Finite Group Databasebeta

← #11805513

Subgroups — #11805513

Order 1152.

1573 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×C4×#626C212yesmaximal
2C2×C4×#626C211yesmaximal, characteristic
3C3⋊D3×#95C211yesmaximal, characteristic, complemented
4C3×D3×#95C211yesmaximal, characteristic, complemented
5C3×#4649C211yesmaximal, characteristic, complemented
6#10591355C211yesmaximal, characteristic, complemented
7#10591327C212yesmaximal, complemented
8#10591295C211yesmaximal, characteristic, complemented
9#10591290C212yesmaximal, complemented
10#10591277C212yesmaximal, complemented
11#10591206C211yesmaximal, characteristic, complemented
12#73770—31nomaximal
13#73369—31nomaximal
14C22×C4×C3⋊D3C2212yes—
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×#626C2211yescharacteristic
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×#3724C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic3⋊Dic3C2211yescharacteristic
26C2×#3722C2212yes—
27C2×#3722C2211yescharacteristic
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2211yescharacteristic
30C4×#626—28no—
31C4×#626C418yescomplemented
32C32×#95C2211yescharacteristic
33#63658C2212yes—
34#63658C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2211yescharacteristic
38#63579C2212yes—
39C2×C4×#67—31no—
40C2×C4×#67—32no—
41C2×C4×D12—31no—
42C2×C4×D12—32no—
43C3×C4×C4⋊C4—31no—
44C2×C3×#95—31no—
45#5212—31no—
46#5210—32no—
47#4989—32no—
48#4989—32no—
49#4936—31no—
50#4928—32no—
51#4668—32no—
52#4667—31no—
53#4667—31no—
54#4667—31no—
55D3×#95—31no—
56D3×#95—31no—
57D3×#95—61no—
58D3×#95D311yescharacteristic, complemented
59#4650—31no—
60#4649D311yescharacteristic, complemented
61#4647—32no—
62C23×C3⋊D3C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—24no—
69C2×C4×C3⋊D3—24no—
70C2×C4×C3⋊D3—42no—
71C2×C4×C3⋊D3—42no—
72C2×C4×C3⋊D3C2×C414yescomplemented
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3—42no—
81C2×C3×C4×D3—42no—
82C2×C3×C4×D3C2×C414yescomplemented
83C2×#626C2×C414yes—
84C2×#626D414yes—
85C2×#626Q814yes—
86C3×Dic3⋊C4—24no—
87C3×C4×Dic3—24no—
88C3×C4×Dic3C2×C414yescomplemented
89#3724—42no—
90Dic3⋊Dic3—24no—
91Dic3⋊Dic3—42no—
92Dic3⋊Dic3C2×C414yescomplemented
93#3722—24no—
94#3722C2×C414yescomplemented
95(C2×D3)⋊Dic3—24no—
96(C2×D3)⋊Dic3C2×C414yescomplemented
97#2349—91noSylow
98C23×C3×C4—31no—
99C23×C3×C4—32no—
100C22×#67—31no—
101C22×D12—31no—
102C22×C4×D3—31no—
103C22×C4×D3—31no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—61no—
107C22×C4×D3—62no—
108C22×C4×D3C2×D312yes—
109C22×C4×D3C2×D311yescharacteristic
110C2×C3×C4⋊C4—32no—
111C2×C3×C42—31no—
112C2×C3×C42—32no—
113C2×#217—31no—
114C2×#217—32no—
115C4×#67—38no—
116C4×#67—68no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—31no—
119C2×(C2×D3)⋊C4—31no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—32no—
126C2×Dic3⋊C4—31no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4C2×D312yes—
132C2×C4×Dic3C2×D312yes—
133C2×C4×Dic3C2×D311yescharacteristic
134C4×D12—38no—
135C4×D12—68no—
136C3×#95—21no—
137C3×#95—32no—
138C3×#95—31no—
139C3×#95—31no—
140C3×#95C2×D311yescharacteristic
141C3×#95C2×D311yescharacteristic
142C3⋊#95—32no—
143C3⋊#95—31no—
144C3⋊#95—31no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—61no—
149C3⋊#95—62no—
150C3⋊#95C2×D311yescharacteristic
151C3⋊#95C2×D311yescharacteristic
152C3⋊#95C2×D312yes—
153C23×C32C2411yescharacteristic
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3C22×C412yes—
157C22×C3⋊D3C2×D412yes—
158C22×C3⋊D3C2×Q812yes—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3C22×C412yes—
162C22×C3×D3C2×D412yes—
163C22×C3×D3C2×Q812yes—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4C22×C412yes—
168C2×C32×C4#4114yes—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C22×C412yes—
174C4×C3⋊D3—44no—
175C4×C3⋊D3—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×C412yes—
185C2×C3×Dic3C22×C412yes—
186C2×C3×Dic3C22×C412yes—
187C2×C3×Dic3C2×D412yes—
188C2×C3×Dic3C2×Q812yes—
189C3×C4×D3—44no—
190C3×C4×D3—48no—
191#626C4⋊C4116yescomplemented
192C2×C4×D4—91no—
193C2×C4×D4—92no—
194#389—92no—
195#385—92no—
196#385—92no—
197#382—91no—
198#380—91no—
199#380—91no—
200C4×C4⋊C4—31no—
201C2×#95—31no—
202C2×#95—91no—
203C24×C3—31no—
204C23×D3—31no—
205C23×D3—31no—
206C23×D3—61no—
207C23×D3C22×D311yescharacteristic
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—34no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—64no—
217C22×C3×C4—64no—
218C22×C3×C4—122no—
219C22×C3×C4—122no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D312yes—
224C2×#67—34no—
225C2×#67—34no—
226C2×#67—34no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—32no—
230C22×Dic3—32no—
231C22×Dic3—61no—
232C22×Dic3—62no—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D311yescharacteristic
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D311yescharacteristic
238C2×D12—34no—
239C2×D12—34no—
240C2×D12—34no—
241C2×C4×D3—24no—
242C2×C4×D3—24no—
243C2×C4×D3—34no—
244C2×C4×D3—34no—
245C2×C4×D3—42no—
246C2×C4×D3—42no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—64no—
250C2×C4×D3—68no—
251C2×C4×D3—64no—
252C2×C4×D3—64no—
253C2×C4×D3—124no—
254C2×C4×D3—122no—
255C2×C4×D3—122no—
256C2×C4×D3—122no—
257C2×C4×D3—122no—
258C2×C4×D3—124no—
259C2×C4×D3—124no—
260C2×C4×D3C4×D314yescomplemented
261C3×C4⋊C4—64no—
262C3×C42—34no—
263C3×C42—64no—
264#217—34no—
265#217—64no—
266(C2×D3)⋊C4—34no—
267(C2×D3)⋊C4—34no—
268(C2×D3)⋊C4—34no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272C4⋊Dic3—34no—
273C4⋊Dic3—64no—
274C4⋊Dic3—122no—
275Dic3⋊C4—24no—
276Dic3⋊C4—34no—
277Dic3⋊C4—64no—
278Dic3⋊C4—122no—
279Dic3⋊C4—122no—
280Dic3⋊C4—122no—
281C4×Dic3—24no—
282C4×Dic3C4×D314yescomplemented
283C22×C32C23×C411yescharacteristic
284C22×C32C22×D411yescharacteristic
285C22×C32C22×Q811yescharacteristic
286C22×C32C2×#4112yes—
287C22×C32H(5,𝔽2)12yes—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—24no—
291C2×C3⋊D3—24no—
292C2×C3⋊D3C2×C4⋊C414yes—
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3C2×C4⋊C414yes—
298C32×C4—22no—
299C32×C4—24no—
300C3⋊Dic3—22no—
301C3⋊Dic3—42no—
302C3×Dic3—22no—
303C3×Dic3—22no—
304C3×Dic3—42no—
305C3×Dic3—42no—
306C3×Dic3C2×C4⋊C414yes—
307C22×D4—91no—
308C23×C4—31no—
309C23×C4—32no—
310C23×C4—91no—
311C23×C4—92no—
312C4×D4—98no—
313C4×D4—188no—
314C2×C4⋊C4—32no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4—92no—
317C2×C4⋊C4—92no—
318C2×C4⋊C4—92no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—92no—
322C2×C22⋊C4—92no—
323C2×C42—31no—
324C2×C42—32no—
325#95—31no—
326#95—32no—
327#95—31no—
328#95—92no—
329#95—91no—
330#95—92no—
331#95D3211yescharacteristic
332C23×C3—21no—
333C23×C3—32no—
334C23×C3—32no—
335C23×C3—32no—
336C23×C3—62no—
337C23×C3—62no—
338C23×C3C23×D311yescharacteristic
339C23×C3C23×D311yescharacteristic
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—32no—
343C22×D3—32no—
344C22×D3—32no—
345C22×D3—32no—
346C22×D3—32no—
347C22×D3—32no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—64no—
352C22×D3—64no—
353C22×D3—62no—
354C22×D3—62no—
355C22×D3—62no—
356C22×D3—62no—
357C22×D3C2×C4×D312yes—
358C22×D3D3×D412yes—
359C22×D3D3×Q812yes—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—22no—
368C2×C3×C4—32no—
369C2×C3×C4—32no—
370C2×C3×C4—32no—
371C2×C3×C4—32no—
372C2×C3×C4—32no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—124no—
385C2×C3×C4—128no—
386C2×C3×C4C2×C4×D312yes—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4#23514yes—
389C2×C3×C4#23514yes—
390#67—316no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—32no—
400C2×Dic3—32no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—64no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3C2×C4×D312yes—
415C2×Dic3C2×C4×D312yes—
416C2×Dic3C2×C4×D312yes—
417C2×Dic3D3×D412yes—
418C2×Dic3D3×Q812yes—
419D12—316no—
420C4×D3—44no—
421C4×D3—48no—
422C4×D3—124no—
423C4×D3—124no—
424C4×D3—128no—
425C4×D3—128no—
426C4×D3—128no—
427C4×D3—1216no—
428C2×C32C22×C4⋊C411yescharacteristic
429C2×C32C4×#4111yescharacteristic
430C2×C32#51811yescharacteristic
431C2×C32#54612yes—
432C2×C32#55412yes—
433C3⋊D3—24no—
434C3×D3—24no—
435C24—31no—
436C24—91no—
437C2×D4—94no—
438C2×D4—94no—
439C2×D4—94no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—34no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—64no—
447C22×C4—64no—
448C22×C4—91no—
449C22×C4—94no—
450C22×C4—92no—
451C22×C4—122no—
452C22×C4—122no—
453C22×C4—184no—
454C22×C4—184no—
455C22×C4—362no—
456C22×C4—362no—
457C22×C4C2×D3212yes—
458C22×C4C2×D3211yescharacteristic
459C4⋊C4—64no—
460C4⋊C4—94no—
461C4⋊C4—184no—
462C4⋊C4—362no—
463C4⋊C4—362no—
464C22⋊C4—94no—
465C22⋊C4—94no—
466C22⋊C4—184no—
467C22⋊C4—184no—
468C42—34no—
469C42—64no—
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—22no—
474C22×C3—21no—
475C22×C3—34no—
476C22×C3—62no—
477C22×C3—62no—
478C22×C3—64no—
479C22×C3—64no—
480C22×C3C22×C4×D311yescharacteristic
481C22×C3C22×C4×D311yescharacteristic
482C22×C3C2×#23512yes—
483C22×C3C2×#23512yes—
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C2×D3×D411yescharacteristic
486C22×C3#100412yes—
487C22×C3C2×D3×Q811yescharacteristic
488C22×C3C2×D3×Q811yescharacteristic
489C22×C3#100912yes—
490C2×D3—22no—
491C2×D3—22no—
492C2×D3—24no—
493C2×D3—24no—
494C2×D3—34no—
495C2×D3—34no—
496C2×D3—64no—
497C2×D3—64no—
498C2×D3—68no—
499C2×D3—64no—
500C2×D3—68no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—62no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—62no—
507C2×D3—64no—
508C2×D3—64no—
509C2×D3D3×C4⋊C414yes—
510C3×C4—22no—
511C3×C4—24no—
512C3×C4—22no—
513C3×C4—24no—
514C3×C4—34no—
515C3×C4—42no—
516C3×C4—44no—
517C3×C4—62no—
518C3×C4—62no—
519C3×C4—122no—
520C3×C4—122no—
521Dic3—22no—
522Dic3—22no—
523Dic3—42no—
524Dic3—42no—
525Dic3—62no—
526Dic3—62no—
527Dic3—122no—
528Dic3—124no—
529Dic3—122no—
530Dic3—122no—
531Dic3D3×C4⋊C414yes—
532C32#234911yescharacteristic, complemented, Sylow
533C23—32no—
534C23—32no—
535C23—32no—
536C23—62no—
537C23—62no—
538C23—92no—
539C23—92no—
540C23—92no—
541C23—182no—
542C23—182no—
543C23C22×D3211yescharacteristic
544D4—916no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—32no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—92no—
562C2×C4—124no—
563C2×C4—128no—
564C2×C4—182no—
565C2×C4—182no—
566C2×C4—182no—
567C2×C4—182no—
568C2×C4—364no—
569C2×C4—368no—
570C2×C4#379814yes—
571C2×C4C4×D3212yes—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—22no—
575C2×C3—21no—
576C2×C3—22no—
577C2×C3—64no—
578C2×C3C4×#23511yescharacteristic
579C2×C3C4×#23511yescharacteristic
580C2×C3#548611yescharacteristic
581C2×C3#549012yes—
582C2×C3C2×D3×C4⋊C411yescharacteristic
583C2×C3C2×D3×C4⋊C411yescharacteristic
584C2×C3#551112yes—
585C2×C3#552111yescharacteristic
586C2×C3#555012yes—
587C2×C3#557912yes—
588D3—24no—
589D3—68no—
590D3—64no—
591D3—64no—
592C22—34no—
593C22—62no—
594C22—64no—
595C22—62no—
596C22—64no—
597C22—94no—
598C22—182no—
599C22—184no—
600C22—182no—
601C22—184no—
602C22C2×#379812yes—
603C22C2×C4×D3211yescharacteristic
604C22D32×D411yescharacteristic
605C22#6431412yes—
606C22D32×Q811yescharacteristic
607C4—22no—
608C4—24no—
609C4—34no—
610C4—62no—
611C4—62no—
612C4—122no—
613C4—122no—
614C4—182no—
615C4—362no—
616C3—21no—
617C3#7336911yescharacteristic, complemented
618C3#7377011yescharacteristic, complemented
619C2—64no—
620C2—184no—
621C2C4×#379811yescharacteristic
622C2#1059418211yescharacteristic
623C2#1059418612yes—
624C2#1059453612yes—
625C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3⋊D3×#95C2semidirect
4. C3×D3×#95C2semidirect
5. C3×#4649C2semidirect
6. #10591355C2semidirect
7. #10591327C2semidirect
8. #10591295C2semidirect
9. #10591290C2semidirect
10. #10591277C2semidirect
11. #10591206C2semidirect
31. C4×#626C4semidirect
58. D3×#95D3semidirect
60. #4649D3semidirect
72. C2×C4×C3⋊D3C2×C4semidirect
82. C2×C3×C4×D3C2×C4semidirect
88. C3×C4×Dic3C2×C4semidirect
92. Dic3⋊Dic3C2×C4semidirect
94. #3722C2×C4semidirect
96. (C2×D3)⋊Dic3C2×C4semidirect
191. #626C4⋊C4semidirect
260. C2×C4×D3C4×D3semidirect
282. C4×Dic3C4×D3semidirect
532. C32#2349semidirect
617. C3#73369semidirect
618. C3#73770semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
C3⋊D3×#952
C3×D3×#952
C3×#46492
#105913552
#105913272
#105912952
#105912902
#105912772
#105912062
#737703
#733693