Finite Group Databasebeta

← #11803490

Subgroups — #11803490

Order 1152.

1273 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic
5#10591703C212yesmaximal
6#10591703C212yesmaximal
7Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8#10591264C212yesmaximal, complemented
9#10591263C212yesmaximal, complemented
10#10591213C211yesmaximal, characteristic, complemented
11#10591212C211yesmaximal, characteristic, complemented
12#82235—31nomaximal
13#73871—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C2×#3757C2212yes—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18#64133C418yescomplemented
19C2×#3750C2212yes—
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2212yes—
23C3×#926—24no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×#3724C2212yes—
31C2×#3724C2212yes—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34#63844—24no—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×#926D311yescharacteristic
42C2×#924—31no—
43C2×#924—31no—
44C2×#924—61no—
45C2×#887—31no—
46C2×C4×Dic6—31no—
47C3×#380—31no—
48#5212D311yescharacteristic
49#4978—32no—
50#4976—32no—
51Dic3×C4⋊C4—31no—
52#4973—31no—
53#4972—31no—
54#4945—32no—
55#4945—32no—
56#4944—32no—
57#4944—32no—
58C4×C4⋊Dic3—31no—
59#4929—31no—
60#4928—31no—
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⋊Dic3C2312yes—
70C22×C3⋊Dic3C2312yes—
71C2×#634—22no—
72C2×#634—22no—
73C2×#634C2×C414yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80#3757C2×C418yes—
81C4⋊(C3⋊Dic3)C2×C414yes—
82#3750C2×C418yes—
83C3×#217—22no—
84C3×#217—22no—
85C3×#217—42no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—22no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3D414yes—
92#3724—24no—
93#3724—42no—
94Dic32—24no—
95Dic32—42no—
96#2323—91noSylow
97C23×C3×C4—21no—
98C23×C3×C4C2×D311yescharacteristic
99C23×C3×C4C2×D311yescharacteristic
100C22×Dic6—31no—
101C22×Dic6—31no—
102C22×Dic6—61no—
103C3×#117—64no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C22⋊C4—31no—
109C2×C3×C22⋊C4—31no—
110C2×C3×C22⋊C4—32no—
111C2×C3×C42—31no—
112C2×C3×C42—31no—
113C2×#217—32no—
114C2×#217—32no—
115C2×#217—62no—
116C2×#217C2×D311yescharacteristic
117C2×#217C2×D311yescharacteristic
118C2×#217C2×D312yes—
119#926—24no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—61no—
123C2×C4⋊Dic3C2×D311yescharacteristic
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×C4⋊Dic3C2×D311yescharacteristic
126C2×C4⋊Dic3C2×D311yescharacteristic
127#924—38no—
128#924—38no—
129#924—68no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—62no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3C2×D311yescharacteristic
142C2×C4×Dic3C2×D311yescharacteristic
143#887—64no—
144C4×Dic6—64no—
145C3×#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95C2×D312yes—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32—21no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32C22×C412yes—
162C23×C32C2411yescharacteristic
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—28no—
166C2×C32×C4C22×C412yes—
167C2×C32×C4C22×C412yes—
168C2×C32×C4C2×D412yes—
169C2×C32×C4#4112yes—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3C22×C414yes—
175C2×C3⋊Dic3C22×C414yes—
176#634—28no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D412yes—
195C2×C22⋊Q8—91no—
196C2×C4×Q8—91no—
197C2×#117—31no—
198#391—91no—
199#389—92no—
200#389—91no—
201#388—92no—
202#388—92no—
203#387—92no—
204#380—31no—
205C4×C4⋊C4—91no—
206C24×C3—21no—
207C24×C3C22×D311yescharacteristic
208C24×C3C22×D311yescharacteristic
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—24no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—31no—
221C22×C3×C4—32no—
222C22×C3×C4—42no—
223C22×C3×C4—42no—
224C22×C3×C4C4×D314yes—
225C22×C3×C4C4×D314yes—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—32no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D311yescharacteristic
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D311yescharacteristic
241C22×Dic3C22×D311yescharacteristic
242C2×Dic6—34no—
243C2×Dic6—34no—
244C2×Dic6—64no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C2×Dic6—122no—
250C2×Dic6—122no—
251C3×C4⋊C4—62no—
252C3×C4⋊C4—62no—
253C3×C4⋊C4—62no—
254C3×C4⋊C4—62no—
255C3×C22⋊C4—62no—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—122no—
258C3×C42—34no—
259C3×C42—62no—
260#217—22no—
261#217—22no—
262#217—38no—
263#217—38no—
264#217—42no—
265#217—68no—
266C4⋊Dic3—22no—
267C4⋊Dic3—22no—
268C4⋊Dic3—22no—
269C4⋊Dic3—22no—
270C4⋊Dic3—34no—
271C4⋊Dic3—34no—
272C4⋊Dic3—64no—
273Dic3⋊C4—38no—
274Dic3⋊C4—38no—
275Dic3⋊C4—68no—
276Dic3⋊C4—64no—
277Dic3⋊C4—64no—
278Dic3⋊C4—122no—
279Dic3⋊C4—122no—
280C4×Dic3—22no—
281C4×Dic3—64no—
282C4×Dic3—64no—
283C4×Dic3—122no—
284C4×Dic3—122no—
285C4×Dic3#6714yes—
286C22×C32—22no—
287C22×C32—22no—
288C22×C32—22no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32C23×C411yescharacteristic
294C22×C32C22×D411yescharacteristic
295C22×C32C2×#4111yescharacteristic
296C22×C32H(5,𝔽2)11yescharacteristic
297C22×C322−1+411yescharacteristic
298C22×C322−1+411yescharacteristic
299C22×C322−1+411yescharacteristic
300C32×C4—22no—
301C32×C4C4×D414yes—
302C3⋊Dic3—24no—
303C3⋊Dic3—24no—
304C3×Dic3—22no—
305C3×Dic3—22no—
306C3×Dic3—41no—
307C3×Dic3—41no—
308C3×Dic3—42no—
309C3×Dic3—42no—
310C22×Q8—91no—
311C23×C4D3211yescharacteristic
312C22⋊Q8—98no—
313C4×Q8—184no—
314#117—64no—
315C2×C4⋊C4—31no—
316C2×C4⋊C4—31no—
317C2×C4⋊C4—31no—
318C2×C4⋊C4—31no—
319C2×C4⋊C4—91no—
320C2×C4⋊C4—92no—
321C2×C4⋊C4—92no—
322C2×C4⋊C4—92no—
323C2×C22⋊C4—31no—
324C2×C22⋊C4—31no—
325C2×C22⋊C4—32no—
326C2×C22⋊C4—92no—
327C2×C42—31no—
328C2×C42—31no—
329C2×C42—92no—
330C2×C42—92no—
331#95—32no—
332#95—92no—
333#95—92no—
334#95—92no—
335#95—92no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
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—22no—
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3C2×C4×D312yes—
357C23×C3C2×C4×D312yes—
358C23×C3C23×D311yescharacteristic
359C23×C3C23×D311yescharacteristic
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—28no—
365C2×C3×C4—28no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—32no—
371C2×C3×C4—32no—
372C2×C3×C4—48no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—61no—
389C2×C3×C4—61no—
390C2×C3×C4—62no—
391C2×C3×C4C2×C4×D312yes—
392C2×C3×C4C2×C4×D312yes—
393C2×C3×C4C2×C4×D312yes—
394C2×C3×C4C2×C4×D312yes—
395C2×C3×C4#23512yes—
396C2×C3×C4D3×D412yes—
397C2×C3×C4#23712yes—
398C2×C3×C4C2×#6712yes—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—21no—
410C2×Dic3—21no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—34no—
416C2×Dic3—34no—
417C2×Dic3—34no—
418C2×Dic3—34no—
419C2×Dic3—64no—
420C2×Dic3—64no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—122no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432C2×Dic3—122no—
433C2×Dic3C2×#6712yes—
434C2×Dic3C2×#6712yes—
435Dic6—68no—
436Dic6—68no—
437Dic6—128no—
438C2×C32—42no—
439C2×C32C2×C4×D411yescharacteristic
440C2×C32#51911yescharacteristic
441C2×C32#52011yescharacteristic
442C2×C32#53611yescharacteristic
443C2×C32#53711yescharacteristic
444C2×C32#54111yescharacteristic
445C2×C32#54211yescharacteristic
446C24C2×D3211yescharacteristic
447C2×Q8—94no—
448C2×Q8—182no—
449C2×Q8—182no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—32no—
455C22×C4—32no—
456C22×C4—31no—
457C22×C4—31no—
458C22×C4—92no—
459C22×C4—92no—
460C22×C4#62414yes—
461C22×C4C2×D3211yescharacteristic
462C22×C4C2×D3211yescharacteristic
463C4⋊C4—62no—
464C4⋊C4—62no—
465C4⋊C4—62no—
466C4⋊C4—62no—
467C4⋊C4—98no—
468C4⋊C4—94no—
469C4⋊C4—184no—
470C4⋊C4—362no—
471C22⋊C4—62no—
472C22⋊C4—62no—
473C22⋊C4—98no—
474C22⋊C4—122no—
475C42—34no—
476C42—62no—
477C42—184no—
478C42—362no—
479C22×C3—24no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3C22×C4×D311yescharacteristic
508C22×C3C22×C4×D311yescharacteristic
509C22×C3C2×#23511yescharacteristic
510C22×C3C2×D3×D411yescharacteristic
511C22×C3C2×#23711yescharacteristic
512C22×C3#100411yescharacteristic
513C22×C3#100711yescharacteristic
514C22×C3#100911yescharacteristic
515C22×C3#101011yescharacteristic
516C22×C3#101011yescharacteristic
517C22×C3#101011yescharacteristic
518C22×C3#101011yescharacteristic
519C22×C3#101011yescharacteristic
520C22×C3C22×#6711yescharacteristic
521C3×C4—22no—
522C3×C4—22no—
523C3×C4—24no—
524C3×C4—42no—
525C3×C4—62no—
526C3×C4—62no—
527C3×C4—122no—
528C3×C4—122no—
529C3×C4—121no—
530C3×C4—121no—
531C3×C4#67⋊C414yes—
532C3×C4C4×#6714yes—
533Dic3—22no—
534Dic3—22no—
535Dic3—41no—
536Dic3—41no—
537Dic3—42no—
538Dic3—42no—
539Dic3—64no—
540Dic3—64no—
541Dic3—64no—
542Dic3—64no—
543Dic3—124no—
544Dic3—124no—
545C32#232311yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23C2×#62412yes—
553C23C22×D3211yescharacteristic
554Q8—188no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—28no—
558C2×C4—32no—
559C2×C4—32no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—61no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—61no—
572C2×C4—62no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—62no—
576C2×C4—94no—
577C2×C4—94no—
578C2×C4—182no—
579C2×C4—182no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4#380412yes—
583C2×C4C2×#62412yes—
584C2×C4C2×#62412yes—
585C2×C4D3×#6712yes—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—44no—
594C2×C3—42no—
595C2×C3—42no—
596C2×C3C2×#67⋊C411yescharacteristic
597C2×C3#550411yescharacteristic
598C2×C3#551611yescharacteristic
599C2×C3#551611yescharacteristic
600C2×C3#551811yescharacteristic
601C2×C3#552311yescharacteristic
602C2×C3#553411yescharacteristic
603C2×C3#560311yescharacteristic
604C2×C3#560811yescharacteristic
605C2×C3#562511yescharacteristic
606C2×C3#562811yescharacteristic
607C2×C3C2×C4×#6711yescharacteristic
608C2×C3#582511yescharacteristic
609C2×C3#583311yescharacteristic
610C22—22no—
611C22—22no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22#6429711yescharacteristic
618C22#6429811yescharacteristic
619C22#6429811yescharacteristic
620C22#6430711yescharacteristic
621C22C2×#380411yescharacteristic
622C22C22×#62411yescharacteristic
623C22C2×D3×#6711yescharacteristic
624C4—22no—
625C4—62no—
626C4—62no—
627C4—121no—
628C4—122no—
629C4—122no—
630C4—121no—
631C4—184no—
632C4—184no—
633C4#6395214yes—
634C3—21no—
635C3#7387111yescharacteristic, complemented
636C3#8223511yescharacteristic, complemented
637C2—42no—
638C2#1059482411yescharacteristic
639C2#1059482811yescharacteristic
640C2#1059488411yescharacteristic
641C2#1059498311yescharacteristic
642C2#1059499011yescharacteristic
643C2#1059500411yescharacteristic
644C2C2×#6395211yescharacteristic
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×#63844C2semidirect
7. Dic3×C4⋊Dic3C2semidirect
8. #10591264C2semidirect
9. #10591263C2semidirect
10. #10591213C2semidirect
11. #10591212C2semidirect
18. #64133C4semidirect
545. C32#2323semidirect
635. C3#73871semidirect
636. C3#82235semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9262
C2×#638442
C3×#52122
#105917032
Dic3×C4⋊Dic32
#105912642
#105912632
#105912132
#105912122
#822353
#738713