Finite Group Databasebeta

← #11803489

Subgroups — #11803489

Order 1152.

1277 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
1C2×#64135C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C2×#63843C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic
5#10591702C212yesmaximal
6#10591701C212yesmaximal
7#10591357C211yesmaximal, characteristic, complemented
8#10591274C211yesmaximal, characteristic, complemented
9#10591272C212yesmaximal, complemented
10#10591268C212yesmaximal, complemented
11#10591221C211yesmaximal, characteristic, complemented
12#82744—31nomaximal
13#73871—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×#3757C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18#64135—24no—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C418yescomplemented
29C2×C3×Dic3⋊C4C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34#63843—24no—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C22⋊Q8—31no—
41C2×Q8×Dic3—31no—
42C2×#926—31no—
43C2×#926—31no—
44C2×#926—61no—
45C2×#924D311yescharacteristic
46C2×#887—31no—
47C3×#380—31no—
48#5229—31no—
49#5212D311yescharacteristic
50#4984—31no—
51#4984—32no—
52#4980—32no—
53Dic3×C4⋊C4—31no—
54Dic3×C4⋊C4—31no—
55#4973—31no—
56#4972—31no—
57#4951—32no—
58#4951—32no—
59#4945—32no—
60#4944—32no—
61#4655—32no—
62#4647—32no—
63C24×C32C2311yescharacteristic
64C22×C32×C4—22no—
65C22×C32×C4—22no—
66C22×C32×C4C2×C414yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2×C414yes—
80#3757—22no—
81#3757—22no—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)—22no—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3D414yes—
86C3×#217—42no—
87C3×#217C2×C418yes—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3C2×C414yes—
91C3×Dic3⋊C4C2×C418yes—
92Dic3⋊Dic3—24no—
93Dic3⋊Dic3—42no—
94Dic32—24no—
95Dic32—42no—
96#2323—91noSylow
97C22×C3×Q8—31no—
98C23×C3×C4—21no—
99C23×C3×C4C2×D311yescharacteristic
100C23×C3×C4C2×D311yescharacteristic
101C22×Dic6C2×D311yescharacteristic
102C3×C22⋊Q8—38no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C22⋊C4—32no—
108C2×C3×C22⋊C4—32no—
109C2×#217—31no—
110C2×#217—31no—
111C2×#217—31no—
112C2×#217—31no—
113C2×#217—61no—
114C2×#217—61no—
115C2×#217C2×D312yes—
116C2×#217C2×D312yes—
117Q8×Dic3—64no—
118#926—64no—
119#926—64no—
120#926—68no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3—61no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×C4⋊Dic3C2×D311yescharacteristic
132#924Dic318yescomplemented
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4C2×D312yes—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—31no—
138C2×C4×Dic3—31no—
139C2×C4×Dic3—31no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—61no—
145C2×C4×Dic3—61no—
146#887—64no—
147C3×#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95C2×D312yes—
157C23×C32—21no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32C22×C412yes—
164C23×C32C2411yescharacteristic
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—28no—
168C2×C32×C4C22×C412yes—
169C2×C32×C4C22×C412yes—
170C2×C32×C4C2×D412yes—
171C2×C32×C4#4112yes—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3C2×D412yes—
183C2×C3⋊Dic3C2×D412yes—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3C22×C414yes—
195C2×C3×Dic3C22×C414yes—
196C3×Dic6—28no—
197C2×C22⋊Q8—31no—
198C2×C4×Q8—91no—
199C2×#117—91no—
200#391—91no—
201#389—92no—
202#389—91no—
203#388—92no—
204#388—92no—
205#387—92no—
206#380—31no—
207C4×C4⋊C4—91no—
208C24×C3—21no—
209C24×C3C22×D311yescharacteristic
210C24×C3C22×D311yescharacteristic
211C2×C3×Q8—34no—
212C2×C3×Q8—62no—
213C2×C3×Q8—62no—
214C22×C3×C4—24no—
215C22×C3×C4—24no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—24no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4C4×D314yes—
228C22×C3×C4C2×Dic314yes—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D312yes—
249C2×Dic6—22no—
250C2×Dic6—22no—
251C2×Dic6C2×Dic314yes—
252C3×C4⋊C4—38no—
253C3×C4⋊C4—34no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—62no—
256C3×C22⋊C4—38no—
257C3×C22⋊C4—122no—
258#217—42no—
259#217—62no—
260#217—62no—
261#217—62no—
262#217—62no—
263#217—64no—
264#217—64no—
265#217C2×Dic318yes—
266C4⋊Dic3—22no—
267C4⋊Dic3—22no—
268C4⋊Dic3—64no—
269C4⋊Dic3—62no—
270C4⋊Dic3—62no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3—64no—
274C4⋊Dic3—64no—
275C4⋊Dic3—122no—
276C4⋊Dic3C2×Dic314yes—
277Dic3⋊C4—64no—
278Dic3⋊C4—122no—
279Dic3⋊C4C2×Dic318yes—
280C4×Dic3—34no—
281C4×Dic3—34no—
282C4×Dic3—64no—
283C4×Dic3—64no—
284C4×Dic3—64no—
285C4×Dic3—64no—
286C4×Dic3—62no—
287C4×Dic3—62no—
288C4×Dic3—122no—
289C4×Dic3—122no—
290C22×C32—22no—
291C22×C32—22no—
292C22×C32—22no—
293C22×C32—41no—
294C22×C32—41no—
295C22×C32—41no—
296C22×C32—41no—
297C22×C32C23×C411yescharacteristic
298C22×C32C22×D411yescharacteristic
299C22×C32C2×#4111yescharacteristic
300C22×C32H(5,𝔽2)11yescharacteristic
301C22×C322−1+411yescharacteristic
302C22×C322−1+411yescharacteristic
303C22×C322−1+411yescharacteristic
304C32×C4—22no—
305C32×C4C4×D414yes—
306C3⋊Dic3—22no—
307C3⋊Dic3—22no—
308C3⋊Dic3—41no—
309C3⋊Dic3—41no—
310C3×Dic3—24no—
311C3×Dic3—24no—
312C3×Dic3—42no—
313C3×Dic3—42no—
314C22×Q8—31no—
315C23×C4D3211yescharacteristic
316C22⋊Q8—38no—
317C4×Q8—184no—
318#117—184no—
319C2×C4⋊C4—31no—
320C2×C4⋊C4—32no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—92no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—92no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—91no—
330C2×C22⋊C4—91no—
331C2×C42—91no—
332C2×C42—92no—
333C2×C42—91no—
334C2×C42—92no—
335#95—32no—
336#95—92no—
337#95—92no—
338#95—92no—
339#95—92no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—22no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3C2×C4×D312yes—
361C23×C3C22×Dic312yes—
362C23×C3C23×D311yescharacteristic
363C23×C3C23×D311yescharacteristic
364C3×Q8—68no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—216no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—28no—
373C2×C3×C4—28no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—34no—
379C2×C3×C4—34no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4C2×C4×D312yes—
391C2×C3×C4C2×C4×D312yes—
392C2×C3×C4D3×D412yes—
393C2×C3×C4D3×D412yes—
394C2×C3×C4#23712yes—
395C2×C3×C4#23712yes—
396C2×C3×C4C22×Dic312yes—
397C2×C3×C4C22×Dic312yes—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—32no—
409C2×Dic3—32no—
410C2×Dic3—32no—
411C2×Dic3—32no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—121no—
437C2×Dic3—121no—
438C2×Dic3—121no—
439C2×Dic3—121no—
440C2×Dic3—121no—
441C2×Dic3—121no—
442C2×Dic3—121no—
443C2×Dic3—121no—
444C2×Dic3C22×Dic314yes—
445C2×Dic3C22×Dic314yes—
446Dic6—28no—
447C2×C32—42no—
448C2×C32C2×C4×D411yescharacteristic
449C2×C32#51911yescharacteristic
450C2×C32#52011yescharacteristic
451C2×C32#53611yescharacteristic
452C2×C32#53711yescharacteristic
453C2×C32#54111yescharacteristic
454C2×C32#54211yescharacteristic
455C24C2×D3211yescharacteristic
456C2×Q8—34no—
457C2×Q8—62no—
458C2×Q8—62no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—32no—
462C22×C4—32no—
463C22×C4—32no—
464C22×C4—32no—
465C22×C4—91no—
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4D3×Dic314yes—
470C22×C4C2×D3211yescharacteristic
471C22×C4C2×D3211yescharacteristic
472C4⋊C4—38no—
473C4⋊C4—34no—
474C4⋊C4—62no—
475C4⋊C4—62no—
476C4⋊C4—182no—
477C4⋊C4—182no—
478C4⋊C4—184no—
479C4⋊C4—362no—
480C22⋊C4—38no—
481C22⋊C4—122no—
482C22⋊C4—182no—
483C22⋊C4—182no—
484C42—94no—
485C42—184no—
486C42—182no—
487C42—362no—
488C22×C3—24no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3C22×C4×D311yescharacteristic
517C22×C3C2×D3×D411yescharacteristic
518C22×C3C2×D3×D411yescharacteristic
519C22×C3C2×#23711yescharacteristic
520C22×C3C2×#23711yescharacteristic
521C22×C3#100411yescharacteristic
522C22×C3#100711yescharacteristic
523C22×C3#100711yescharacteristic
524C22×C3#100711yescharacteristic
525C22×C3#100911yescharacteristic
526C22×C3#101011yescharacteristic
527C22×C3#101011yescharacteristic
528C22×C3#101011yescharacteristic
529C22×C3C23×Dic311yescharacteristic
530C3×C4—24no—
531C3×C4—22no—
532C3×C4—22no—
533C3×C4—24no—
534C3×C4—64no—
535C3×C4—64no—
536C3×C4—122no—
537C3×C4—122no—
538C3×C4#67⋊C414yes—
539C3×C4D4×Dic314yes—
540Dic3—24no—
541Dic3—24no—
542Dic3—42no—
543Dic3—42no—
544Dic3—62no—
545Dic3—62no—
546Dic3—62no—
547Dic3—62no—
548Dic3—122no—
549Dic3—122no—
550Dic3—122no—
551Dic3—122no—
552Dic3—121no—
553Dic3—121no—
554Dic3—121no—
555Dic3—121no—
556C32#232311yescharacteristic, complemented, Sylow
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23C2×D3×Dic312yes—
564C23C22×D3211yescharacteristic
565Q8—68no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—28no—
569C2×C4—34no—
570C2×C4—34no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4C2×D3×Dic312yes—
594C2×C4C2×D3×Dic312yes—
595C2×C4#380512yes—
596C2×C4#381112yes—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—44no—
605C2×C3—42no—
606C2×C3—42no—
607C2×C3C2×#67⋊C411yescharacteristic
608C2×C3#550411yescharacteristic
609C2×C3#551611yescharacteristic
610C2×C3#560311yescharacteristic
611C2×C3#560811yescharacteristic
612C2×C3#562511yescharacteristic
613C2×C3#562511yescharacteristic
614C2×C3#562811yescharacteristic
615C2×C3#562811yescharacteristic
616C2×C3#562911yescharacteristic
617C2×C3#564311yescharacteristic
618C2×C3C2×D4×Dic311yescharacteristic
619C2×C3#581211yescharacteristic
620C2×C3#582711yescharacteristic
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22#6429711yescharacteristic
629C22#6429711yescharacteristic
630C22#6429711yescharacteristic
631C22#6430711yescharacteristic
632C22C22×D3×Dic311yescharacteristic
633C22C2×#380511yescharacteristic
634C22C2×#381111yescharacteristic
635C4—22no—
636C4—64no—
637C4—64no—
638C4—122no—
639C4—122no—
640C4—182no—
641C4—182no—
642C4—361no—
643C4—361no—
644C4#67⋊Dic314yes—
645C3—21no—
646C3#7387111yescharacteristic, complemented
647C3#8274411yescharacteristic, complemented
648C2—42no—
649C2#1059480511yescharacteristic
650C2#1059481811yescharacteristic
651C2#1059482611yescharacteristic
652C2#1059492311yescharacteristic
653C2#1059498411yescharacteristic
654C2#1059498611yescharacteristic
655C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63843C2semidirect
7. #10591357C2semidirect
8. #10591274C2semidirect
9. #10591272C2semidirect
10. #10591268C2semidirect
11. #10591221C2semidirect
28. C3×#924C4semidirect
132. #924Dic3semidirect
556. C32#2323semidirect
646. C3#73871semidirect
647. C3#82744semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×#9242
C2×#638432
C3×#52122
#105917022
#105917012
#105913572
#105912742
#105912722
#105912682
#105912212
#827443
#738713