteristic
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—42no—
543C3×C4—41no—
544C3×C4—41no—
545C3×C4—122no—
546C3×C4—122no—
547C3×C4#88411yescharacteristic
548C3×C4#88411yescharacteristic
549C3×C4#93711yescharacteristic
550C3×C4#93711yescharacteristic
551C3×C4#93811yescharacteristic
552C3×C4#93911yescharacteristic
553C3×C4#94011yescharacteristic
554C3×C4#94011yescharacteristic
555Dic3—42no—
556Dic3—42no—
557Dic3—124no—
558Dic3—124no—
559Dic3—122no—
560Dic3—122no—
561Dic3—122no—
562Dic3—122no—
563C32#200111yescharacteristic, complemented, Sylow
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23#371912yescomplemented
571C23C2×#62611yescharacteristic
572Q8—62no—
573Q8—62no—
574Q8—121no—
575Q8—121no—
576Q8—182no—
577Q8—182no—
578Q8—361no—
579Q8—361no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—121no—
590C2×C4—121no—
591C2×C4—121no—
592C2×C4—121no—
593C2×C4—182no—
594C2×C4—182no—
595C2×C4—361no—
596C2×C4—361no—
597C2×C4—361no—
598C2×C4—361no—
599C2×C4#380411yescharacteristic
600C2×C4D3×#6711yescharacteristic
601C2×C4D3×#6711yescharacteristic
602C2×C4D3×#6711yescharacteristic
603C2×C4#381111yescharacteristic
604C2×C4#381111yescharacteristic
605C8—62no—
606C8—121no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—44no—
615C2×C3—42no—
616C2×C3—42no—
617C2×C3#473311yescharacteristic
618C2×C3#473311yescharacteristic
619C2×C3#473911yescharacteristic
620C2×C3#473911yescharacteristic
621C2×C3#496011yescharacteristic
622C2×C3#504711yescharacteristic
623C2×C3#505011yescharacteristic
624C2×C3#505111yescharacteristic
625C2×C3#505211yescharacteristic
626C2×C3#511611yescharacteristic
627C2×C3#513711yescharacteristic
628C2×C3#522311yescharacteristic
629C2×C3#522811yescharacteristic
630C2×C3#523911yescharacteristic
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22#6382911yescharacteristic
639C22#6383111yescharacteristic
640C22#6383311yescharacteristic
641C22C2×#371911yescharacteristic
642C22#6397711yescharacteristic
643C22#6397811yescharacteristic
644C22#6398111yescharacteristic
645C4—41no—
646C4—122no—
647C4—122no—
648C4—362no—
649C4—362no—
650C4#6395811yescharacteristic
651C4#6397111yescharacteristic
652C4#6397911yescharacteristic
653C4#6398311yescharacteristic
654C3—21no—
655C3#6996411yescharacteristic, complemented
656C3#7170011yescharacteristic, complemented
657C2—42no—
658C2#1059112111yescharacteristic
659C2#1059117311yescharacteristic
660C2#1059118411yescharacteristic
661C2#1059118611yescharacteristic
662C2#1059118711yescharacteristic
663C2#1059119011yescharacteristic
664C2#1059172411yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC23×C4D32
hypocenterC32#2001
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C22×#3719C2semidirect
5. C2×#63567C2semidirect
6. C2×#63566C2semidirect
7. #10589164C2semidirect
142. C23×C32Q16semidirect
351. C23×C3Dic12semidirect
352. C23×C3#216semidirect
563. C32#2001semidirect
570. C23#3719semidirect
655. C3#69964semidirect
656. C3#71700semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9242
C22×#37192
C2×C3×#8302
C2×#635672
C2×#635662
#105891642
#717003
#699643