Finite Group Databasebeta

← #11773318

Subgroups — #11773318

Order 1152.

1897 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic, complemented
3C22×#3722C212yesmaximal
4C2×C3×C3⋊#95C212yesmaximal, complemented
5C2×#63579C211yesmaximal, characteristic, complemented
6#69428—32nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2212yes—
12C2×#3752—22no—
13C2×#3752—22no—
14C2×#3752C414yescomplemented
15C2×#3724—22no—
16C2×#3724—24no—
17C2×#3722—24no—
18C2×#3722—24no—
19C2×#3722—24no—
20C3×C3⋊#95—24no—
21#63579—22no—
22C22×(C2×D3)⋊C4—32no—
23C22×(C2×D3)⋊C4—32no—
24C22×(C2×D3)⋊C4—32no—
25C22×(C2×D3)⋊C4—61no—
26C22×Dic3⋊C4—32no—
27C2×C3×#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95D312yescomplemented
30C24×C32C2311yescharacteristic
31C23×C3⋊D3—21no—
32C23×C3⋊D3—21no—
33C23×C3⋊D3—22no—
34C23×C3⋊D3—22no—
35C23×C3⋊D3—21no—
36C23×C3⋊D3—21no—
37C23×C3⋊D3—22no—
38C23×C3⋊D3—22no—
39C23×C3⋊D3C2×C412yes—
40C23×C3⋊D3D412yes—
41C23×C3⋊D3Q812yes—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—22no—
45C22×C32×C4—22no—
46C22×C32×C4C2×C412yes—
47C22×C3⋊Dic3—22no—
48C22×C3⋊Dic3—22no—
49C22×C3⋊Dic3C2×C412yes—
50C22×C3⋊Dic3D412yes—
51C22×C3⋊Dic3D412yes—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—22no—
58C22×C3×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3D414yes—
65C22×C3×Dic3D414yes—
66#3752—28no—
67#3724—28no—
68#3722—216no—
69#1439—91noSylow
70C24×D3—32no—
71C24×D3—61no—
72C23×C3×C4—21no—
73C23×C3×C4—32no—
74C23×C3×C4—32no—
75C23×C3×C4C2×D312yes—
76C23×Dic3—32no—
77C23×Dic3—61no—
78C23×Dic3C2×D312yes—
79C23×Dic3C2×D312yes—
80C2×(C2×D3)⋊C4—38no—
81C2×(C2×D3)⋊C4—64no—
82C2×(C2×D3)⋊C4—64no—
83C2×(C2×D3)⋊C4—64no—
84C2×(C2×D3)⋊C4—64no—
85C2×(C2×D3)⋊C4—64no—
86C2×(C2×D3)⋊C4—64no—
87C2×(C2×D3)⋊C4—64no—
88C2×(C2×D3)⋊C4—64no—
89C2×(C2×D3)⋊C4—64no—
90C2×(C2×D3)⋊C4—64no—
91C2×(C2×D3)⋊C4—64no—
92C2×Dic3⋊C4—64no—
93C2×Dic3⋊C4—64no—
94C2×Dic3⋊C4—64no—
95C3×#95—64no—
96C3⋊#95—24no—
97C3⋊#95—64no—
98C23×C32C22×C411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32C2×D411yescharacteristic
101C23×C32C2×D411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×D412yes—
104C23×C32C2×Q811yescharacteristic
105C23×C32#4111yescharacteristic
106C23×C32#4111yescharacteristic
107C23×C32#4112yes—
108C23×C32#4112yes—
109C22×C3⋊D3—22no—
110C22×C3⋊D3—22no—
111C22×C3⋊D3—22no—
112C22×C3⋊D3—22no—
113C22×C3⋊D3—22no—
114C22×C3⋊D3—22no—
115C22×C3⋊D3—24no—
116C22×C3⋊D3—24no—
117C22×C3⋊D3—24no—
118C22×C3⋊D3—24no—
119C22×C3⋊D3—24no—
120C22×C3⋊D3—24no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—42no—
123C22×C3⋊D3—42no—
124C22×C3⋊D3—42no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—42no—
127C22×C3⋊D3—42no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—42no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3C4⋊C414yescomplemented
132C2×C32×C4—22no—
133C2×C32×C4—24no—
134C2×C32×C4—42no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C3⋊Dic3—24no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—24no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3C22⋊C414yescomplemented
142C2×C3×Dic3—24no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—24no—
148C2×C3×Dic3—42no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3—42no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—42no—
156C22×C4⋊C4—91no—
157C22×C22⋊C4—91no—
158C22×C22⋊C4—92no—
159C2×#95—32no—
160C2×#95—91no—
161C24×C3—21no—
162C24×C3C22×D312yes—
163C23×D3—34no—
164C23×D3—34no—
165C23×D3—34no—
166C23×D3—62no—
167C23×D3—62no—
168C23×D3—62no—
169C23×D3—62no—
170C23×D3—62no—
171C23×D3—62no—
172C23×D3—62no—
173C23×D3—62no—
174C23×D3—62no—
175C23×D3—62no—
176C23×D3—62no—
177C23×D3—62no—
178C23×D3—62no—
179C23×D3—62no—
180C23×D3—62no—
181C23×D3—62no—
182C23×D3—62no—
183C23×D3—62no—
184C23×D3—62no—
185C23×D3—122no—
186C23×D3—122no—
187C23×D3—122no—
188C23×D3—122no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—34no—
199C22×C3×C4—34no—
200C22×C3×C4—42no—
201C22×C3×C4—42no—
202C22×C3×C4—62no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4—62no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4—62no—
209C22×C3×C4—62no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C22×C3×C4—62no—
213C22×C3×C4—62no—
214C22×C3×C4C4×D314yes—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—34no—
228C22×Dic3—34no—
229C22×Dic3—34no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3—122no—
238C22×Dic3—122no—
239C22×Dic3D1214yes—
240C22×Dic3#6714yes—
241(C2×D3)⋊C4—616no—
242(C2×D3)⋊C4—616no—
243(C2×D3)⋊C4—616no—
244(C2×D3)⋊C4—616no—
245Dic3⋊C4—616no—
246C22×C32C2×C22⋊C411yescharacteristic
247C22×C32C2×C4⋊C411yescharacteristic
248C22×C32#11711yescharacteristic
249C22×C32C4×D412yes—
250C22×C32C4×D412yes—
251C22×C32#12011yescharacteristic
252C22×C32#12012yes—
253C22×C32#12111yescharacteristic
254C22×C32#12111yescharacteristic
255C22×C32#12112yes—
256C22×C32#12112yes—
257C22×C32#12112yes—
258C22×C32C22⋊Q811yescharacteristic
259C22×C32C22⋊Q811yescharacteristic
260C22×C32C22⋊Q812yes—
261C22×C32C22⋊Q812yes—
262C22×C32#12312yes—
263C22×C32#12311yescharacteristic
264C22×C32#12312yes—
265C22×C32#12412yes—
266C22×C32#12411yescharacteristic
267C22×C32#12612yes—
268C22×C32#12711yescharacteristic
269C2×C3⋊D3—24no—
270C2×C3⋊D3—28no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—44no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—44no—
277C2×C3⋊D3—44no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C32×C4—42no—
281C3⋊Dic3—24no—
282C3×Dic3—44no—
283C3×Dic3—44no—
284C25—91no—
285C23×C4—32no—
286C23×C4—32no—
287C23×C4—91no—
288C23×C4D3211yescharacteristic
289C2×C4⋊C4—184no—
290C2×C4⋊C4—182no—
291C2×C22⋊C4—94no—
292C2×C22⋊C4—182no—
293C2×C22⋊C4—182no—
294C2×C22⋊C4—184no—
295C2×C22⋊C4—184no—
296C2×C22⋊C4—184no—
297#95—64no—
298#95—182no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—21no—
305C23×C3—22no—
306C23×C3—21no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3C2×C4×D312yes—
311C23×C3C2×D1212yes—
312C23×C3#23512yes—
313C23×C3#23512yes—
314C23×C3#23512yes—
315C23×C3#23512yes—
316C23×C3D3×D412yes—
317C23×C3D3×D412yes—
318C23×C3D3×D412yes—
319C23×C3D3×D412yes—
320C23×C3D3×D412yes—
321C23×C3#23712yes—
322C23×C3D3×Q812yes—
323C23×C3#23912yes—
324C23×C3C2×#6712yes—
325C22×D3—38no—
326C22×D3—64no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3—64no—
330C22×D3—64no—
331C22×D3—64no—
332C22×D3—64no—
333C22×D3—64no—
334C22×D3—64no—
335C22×D3—64no—
336C22×D3—64no—
337C22×D3—64no—
338C22×D3—64no—
339C22×D3—64no—
340C22×D3—64no—
341C22×D3—64no—
342C22×D3—64no—
343C22×D3—64no—
344C22×D3—64no—
345C22×D3—64no—
346C22×D3—64no—
347C22×D3—64no—
348C22×D3—64no—
349C22×D3—64no—
350C22×D3—64no—
351C22×D3—124no—
352C22×D3—124no—
353C22×D3—124no—
354C22×D3—124no—
355C22×D3—124no—
356C22×D3—124no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3—124no—
360C22×D3—122no—
361C22×D3—124no—
362C22×D3—124no—
363C22×D3—122no—
364C22×D3—122no—
365C22×D3—124no—
366C22×D3—122no—
367C22×D3—122no—
368C22×D3—122no—
369C22×D3—122no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3—122no—
378C22×D3—122no—
379C22×D3—122no—
380C22×D3—122no—
381C22×D3—122no—
382C22×D3—122no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—44no—
388C2×C3×C4—42no—
389C2×C3×C4—44no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—64no—
396C2×C3×C4—64no—
397C2×C3×C4—64no—
398C2×C3×C4—64no—
399C2×C3×C4—64no—
400C2×C3×C4—64no—
401C2×C3×C4—122no—
402C2×C3×C4—122no—
403C2×C3×C4—122no—
404C2×C3×C4—122no—
405C2×C3×C4—122no—
406C2×C3×C4—122no—
407C2×C3×C4—122no—
408C2×C3×C4—122no—
409C2×Dic3—24no—
410C2×Dic3—24no—
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—24no—
414C2×Dic3—24no—
415C2×Dic3—38no—
416C2×Dic3—42no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—64no—
425C2×Dic3—64no—
426C2×Dic3—64no—
427C2×Dic3—64no—
428C2×Dic3—64no—
429C2×Dic3—64no—
430C2×Dic3—64no—
431C2×Dic3—124no—
432C2×Dic3—122no—
433C2×Dic3—124no—
434C2×Dic3—122no—
435C2×C32#38011yescharacteristic
436C2×C32#38512yes—
437C2×C32#38611yescharacteristic
438C2×C32#38812yes—
439C2×C32#39011yescharacteristic
440C2×C32#39211yescharacteristic
441C2×C32#39311yescharacteristic
442C2×C32#39412yes—
443C2×C32#39612yes—
444C2×C32#39711yescharacteristic
445C2×C32#39911yescharacteristic
446C3⋊D3—44no—
447C24—92no—
448C24—92no—
449C24—92no—
450C24—181no—
451C24—181no—
452C24—182no—
453C24—182no—
454C24—182no—
455C24—182no—
456C24—181no—
457C24—181no—
458C24C2×D3211yescharacteristic
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—34no—
464C22×C4—34no—
465C22×C4—62no—
466C22×C4—62no—
467C22×C4—62no—
468C22×C4—62no—
469C22×C4—62no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—62no—
475C22×C4—62no—
476C22×C4—62no—
477C22×C4—92no—
478C22×C4—92no—
479C22×C4—92no—
480C22×C4—182no—
481C22×C4—182no—
482C22×C4#62412yes—
483C4⋊C4—188no—
484C22⋊C4—188no—
485C22⋊C4—1816no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—22no—
492C22×C3—21no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—21no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3#87212yes—
510C22×C3C4×D1212yes—
511C22×C3#87512yes—
512C22×C3#87612yes—
513C22×C3D3×C22⋊C412yes—
514C22×C3#67⋊C412yes—
515C22×C3#88212yes—
516C22×C3#88212yes—
517C22×C3#88312yes—
518C22×C3#88412yes—
519C22×C3#88412yes—
520C22×C3#88412yes—
521C22×C3#88412yes—
522C22×C3#88412yes—
523C22×C3#88512yes—
524C22×C3#88512yes—
525C22×C3D3×C4⋊C412yes—
526C22×C3#89312yes—
527C22×C3#89412yes—
528C22×C3#89412yes—
529C22×C3#89412yes—
530C22×C3#89512yes—
531C22×C3#89612yes—
532C22×C3#89612yes—
533C22×C3#89612yes—
534C22×C3#89612yes—
535C22×C3#89712yes—
536C22×C3#89812yes—
537C22×C3C4×#6712yes—
538C22×C3#92912yes—
539C22×C3#93012yes—
540C22×C3#93712yes—
541C22×C3#93912yes—
542C22×C3#94012yes—
543C22×C3#94612yes—
544C2×D3—68no—
545C2×D3—68no—
546C2×D3—68no—
547C2×D3—68no—
548C2×D3—128no—
549C2×D3—128no—
550C2×D3—128no—
551C2×D3—124no—
552C2×D3—124no—
553C2×D3—124no—
554C2×D3—128no—
555C2×D3—124no—
556C2×D3—124no—
557C2×D3—124no—
558C2×D3—124no—
559C2×D3—124no—
560C2×D3—124no—
561C2×D3—124no—
562C2×D3—124no—
563C2×D3—124no—
564C2×D3—124no—
565C2×D3—124no—
566C2×D3—124no—
567C2×D3—124no—
568C2×D3—124no—
569C2×D3—124no—
570C3×C4—44no—
571C3×C4—44no—
572C3×C4—124no—
573C3×C4—124no—
574Dic3—44no—
575Dic3—44no—
576Dic3—68no—
577Dic3—124no—
578C32#143911yescharacteristic, complemented, Sylow
579C23—94no—
580C23—184no—
581C23—182no—
582C23—182no—
583C23—182no—
584C23—184no—
585C23—184no—
586C23—184no—
587C23—182no—
588C23—182no—
589C23—184no—
590C23—184no—
591C23—182no—
592C23—362no—
593C23—362no—
594C23—362no—
595C23—361no—
596C23—362no—
597C23—362no—
598C23—361no—
599C23—361no—
600C23—362no—
601C23—361no—
602C23#379711yescharacteristic
603C23#379811yescharacteristic
604C23#379811yescharacteristic
605C23#379912yes—
606C23D3×D1212yes—
607C23#380211yescharacteristic
608C23#380412yes—
609C23C2×#62411yescharacteristic
610C23D3×#6712yes—
611C23#381111yescharacteristic
612C23#381111yescharacteristic
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—64no—
619C2×C4—64no—
620C2×C4—64no—
621C2×C4—64no—
622C2×C4—64no—
623C2×C4—64no—
624C2×C4—94no—
625C2×C4—122no—
626C2×C4—122no—
627C2×C4—122no—
628C2×C4—122no—
629C2×C4—122no—
630C2×C4—122no—
631C2×C4—122no—
632C2×C4—122no—
633C2×C4—184no—
634C2×C4—182no—
635C2×C4—184no—
636C2×C4—182no—
637C2×C3—22no—
638C2×C3—22no—
639C2×C3—21no—
640C2×C3—22no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—22no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3#466512yes—
649C2×C3#466712yes—
650C2×C3#466812yes—
651C2×C3#466912yes—
652C2×C3#467212yes—
653C2×C3#467312yes—
654C2×C3#467512yes—
655C2×C3#467612yes—
656C2×C3#494012yes—
657C2×C3#495712yes—
658C2×C3#495912yes—
659C2×C3#496012yes—
660C2×C3#498912yes—
661C2×C3#499312yes—
662C2×C3#499412yes—
663D3—128no—
664D3—128no—
665C22—184no—
666C22—188no—
667C22—364no—
668C22—364no—
669C22—362no—
670C22—362no—
671C22—362no—
672C22—364no—
673C22—362no—
674C22—362no—
675C22—362no—
676C22#6385012yes—
677C22#6385212yes—
678C22#6385412yes—
679C22#6386511yescharacteristic
680C22#6386511yescharacteristic
681C22#6386812yes—
682C22#6387411yescharacteristic
683C22#6388812yes—
684C22#6389412yes—
685C22#6389512yes—
686C22#6389711yescharacteristic
687C22#6390011yescharacteristic
688C22#6390612yes—
689C22#6391012yes—
690C22#6391211yescharacteristic
691C22#6391211yescharacteristic
692C22#6392212yes—
693C22#6392311yescharacteristic
694C22#6395212yes—
695C22#6395311yescharacteristic
696C22#6397112yes—
697C22#6397411yescharacteristic
698C22#6397911yescharacteristic
699C4—42no—
700C4—124no—
701C4—124no—
702C4—184no—
703C3—21no—
704C3#6942812yescomplemented
705C2—364no—
706C2#1059120212yes—
707C2#1059120311yescharacteristic
708C2#1059120511yescharacteristic
709C2#1059121611yescharacteristic
710C2#1059129212yes—
711C2#1059134712yes—
712C2#1059135511yescharacteristic
713C2#1059137812yes—
714C2#1059138011yescharacteristic
715C2#1059139311yescharacteristic
716C2#1059170411yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, cosocleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32#1439
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3724C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. C2×#63579C2semidirect
14. C2×#3752C4semidirect
29. C2×C3⋊#95D3semidirect
131. C22×C3⋊D3C4⋊C4semidirect
141. C2×C3⋊Dic3C22⋊C4semidirect
578. C32#1439semidirect
704. C3#69428semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C22×#37242
C22×#37222
C2×C3×C3⋊#952
C2×#635792
#694283