Finite Group Databasebeta

← #11805764

Subgroups — #11805764

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2#10592631C211yesmaximal, characteristic, complemented
3C3×#4937C211yesmaximal, characteristic, complemented
4#10591376C212yesmaximal
5#10591368C212yesmaximal, complemented
6D3×C3⋊#95C211yesmaximal, characteristic, complemented
7#10591295C211yesmaximal, characteristic, complemented
8#10591294C211yesmaximal, characteristic, complemented
9#10591286C212yesmaximal, complemented
10#10591269C212yesmaximal, complemented
11#10591237C211yesmaximal, characteristic, complemented
12#82336—31nomaximal
13#74297—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×C4×C3⋊Dic3C2212yes—
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C3×C4×D12C418yescomplemented
24C2×Dic3⋊Dic3C2212yes—
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29#63658C2211yescharacteristic
30#63658C2212yes—
31#63658C2211yescharacteristic
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×C4×D4—31no—
39C2×C4×D12D311yescharacteristic
40C3×#383—31no—
41#5220—32no—
42#5212—31no—
43#5211—31no—
44C4×#217—31no—
45C2×C3⋊#95—31no—
46#4980—32no—
47#4951—32no—
48Dic3×C22⋊C4—32no—
49#4937D311yescharacteristic, complemented
50#4932—31no—
51#4932—31no—
52#4932—61no—
53#4669—32no—
54#4667—31no—
55#4666—31no—
56#4666—32no—
57#4665—32no—
58#4664—31no—
59D3×#95—31no—
60#4653—32no—
61C23×C3×D3C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×D12—22no—
73C2×C3×D12—22no—
74C2×C3×D12C2×C414yes—
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3—42no—
77C2×C3×C4×D3C2×C414yes—
78C2×C3×C4×D3C2×C414yescomplemented
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81C2×D3×Dic3—42no—
82C32×C42C2×C414yescomplemented
83C4×C3⋊Dic3—24no—
84C3×(C2×D3)⋊C4C2×C414yes—
85C3×(C2×D3)⋊C4C2×C414yescomplemented
86C3×C4⋊Dic3C2×C414yescomplemented
87Dic3⋊Dic3—42no—
88(C2×D3)⋊Dic3—24no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—42no—
91Dic32—42no—
92#2353—91noSylow
93C22×C3×D4—31no—
94C23×C3×C4—31no—
95C23×C3×C4—31no—
96C23×Dic3—32no—
97C22×D12C2×D311yescharacteristic
98C22×C4×D3—32no—
99C22×C4×D3C2×D311yescharacteristic
100C22×C4×D3C2×D311yescharacteristic
101C3×C4×D4—38no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C42—21no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C2×D311yescharacteristic
108C2×#217—32no—
109C2×#217—32no—
110C2×#217—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4C2×D311yescharacteristic
115C2×(C2×D3)⋊C4C2×D311yescharacteristic
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×Dic3⋊C4—32no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—62no—
124C4×D12Dic318yescomplemented
125C3×#95—32no—
126C3×#95—31no—
127C3×#95—31no—
128C3×#95—32no—
129C3⋊#95—32no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—31no—
133C3⋊#95—31no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—61no—
140C3⋊#95—61no—
141C3⋊#95—62no—
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D312yes—
146C23×C32C2411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—21no—
151C22×C3×D3—21no—
152C22×C3×D3—22no—
153C22×C3×D3C22×C412yes—
154C22×C3×D3C22×C412yes—
155C22×C3×D3#4112yes—
156C22×C3×D3#4112yes—
157C2×C32×C4—22no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—22no—
161C2×C32×C4C22×C412yes—
162C2×C32×C4C22×C412yes—
163C2×C32×C4C22×C412yes—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3#4114yes—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
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×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C3×D12—28no—
181C3×C4×D3—44no—
182C3×C4×D3—44no—
183D3×Dic3—48no—
184C2×C4×D4—31no—
185#388—92no—
186#387—92no—
187#386—92no—
188#383—31no—
189#381—91no—
190#380—91no—
191C4×C22⋊C4—92no—
192C4×C22⋊C4—91no—
193#376—91no—
194C2×#95—91no—
195C24×C3—31no—
196C24×C3—31no—
197C23×D3C22×D311yescharacteristic
198C23×D3C22×D311yescharacteristic
199C2×C3×D4—34no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—34no—
208C22×C3×C4—34no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—122no—
212C22×C3×C4—122no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—64no—
226C22×Dic3—64no—
227C22×Dic3—122no—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D311yescharacteristic
232C2×D12—22no—
233C2×D12—22no—
234C2×D12C2×Dic314yes—
235C2×C4×D3—42no—
236C2×C4×D3—42no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—122no—
240C2×C4×D3C2×Dic314yes—
241C2×C4×D3C2×Dic314yescomplemented
242C3×C4⋊C4—34no—
243C3×C22⋊C4—34no—
244C3×C22⋊C4—34no—
245C3×C42—24no—
246C3×C42C4×D314yescomplemented
247C3×C42C2×Dic314yescomplemented
248#217—64no—
249#217—64no—
250#217—122no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—122no—
254(C2×D3)⋊C4C2×Dic314yes—
255(C2×D3)⋊C4C2×Dic314yescomplemented
256C4⋊Dic3—122no—
257C4⋊Dic3C2×Dic314yescomplemented
258Dic3⋊C4—122no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C4×Dic3—68no—
262C4×Dic3—122no—
263C4×Dic3—122no—
264C22×C32C23×C411yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32C2×#4112yes—
268C22×C32H(5,𝔽2)12yes—
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—24no—
272C2×C3×D3—24no—
273C2×C3×D3—22no—
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3#11714yes—
279C32×C4—22no—
280C32×C4—22no—
281C32×C4—22no—
282C3⋊Dic3—24no—
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C22×D4—31no—
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—92no—
292C4×D4—38no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—92no—
295C2×C22⋊C4—31no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—92no—
299C2×C22⋊C4—92no—
300C2×C42—92no—
301C2×C42—92no—
302C2×C42D3211yescharacteristic
303#95—31no—
304#95—31no—
305#95—32no—
306#95—32no—
307#95—92no—
308#95—92no—
309#95—91no—
310#95—91no—
311#95—92no—
312C23×C3—21no—
313C23×C3—32no—
314C23×C3—32no—
315C23×C3—32no—
316C23×C3—32no—
317C23×C3—62no—
318C23×C3—62no—
319C23×C3—62no—
320C23×C3—61no—
321C23×C3—61no—
322C23×C3—62no—
323C23×C3C23×D311yescharacteristic
324C23×C3C23×D311yescharacteristic
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—21no—
328C22×D3—21no—
329C22×D3—22no—
330C22×D3—22no—
331C22×D3#23512yes—
332C22×D3#23512yes—
333C22×D3C22×Dic312yes—
334C22×D3C22×Dic312yes—
335C3×D4—68no—
336C2×C3×C4—24no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—42no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—124no—
362C2×C3×C4—124no—
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4C2×C4×D312yes—
365C2×C3×C4C2×C4×D312yes—
366C2×C3×C4C22×Dic312yes—
367C2×C3×C4C22×Dic312yes—
368C2×C3×C4C22×Dic312yes—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—34no—
378C2×Dic3—34no—
379C2×Dic3—64no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—64no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3—122no—
395C2×Dic3—128no—
396C2×Dic3C22×Dic312yes—
397C2×Dic3C22×Dic312yes—
398D12—28no—
399C4×D3—44no—
400C4×D3—44no—
401C4×D3—128no—
402C2×C32C2×#11711yescharacteristic
403C2×C32C4×#4111yescharacteristic
404C2×C32#51811yescharacteristic
405C2×C32#55112yes—
406C2×C32#55312yes—
407C3×D3—24no—
408C3×D3—42no—
409C24—31no—
410C24—31no—
411C2×D4—34no—
412C2×D4—62no—
413C2×D4—62no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—34no—
417C22×C4—34no—
418C22×C4—32no—
419C22×C4—32no—
420C22×C4—92no—
421C22×C4—92no—
422C22×C4—122no—
423C22×C4—122no—
424C22×C4—184no—
425C22×C4—184no—
426C22×C4—362no—
427C22×C4C2×D3211yescharacteristic
428C22×C4C2×D3211yescharacteristic
429C22×C4C2×D3211yescharacteristic
430C4⋊C4—34no—
431C4⋊C4—362no—
432C22⋊C4—34no—
433C22⋊C4—34no—
434C22⋊C4—184no—
435C22⋊C4—184no—
436C22⋊C4—362no—
437C42—184no—
438C42—362no—
439C42D3×Dic314yescomplemented
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—21no—
445C22×C3—34no—
446C22×C3—64no—
447C22×C3—64no—
448C22×C3—62no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—62no—
453C22×C3—122no—
454C22×C3—122no—
455C22×C3C22×C4×D311yescharacteristic
456C22×C3C2×#23511yescharacteristic
457C22×C3C2×#23511yescharacteristic
458C22×C3#100412yes—
459C22×C3D3×#4111yescharacteristic
460C22×C3D3×#4111yescharacteristic
461C22×C3D3×#4112yes—
462C22×C3D3×#4112yes—
463C22×C3#100912yes—
464C22×C3C23×Dic311yescharacteristic
465C2×D3—24no—
466C2×D3—22no—
467C2×D3—24no—
468C2×D3—22no—
469C2×D3—22no—
470C2×D3—22no—
471C2×D3—22no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3#92614yes—
475C3×C4—24no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—22no—
479C3×C4—22no—
480C3×C4—22no—
481C3×C4—22no—
482C3×C4—42no—
483C3×C4—42no—
484C3×C4—62no—
485C3×C4—62no—
486C3×C4—122no—
487C3×C4—122no—
488Dic3—22no—
489Dic3—22no—
490Dic3—42no—
491Dic3—42no—
492Dic3—64no—
493Dic3—64no—
494Dic3—124no—
495Dic3—124no—
496Dic3—122no—
497Dic3—122no—
498C32#235311yescharacteristic, complemented, Sylow
499C23—32no—
500C23—32no—
501C23—32no—
502C23—32no—
503C23—62no—
504C23—62no—
505C23—61no—
506C23—61no—
507C23—62no—
508C23—62no—
509C23C22×D3211yescharacteristic
510D4—68no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—94no—
526C2×C4—124no—
527C2×C4—124no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4—368no—
534C2×C4C2×D3×Dic312yes—
535C2×C4C2×D3×Dic312yes—
536C2×C4C2×D3×Dic312yes—
537C2×C3—21no—
538C2×C3—22no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—22no—
542C2×C3—64no—
543C2×C3—122no—
544C2×C3D3×#11711yescharacteristic
545C2×C3#552111yescharacteristic
546C2×C3#552211yescharacteristic
547C2×C3#554012yes—
548C2×C3#555612yes—
549C2×C3#570512yes—
550C2×C3#570912yes—
551C2×C3C2×#92611yescharacteristic
552C2×C3#579811yescharacteristic
553C2×C3Dic3×#4111yescharacteristic
554D3—24no—
555D3—42no—
556C22—34no—
557C22—64no—
558C22—62no—
559C22—62no—
560C22—64no—
561C22—62no—
562C22—62no—
563C22—62no—
564C22—122no—
565C22—122no—
566C22D3×#23511yescharacteristic
567C22D3×#23511yescharacteristic
568C22#6430612yes—
569C22#6430712yes—
570C22C22×D3×Dic311yescharacteristic
571C4—22no—
572C4—22no—
573C4—22no—
574C4—62no—
575C4—62no—
576C4—122no—
577C4—122no—
578C4—184no—
579C4—362no—
580C3—21no—
581C3#7429711yescharacteristic, complemented
582C3#8233611yescharacteristic, complemented
583C2—64no—
584C2—122no—
585C2#1059392412yes—
586C2#1059401812yes—
587C2D3×#92611yescharacteristic
588C2#1059495811yescharacteristic
589C2#1059498211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592631C2semidirect
3. C3×#4937C2semidirect
5. #10591368C2semidirect
6. D3×C3⋊#95C2semidirect
7. #10591295C2semidirect
8. #10591294C2semidirect
9. #10591286C2semidirect
10. #10591269C2semidirect
11. #10591237C2semidirect
23. C3×C4×D12C4semidirect
49. #4937D3semidirect
78. C2×C3×C4×D3C2×C4semidirect
82. C32×C42C2×C4semidirect
85. C3×(C2×D3)⋊C4C2×C4semidirect
86. C3×C4⋊Dic3C2×C4semidirect
124. C4×D12Dic3semidirect
241. C2×C4×D3C2×Dic3semidirect
246. C3×C42C4×D3semidirect
247. C3×C42C2×Dic3semidirect
255. (C2×D3)⋊C4C2×Dic3semidirect
257. C4⋊Dic3C2×Dic3semidirect
439. C42D3×Dic3semidirect
498. C32#2353semidirect
581. C3#74297semidirect
582. C3#82336semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
#105926312
C3×#49372
#105913762
#105913682
D3×C3⋊#952
#105912952
#105912942
#105912862
#105912692
#105912372
#823363
#742973