Finite Group Databasebeta

← #11787082

Subgroups — #11787082

Order 1152.

819 conjugacy classes of subgroups.

The subgroup lattice has 697 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595506C211yesmaximal, characteristic
2C2×C3×#806C211yesmaximal, characteristic
3C3×#4950C211yesmaximal, characteristic, complemented
4#10591718C211yesmaximal, characteristic, complemented
5#10591710C211yesmaximal, characteristic
6#10589393C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#70021—31nomaximal
9#69595—31nomaximal
10C22×C3×#67C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×C4⋊Dic3—21no—
18#67⋊Dic3—21no—
19#67⋊Dic3—21no—
20Dic3×#67—21no—
21Dic3×#67—21no—
22D3×#217—21no—
23C2×Dic3⋊Dic3—21no—
24C2×(C2×D3)⋊Dic3—21no—
25#63955—21no—
26C3×C3⋊#95—21no—
27C3×#806C414yescomplemented
28#63579—21no—
29#63579—21no—
30#5798—31no—
31#5486—31no—
32C2×C3×#99—31no—
33C3×#385—31no—
34#5220—31no—
35#5213—31no—
36#5210—31no—
37C2×#806D311yescharacteristic
38#4950—31no—
39#4950D311yescharacteristic, complemented
40#4527—31no—
41#4527—31no—
42#4527—31no—
43#4527—61no—
44#4526—31no—
45C24×C32C2311yescharacteristic
46C23×C3×D3D411yescharacteristic
47C22×C32×C4—21no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C2×C3×#67—21no—
55C2×C3×#67C2×C412yes—
56C2×C3×#67Q812yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—42no—
62C22×C3×Dic3D411yescharacteristic
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×D3×Dic3—21no—
66C2×D3×Dic3—21no—
67C32×C22⋊C4—21no—
68C32×C22⋊C4C2×C412yescomplemented
69#3757—21no—
70#3757—21no—
71#3757—21no—
72#3757—21no—
73C3×#217—21no—
74C3×#217—21no—
75C3×#217—21no—
76C3×#217C2×C412yescomplemented
77C3×C4⋊Dic3—42no—
78Dic3⋊Dic3—21no—
79Dic3⋊Dic3—21no—
80Dic3⋊Dic3—42no—
81(C2×D3)⋊Dic3—21no—
82(C2×D3)⋊Dic3—21no—
83(C2×D3)⋊Dic3—42no—
84Dic32—21no—
85Dic32—21no—
86#1867—91noSylow
87C22×C3×D4—31no—
88C23×C3×C4—31no—
89C22×#67C2×D311yescharacteristic
90C23×Dic3C2×D311yescharacteristic
91C2×C3×C4⋊C4—61no—
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4—31no—
94C2×C3×C22⋊C4—31no—
95C2×C3×C22⋊C4C2×D311yescharacteristic
96C2×C3×C22⋊C4C2×D311yescharacteristic
97C2×#217—31no—
98C2×#217—31no—
99C2×#217—31no—
100C2×#217—31no—
101C2×#217—61no—
102C2×#217—61no—
103C2×#217—61no—
104C2×#217—61no—
105C2×#217C2×D311yescharacteristic
106C2×#217C2×D311yescharacteristic
107D4×Dic3—61no—
108D4×Dic3—61no—
109D4×Dic3—61no—
110D4×Dic3—61no—
111C4×#67—61no—
112C4×#67—61no—
113C2×(C2×D3)⋊C4—61no—
114#926—61no—
115C2×C4⋊Dic3—21no—
116C2×C4⋊Dic3—61no—
117C2×Dic3⋊C4—61no—
118#67⋊C4—61no—
119#67⋊C4—61no—
120D3×C22⋊C4—61no—
121#877—61no—
122C3×#99—34no—
123C3×#95—61no—
124C3⋊#95—21no—
125C3⋊#95—61no—
126C3⋊#95—61no—
127C3⋊#95—61no—
128C3⋊#95—61no—
129#806Dic314yescomplemented
130C23×C32—41no—
131C23×C32—41no—
132C23×C32C22×C411yescharacteristic
133C23×C32C2×D411yescharacteristic
134C23×C32C2×D411yescharacteristic
135C23×C32C2×D411yescharacteristic
136C23×C32C2×Q811yescharacteristic
137C23×C32#4111yescharacteristic
138C23×C32#4111yescharacteristic
139C22×C3×D3—21no—
140C22×C3×D3—21no—
141C22×C3×D3—41no—
142C22×C3×D3—41no—
143C22×C3×D3C4⋊C412yescomplemented
144C2×C32×C4—22no—
145C2×C32×C4—41no—
146C2×C32×C4—41no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3—41no—
152C2×C3⋊Dic3—41no—
153C2×C3⋊Dic3—41no—
154C3×#67—22no—
155C3×#67—22no—
156C3×#67—22no—
157C3×#67—22no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—41no—
167C2×C3×Dic3—41no—
168C2×C3×Dic3—41no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C2×C3×Dic3—41no—
174C2×C3×Dic3C4⋊C412yescomplemented
175D3×Dic3—81no—
176D3×Dic3—81no—
177#518—91no—
178C2×#99—31no—
179#386—91no—
180#385—31no—
181#385—91no—
182#342—91no—
183#342—91no—
184C24×C3—21no—
185C24×C3—31no—
186C24×C3C22×D311yescharacteristic
187C24×C3C22×D311yescharacteristic
188C23×D3D1211yescharacteristic
189C2×C3×D4—32no—
190C2×C3×D4—32no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—41no—
201C22×C3×C4—61no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4—122no—
206C2×#67—21no—
207C2×#67—21no—
208C2×#67—21no—
209C2×#67—21no—
210C2×#67Dic612yes—
211C2×#67C2×Dic312yes—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—42no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—121no—
228C22×Dic3D1211yescharacteristic
229C22×Dic3#6711yescharacteristic
230C22×Dic3#6711yescharacteristic
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C3×C4⋊C4—122no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—21no—
236C3×C22⋊C4—22no—
237C3×C22⋊C4—32no—
238C3×C22⋊C4—41no—
239C3×C22⋊C4—61no—
240C3×C22⋊C4—61no—
241C3×C22⋊C4—61no—
242C3×C22⋊C4C4×D312yescomplemented
243C3×C22⋊C4C2×Dic312yescomplemented
244#217—21no—
245#217—21no—
246#217—21no—
247#217—61no—
248#217—61no—
249#217—61no—
250#217—61no—
251#217—61no—
252#217—61no—
253#217—62no—
254#217—61no—
255#217—61no—
256#217—61no—
257#217—61no—
258#217—121no—
259#217—121no—
260#217—121no—
261#217—122no—
262#217C2×Dic312yescomplemented
263(C2×D3)⋊C4—61no—
264(C2×D3)⋊C4—61no—
265(C2×D3)⋊C4—122no—
266C4⋊Dic3—42no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3—122no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—122no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C4×Dic3—61no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32C2×C4⋊C411yescharacteristic
288C22×C32C4×D411yescharacteristic
289C22×C32C4×D411yescharacteristic
290C22×C32#12011yescharacteristic
291C22×C32C22⋊Q811yescharacteristic
292C22×C32C22⋊Q811yescharacteristic
293C22×C32#12311yescharacteristic
294C2×C3×D3—22no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C2×C3×D3—42no—
298C2×C3×D3—81no—
299C32×C4—42no—
300C3⋊Dic3—41no—
301C3⋊Dic3—41no—
302C3⋊Dic3—81no—
303C3×Dic3—22no—
304C3×Dic3—42no—
305C3×Dic3—41no—
306C3×Dic3—42no—
307C3×Dic3—41no—
308C22×D4—31no—
309C23×C4—31no—
310C4×D4—181no—
311C4×D4—181no—
312C4×D4—181no—
313C4×D4—181no—
314#117—181no—
315C2×C4⋊C4—61no—
316C2×C4⋊C4—181no—
317C2×C22⋊C4—31no—
318C2×C22⋊C4—31no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—181no—
322C2×C22⋊C4—181no—
323C2×C22⋊C4D3211yescharacteristic
324#99—34no—
325#95—61no—
326#95—181no—
327#95—181no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—32no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—61no—
341C23×C3—61no—
342C23×C3—81no—
343C23×C3—81no—
344C23×C3—121no—
345C23×C3—121no—
346C23×C3C2×Dic611yescharacteristic
347C23×C3C2×C4×D311yescharacteristic
348C23×C3C2×D1211yescharacteristic
349C23×C3#23511yescharacteristic
350C23×C3D3×D411yescharacteristic
351C23×C3D3×D411yescharacteristic
352C23×C3D3×D411yescharacteristic
353C23×C3D3×D411yescharacteristic
354C23×C3#23711yescharacteristic
355C23×C3#23711yescharacteristic
356C23×C3D3×Q811yescharacteristic
357C23×C3#23911yescharacteristic
358C23×C3C22×Dic311yescharacteristic
359C23×C3C2×#6711yescharacteristic
360C22×D3—21no—
361C22×D3—21no—
362C22×D3—41no—
363C22×D3—41no—
364C22×D3C4⋊Dic312yescomplemented
365C3×D4—62no—
366C3×D4—62no—
367C3×D4—62no—
368C3×D4—62no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—32no—
372C2×C3×C4—42no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—62no—
385C2×C3×C4—81no—
386C2×C3×C4—81no—
387C2×C3×C4—121no—
388C2×C3×C4—121no—
389C2×C3×C4—121no—
390C2×C3×C4—121no—
391C2×C3×C4—121no—
392C2×C3×C4—121no—
393C2×C3×C4—121no—
394C2×C3×C4—121no—
395#67—22no—
396#67—22no—
397#67—22no—
398#67—22no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—41no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C2×Dic3—41no—
413C2×Dic3—41no—
414C2×Dic3—41no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—121no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3—121no—
425C2×Dic3—121no—
426C2×Dic3—122no—
427C2×Dic3—121no—
428C2×Dic3—121no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—121no—
432C2×Dic3—241no—
433C2×Dic3—241no—
434C2×Dic3—241no—
435C2×Dic3—241no—
436C2×Dic3—241no—
437C2×Dic3—241no—
438C2×Dic3C4⋊Dic312yescomplemented
439C4×D3—241no—
440C4×D3—241no—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32—21no—
444C2×C32—21no—
445C2×C32—21no—
446C2×C32—21no—
447C2×C32#38511yescharacteristic
448C2×C32B(4,𝔽2)11yescharacteristic
449C2×C32#45811yescharacteristic
450C3×D3—42no—
451C24—31no—
452C24C2×D3211yescharacteristic
453C2×D4—32no—
454C2×D4—32no—
455C2×D4—61no—
456C2×D4—61no—
457C2×D4—61no—
458C2×D4—61no—
459C22×C4—21no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—122no—
470C22×C4—181no—
471C22×C4—181no—
472C22×C4—181no—
473C4⋊C4—122no—
474C4⋊C4—181no—
475C4⋊C4—181no—
476C4⋊C4—362no—
477C22⋊C4—21no—
478C22⋊C4—32no—
479C22⋊C4—61no—
480C22⋊C4—61no—
481C22⋊C4—61no—
482C22⋊C4—181no—
483C22⋊C4—181no—
484C22⋊C4—181no—
485C22⋊C4—181no—
486C22⋊C4—181no—
487C22⋊C4—181no—
488C22⋊C4—362no—
489C22⋊C4D3×Dic312yescomplemented
490C42—181no—
491C42—181no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—41no—
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—41no—
525C22×C3—62no—
526C22×C3—81no—
527C22×C3—81no—
528C22×C3—81no—
529C22×C3—81no—
530C22×C3—122no—
531C22×C3—121no—
532C22×C3—121no—
533C22×C3—241no—
534C22×C3#87811yescharacteristic
535C22×C3#87811yescharacteristic
536C22×C3#88211yescharacteristic
537C22×C3#88611yescharacteristic
538C22×C3D3×C4⋊C411yescharacteristic
539C22×C3#89311yescharacteristic
540C22×C3#89411yescharacteristic
541C22×C3#89611yescharacteristic
542C22×C3C2×C4⋊Dic311yescharacteristic
543C22×C3C4×#6711yescharacteristic
544C22×C3D4×Dic311yescharacteristic
545C22×C3D4×Dic311yescharacteristic
546C22×C3#93711yescharacteristic
547C22×C3#94611yescharacteristic
548C2×D3—22no—
549C2×D3—41no—
550C2×D3—41no—
551C2×D3—42no—
552C2×D3—81no—
553C3×C4—42no—
554C3×C4—42no—
555C3×C4—62no—
556C3×C4—82no—
557C3×C4—122no—
558C3×C4—121no—
559C3×C4—122no—
560C3×C4—121no—
561Dic3—22no—
562Dic3—42no—
563Dic3—42no—
564Dic3—41no—
565Dic3—41no—
566Dic3—121no—
567Dic3—121no—
568Dic3—121no—
569Dic3—121no—
570Dic3—241no—
571Dic3—241no—
572Dic3—241no—
573Dic3—241no—
574Dic3—242no—
575C32#186711yescharacteristic, complemented, Sylow
576C23—32no—
577C23—41no—
578C23—41no—
579C23—61no—
580C23—61no—
581C23—121no—
582C23—121no—
583C23D3×Dic611yescharacteristic
584C23#379611yescharacteristic
585C23D3×D1211yescharacteristic
586C23#380211yescharacteristic
587C23C2×D3×Dic311yescharacteristic
588C23#380411yescharacteristic
589C23D3×#6711yescharacteristic
590D4—62no—
591D4—62no—
592D4—62no—
593D4—62no—
594C2×C4—22no—
595C2×C4—32no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—61no—
599C2×C4—61no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—62no—
604C2×C4—61no—
605C2×C4—61no—
606C2×C4—121no—
607C2×C4—121no—
608C2×C4—121no—
609C2×C4—121no—
610C2×C4—121no—
611C2×C4—121no—
612C2×C4—121no—
613C2×C4—121no—
614C2×C4—181no—
615C2×C4—181no—
616C2×C4—361no—
617C2×C4—361no—
618C2×C4—361no—
619C2×C4—361no—
620C2×C4—361no—
621C2×C4—721no—
622C2×C4—721no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—41no—
639C2×C3—41no—
640C2×C3—41no—
641C2×C3—41no—
642C2×C3—41no—
643C2×C3—41no—
644C2×C3—122no—
645C2×C3#474111yescharacteristic
646C2×C3#474211yescharacteristic
647C2×C3#495011yescharacteristic
648C2×C3#498911yescharacteristic
649C2×C3#503211yescharacteristic
650C2×C3#505311yescharacteristic
651D3—42no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—62no—
663C22—122no—
664C22—121no—
665C22—121no—
666C22—241no—
667C22#6388711yescharacteristic
668C22D3×C4⋊Dic311yescharacteristic
669C22#6389011yescharacteristic
670C22#6389811yescharacteristic
671C22#6389911yescharacteristic
672C22#6392211yescharacteristic
673C22Dic3×#6711yescharacteristic
674C4—42no—
675C4—62no—
676C4—122no—
677C4—122no—
678C4—121no—
679C4—121no—
680C4—361no—
681C4—361no—
682C4—721no—
683C3—21no—
684C3#6959511yescharacteristic, complemented
685C3#7002111yescharacteristic, complemented
686C2—21no—
687C2—21no—
688C2—21no—
689C2—21no—
690C2—21no—
691C2—21no—
692C2—122no—
693C2#1059040711yescharacteristic
694C2#1059040811yescharacteristic
695C2#1059137711yescharacteristic
subgroupG/H
centerC22#63922
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC22×C3×#67C22
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1867
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4950C2semidirect
4. #10591718C2semidirect
6. #10589393C2semidirect
7. #10589186C2semidirect
27. C3×#806C4semidirect
39. #4950D3semidirect
68. C32×C22⋊C4C2×C4semidirect
76. C3×#217C2×C4semidirect
129. #806Dic3semidirect
143. C22×C3×D3C4⋊C4semidirect
174. C2×C3×Dic3C4⋊C4semidirect
242. C3×C22⋊C4C4×D3semidirect
243. C3×C22⋊C4C2×Dic3semidirect
262. #217C2×Dic3semidirect
364. C22×D3C4⋊Dic3semidirect
438. C2×Dic3C4⋊Dic3semidirect
489. C22⋊C4D3×Dic3semidirect
575. C32#1867semidirect
684. C3#69595semidirect
685. C3#70021semidirect

Maximal subgroups

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

subgroupindex
#105955062
C2×C3×#8062
C3×#49502
#105917182
#105917102
#105893932
#105891862
#700213
#695953