Finite Group Databasebeta

← #11803057

Subgroups — #11803057

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2#10592910C211yesmaximal, characteristic, complemented
3C3×#5212C211yesmaximal, characteristic, complemented
4#10591721C212yesmaximal
5#10591702C212yesmaximal, complemented
6#10591377C212yesmaximal, complemented
7D3×C3⋊#95C211yesmaximal, characteristic, complemented
8#10591262C212yesmaximal, complemented
9#10591237C211yesmaximal, characteristic, complemented
10#10591223C211yesmaximal, characteristic, complemented
11#10591206C211yesmaximal, characteristic, complemented
12#82324—31nomaximal
13#74006—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×#3757C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2211yescharacteristic
21C3×C4×#67C418yescomplemented
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29#63658C2211yescharacteristic
30#63658C2212yes—
31#63658C2211yescharacteristic
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×C4×D4—31no—
39C2×C4×#67D311yescharacteristic
40C3×#380—31no—
41#5220—32no—
42#5212D311yescharacteristic, complemented
43#5211—31no—
44#5211—31no—
45#5211—61no—
46C4×#217—31no—
47C2×C3⋊#95—31no—
48#4989—32no—
49#4980—32no—
50#4978—32no—
51#4956—32no—
52#4951—32no—
53#4950—32no—
54#4945—32no—
55#4937—31no—
56#4936—31no—
57#4666—31no—
58D3×#95—31no—
59#4651—31no—
60#4650—31no—
61C24×C32C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4—42no—
64C22×C32×C4C2×C414yescomplemented
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C2×C3×#67—24no—
70C2×C3×#67C2×C414yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C2×C3×C4×D3—42no—
77C2×C3×C4×D3C2×C414yes—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—42no—
80C2×D3×Dic3—42no—
81#3757—42no—
82C3×#217—42no—
83C3×#217C2×C414yescomplemented
84C3×(C2×D3)⋊C4C2×C414yes—
85C3×C4⋊Dic3—42no—
86C3×Dic3⋊C4C2×C414yescomplemented
87C3×C4×Dic3C2×C414yescomplemented
88Dic3⋊Dic3—42no—
89(C2×D3)⋊Dic3—24no—
90Dic32—42no—
91#2318—91noSylow
92C22×C3×D4—31no—
93C23×C3×C4—21no—
94C23×C3×C4—31no—
95C23×C3×C4C2×D311yescharacteristic
96C23×C3×C4C2×D311yescharacteristic
97C22×#67C2×D311yescharacteristic
98C23×Dic3—32no—
99C22×C4×D3—32no—
100C22×C4×D3C2×D311yescharacteristic
101C3×C4×D4—38no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C42—31no—
108C2×#217—32no—
109C2×#217—32no—
110C2×#217—32no—
111C2×#217—62no—
112C2×#217C2×D312yes—
113C2×#217C2×D311yescharacteristic
114C4×#67Dic318yescomplemented
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4C2×D311yescharacteristic
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3C2×D312yes—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4C2×D311yescharacteristic
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3C2×D311yescharacteristic
124C3×#95—31no—
125C3×#95—31no—
126C3⋊#95—31no—
127C3⋊#95—31no—
128C3⋊#95—31no—
129C3⋊#95—31no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—61no—
141C3⋊#95—61no—
142C3⋊#95—62no—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D311yescharacteristic
145C23×C32—22no—
146C23×C32—22no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32C22×C412yes—
150C23×C32C2411yescharacteristic
151C22×C3×D3—21no—
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3C22×C412yes—
155C22×C3×D3#4114yes—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—44no—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C22×C412yes—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C3×#67—28no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
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—
180C2×C3×Dic3C22×C412yes—
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—91no—
189#382—91no—
190#381—91no—
191#380—31no—
192C4×C22⋊C4—91no—
193C2×#95—91no—
194C24×C3—21no—
195C24×C3—31no—
196C24×C3C22×D311yescharacteristic
197C24×C3C22×D311yescharacteristic
198C23×D3C22×D311yescharacteristic
199C2×C3×D4—34no—
200C2×C3×D4—64no—
201C22×C3×C4—24no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—34no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—42no—
211C22×C3×C4—42no—
212C22×C3×C4—44no—
213C22×C3×C4—122no—
214C22×C3×C4C4×D314yescomplemented
215C22×C3×C4C2×Dic314yescomplemented
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—24no—
221C2×#67C2×Dic314yes—
222C22×Dic3—32no—
223C22×Dic3—32no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—62no—
227C22×Dic3—62no—
228C22×Dic3—64no—
229C22×Dic3—122no—
230C22×Dic3—122no—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D311yescharacteristic
235C22×Dic3C22×D311yescharacteristic
236C2×C4×D3—42no—
237C2×C4×D3—64no—
238C2×C4×D3—122no—
239C2×C4×D3—122no—
240C2×C4×D3C2×Dic314yes—
241C3×C4⋊C4—34no—
242C3×C4⋊C4—122no—
243C3×C22⋊C4—34no—
244C3×C22⋊C4—34no—
245C3×C22⋊C4—122no—
246C3×C42—34no—
247#217—42no—
248#217—64no—
249#217—122no—
250#217—122no—
251#217—124no—
252#217C2×Dic314yescomplemented
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4C2×Dic314yes—
255C4⋊Dic3—42no—
256C4⋊Dic3—122no—
257Dic3⋊C4—122no—
258Dic3⋊C4C2×Dic314yescomplemented
259C4×Dic3—122no—
260C4×Dic3—122no—
261C4×Dic3C2×Dic314yescomplemented
262C22×C32—22no—
263C22×C32—22no—
264C22×C32—22no—
265C22×C32—42no—
266C22×C32—42no—
267C22×C32C23×C411yescharacteristic
268C22×C32C2×#4112yes—
269C22×C32H(5,𝔽2)12yes—
270C22×C32H(5,𝔽2)11yescharacteristic
271C22×C322−1+411yescharacteristic
272C2×C3×D3—22no—
273C2×C3×D3—22no—
274C2×C3×D3—24no—
275C2×C3×D3—24no—
276C2×C3×D3#11714yes—
277C32×C4—22no—
278C32×C4—22no—
279C3⋊Dic3—42no—
280C3⋊Dic3—42no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—42no—
285C3×Dic3—42no—
286C22×D4—31no—
287C23×C4—31no—
288C23×C4—92no—
289C23×C4D3211yescharacteristic
290C4×D4—38no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—92no—
294C2×C22⋊C4—31no—
295C2×C22⋊C4—31no—
296C2×C22⋊C4—32no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—92no—
299C2×C42—31no—
300C2×C42—92no—
301#95—31no—
302#95—31no—
303#95—92no—
304#95—92no—
305#95—92no—
306#95—92no—
307#95—91no—
308#95—91no—
309#95—92no—
310C23×C3—24no—
311C23×C3—22no—
312C23×C3—21no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—21no—
316C23×C3—22no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—22no—
321C23×C3—32no—
322C23×C3—34no—
323C23×C3—41no—
324C23×C3—42no—
325C23×C3—41no—
326C23×C3—61no—
327C23×C3—62no—
328C23×C3—61no—
329C23×C3C2×C4×D312yes—
330C23×C3C22×Dic312yes—
331C23×C3C23×D311yescharacteristic
332C23×C3C23×D311yescharacteristic
333C22×D3—22no—
334C22×D3—21no—
335C22×D3—21no—
336C22×D3#23514yes—
337C22×D3C22×Dic312yes—
338C3×D4—68no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—32no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—44no—
351C2×C3×C4—44no—
352C2×C3×C4—48no—
353C2×C3×C4—62no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—124no—
364C2×C3×C4C2×C4×D312yes—
365C2×C3×C4C2×C4×D312yes—
366C2×C3×C4C22×Dic312yes—
367C2×C3×C4C22×Dic312yes—
368#67—28no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
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—122no—
396C2×Dic3—122no—
397C2×Dic3—128no—
398C2×Dic3C22×Dic312yes—
399C2×Dic3C22×Dic312yes—
400C2×Dic3C22×Dic312yes—
401C4×D3—44no—
402C4×D3—128no—
403C2×C32—42no—
404C2×C32C2×#11711yescharacteristic
405C2×C32#51811yescharacteristic
406C2×C32#52011yescharacteristic
407C2×C32#53812yes—
408C2×C32#53912yes—
409C3×D3—24no—
410C24—31no—
411C24C2×D3211yescharacteristic
412C2×D4—34no—
413C2×D4—64no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—34no—
418C22×C4—32no—
419C22×C4—32no—
420C22×C4—42no—
421C22×C4—92no—
422C22×C4—92no—
423C22×C4—122no—
424C22×C4—184no—
425C22×C4—362no—
426C22×C4—362no—
427C22×C4D3×Dic314yescomplemented
428C22×C4C2×D3211yescharacteristic
429C22×C4C2×D3211yescharacteristic
430C4⋊C4—34no—
431C4⋊C4—122no—
432C4⋊C4—362no—
433C22⋊C4—34no—
434C22⋊C4—34no—
435C22⋊C4—122no—
436C22⋊C4—184no—
437C22⋊C4—362no—
438C42—34no—
439C42—362no—
440C22×C3—24no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—21no—
448C22×C3—22no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—22no—
452C22×C3—34no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—44no—
456C22×C3—44no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—64no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—64no—
465C22×C3C22×C4×D311yescharacteristic
466C22×C3C2×#23512yes—
467C22×C3#100411yescharacteristic
468C22×C3#100412yes—
469C22×C3#100412yes—
470C22×C3#100711yescharacteristic
471C22×C3D3×#4112yes—
472C22×C3#100911yescharacteristic
473C22×C3#101011yescharacteristic
474C22×C3C23×Dic311yescharacteristic
475C2×D3—22no—
476C2×D3—24no—
477C2×D3—24no—
478C2×D3—22no—
479C2×D3#92614yes—
480C3×C4—22no—
481C3×C4—22no—
482C3×C4—22no—
483C3×C4—22no—
484C3×C4—42no—
485C3×C4—42no—
486C3×C4—62no—
487C3×C4—62no—
488C3×C4—62no—
489C3×C4—122no—
490C3×C4—122no—
491Dic3—22no—
492Dic3—22no—
493Dic3—22no—
494Dic3—42no—
495Dic3—42no—
496Dic3—122no—
497Dic3—122no—
498Dic3—122no—
499Dic3—122no—
500Dic3—242no—
501Dic3—242no—
502C32#231811yescharacteristic, complemented, Sylow
503C23—21no—
504C23—22no—
505C23—21no—
506C23—22no—
507C23—34no—
508C23—32no—
509C23—61no—
510C23—61no—
511C23—62no—
512C23C2×D3×Dic312yes—
513C23C22×D3211yescharacteristic
514D4—68no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—44no—
521C2×C4—61no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—124no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—182no—
535C2×C4—182no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—368no—
539C2×C4C2×D3×Dic312yes—
540C2×C4C2×D3×Dic312yes—
541C2×C3—22no—
542C2×C3—21no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—44no—
547C2×C3—42no—
548C2×C3—42no—
549C2×C3—64no—
550C2×C3#548611yescharacteristic
551C2×C3#550411yescharacteristic
552C2×C3D3×#11711yescharacteristic
553C2×C3#556012yes—
554C2×C3#556412yes—
555C2×C3#561312yes—
556C2×C3#563812yes—
557C2×C3C2×#92611yescharacteristic
558C2×C3#579811yescharacteristic
559C2×C3#582711yescharacteristic
560D3—24no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—34no—
565C22—42no—
566C22—42no—
567C22—64no—
568C22—64no—
569C22—62no—
570C22—62no—
571C22#6429711yescharacteristic
572C22D3×#23512yes—
573C22#6430711yescharacteristic
574C22C22×D3×Dic311yescharacteristic
575C22#6433012yes—
576C4—22no—
577C4—22no—
578C4—62no—
579C4—62no—
580C4—62no—
581C4—122no—
582C4—122no—
583C4—362no—
584C4—362no—
585C3—21no—
586C3#7400611yescharacteristic, complemented
587C3#8232411yescharacteristic, complemented
588C2—42no—
589C2—64no—
590C2D3×#92611yescharacteristic
591C2#1059493612yes—
592C2#1059498611yescharacteristic
593C2#1059508612yes—
594C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592910C2semidirect
3. C3×#5212C2semidirect
5. #10591702C2semidirect
6. #10591377C2semidirect
7. D3×C3⋊#95C2semidirect
8. #10591262C2semidirect
9. #10591237C2semidirect
10. #10591223C2semidirect
11. #10591206C2semidirect
21. C3×C4×#67C4semidirect
42. #5212D3semidirect
64. C22×C32×C4C2×C4semidirect
83. C3×#217C2×C4semidirect
86. C3×Dic3⋊C4C2×C4semidirect
87. C3×C4×Dic3C2×C4semidirect
114. C4×#67Dic3semidirect
214. C22×C3×C4C4×D3semidirect
215. C22×C3×C4C2×Dic3semidirect
252. #217C2×Dic3semidirect
258. Dic3⋊C4C2×Dic3semidirect
261. C4×Dic3C2×Dic3semidirect
427. C22×C4D3×Dic3semidirect
502. C32#2318semidirect
586. C3#74006semidirect
587. 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×#672
#105929102
C3×#52122
#105917212
#105917022
#105913772
D3×C3⋊#952
#105912622
#105912372
#105912232
#105912062
#823243
#740063