Finite Group Databasebeta

← #11803068

Subgroups — #11803068

Order 1152.

1213 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2#10592635C211yesmaximal, characteristic, complemented
3C3×#4937C211yesmaximal, characteristic, complemented
4#10591379C212yesmaximal, complemented
5#10591376C212yesmaximal
6D3×C3⋊#95C211yesmaximal, characteristic, complemented
7#10591316C212yesmaximal, complemented
8#10591295C211yesmaximal, characteristic, complemented
9#10591294C211yesmaximal, characteristic, complemented
10#10591270C212yesmaximal, complemented
11#10591237C211yesmaximal, characteristic, complemented
12#82324—31nomaximal
13#74295—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2212yes—
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⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
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—
48#4950—32no—
49#4937D311yescharacteristic, complemented
50#4936—31no—
51#4936—31no—
52#4936—61no—
53#4670—32no—
54#4668—32no—
55#4667—31no—
56#4666—31no—
57#4665—32no—
58#4664—31no—
59D3×#95—31no—
60#4654—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—24no—
73C2×C3×D12C2×C414yes—
74C2×C3×C4×D3—42no—
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3C2×C414yes—
77C2×C3×C4×D3C2×C414yescomplemented
78C2×D3×Dic3—24no—
79C2×D3×Dic3—42no—
80C2×D3×Dic3—42no—
81C32×C42C2×C414yescomplemented
82C4⋊(C3⋊Dic3)—42no—
83C3×(C2×D3)⋊C4C2×C414yes—
84C3×(C2×D3)⋊C4C2×C414yescomplemented
85C3×C4⋊Dic3C2×C414yescomplemented
86Dic3⋊Dic3—42no—
87(C2×D3)⋊Dic3—24no—
88(C2×D3)⋊Dic3—42no—
89(C2×D3)⋊Dic3—42no—
90Dic32—42no—
91#2318—91noSylow
92C22×C3×D4—31no—
93C23×C3×C4—31no—
94C23×C3×C4—31no—
95C23×Dic3—32no—
96C22×D12C2×D311yescharacteristic
97C22×C4×D3—32no—
98C22×C4×D3C2×D311yescharacteristic
99C22×C4×D3C2×D311yescharacteristic
100C3×C4×D4—38no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C42—21no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×#217—32no—
108C2×#217—32no—
109C2×#217—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4C2×D311yescharacteristic
114C2×(C2×D3)⋊C4C2×D311yescharacteristic
115C2×C4⋊Dic3—32no—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—62no—
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×Dic3⋊C4—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C4×D12Dic318yescomplemented
124C3×#95—32no—
125C3×#95—31no—
126C3×#95—31no—
127C3×#95—32no—
128C3⋊#95—32no—
129C3⋊#95—31no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—31no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—61no—
139C3⋊#95—61no—
140C3⋊#95—62no—
141C3⋊#95C2×D312yes—
142C3⋊#95C2×D311yescharacteristic
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C22×C3×D3—21no—
147C22×C3×D3—22no—
148C22×C3×D3—21no—
149C22×C3×D3—22no—
150C22×C3×D3—21no—
151C22×C3×D3—22no—
152C22×C3×D3—21no—
153C22×C3×D3C22×C412yes—
154C22×C3×D3C22×C412yes—
155C22×C3×D3#4114yes—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4C22×C412yes—
161C2×C32×C4C22×C412yes—
162C2×C32×C4C22×C412yes—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3×Dic3—22no—
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×Dic3C22×C412yes—
178C2×C3×Dic3C22×C412yes—
179C3×D12—28no—
180C3×C4×D3—44no—
181C3×C4×D3—44no—
182D3×Dic3—48no—
183C2×C4×D4—31no—
184#388—92no—
185#387—92no—
186#386—92no—
187#385—92no—
188#383—31no—
189#382—91no—
190#381—91no—
191#380—91no—
192C4×C22⋊C4—91no—
193C2×#95—91no—
194C24×C3—31no—
195C24×C3—31no—
196C23×D3C22×D311yescharacteristic
197C23×D3C22×D311yescharacteristic
198C2×C3×D4—34no—
199C2×C3×D4—64no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—34no—
206C22×C3×C4—34no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—122no—
210C22×C3×C4—122no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—64no—
224C22×Dic3—122no—
225C22×Dic3—122no—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D311yescharacteristic
230C2×D12—24no—
231C2×D12C2×Dic314yes—
232C2×C4×D3—42no—
233C2×C4×D3—42no—
234C2×C4×D3—64no—
235C2×C4×D3—122no—
236C2×C4×D3—122no—
237C2×C4×D3C2×Dic314yes—
238C2×C4×D3C2×Dic314yescomplemented
239C3×C4⋊C4—34no—
240C3×C22⋊C4—34no—
241C3×C22⋊C4—34no—
242C3×C42—24no—
243C3×C42C4×D314yescomplemented
244C3×C42C2×Dic314yescomplemented
245#217—64no—
246#217—122no—
247#217—122no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—122no—
250(C2×D3)⋊C4—122no—
251(C2×D3)⋊C4C2×Dic314yes—
252(C2×D3)⋊C4C2×Dic314yescomplemented
253C4⋊Dic3—122no—
254C4⋊Dic3—122no—
255C4⋊Dic3—122no—
256C4⋊Dic3—124no—
257C4⋊Dic3C2×Dic314yescomplemented
258Dic3⋊C4—122no—
259C4×Dic3—122no—
260C4×Dic3—122no—
261C22×C32C23×C411yescharacteristic
262C22×C32C2×#4112yes—
263C22×C32H(5,𝔽2)12yes—
264C22×C32H(5,𝔽2)11yescharacteristic
265C22×C322−1+411yescharacteristic
266C2×C3×D3—22no—
267C2×C3×D3—22no—
268C2×C3×D3—24no—
269C2×C3×D3—24no—
270C2×C3×D3—22no—
271C2×C3×D3—22no—
272C2×C3×D3—22no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3#11714yes—
276C32×C4—22no—
277C32×C4—22no—
278C32×C4—22no—
279C3⋊Dic3—42no—
280C3⋊Dic3—42no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—42no—
284C3×Dic3—42no—
285C22×D4—31no—
286C23×C4—31no—
287C23×C4—31no—
288C23×C4—92no—
289C4×D4—38no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—92no—
293C2×C22⋊C4—31no—
294C2×C22⋊C4—31no—
295C2×C22⋊C4—92no—
296C2×C22⋊C4—92no—
297C2×C22⋊C4—92no—
298C2×C42—92no—
299C2×C42D3211yescharacteristic
300#95—31no—
301#95—31no—
302#95—32no—
303#95—32no—
304#95—92no—
305#95—92no—
306#95—91no—
307#95—91no—
308#95—92no—
309C23×C3—21no—
310C23×C3—32no—
311C23×C3—34no—
312C23×C3—32no—
313C23×C3—61no—
314C23×C3—62no—
315C23×C3—61no—
316C23×C3—62no—
317C23×C3—61no—
318C23×C3—62no—
319C23×C3—61no—
320C23×C3C23×D311yescharacteristic
321C23×C3C23×D311yescharacteristic
322C22×D3—22no—
323C22×D3—21no—
324C22×D3—21no—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—21no—
328C22×D3—21no—
329C22×D3#23514yes—
330C22×D3C22×Dic312yes—
331C22×D3C22×Dic312yes—
332C3×D4—68no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—124no—
359C2×C3×C4—124no—
360C2×C3×C4C2×C4×D312yes—
361C2×C3×C4C2×C4×D312yes—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4C22×Dic312yes—
364C2×C3×C4C22×Dic312yes—
365C2×C3×C4C22×Dic312yes—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3—122no—
390C2×Dic3—122no—
391C2×Dic3—122no—
392C2×Dic3—128no—
393C2×Dic3C22×Dic312yes—
394C2×Dic3C22×Dic312yes—
395D12—28no—
396C4×D3—44no—
397C4×D3—44no—
398C4×D3—128no—
399C2×C32C2×#11711yescharacteristic
400C2×C32#51811yescharacteristic
401C2×C32#52011yescharacteristic
402C2×C32#53812yes—
403C2×C32#53912yes—
404C3×D3—24no—
405C3×D3—42no—
406C24—31no—
407C24—31no—
408C2×D4—34no—
409C2×D4—64no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—34no—
413C22×C4—34no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—92no—
417C22×C4—92no—
418C22×C4—122no—
419C22×C4—122no—
420C22×C4—184no—
421C22×C4—362no—
422C22×C4—362no—
423C22×C4C2×D3211yescharacteristic
424C22×C4C2×D3211yescharacteristic
425C22×C4C2×D3211yescharacteristic
426C4⋊C4—34no—
427C4⋊C4—362no—
428C4⋊C4—362no—
429C22⋊C4—34no—
430C22⋊C4—34no—
431C22⋊C4—184no—
432C22⋊C4—362no—
433C22⋊C4—362no—
434C42—362no—
435C42D3×Dic314yescomplemented
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—34no—
442C22×C3—64no—
443C22×C3—64no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—62no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3C22×C4×D311yescharacteristic
452C22×C3C2×#23512yes—
453C22×C3#100412yes—
454C22×C3D3×#4112yes—
455C22×C3#100912yes—
456C22×C3#100911yescharacteristic
457C22×C3#100911yescharacteristic
458C22×C3#101011yescharacteristic
459C22×C3#101011yescharacteristic
460C22×C3C23×Dic311yescharacteristic
461C2×D3—22no—
462C2×D3—24no—
463C2×D3—24no—
464C2×D3—22no—
465C2×D3—22no—
466C2×D3—22no—
467C2×D3—22no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3#92614yes—
471C3×C4—24no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—62no—
481C3×C4—62no—
482C3×C4—122no—
483C3×C4—122no—
484Dic3—22no—
485Dic3—22no—
486Dic3—42no—
487Dic3—42no—
488Dic3—122no—
489Dic3—122no—
490Dic3—122no—
491Dic3—122no—
492Dic3—242no—
493Dic3—242no—
494C32#231811yescharacteristic, complemented, Sylow
495C23—34no—
496C23—32no—
497C23—32no—
498C23—61no—
499C23—62no—
500C23—61no—
501C23—61no—
502C23—62no—
503C23—62no—
504C23—61no—
505C23C22×D3211yescharacteristic
506D4—68no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—32no—
512C2×C4—32no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—124no—
522C2×C4—124no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4—182no—
526C2×C4—182no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—368no—
530C2×C4C2×D3×Dic312yes—
531C2×C4C2×D3×Dic312yes—
532C2×C4C2×D3×Dic312yes—
533C2×C3—21no—
534C2×C3—22no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—64no—
539C2×C3—122no—
540C2×C3D3×#11711yescharacteristic
541C2×C3#552111yescharacteristic
542C2×C3#552311yescharacteristic
543C2×C3#556012yes—
544C2×C3#556412yes—
545C2×C3#570412yes—
546C2×C3#570712yes—
547C2×C3C2×#92611yescharacteristic
548C2×C3#579811yescharacteristic
549C2×C3#582711yescharacteristic
550D3—24no—
551D3—42no—
552C22—34no—
553C22—64no—
554C22—62no—
555C22—62no—
556C22—64no—
557C22—62no—
558C22—62no—
559C22—62no—
560C22—122no—
561C22—122no—
562C22#6429811yescharacteristic
563C22D3×#23512yes—
564C22#6430712yes—
565C22#6430811yescharacteristic
566C22C22×D3×Dic311yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—62no—
571C4—62no—
572C4—122no—
573C4—122no—
574C4—362no—
575C4—362no—
576C3—21no—
577C3#7429511yescharacteristic, complemented
578C3#8232411yescharacteristic, complemented
579C2—64no—
580C2—122no—
581C2#1059391412yes—
582C2#1059401312yes—
583C2D3×#92611yescharacteristic
584C2#1059498211yescharacteristic
585C2#1059499211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592635C2semidirect
3. C3×#4937C2semidirect
4. #10591379C2semidirect
6. D3×C3⋊#95C2semidirect
7. #10591316C2semidirect
8. #10591295C2semidirect
9. #10591294C2semidirect
10. #10591270C2semidirect
11. #10591237C2semidirect
23. C3×C4×D12C4semidirect
49. #4937D3semidirect
77. C2×C3×C4×D3C2×C4semidirect
81. C32×C42C2×C4semidirect
84. C3×(C2×D3)⋊C4C2×C4semidirect
85. C3×C4⋊Dic3C2×C4semidirect
123. C4×D12Dic3semidirect
238. C2×C4×D3C2×Dic3semidirect
243. C3×C42C4×D3semidirect
244. C3×C42C2×Dic3semidirect
252. (C2×D3)⋊C4C2×Dic3semidirect
257. C4⋊Dic3C2×Dic3semidirect
435. C42D3×Dic3semidirect
494. C32#2318semidirect
577. C3#74295semidirect
578. C3#82324semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
#105926352
C3×#49372
#105913792
#105913762
D3×C3⋊#952
#105913162
#105912952
#105912942
#105912702
#105912372
#823243
#742953