Finite Group Databasebeta

← #11803581

Subgroups — #11803581

Order 1152.

1501 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic, complemented
2C2×#63980C211yesmaximal, characteristic
3C2×C4×#625C211yesmaximal, characteristic, complemented
4C3×#4956C212yesmaximal, complemented
5#10591720C211yesmaximal, characteristic, complemented
6#10591707C212yesmaximal, complemented
7#10591385C211yesmaximal, characteristic, complemented
8#10591328C211yesmaximal, characteristic, complemented
9#10591281C212yesmaximal, complemented
10#10591278C212yesmaximal, complemented
11#10591257C211yesmaximal, characteristic, complemented
12#74665—32nomaximal
13C23×C3⋊Dic3C2211yescharacteristic
14C22×C3×#67C2212yes—
15C22×C3×C4×D3C2212yes—
16C22×#625C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64086—24no—
24C2×C3×#217C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26#63980C418yescomplemented
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×#3724C2211yescharacteristic
30C2×Dic3⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35C4×#625—24no—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39C2×#939—32no—
40C2×C4×#67—32no—
41C2×#877—32no—
42C2×#877—61no—
43C3×#386—32no—
44#5221—32no—
45#5210—32no—
46#4957—32no—
47#4957—32no—
48#4956D312yescomplemented
49#4944—32no—
50#4942—32no—
51#4669—32no—
52#4668—32no—
53#4649—32no—
54#4647—32no—
55C24×C32C2311yescharacteristic
56C23×C3×D3C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—22no—
60C22×C3⋊Dic3—22no—
61C22×C3⋊Dic3C2×C414yescomplemented
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C3×#67—42no—
67C2×C3×#67—42no—
68C2×C3×#67C2×C418yescomplemented
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3—42no—
74C2×C3×C4×D3—42no—
75C2×#625—22no—
76C2×#625—22no—
77C2×#625C2×C414yes—
78C32×C22⋊C4—22no—
79#3757—22no—
80#3750—22no—
81#3750—22no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3D414yescomplemented
84C3×#217—42no—
85C3×(C2×D3)⋊C4—42no—
86#3724—22no—
87#3724—22no—
88#3724C2×C414yescomplemented
89Dic3⋊Dic3—42no—
90(C2×D3)⋊Dic3—24no—
91(C2×D3)⋊Dic3—42no—
92(C2×D3)⋊Dic3C2×C418yescomplemented
93Dic32—42no—
94#2324—91noSylow
95C22×C3×D4—32no—
96C23×C3×C4—32no—
97C22×#67—32no—
98C22×#67C2×D312yes—
99C23×Dic3—32no—
100C23×Dic3—61no—
101C22×C4×D3C2×D312yes—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4—32no—
105C2×C3×C22⋊C4C2×D312yes—
106C2×#217—32no—
107C2×#217—32no—
108C2×#217—32no—
109C2×#217—32no—
110C2×#217—61no—
111C2×#217C2×D312yes—
112#939—316no—
113C4×#67—68no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4C2×D312yes—
118C2×C4⋊Dic3—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—61no—
126C2×Dic3⋊C4—61no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—61no—
132C2×C4×Dic3—61no—
133#877—68no—
134#877—68no—
135C3×#95—32no—
136C3×#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95C2×D312yes—
140C3⋊#95C2×D312yes—
141C23×C32—21no—
142C23×C32—21no—
143C23×C32—21no—
144C23×C32—21no—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32C22×C412yes—
148C23×C32C2411yescharacteristic
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3C22×C414yes—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4C2×D412yes—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—28no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3C22×C412yes—
171C2×C3⋊Dic3C22×C412yes—
172C2×C3⋊Dic3C2×D412yes—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3#4112yes—
175C3×#67—48no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3C22×C414yes—
185C3×C4×D3—48no—
186#625—28no—
187C2×#121—91no—
188C2×C4×D4—91no—
189C2×#117—91no—
190#390—91no—
191#390—92no—
192#389—91no—
193#388—92no—
194#386—32no—
195#385—92no—
196#380—91no—
197C4×C4⋊C4—91no—
198C24×C3—21no—
199C24×C3—32no—
200C24×C3C22×D312yes—
201C23×D3C22×D312yes—
202C2×C3×D4—38no—
203C2×C3×D4—122no—
204C2×C3×D4—122no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—64no—
211C22×C3×C4—122no—
212C22×C3×C4—122no—
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D312yes—
215C2×#67—38no—
216C2×#67—42no—
217C2×#67—42no—
218C2×#67—64no—
219C2×#67—64no—
220C2×#67C4×D318yescomplemented
221C22×Dic3—32no—
222C22×Dic3—38no—
223C22×Dic3—32no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—64no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231C22×Dic3—64no—
232C22×Dic3—64no—
233C22×Dic3—64no—
234C22×Dic3—64no—
235C22×Dic3C22×D312yes—
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238C2×C4×D3—24no—
239C2×C4×D3—42no—
240C2×C4×D3—42no—
241C3×C22⋊C4—24no—
242C3×C22⋊C4—24no—
243C3×C22⋊C4—122no—
244C3×C22⋊C4—122no—
245#217—38no—
246#217—42no—
247#217—64no—
248#217—64no—
249#217—64no—
250#217—122no—
251(C2×D3)⋊C4—38no—
252(C2×D3)⋊C4—42no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—122no—
255C4⋊Dic3—122no—
256Dic3⋊C4—38no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—122no—
264C4×Dic3—38no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268C4×Dic3—122no—
269C4×Dic3—122no—
270C22×C32—22no—
271C22×C32—22no—
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32C23×C411yescharacteristic
278C22×C32C22×D411yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32H(5,𝔽2)11yescharacteristic
281C22×C32H(5,𝔽2)11yescharacteristic
282C22×C32H(5,𝔽2)11yescharacteristic
283C22×C322−1+411yescharacteristic
284C2×C3×D3—24no—
285C2×C3×D3—24no—
286C2×C3×D3—24no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C32×C4—22no—
292C32×C4—41no—
293C3⋊Dic3—22no—
294C3⋊Dic3—22no—
295C3⋊Dic3—41no—
296C3⋊Dic3C4×D414yes—
297C3×Dic3—24no—
298C3×Dic3—42no—
299C3×Dic3—42no—
300C22×D4—32no—
301C22×D4—91no—
302C23×C4—32no—
303C23×C4—91no—
304#121—98no—
305C4×D4—184no—
306#117—184no—
307C2×C4⋊C4—91no—
308C2×C4⋊C4—91no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—92no—
313C2×C22⋊C4—32no—
314C2×C22⋊C4—32no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—91no—
318C2×C22⋊C4—92no—
319C2×C22⋊C4D3211yescharacteristic
320C2×C42—91no—
321C2×C42—91no—
322C2×C42—92no—
323#95—32no—
324#95—32no—
325#95—92no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—21no—
335C23×C3—22no—
336C23×C3—34no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—62no—
342C23×C3—62no—
343C23×C3—62no—
344C23×C3—62no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3C2×C4×D314yes—
348C23×C3C23×D312yes—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3C2×C4×D314yes—
356C3×D4—128no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—34no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—128no—
378C2×C3×C4D3×D414yes—
379#67—48no—
380#67—616no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—34no—
390C2×Dic3—34no—
391C2×Dic3—34no—
392C2×Dic3—34no—
393C2×Dic3—34no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—616no—
400C2×Dic3—62no—
401C2×Dic3—616no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—121no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3—121no—
415C2×Dic3C2×C4×D314yes—
416C4×D3—48no—
417C2×C32—42no—
418C2×C32C2×C4×D411yescharacteristic
419C2×C32#51811yescharacteristic
420C2×C32#52011yescharacteristic
421C2×C32#53511yescharacteristic
422C2×C32#53711yescharacteristic
423C2×C32#54011yescharacteristic
424C2×C32#54211yescharacteristic
425C3×D3—44no—
426C24—32no—
427C24C2×D3211yescharacteristic
428C2×D4—38no—
429C2×D4—94no—
430C2×D4—122no—
431C2×D4—122no—
432C2×D4—182no—
433C2×D4—182no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—64no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—94no—
442C22×C4—91no—
443C22×C4—122no—
444C22×C4—122no—
445C22×C4—182no—
446C22×C4—182no—
447C22×C4C2×D3211yescharacteristic
448C22×C4C2×D3211yescharacteristic
449C4⋊C4—94no—
450C4⋊C4—182no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C4⋊C4—182no—
454C4⋊C4—362no—
455C22⋊C4—22no—
456C22⋊C4—98no—
457C22⋊C4—122no—
458C22⋊C4—122no—
459C22⋊C4—184no—
460C22⋊C4—182no—
461C22⋊C4—362no—
462C42—94no—
463C42—182no—
464C42—362no—
465C22×C3—24no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—24no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—64no—
487C22×C3—64no—
488C22×C3—64no—
489C22×C3—122no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3C22×C4×D312yes—
494C22×C3C2×D3×D412yes—
495C22×C3#100412yes—
496C22×C3#100412yes—
497C22×C3#100412yes—
498C22×C3D3×#4112yes—
499C22×C3#101012yes—
500C2×D3—24no—
501C2×D3—24no—
502C2×D3—24no—
503C2×D3—42no—
504C2×D3—42no—
505C2×D3—42no—
506C2×D3—42no—
507C3×C4—24no—
508C3×C4—42no—
509C3×C4—42no—
510C3×C4—42no—
511C3×C4—64no—
512C3×C4—122no—
513C3×C4—122no—
514Dic3—24no—
515Dic3—38no—
516Dic3—42no—
517Dic3—42no—
518Dic3—64no—
519Dic3—64no—
520Dic3—64no—
521Dic3—64no—
522Dic3—122no—
523Dic3—122no—
524Dic3—122no—
525C32#232411yescharacteristic, complemented, Sylow
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—34no—
533C23—62no—
534C23—62no—
535C23—62no—
536C23—62no—
537C23—62no—
538C23—62no—
539C23C4×D3212yes—
540C23C22×D3211yescharacteristic
541D4—128no—
542D4—188no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—34no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—128no—
563C2×C4—188no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—181no—
568C2×C4—181no—
569C2×C4—181no—
570C2×C4—181no—
571C2×C4#381112yes—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—44no—
580C2×C3—44no—
581C2×C3—124no—
582C2×C3#548612yes—
583C2×C3C4×D3×D412yes—
584C2×C3#554612yes—
585C2×C3#559212yes—
586C2×C3#560812yes—
587C2×C3#561512yes—
588C2×C3#566212yes—
589D3—44no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—64no—
598C22—64no—
599C22—64no—
600C22—122no—
601C22—122no—
602C22—122no—
603C22—122no—
604C22C2×C4×D3211yescharacteristic
605C22#6430611yescharacteristic
606C22#6430911yescharacteristic
607C22#6431311yescharacteristic
608C22#6431311yescharacteristic
609C22#6431311yescharacteristic
610C22C2×#381111yescharacteristic
611C4—22no—
612C4—41no—
613C4—64no—
614C4—94no—
615C4—122no—
616C4—122no—
617C4—182no—
618C4—182no—
619C4—361no—
620C3—21no—
621C3#7466512yescomplemented
622C2—42no—
623C2—124no—
624C2#1059405111yescharacteristic
625C2#1059418111yescharacteristic
626C2#1059422211yescharacteristic
627C2#1059422311yescharacteristic
628C2C4×#381111yescharacteristic
629C2#1059523911yescharacteristic
630C2#1059524011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63980C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64086C2semidirect
3. C2×C4×#625C2semidirect
4. C3×#4956C2semidirect
5. #10591720C2semidirect
6. #10591707C2semidirect
7. #10591385C2semidirect
8. #10591328C2semidirect
9. #10591281C2semidirect
10. #10591278C2semidirect
11. #10591257C2semidirect
26. #63980C4semidirect
48. #4956D3semidirect
61. C22×C3⋊Dic3C2×C4semidirect
68. C2×C3×#67C2×C4semidirect
83. C4×C3⋊Dic3D4semidirect
88. #3724C2×C4semidirect
92. (C2×D3)⋊Dic3C2×C4semidirect
220. C2×#67C4×D3semidirect
525. C32#2324semidirect
621. C3#74665semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C2×#639802
C2×C4×#6252
C3×#49562
#105917202
#105917072
#105913852
#105913282
#105912812
#105912782
#105912572
#746653