Finite Group Databasebeta

← #11805706

Subgroups — #11805706

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 627 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic, complemented
3C2×#63874C211yesmaximal, characteristic, complemented
4C3×#4980C212yesmaximal, complemented
5#10591380C212yesmaximal
6#10591360C211yesmaximal, characteristic, complemented
7#10591355C211yesmaximal, characteristic, complemented
8#10591355C211yesmaximal, characteristic, complemented
9#10591266C212yesmaximal, complemented
10#10591257C211yesmaximal, characteristic, complemented
11#10591233C212yesmaximal, complemented
12#75305—32nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#624C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64102C418yescomplemented
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×#3724C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×#3724C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×#3722C2212yes—
29C2×#3722C2212yes—
30C2×#3722C2212yes—
31C2×Dic32C2212yes—
32#63900—24no—
33#63874—24no—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39C2×#893—32no—
40C2×#893—61no—
41C2×D3×C4⋊C4—32no—
42C2×#872—32no—
43C3×#387—32no—
44#4990—32no—
45#4980D312yescomplemented
46C4×(C2×D3)⋊C4—32no—
47#4670—32no—
48#4667—32no—
49#4667—32no—
50#4666—32no—
51#4665—32no—
52#4665—32no—
53#4650—32no—
54#4649—32no—
55C23×C3⋊D3C2311yescharacteristic
56C23×C3⋊D3C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)C2×C414yes—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3C2×C414yes—
70C2×C4×C3⋊D3C2×C414yescomplemented
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×#624—24no—
76C2×#624—24no—
77C2×#624—42no—
78C32×C4⋊C4C2×C414yescomplemented
79#3752C2×C414yes—
80#3752C2×C414yescomplemented
81C4×C3⋊Dic3C2×C414yescomplemented
82C3×C4⋊Dic3—24no—
83C3×C4×Dic3—24no—
84#3724—22no—
85#3724—22no—
86#3724—22no—
87#3724D414yescomplemented
88#3722—24no—
89#3722—24no—
90#3722—42no—
91Dic32—42no—
92#2352—91noSylow
93C22×D12—32no—
94C22×D12—61no—
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—61no—
100C22×C4×D3—61no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4C2×D312yes—
104C2×C3×C42—32no—
105C2×(C2×D3)⋊C4—32no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4⋊Dic3C2×D312yes—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—61no—
124C2×C4×Dic3C2×D312yes—
125#893—316no—
126#893—68no—
127D3×C4⋊C4—68no—
128#872—68no—
129C3×#95—32no—
130C3×#95—32no—
131C3×#95—32no—
132C3×#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95C2×D312yes—
136C3⋊#95C2×D312yes—
137C3⋊#95C2×D312yes—
138C3⋊#95C2×D312yes—
139C23×C32C2411yescharacteristic
140C22×C3⋊D3—21no—
141C22×C3⋊D3—21no—
142C22×C3⋊D3—21no—
143C22×C3⋊D3—21no—
144C22×C3⋊D3—21no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3—21no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3C22×C412yes—
151C22×C3⋊D3C22×C412yes—
152C22×C3⋊D3#4112yes—
153C22×C3⋊D3#4112yes—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4C22×C412yes—
161C2×C32×C4C22×C412yes—
162C2×C32×C4C22×C412yes—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3C22×C412yes—
166C2×C3⋊Dic3C22×C412yes—
167C2×C3⋊Dic3C2×D412yes—
168C2×C3⋊Dic3#4112yes—
169C4⋊(C3⋊D3)—28no—
170C4×C3⋊D3—28no—
171C4×C3⋊D3—28no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
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×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3C2×D414yes—
184#624—48no—
185C2×C4×D4—91no—
186C2×#117—91no—
187C22×C4⋊C4—91no—
188#388—92no—
189#387—32no—
190#386—92no—
191#382—91no—
192#380—91no—
193#380—91no—
194C4×C4⋊C4—91no—
195C4×C22⋊C4—92no—
196C23×D3—32no—
197C23×D3—32no—
198C23×D3—61no—
199C23×D3—61no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—32no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D312yes—
218C2×D12—38no—
219C2×D12—64no—
220C2×D12—64no—
221C2×D12—64no—
222C2×D12—64no—
223C2×D12—64no—
224C2×C4×D3—38no—
225C2×C4×D3—38no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—122no—
237C2×C4×D3—122no—
238C2×C4×D3—122no—
239C2×C4×D3—122no—
240C2×C4×D3—122no—
241C2×C4×D3—122no—
242C3×C4⋊C4—24no—
243C3×C4⋊C4—64no—
244C3×C4⋊C4C4×D318yescomplemented
245C3×C42—64no—
246(C2×D3)⋊C4—38no—
247(C2×D3)⋊C4—38no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—122no—
255(C2×D3)⋊C4—122no—
256C4⋊Dic3—24no—
257Dic3⋊C4—38no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261C4×Dic3—24no—
262C4×Dic3—38no—
263C4×Dic3—64no—
264C4×Dic3—122no—
265C4×Dic3—122no—
266C22×C32C23×C411yescharacteristic
267C22×C32C22×D411yescharacteristic
268C22×C32C2×#4111yescharacteristic
269C22×C32C2×#4111yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C32H(5,𝔽2)11yescharacteristic
272C22×C322−1+411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—22no—
277C2×C3⋊D3—22no—
278C2×C3⋊D3—22no—
279C2×C3⋊D3—22no—
280C2×C3⋊D3—22no—
281C2×C3⋊D3—22no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3#11714yescomplemented
287C32×C4—22no—
288C32×C4—22no—
289C32×C4—22no—
290C3⋊Dic3—22no—
291C3⋊Dic3C4×D414yes—
292C3×Dic3—24no—
293C3×Dic3—42no—
294C3×Dic3—42no—
295C3×Dic3—42no—
296C22×D4—91no—
297C23×C4—92no—
298C23×C4—91no—
299C23×C4—91no—
300C4×D4—98no—
301#117—184no—
302C2×C4⋊C4—32no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—91no—
305C2×C4⋊C4—91no—
306C2×C4⋊C4—91no—
307C2×C4⋊C4—184no—
308C2×C4⋊C4D3211yescharacteristic
309C2×C22⋊C4—91no—
310C2×C22⋊C4—91no—
311C2×C22⋊C4—92no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—92no—
314C2×C42—32no—
315C2×C42—91no—
316C2×C42—92no—
317#95—32no—
318#95—32no—
319#95—32no—
320#95—32no—
321#95—92no—
322C23×C3—21no—
323C23×C3C23×D312yes—
324C22×D3—34no—
325C22×D3—34no—
326C22×D3—34no—
327C22×D3—34no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—121no—
345C22×D3—121no—
346C22×D3—121no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—121no—
350C22×D3—121no—
351C22×D3—121no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
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—34no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—62no—
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—62no—
378C2×C3×C4—62no—
379C2×C3×C4C2×C4×D314yes—
380C2×C3×C4C2×C4×D314yes—
381C2×C3×C4C2×C4×D314yes—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—34no—
396C2×Dic3—34no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3D3×D414yes—
406D12—616no—
407D12—616no—
408C4×D3—616no—
409C4×D3—616no—
410C4×D3—128no—
411C4×D3—128no—
412C4×D3—128no—
413C4×D3—128no—
414C2×C32C2×#11711yescharacteristic
415C2×C32C2×C4×D411yescharacteristic
416C2×C32#52011yescharacteristic
417C2×C32#54611yescharacteristic
418C2×C32#54811yescharacteristic
419C2×C32#55211yescharacteristic
420C2×C32#55311yescharacteristic
421C3⋊D3—24no—
422C3⋊D3—42no—
423C24—91no—
424C24—91no—
425C2×D4—94no—
426C2×D4—182no—
427C2×D4—182no—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4—32no—
431C22×C4—32no—
432C22×C4—91no—
433C22×C4—91no—
434C22×C4—94no—
435C22×C4—94no—
436C22×C4—182no—
437C22×C4—182no—
438C22×C4—182no—
439C22×C4—182no—
440C22×C4—184no—
441C22×C4—184no—
442C22×C4—362no—
443C22×C4C2×D3211yescharacteristic
444C22×C4C2×D3211yescharacteristic
445C22×C4C2×D3211yescharacteristic
446C4⋊C4—64no—
447C4⋊C4—94no—
448C4⋊C4—182no—
449C4⋊C4—182no—
450C4⋊C4—182no—
451C4⋊C4#62414yescomplemented
452C22⋊C4—94no—
453C22⋊C4—94no—
454C22⋊C4—184no—
455C22⋊C4—184no—
456C22⋊C4—362no—
457C42—64no—
458C42—94no—
459C42—362no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3C22×C4×D312yes—
468C22×C3C2×D3×D412yes—
469C22×C3#100712yes—
470C22×C3D3×#4112yes—
471C22×C3D3×#4112yes—
472C22×C3D3×#4112yes—
473C22×C3#100912yes—
474C2×D3—38no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—64no—
478C2×D3—64no—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—64no—
485C2×D3—64no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C3×C4—24no—
503C3×C4—24no—
504C3×C4—24no—
505C3×C4—24no—
506C3×C4—42no—
507C3×C4—42no—
508C3×C4—64no—
509C3×C4—122no—
510C3×C4—122no—
511C3×C4—122no—
512Dic3—24no—
513Dic3—38no—
514Dic3—42no—
515Dic3—42no—
516Dic3—42no—
517Dic3—64no—
518Dic3—64no—
519Dic3—122no—
520C32#235211yescharacteristic, complemented, Sylow
521C23—92no—
522C23—92no—
523C23—92no—
524C23—92no—
525C23—181no—
526C23—181no—
527C23—181no—
528C23—181no—
529C23—181no—
530C23—181no—
531C23—181no—
532C23—181no—
533C23—181no—
534C23—181no—
535C23C22×D3211yescharacteristic
536D4—188no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—34no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—92no—
556C2×C4—92no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—188no—
560C2×C4—188no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—368no—
564C2×C4C2×#62412yes—
565C2×C4C2×#62412yes—
566C2×C4C2×#62412yes—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3D3×#11712yes—
575C2×C3C4×D3×D412yes—
576C2×C3#557412yes—
577C2×C3#563312yes—
578C2×C3#565412yes—
579C2×C3#569312yes—
580C2×C3#570912yes—
581D3—68no—
582D3—124no—
583D3—124no—
584D3—124no—
585C22—94no—
586C22—182no—
587C22—182no—
588C22—182no—
589C22—182no—
590C22—182no—
591C22—182no—
592C22—182no—
593C22—182no—
594C22—182no—
595C22—361no—
596C22—361no—
597C22—361no—
598C22—361no—
599C22#6430611yescharacteristic
600C22#6430611yescharacteristic
601C22D32×D411yescharacteristic
602C22#6431211yescharacteristic
603C22#6431611yescharacteristic
604C22#6432011yescharacteristic
605C22C22×#62411yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—64no—
610C4—94no—
611C4—122no—
612C4—122no—
613C4—122no—
614C4—182no—
615C3—21no—
616C3#7530512yescomplemented
617C2—184no—
618C2—362no—
619C2#1059447511yescharacteristic
620C2#1059447611yescharacteristic
621C2#1059452111yescharacteristic
622C2#1059461611yescharacteristic
623C2#1059496911yescharacteristic
624C2D4×#62411yescharacteristic
625C2#1059535311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63900C2semidirect
3. C2×#63874C2semidirect
4. C3×#4980C2semidirect
6. #10591360C2semidirect
7. #10591355C2semidirect
8. #10591355C2semidirect
9. #10591266C2semidirect
10. #10591257C2semidirect
11. #10591233C2semidirect
21. #64102C4semidirect
45. #4980D3semidirect
70. C2×C4×C3⋊D3C2×C4semidirect
78. C32×C4⋊C4C2×C4semidirect
80. #3752C2×C4semidirect
81. C4×C3⋊Dic3C2×C4semidirect
87. #3724D4semidirect
244. C3×C4⋊C4C4×D3semidirect
286. C2×C3⋊D3#117semidirect
451. C4⋊C4#624semidirect
520. C32#2352semidirect
616. C3#75305semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#639002
C2×#638742
C3×#49802
#105913802
#105913602
#105913552
#105912662
#105912572
#105912332
#753053