Finite Group Databasebeta

← #11824558

Subgroups — #11824558

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic, complemented
2C2×#63958C212yesmaximal, complemented
3C2×#63881C211yesmaximal, characteristic, complemented
4C3×#5223C211yesmaximal, characteristic, complemented
5C3×#5222C211yesmaximal, characteristic, complemented
6#10591722C212yesmaximal, complemented
7#10591721C212yesmaximal, complemented
8#10591702C212yesmaximal, complemented
9#10591370C211yesmaximal, characteristic, complemented
10#10591353C211yesmaximal, characteristic, complemented
11#10591315C211yesmaximal, characteristic, complemented
12#77120—31nomaximal
13#76759—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×#638C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×#626C2211yescharacteristic
19C22×#624C2212yes—
20C22×D3×Dic3C2211yescharacteristic
21C2×#3757C2212yes—
22#64147—24no—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×#3722C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2212yes—
32#63958—28no—
33C2×Dic32C2211yescharacteristic
34#63881—24no—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×#938—31no—
41C2×#938—31no—
42C2×#938—32no—
43C2×#938—61no—
44C2×#893—31no—
45C2×#884—32no—
46C2×#67⋊C4—31no—
47C3×#394—31no—
48C3×#392—31no—
49#5223D311yescharacteristic, complemented
50#5222D311yescharacteristic, complemented
51#5220—32no—
52#4981—31no—
53#4956—32no—
54#4956—32no—
55#4956—32no—
56#4953—31no—
57#4951—32no—
58#4945—32no—
59#4674—31no—
60D3×#95—31no—
61D3×#95—31no—
62#4661—31no—
63C24×C32C2312yes—
64C23×C3⋊D3C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C2×C32×D4—22no—
67C2×C32×D4—42no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—24no—
70C2×#638—24no—
71C2×#638—24no—
72C22×C3⋊Dic3C2312yes—
73C22×C3⋊Dic3C2311yescharacteristic
74C2×C4×C3⋊D3—42no—
75C2×C4×C3⋊D3D414yescomplemented
76C2×C3×#67—24no—
77C2×C3×#67—24no—
78C2×C3×#67—42no—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C2×#626—22no—
85C2×#626—22no—
86C2×#626D414yescomplemented
87C2×#624—24no—
88C2×#624—24no—
89C2×#624—42no—
90C2×D3×Dic3—22no—
91C2×D3×Dic3—42no—
92#3757—24no—
93C4⋊(C3⋊Dic3)—22no—
94C3×#217—24no—
95C3×#217—24no—
96C3×#217—42no—
97C3×(C2×D3)⋊C4—22no—
98C3×Dic3⋊C4—22no—
99Dic3⋊Dic3—24no—
100#3722—22no—
101(C2×D3)⋊Dic3—24no—
102Dic32—22no—
103#2543—91noSylow
104C22×C3×D4—21no—
105C22×C3×D4—32no—
106C22×C3×D4C2×D311yescharacteristic
107C22×C3×D4C2×D311yescharacteristic
108C22×#67—32no—
109C22×#67—32no—
110C22×#67—31no—
111C22×#67—62no—
112C22×#67C2×D312yes—
113C23×Dic3—31no—
114C22×D12—31no—
115C22×C4×D3—31no—
116C22×C4×D3—31no—
117C22×C4×D3—32no—
118C22×C4×D3—32no—
119C22×C4×D3—31no—
120C22×C4×D3—61no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4—32no—
126C2×#217—32no—
127C2×#217—32no—
128C2×#217—32no—
129C2×#217—62no—
130C2×#217C2×D312yes—
131C2×#217C2×D312yes—
132C2×#217C2×D312yes—
133#938—68no—
134#938—64no—
135#938—64no—
136#938—68no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4C2×D311yescharacteristic
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3—61no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4C2×D311yescharacteristic
147C2×C4×Dic3—31no—
148C2×C4×Dic3—31no—
149#893—64no—
150#884—68no—
151#67⋊C4—64no—
152C3×#95—31no—
153C3×#95—31no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95C2×D311yescharacteristic
161C3⋊#95C2×D311yescharacteristic
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32C2411yescharacteristic
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3C2×D412yes—
173C22×C3⋊D3C2×D412yes—
174C22×C3⋊D3#4112yes—
175C22×C3×D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3C2×D412yes—
180C32×D4—44no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D412yes—
183#638—48no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3C2×D412yes—
189C4×C3⋊D3—44no—
190C3×#67—48no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3C2×D412yes—
203C2×C3×Dic3#4114yes—
204#626—28no—
205#624—48no—
206D3×Dic3—44no—
207C2×#121—92no—
208C2×#121—91no—
209C2×C4×D4—91no—
210#398—91no—
211#397—91no—
212#394—31no—
213#392—31no—
214#388—92no—
215#386—92no—
216#386—92no—
217C2×#95—91no—
218C24×C3—22no—
219C24×C3—31no—
220C24×C3C22×D312yes—
221C24×C3C22×D312yes—
222C23×D3—31no—
223C23×D3—31no—
224C23×D3—61no—
225C23×D3C22×D311yescharacteristic
226C2×C3×D4—24no—
227C2×C3×D4—22no—
228C2×C3×D4—22no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—44no—
232C2×C3×D4—64no—
233C2×C3×D4—64no—
234C2×C3×D4—122no—
235C22×C3×C4—21no—
236C22×C3×C4—32no—
237C22×C3×C4—31no—
238C22×C3×C4—32no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C2×#67—24no—
244C2×#67—24no—
245C2×#67—34no—
246C2×#67—42no—
247C2×#67—62no—
248C2×#67—62no—
249C2×#67—64no—
250C2×#67—64no—
251C2×#67—64no—
252C2×#67—64no—
253C2×#67—64no—
254C2×#67—64no—
255C2×#67—68no—
256C2×#67—124no—
257C2×#67—124no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—62no—
263C22×Dic3—61no—
264C22×Dic3—62no—
265C22×Dic3—122no—
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D311yescharacteristic
269C22×Dic3C22×D311yescharacteristic
270C22×Dic3C22×D312yes—
271C2×D12—34no—
272C2×D12—62no—
273C2×D12—62no—
274C2×C4×D3—34no—
275C2×C4×D3—34no—
276C2×C4×D3—64no—
277C2×C4×D3—64no—
278C2×C4×D3—64no—
279C2×C4×D3—64no—
280C2×C4×D3—62no—
281C2×C4×D3—64no—
282C2×C4×D3—122no—
283C2×C4×D3—122no—
284C2×C4×D3—122no—
285C2×C4×D3—122no—
286C2×C4×D3—122no—
287C2×C4×D3—124no—
288C3×C4⋊C4—62no—
289C3×C22⋊C4—64no—
290C3×C22⋊C4—64no—
291C3×C22⋊C4—62no—
292C3×C22⋊C4—122no—
293#217—24no—
294#217—24no—
295#217—42no—
296#217—64no—
297#217—64no—
298#217—64no—
299#217—68no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303(C2×D3)⋊C4—64no—
304C4⋊Dic3—64no—
305C4⋊Dic3—62no—
306C4⋊Dic3—62no—
307C4⋊Dic3—64no—
308Dic3⋊C4—22no—
309Dic3⋊C4—64no—
310C4×Dic3—62no—
311C4×Dic3—62no—
312C22×C32—42no—
313C22×C32—42no—
314C22×C32—42no—
315C22×C32—42no—
316C22×C32—42no—
317C22×C32—42no—
318C22×C32—42no—
319C22×C32C22×D411yescharacteristic
320C22×C32C22×D411yescharacteristic
321C22×C32C2×#4112yes—
322C22×C32C2×#4111yescharacteristic
323C22×C32H(5,𝔽2)12yes—
324C2×C3⋊D3—22no—
325C2×C3⋊D3—22no—
326C2×C3⋊D3—24no—
327C2×C3⋊D3—24no—
328C2×C3⋊D3#12114yes—
329C2×C3×D3—22no—
330C2×C3×D3—24no—
331C2×C3×D3—41no—
332C2×C3×D3—41no—
333C2×C3×D3—42no—
334C32×C4—22no—
335C3⋊Dic3—22no—
336C3⋊Dic3—42no—
337C3×Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—41no—
340C3×Dic3—41no—
341C3×Dic3—42no—
342C22×D4—32no—
343C22×D4—91no—
344C22×D4—92no—
345C22×D4D3211yescharacteristic
346C23×C4—92no—
347C23×C4—91no—
348C23×C4—91no—
349#121—188no—
350#121—184no—
351C4×D4—184no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—92no—
354C2×C4⋊C4—91no—
355C2×C22⋊C4—32no—
356C2×C22⋊C4—32no—
357C2×C22⋊C4—31no—
358C2×C22⋊C4—32no—
359C2×C22⋊C4—91no—
360C2×C22⋊C4—92no—
361C2×C22⋊C4—92no—
362C2×C42—91no—
363#95—31no—
364#95—31no—
365#95—92no—
366#95—92no—
367#95—92no—
368C23×C3—24no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—21no—
384C23×C3—32no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—61no—
392C23×C3—62no—
393C23×C3—61no—
394C23×C3—62no—
395C23×C3C23×D311yescharacteristic
396C23×C3C23×D311yescharacteristic
397C22×D3—21no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—21no—
401C22×D3—32no—
402C22×D3—32no—
403C22×D3—32no—
404C22×D3—32no—
405C22×D3—32no—
406C22×D3—32no—
407C22×D3—62no—
408C22×D3—62no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—62no—
412C22×D3—62no—
413C22×D3—62no—
414C22×D3—122no—
415C22×D3—122no—
416C22×D3D3×D412yes—
417C3×D4—48no—
418C3×D4—44no—
419C3×D4—44no—
420C3×D4—128no—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—32no—
426C2×C3×C4—34no—
427C2×C3×C4—61no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—62no—
433C2×C3×C4—61no—
434C2×C3×C4—62no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4—62no—
438C2×C3×C4D3×D412yes—
439C2×C3×C4D3×D412yes—
440#67—48no—
441#67—68no—
442#67—128no—
443#67—128no—
444#67—1216no—
445C2×Dic3—21no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—32no—
457C2×Dic3—32no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—64no—
462C2×Dic3—62no—
463C2×Dic3—62no—
464C2×Dic3—62no—
465C2×Dic3—62no—
466C2×Dic3—62no—
467C2×Dic3—62no—
468C2×Dic3—122no—
469C2×Dic3—122no—
470C2×Dic3—122no—
471C2×Dic3—124no—
472C2×Dic3D3×D412yes—
473C2×Dic3#23714yes—
474D12—68no—
475C4×D3—128no—
476C4×D3—128no—
477C4×D3—124no—
478C4×D3—124no—
479C4×D3—124no—
480C4×D3—128no—
481C2×C32—82no—
482C2×C32C2×#12111yescharacteristic
483C2×C32#53211yescharacteristic
484C2×C32#53411yescharacteristic
485C2×C32#54612yes—
486C2×C32#55312yes—
487C3⋊D3—24no—
488C3×D3—42no—
489C24—31no—
490C24—91no—
491C24C2×D3212yes—
492C2×D4—22no—
493C2×D4—42no—
494C2×D4—64no—
495C2×D4—64no—
496C2×D4—94no—
497C2×D4—122no—
498C2×D4—182no—
499C2×D4—182no—
500C2×D4—184no—
501C2×D4—184no—
502C2×D4—184no—
503C22×C4—32no—
504C22×C4—31no—
505C22×C4—32no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—91no—
509C22×C4—94no—
510C22×C4—92no—
511C22×C4—184no—
512C22×C4—184no—
513C22×C4—182no—
514C22×C4—362no—
515C22×C4—362no—
516C22×C4—362no—
517C22×C4C2×D3211yescharacteristic
518C4⋊C4—62no—
519C4⋊C4—184no—
520C4⋊C4—182no—
521C22⋊C4—64no—
522C22⋊C4—64no—
523C22⋊C4—62no—
524C22⋊C4—122no—
525C22⋊C4—182no—
526C22⋊C4—184no—
527C22⋊C4—184no—
528C42—182no—
529C22×C3—21no—
530C22×C3—22no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—22no—
534C22×C3—44no—
535C22×C3—44no—
536C22×C3—44no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—62no—
552C22×C3—64no—
553C22×C3—82no—
554C22×C3—82no—
555C22×C3—82no—
556C22×C3—82no—
557C22×C3—122no—
558C22×C3—121no—
559C22×C3—121no—
560C22×C3C2×D3×D411yescharacteristic
561C22×C3C2×D3×D411yescharacteristic
562C22×C3C2×D3×D411yescharacteristic
563C22×C3C2×D3×D411yescharacteristic
564C22×C3C2×#23712yes—
565C22×C3#100412yes—
566C22×C3#100412yes—
567C22×C3D3×#4112yes—
568C22×C3D3×#4111yescharacteristic
569C22×C3D3×#4111yescharacteristic
570C2×D3—24no—
571C2×D3—22no—
572C2×D3—34no—
573C2×D3—34no—
574C2×D3—41no—
575C2×D3—41no—
576C2×D3—42no—
577C2×D3—64no—
578C2×D3—64no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—64no—
584C2×D3—64no—
585C2×D3—64no—
586C2×D3—122no—
587C2×D3—122no—
588C2×D3—124no—
589C2×D3—124no—
590C3×C4—24no—
591C3×C4—22no—
592C3×C4—22no—
593C3×C4—62no—
594C3×C4—64no—
595C3×C4—121no—
596C3×C4—121no—
597C3×C4—122no—
598Dic3—24no—
599Dic3—22no—
600Dic3—41no—
601Dic3—41no—
602Dic3—42no—
603Dic3—62no—
604Dic3—62no—
605Dic3—122no—
606Dic3—124no—
607Dic3—122no—
608Dic3—122no—
609C32#254311yescharacteristic, complemented, Sylow
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—32no—
618C23—62no—
619C23—61no—
620C23—61no—
621C23—62no—
622C23—92no—
623C23—92no—
624C23—92no—
625C23—182no—
626C23—182no—
627C23C22×D3211yescharacteristic
628D4—44no—
629D4—128no—
630D4—188no—
631D4—368no—
632C2×C4—22no—
633C2×C4—32no—
634C2×C4—34no—
635C2×C4—62no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—62no—
639C2×C4—62no—
640C2×C4—62no—
641C2×C4—62no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—92no—
647C2×C4—182no—
648C2×C4—182no—
649C2×C4—182no—
650C2×C4—182no—
651C2×C4—364no—
652C2×C4—368no—
653C2×C4—364no—
654C2×C4#381112yes—
655C2×C3—21no—
656C2×C3—22no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—22no—
660C2×C3—84no—
661C2×C3—82no—
662C2×C3—82no—
663C2×C3—122no—
664C2×C3#558911yescharacteristic
665C2×C3#558911yescharacteristic
666C2×C3#559112yes—
667C2×C3D3×#12111yescharacteristic
668C2×C3D3×#12111yescharacteristic
669C2×C3#561212yes—
670C2×C3#561412yes—
671C2×C3#566112yes—
672C2×C3#566811yescharacteristic
673C2×C3#571611yescharacteristic
674D3—42no—
675D3—64no—
676D3—64no—
677D3—124no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—62no—
686C22—64no—
687C22—94no—
688C22—121no—
689C22—122no—
690C22—121no—
691C22—182no—
692C22—184no—
693C22—182no—
694C22—184no—
695C22D32×D411yescharacteristic
696C22D3×#23712yes—
697C22#6431211yescharacteristic
698C22C2×#381111yescharacteristic
699C22#6433012yes—
700C4—22no—
701C4—62no—
702C4—64no—
703C4—121no—
704C4—121no—
705C4—122no—
706C4—182no—
707C4—362no—
708C3—21no—
709C3#7675911yescharacteristic, complemented
710C3#7712011yescharacteristic, complemented
711C2—82no—
712C2—122no—
713C2—184no—
714C2#1059516711yescharacteristic
715C2#1059519512yes—
716C2#1059528211yescharacteristic
717C2#1059529412yes—
718C2#1059552811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2543
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64147C2semidirect
2. C2×#63958C2semidirect
3. C2×#63881C2semidirect
4. C3×#5223C2semidirect
5. C3×#5222C2semidirect
6. #10591722C2semidirect
7. #10591721C2semidirect
8. #10591702C2semidirect
9. #10591370C2semidirect
10. #10591353C2semidirect
11. #10591315C2semidirect
49. #5223D3semidirect
50. #5222D3semidirect
75. C2×C4×C3⋊D3D4semidirect
86. C2×#626D4semidirect
609. C32#2543semidirect
709. C3#76759semidirect
710. C3#77120semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×#639582
C2×#638812
C3×#52232
C3×#52222
#105917222
#105917212
#105917022
#105913702
#105913532
#105913152
#771203
#767593