Finite Group Databasebeta

← #11802865

Subgroups — #11802865

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic
3C3×#5212C211yesmaximal, characteristic
4#10591702C212yesmaximal
5#10591701C212yesmaximal
6#10591349C211yesmaximal, characteristic, complemented
7#10591270C212yesmaximal, complemented
8#10591269C212yesmaximal, complemented
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591224C211yesmaximal, characteristic, complemented
12#82231—31nomaximal
13#73868—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C2×#3757C2212yes—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C3×#217C2212yes—
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C3×#926C418yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63658C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×#117—31no—
39C2×#926D311yescharacteristic
40C3×#380—31no—
41#5212—31no—
42#5212—31no—
43#5212—61no—
44#5212D311yescharacteristic
45#4980—32no—
46#4980—32no—
47#4977—31no—
48#4975—31no—
49Dic3×C4⋊C4—31no—
50Dic3×C4⋊C4—31no—
51#4951—32no—
52#4951—32no—
53#4945—32no—
54#4944—32no—
55#4936—31no—
56#4935—31no—
57C4×C4⋊Dic3—31no—
58C4×C4⋊Dic3—31no—
59#4654—32no—
60#4653—32no—
61C24×C32C2311yescharacteristic
62C22×C32×C4—22no—
63C22×C32×C4—22no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75#3757—42no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)—22no—
78C3×#217—42no—
79C3×#217C2×C414yes—
80C3×#217C2×C414yes—
81C3×C4⋊Dic3—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3C2×C414yes—
84C3×C4⋊Dic3C2×C414yes—
85C3×C4×Dic3C2×C414yes—
86C3×C4×Dic3C2×C414yes—
87Dic3⋊Dic3—42no—
88Dic3⋊Dic3—42no—
89Dic32—42no—
90Dic32—42no—
91#2314—91noSylow
92C23×C3×C4—21no—
93C23×C3×C4C2×D311yescharacteristic
94C23×C3×C4C2×D311yescharacteristic
95C3×#117—38no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C22⋊C4—31no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C42—31no—
104C2×C3×C42—31no—
105C2×#217—32no—
106C2×#217—32no—
107C2×#217—62no—
108C2×#217C2×D312yes—
109C2×#217C2×D311yescharacteristic
110C2×#217C2×D311yescharacteristic
111#926Dic318yescomplemented
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×C4⋊Dic3C2×D311yescharacteristic
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3C2×D311yescharacteristic
131C2×C4×Dic3C2×D311yescharacteristic
132C3×#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—62no—
144C3⋊#95C2×D312yes—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32C22×C412yes—
152C23×C32C2411yescharacteristic
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—28no—
156C2×C32×C4C22×C412yes—
157C2×C32×C4C22×C412yes—
158C2×C32×C4#4112yes—
159C2×C32×C4#4112yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C412yes—
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3C22×C412yes—
184C2×#117—31no—
185#388—92no—
186#388—92no—
187#387—92no—
188#387—92no—
189#384—91no—
190#382—91no—
191#380—31no—
192#380—91no—
193C4×C4⋊C4—91no—
194C4×C4⋊C4—91no—
195C24×C3—21no—
196C24×C3C22×D311yescharacteristic
197C24×C3C22×D311yescharacteristic
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—24no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—42no—
212C22×C3×C4—42no—
213C22×C3×C4C4×D314yes—
214C22×C3×C4C2×Dic314yes—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D311yescharacteristic
231C3×C4⋊C4—34no—
232C3×C4⋊C4—34no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C22⋊C4—34no—
236C3×C22⋊C4—34no—
237C3×C22⋊C4—122no—
238C3×C42—34no—
239C3×C42—34no—
240#217—42no—
241#217—122no—
242#217—122no—
243#217—124no—
244#217C2×Dic314yes—
245#217C2×Dic314yes—
246C4⋊Dic3—22no—
247C4⋊Dic3—22no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3—122no—
253C4⋊Dic3—122no—
254C4⋊Dic3—122no—
255C4⋊Dic3—122no—
256C4⋊Dic3C2×Dic314yes—
257C4⋊Dic3C2×Dic314yes—
258Dic3⋊C4—122no—
259Dic3⋊C4—122no—
260C4×Dic3—122no—
261C4×Dic3—122no—
262C4×Dic3—122no—
263C4×Dic3—122no—
264C4×Dic3C2×Dic314yes—
265C4×Dic3C2×Dic314yes—
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—22no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32C23×C411yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C32C2×#4111yescharacteristic
276C22×C32H(5,𝔽2)11yescharacteristic
277C22×C32H(5,𝔽2)11yescharacteristic
278C22×C322−1+411yescharacteristic
279C22×C322−1+411yescharacteristic
280C32×C4—22no—
281C32×C4#11714yes—
282C3⋊Dic3—42no—
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—42no—
289C3×Dic3—42no—
290C23×C4D3211yescharacteristic
291#117—38no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—92no—
299C2×C4⋊C4—92no—
300C2×C22⋊C4—31no—
301C2×C22⋊C4—31no—
302C2×C22⋊C4—32no—
303C2×C22⋊C4—92no—
304C2×C42—31no—
305C2×C42—31no—
306C2×C42—92no—
307C2×C42—92no—
308#95—32no—
309#95—92no—
310#95—92no—
311#95—92no—
312#95—92no—
313#95—92no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—22no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3C2×C4×D312yes—
335C23×C3C22×Dic312yes—
336C23×C3C23×D311yescharacteristic
337C23×C3C23×D311yescharacteristic
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—28no—
343C2×C3×C4—28no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—48no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4C2×C4×D312yes—
370C2×C3×C4C2×C4×D312yes—
371C2×C3×C4#23512yes—
372C2×C3×C4#23512yes—
373C2×C3×C4#23712yes—
374C2×C3×C4#23712yes—
375C2×C3×C4C22×Dic312yes—
376C2×C3×C4C22×Dic312yes—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408C2×Dic3—122no—
409C2×Dic3C22×Dic312yes—
410C2×Dic3C22×Dic312yes—
411C2×Dic3C22×Dic312yes—
412C2×Dic3C22×Dic312yes—
413C2×C32—42no—
414C2×C32C2×#11711yescharacteristic
415C2×C32#52011yescharacteristic
416C2×C32#52011yescharacteristic
417C2×C32#54011yescharacteristic
418C2×C32#54111yescharacteristic
419C2×C32#54211yescharacteristic
420C2×C32#54211yescharacteristic
421C24C2×D3211yescharacteristic
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4—92no—
431C22×C4—92no—
432C22×C4D3×Dic314yes—
433C22×C4C2×D3211yescharacteristic
434C22×C4C2×D3211yescharacteristic
435C4⋊C4—34no—
436C4⋊C4—34no—
437C4⋊C4—62no—
438C4⋊C4—62no—
439C4⋊C4—182no—
440C4⋊C4—182no—
441C4⋊C4—362no—
442C4⋊C4—362no—
443C22⋊C4—34no—
444C22⋊C4—34no—
445C22⋊C4—122no—
446C22⋊C4—362no—
447C42—34no—
448C42—34no—
449C42—362no—
450C42—362no—
451C22×C3—24no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3C22×C4×D311yescharacteristic
480C22×C3C2×#23511yescharacteristic
481C22×C3C2×#23511yescharacteristic
482C22×C3C2×#23711yescharacteristic
483C22×C3C2×#23711yescharacteristic
484C22×C3#100411yescharacteristic
485C22×C3#100711yescharacteristic
486C22×C3#100911yescharacteristic
487C22×C3#100911yescharacteristic
488C22×C3#100911yescharacteristic
489C22×C3#101011yescharacteristic
490C22×C3#101011yescharacteristic
491C22×C3#101011yescharacteristic
492C22×C3C23×Dic311yescharacteristic
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—24no—
496C3×C4—42no—
497C3×C4—62no—
498C3×C4—62no—
499C3×C4—62no—
500C3×C4—62no—
501C3×C4—122no—
502C3×C4—122no—
503C3×C4#87714yes—
504C3×C4#92614yes—
505Dic3—22no—
506Dic3—22no—
507Dic3—22no—
508Dic3—22no—
509Dic3—42no—
510Dic3—42no—
511Dic3—122no—
512Dic3—122no—
513Dic3—122no—
514Dic3—122no—
515Dic3—242no—
516Dic3—242no—
517C32#231411yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23C2×D3×Dic312yes—
525C23C22×D3211yescharacteristic
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—28no—
529C2×C4—32no—
530C2×C4—32no—
531C2×C4—32no—
532C2×C4—32no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4—182no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4—182no—
553C2×C4C2×D3×Dic312yes—
554C2×C4C2×D3×Dic312yes—
555C2×C4#380412yes—
556C2×C4#380412yes—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—44no—
565C2×C3—42no—
566C2×C3—42no—
567C2×C3C2×#87711yescharacteristic
568C2×C3#550411yescharacteristic
569C2×C3#551811yescharacteristic
570C2×C3#552311yescharacteristic
571C2×C3#553411yescharacteristic
572C2×C3#553411yescharacteristic
573C2×C3#553511yescharacteristic
574C2×C3#560311yescharacteristic
575C2×C3#561911yescharacteristic
576C2×C3#562511yescharacteristic
577C2×C3#564311yescharacteristic
578C2×C3C2×#92611yescharacteristic
579C2×C3#582711yescharacteristic
580C2×C3#582711yescharacteristic
581C22—22no—
582C22—22no—
583C22—22no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22#6429711yescharacteristic
589C22#6429811yescharacteristic
590C22#6430711yescharacteristic
591C22#6430811yescharacteristic
592C22C22×D3×Dic311yescharacteristic
593C22C2×#380411yescharacteristic
594C22C2×#380411yescharacteristic
595C4—22no—
596C4—62no—
597C4—62no—
598C4—62no—
599C4—62no—
600C4—122no—
601C4—122no—
602C4—362no—
603C4—362no—
604C4#6395514yes—
605C3—21no—
606C3#7386811yescharacteristic, complemented
607C3#8223111yescharacteristic, complemented
608C2—42no—
609C2#1059481411yescharacteristic
610C2#1059482411yescharacteristic
611C2#1059498311yescharacteristic
612C2#1059498511yescharacteristic
613C2#1059498611yescharacteristic
614C2#1059499211yescharacteristic
615C2C2×#6395511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2314
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591349C2semidirect
7. #10591270C2semidirect
8. #10591269C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591224C2semidirect
21. C3×#926C4semidirect
111. #926Dic3semidirect
517. C32#2314semidirect
606. C3#73868semidirect
607. C3#82231semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
#105929112
C3×#52122
#105917022
#105917012
#105913492
#105912702
#105912692
Dic3×C4⋊Dic32
#105912242
#822313
#738683