Finite Group Databasebeta

← #11803267

Subgroups — #11803267

Order 1152.

1829 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic, complemented
2C2×#63923C211yesmaximal, characteristic
3C2×#63921C211yesmaximal, characteristic, complemented
4C3×#4990C212yesmaximal, complemented
5#10591399C211yesmaximal, characteristic, complemented
6#10591387C212yesmaximal, complemented
7#10591383C212yesmaximal, complemented
8#10591380C211yesmaximal, characteristic, complemented
9#10591375C211yesmaximal, characteristic, complemented
10C4×#3722C211yesmaximal, characteristic, complemented
11#10591286C212yesmaximal, complemented
12#75826—32nomaximal
13C23×D32C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic, complemented
17C22×#626C2212yes—
18C22×#624C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic, complemented
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic, complemented
22C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
23#64102—24no—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4×Dic3C2212yescomplemented
28C2×Dic3⋊Dic3C2212yescomplemented
29C2×#3722C2211yescharacteristic
30C2×#3722C2211yescharacteristic
31C2×#3722C2212yescomplemented
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34#63923C418yescomplemented
35#63921—24no—
36C3×C3⋊#95C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38#63579C2212yescomplemented
39C2×#893—32no—
40C2×#893—61no—
41C2×#882—32no—
42C2×D3×C22⋊C4—32no—
43C3×#388—32no—
44#4990D312yescomplemented
45#4957—32no—
46#4956—32no—
47#4955—32no—
48#4951—32no—
49#4939—32no—
50C4×(C2×D3)⋊C4—32no—
51#4669—32no—
52#4668—32no—
53#4665—32no—
54#4665—32no—
55C23×C3⋊D3C2311yescharacteristic
56C23×C3⋊D3C2311yescharacteristic
57C23×C3×D3C2312yes—
58C22×D32—22no—
59C22×D32—22no—
60C22×D32—42no—
61C22×D32—42no—
62C22×D32C2×C414yescomplemented
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)C2×C414yes—
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3—42no—
73C2×C4×C3⋊D3—42no—
74C2×C4×C3⋊D3D414yescomplemented
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C2×#626—42no—
79C2×#626—42no—
80C2×#626C2×C418yescomplemented
81C2×#624—22no—
82C2×#624—42no—
83C32×C4⋊C4—22no—
84#3752—22no—
85#3752—22no—
86C4×C3⋊Dic3—22no—
87C3×(C2×D3)⋊C4—24no—
88C3×(C2×D3)⋊C4—42no—
89C3×(C2×D3)⋊C4C2×C418yescomplemented
90C3×C4×Dic3—42no—
91Dic3⋊Dic3—42no—
92#3722—22no—
93#3722—42no—
94#3722C2×C414yescomplemented
95(C2×D3)⋊Dic3—24no—
96(C2×D3)⋊Dic3—42no—
97#2321—91noSylow
98C24×D3—32no—
99C22×#67—32no—
100C22×D12—32no—
101C22×D12—32no—
102C22×D12—61no—
103C22×C4×D3—32no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—61no—
107C22×C4×D3—61no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2×D312yescomplemented
110C2×C3×C22⋊C4—32no—
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C42—32no—
114C2×#217—32no—
115C2×#217—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—61no—
125C2×(C2×D3)⋊C4—61no—
126C2×(C2×D3)⋊C4C2×D312yes—
127C2×(C2×D3)⋊C4C2×D312yes—
128C2×(C2×D3)⋊C4C2×D312yes—
129C2×C4⋊Dic3—32no—
130C2×Dic3⋊C4—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3C2×D312yescomplemented
134#893—68no—
135#893—68no—
136#882—316no—
137D3×C22⋊C4—68no—
138C3×#95—32no—
139C3×#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95C2×D312yescomplemented
143C3⋊#95C2×D312yescomplemented
144C23×C32C2411yescharacteristic
145C22×C3⋊D3—21no—
146C22×C3⋊D3—21no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3C22×C412yes—
152C22×C3⋊D3C22×C412yes—
153C22×C3⋊D3C2×D412yes—
154C22×C3⋊D3#4112yes—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3C22×C414yes—
162C2×D32—28no—
163C2×D32—48no—
164C2×D32—44no—
165C2×D32—44no—
166C2×D32—48no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4C22×C412yes—
173C2×C32×C4C2×D412yes—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3C2×D412yes—
178C4⋊(C3⋊D3)—28no—
179C4×C3⋊D3—44no—
180C4×C3⋊D3—44no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3C22×C414yes—
190#626—48no—
191#624—44no—
192C2×#120—91no—
193C2×C4×D4—91no—
194C22×C22⋊C4—91no—
195#390—92no—
196#388—32no—
197#388—92no—
198#386—91no—
199#386—92no—
200#385—91no—
201#379—91no—
202C4×C22⋊C4—91no—
203C24×C3—32no—
204C23×D3—32no—
205C23×D3—32no—
206C23×D3—38no—
207C23×D3—61no—
208C23×D3—61no—
209C23×D3—64no—
210C23×D3—64no—
211C23×D3—122no—
212C23×D3—122no—
213C23×D3—122no—
214C23×D3—122no—
215C23×D3C22×D312yes—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D312yes—
225C2×#67—38no—
226C2×#67—122no—
227C2×#67—122no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D312yes—
235C2×D12—38no—
236C2×D12—38no—
237C2×D12—64no—
238C2×D12—64no—
239C2×D12—64no—
240C2×D12—64no—
241C2×D12—64no—
242C2×D12—122no—
243C2×D12—122no—
244C2×C4×D3—38no—
245C2×C4×D3—64no—
246C2×C4×D3—64no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—122no—
250C2×C4×D3—122no—
251C2×C4×D3—122no—
252C2×C4×D3—122no—
253C2×C4×D3—122no—
254C2×C4×D3—122no—
255C2×C4×D3—124no—
256C2×C4×D3—124no—
257C3×C4⋊C4—24no—
258C3×C4⋊C4—24no—
259C3×C22⋊C4—38no—
260C3×C22⋊C4—64no—
261C3×C22⋊C4—122no—
262C3×C42—122no—
263#217—64no—
264#217—122no—
265(C2×D3)⋊C4—24no—
266(C2×D3)⋊C4—38no—
267(C2×D3)⋊C4—42no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—64no—
274(C2×D3)⋊C4—122no—
275(C2×D3)⋊C4—122no—
276(C2×D3)⋊C4—122no—
277(C2×D3)⋊C4C4×D318yescomplemented
278C4⋊Dic3—122no—
279Dic3⋊C4—122no—
280C4×Dic3—42no—
281C4×Dic3—64no—
282C4×Dic3—64no—
283C22×C32C23×C411yescharacteristic
284C22×C32C22×D411yescharacteristic
285C22×C32C2×#4111yescharacteristic
286C22×C32H(5,𝔽2)12yes—
287C22×C32H(5,𝔽2)12yes—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—24no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—22no—
292C2×C3⋊D3—24no—
293C2×C3⋊D3—24no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—42no—
297C2×C3⋊D3C4×D414yes—
298C2×C3×D3—24no—
299C2×C3×D3—24no—
300C2×C3×D3—24no—
301C2×C3×D3—42no—
302C2×C3×D3—42no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305D32—416no—
306C32×C4—22no—
307C32×C4—22no—
308C32×C4—41no—
309C3⋊Dic3—22no—
310C3⋊Dic3—41no—
311C3×Dic3—24no—
312C3×Dic3—42no—
313C3×Dic3—42no—
314C25—91no—
315C22×D4—92no—
316C22×D4—91no—
317C23×C4—91no—
318C23×C4—91no—
319C23×C4—91no—
320#120—98no—
321C4×D4—184no—
322C2×C4⋊C4—92no—
323C2×C4⋊C4D3211yescharacteristic, complemented
324C2×C22⋊C4—32no—
325C2×C22⋊C4—32no—
326C2×C22⋊C4—32no—
327C2×C22⋊C4—91no—
328C2×C22⋊C4—91no—
329C2×C22⋊C4—92no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—184no—
335C2×C42—32no—
336C2×C42—91no—
337#95—32no—
338#95—32no—
339#95—92no—
340C23×C3—21no—
341C23×C3—34no—
342C23×C3—62no—
343C23×C3—62no—
344C23×C3—62no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3C23×D312yes—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—34no—
356C22×D3—34no—
357C22×D3—34no—
358C22×D3—34no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—616no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—122no—
377C22×D3—122no—
378C22×D3—122no—
379C22×D3—122no—
380C22×D3—128no—
381C22×D3—128no—
382C22×D3—128no—
383C22×D3—128no—
384C22×D3—128no—
385C22×D3—128no—
386C22×D3C2×C4×D314yes—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—34no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4C2×C4×D314yes—
411C2×C3×C4D3×D414yes—
412#67—128no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—34no—
422C2×Dic3—62no—
423C2×Dic3—64no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—122no—
431C2×Dic3C2×C4×D314yes—
432D12—616no—
433D12—616no—
434D12—128no—
435C4×D3—128no—
436C4×D3—128no—
437C4×D3—128no—
438C4×D3—128no—
439C4×D3—128no—
440C2×C32C2×C4×D411yescharacteristic
441C2×C32#51812yes—
442C2×C32#53411yescharacteristic
443C2×C32#53511yescharacteristic
444C2×C32#53812yes—
445C3⋊D3—24no—
446C3⋊D3—42no—
447C3×D3—44no—
448C24—32no—
449C24—94no—
450C24—91no—
451C24—91no—
452C24—182no—
453C24—182no—
454C24—362no—
455C24—362no—
456C2×D4—98no—
457C2×D4—94no—
458C2×D4—182no—
459C2×D4—182no—
460C2×D4—362no—
461C2×D4—362no—
462C22×C4—32no—
463C22×C4—32no—
464C22×C4—32no—
465C22×C4—91no—
466C22×C4—94no—
467C22×C4—91no—
468C22×C4—182no—
469C22×C4—182no—
470C22×C4—362no—
471C22×C4—362no—
472C22×C4—362no—
473C22×C4C2×D3211yescharacteristic
474C22×C4C2×D3211yescharacteristic
475C22×C4C2×D3211yescharacteristic
476C4⋊C4—22no—
477C4⋊C4—362no—
478C22⋊C4—38no—
479C22⋊C4—64no—
480C22⋊C4—94no—
481C22⋊C4—122no—
482C22⋊C4—182no—
483C22⋊C4—182no—
484C22⋊C4—184no—
485C22⋊C4—182no—
486C22⋊C4—362no—
487C22⋊C4—362no—
488C42—122no—
489C42—182no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3—64no—
496C22×C3—64no—
497C22×C3—64no—
498C22×C3—122no—
499C22×C3—122no—
500C22×C3—122no—
501C22×C3—122no—
502C22×C3C22×C4×D312yes—
503C22×C3C2×D3×D412yes—
504C22×C3#100412yes—
505C22×C3D3×#4112yes—
506C22×C3#100912yes—
507C22×C3#100912yes—
508C22×C3#100912yes—
509C2×D3—24no—
510C2×D3—24no—
511C2×D3—24no—
512C2×D3—38no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—42no—
516C2×D3—42no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—64no—
520C2×D3—64no—
521C2×D3—64no—
522C2×D3—64no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—64no—
527C2×D3—64no—
528C2×D3—122no—
529C2×D3—124no—
530C2×D3—124no—
531C2×D3—122no—
532C2×D3—124no—
533C2×D3—1232no—
534C2×D3—122no—
535C2×D3—124no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—122no—
541C3×C4—24no—
542C3×C4—24no—
543C3×C4—24no—
544C3×C4—42no—
545C3×C4—42no—
546C3×C4—42no—
547C3×C4—64no—
548C3×C4—122no—
549C3×C4—122no—
550Dic3—24no—
551Dic3—42no—
552Dic3—42no—
553Dic3—64no—
554Dic3—64no—
555Dic3—122no—
556Dic3—122no—
557C32#232111yescharacteristic, complemented, Sylow
558C23—34no—
559C23—62no—
560C23—62no—
561C23—62no—
562C23—62no—
563C23—62no—
564C23—62no—
565C23—92no—
566C23—92no—
567C23—92no—
568C23—92no—
569C23—188no—
570C23—182no—
571C23—182no—
572C23—181no—
573C23—182no—
574C23—182no—
575C23—181no—
576C23—368no—
577C23—368no—
578C23—364no—
579C23—364no—
580C23C22×D3211yescharacteristic
581D4—188no—
582D4—368no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—34no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—92no—
598C2×C4—182no—
599C2×C4—182no—
600C2×C4—181no—
601C2×C4—364no—
602C2×C4—364no—
603C2×C4—364no—
604C2×C4C4×D3212yes—
605C2×C4#381112yes—
606C2×C3—22no—
607C2×C3—22no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—124no—
612C2×C3#552112yes—
613C2×C3C4×D3×D412yes—
614C2×C3#554512yes—
615C2×C3#560512yes—
616C2×C3#565712yes—
617C2×C3#567412yes—
618C2×C3#570412yes—
619D3—44no—
620D3—68no—
621D3—124no—
622D3—124no—
623D3—124no—
624C22—64no—
625C22—64no—
626C22—64no—
627C22—94no—
628C22—122no—
629C22—122no—
630C22—122no—
631C22—122no—
632C22—184no—
633C22—184no—
634C22—182no—
635C22—182no—
636C22—184no—
637C22—182no—
638C22—3616no—
639C22—362no—
640C22—361no—
641C22—361no—
642C22C2×C4×D3211yescharacteristic
643C22#6430611yescharacteristic
644C22#6431412yes—
645C22#6432012yes—
646C22C2×#381111yescharacteristic
647C4—22no—
648C4—22no—
649C4—41no—
650C4—64no—
651C4—122no—
652C4—122no—
653C4—182no—
654C4—361no—
655C3—21no—
656C3#7582612yescomplemented
657C2—124no—
658C2—184no—
659C2—362no—
660C2#1059460412yes—
661C2#1059465712yes—
662C2C4×#381111yescharacteristic
663C2#1059530811yescharacteristic
664C2#1059543311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63923C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
3. C2×#63921C2semidirect
4. C3×#4990C2semidirect
5. #10591399C2semidirect
6. #10591387C2semidirect
7. #10591383C2semidirect
8. #10591380C2semidirect
9. #10591375C2semidirect
10. C4×#3722C2semidirect
11. #10591286C2semidirect
16. C22×C4×C3⋊D3C22semidirect
19. C2×C32×C4⋊C4C22semidirect
21. C2×#3752C22semidirect
22. C2×C4×C3⋊Dic3C22semidirect
27. C2×C3×C4×Dic3C22semidirect
28. C2×Dic3⋊Dic3C22semidirect
31. C2×#3722C22semidirect
34. #63923C4semidirect
36. C3×C3⋊#95C22semidirect
37. C3×C3⋊#95C22semidirect
38. #63579C22semidirect
44. #4990D3semidirect
62. C22×D32C2×C4semidirect
74. C2×C4×C3⋊D3D4semidirect
80. C2×#626C2×C4semidirect
89. C3×(C2×D3)⋊C4C2×C4semidirect
94. #3722C2×C4semidirect
109. C2×C3×C4⋊C4C2×D3semidirect
133. C2×C4×Dic3C2×D3semidirect
142. C3⋊#95C2×D3semidirect
143. C3⋊#95C2×D3semidirect
277. (C2×D3)⋊C4C4×D3semidirect
323. C2×C4⋊C4D32semidirect
557. C32#2321semidirect
656. C3#75826semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#639232
C2×#639212
C3×#49902
#105913992
#105913872
#105913832
#105913802
#105913752
C4×#37222
#105912862
#758263