Finite Group Databasebeta

← #11806053

Subgroups — #11806053

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic, complemented
3C3×#5211C211yesmaximal, characteristic, complemented
4#10591707C212yesmaximal
5#10591701C212yesmaximal, complemented
6#10591294C211yesmaximal, characteristic, complemented
7#10591286C212yesmaximal, complemented
8#10591242C211yesmaximal, characteristic, complemented
9#10591241C212yesmaximal, complemented
10#10591237C211yesmaximal, characteristic, complemented
11#10591206C211yesmaximal, characteristic, complemented
12#82338—31nomaximal
13#74061—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C2×#3757C2212yes—
18C2×C4×C3⋊Dic3C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2211yescharacteristic
21C3×C4×#67C418yescomplemented
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×C4×D4—31no—
39C2×C4×#67D311yescharacteristic
40C3×#381—31no—
41#5221—32no—
42#5211—31no—
43#5211D311yescharacteristic, complemented
44C4×#217—31no—
45C4×#217—31no—
46C4×#217—31no—
47C4×#217—61no—
48Dic3×C4⋊C4—32no—
49#4957—32no—
50#4951—32no—
51#4951—32no—
52#4944—32no—
53#4936—31no—
54C4×C4⋊Dic3—31no—
55#4669—32no—
56#4666—31no—
57#4664—31no—
58#4650—31no—
59#4649—32no—
60#4649—31no—
61C24×C32C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4—42no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C2×C3×#67C2×C414yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×C4×D3—42no—
78C2×C3×C4×D3C2×C414yes—
79#3757—24no—
80C4×C3⋊Dic3—42no—
81C3×#217—42no—
82C3×#217C2×C414yes—
83C3×(C2×D3)⋊C4C2×C414yes—
84C3×Dic3⋊C4C2×C414yes—
85C3×C4×Dic3C2×C414yes—
86Dic3⋊Dic3—24no—
87Dic3⋊Dic3—24no—
88(C2×D3)⋊Dic3—24no—
89(C2×D3)⋊Dic3—42no—
90Dic32—24no—
91Dic32—42no—
92#2357—91noSylow
93C22×C3×D4—31no—
94C23×C3×C4—21no—
95C23×C3×C4—31no—
96C23×C3×C4C2×D311yescharacteristic
97C23×C3×C4C2×D311yescharacteristic
98C22×#67C2×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×C22⋊C4—32no—
105C2×C3×C42—31no—
106C2×#217—32no—
107C2×#217—32no—
108C2×#217—32no—
109C2×#217—32no—
110C2×#217—62no—
111C2×#217C2×D312yes—
112C2×#217C2×D311yescharacteristic
113C4×#67Dic318yescomplemented
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4C2×D311yescharacteristic
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4C2×D311yescharacteristic
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—62no—
129C2×C4×Dic3C2×D311yescharacteristic
130C3×#95—31no—
131C3×#95—32no—
132C3×#95—31no—
133C3⋊#95—31no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—61no—
142C3⋊#95—61no—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D312yes—
146C23×C32—22no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—22no—
150C23×C32C22×C412yes—
151C23×C32C2411yescharacteristic
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—22no—
156C22×C3×D3C22×C412yes—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—44no—
160C2×C32×C4C22×C412yes—
161C2×C32×C4C22×C412yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3#4114yes—
168C3×#67—28no—
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—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3#4112yes—
181C2×C3×Dic3#4112yes—
182C3×C4×D3—44no—
183C2×C4×D4—31no—
184#390—92no—
185#388—92no—
186#388—92no—
187#382—91no—
188#381—31no—
189#381—91no—
190C4×C4⋊C4—91no—
191C4×C4⋊C4—92no—
192C4×C22⋊C4—91no—
193C4×C22⋊C4—91no—
194C24×C3—21no—
195C24×C3—31no—
196C24×C3C22×D311yescharacteristic
197C24×C3C22×D311yescharacteristic
198C23×D3C22×D311yescharacteristic
199C2×C3×D4—34no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C22×C3×C4—24no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—34no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—42no—
212C22×C3×C4—42no—
213C22×C3×C4—44no—
214C22×C3×C4—122no—
215C22×C3×C4C4×D314yes—
216C22×C3×C4C2×Dic314yes—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—22no—
222C2×#67—22no—
223C2×#67C2×Dic314yes—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—62no—
229C22×Dic3—62no—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D311yescharacteristic
235C2×C4×D3—42no—
236C2×C4×D3C2×Dic314yes—
237C3×C4⋊C4—34no—
238C3×C22⋊C4—34no—
239C3×C22⋊C4—34no—
240C3×C22⋊C4—122no—
241C3×C42—34no—
242#217—42no—
243#217—64no—
244#217—64no—
245#217—64no—
246#217—68no—
247#217—122no—
248#217C2×Dic314yes—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—122no—
251(C2×D3)⋊C4C2×Dic314yes—
252C4⋊Dic3—64no—
253C4⋊Dic3—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4C2×Dic314yes—
257C4×Dic3—64no—
258C4×Dic3—64no—
259C4×Dic3—122no—
260C4×Dic3—122no—
261C4×Dic3—122no—
262C4×Dic3—122no—
263C4×Dic3—124no—
264C4×Dic3C2×Dic314yes—
265C22×C32—22no—
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32C23×C411yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4112yes—
274C22×C32H(5,𝔽2)12yes—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—22no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—22no—
281C32×C4—22no—
282C3⋊Dic3—24no—
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C3×Dic3#11714yes—
289C22×D4—31no—
290C23×C4—31no—
291C23×C4D3211yescharacteristic
292C4×D4—38no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—92no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—31no—
298C2×C22⋊C4—32no—
299C2×C22⋊C4—92no—
300C2×C22⋊C4—92no—
301C2×C22⋊C4—92no—
302C2×C42—31no—
303C2×C42—92no—
304C2×C42—92no—
305C2×C42—92no—
306#95—31no—
307#95—31no—
308#95—32no—
309#95—92no—
310#95—92no—
311#95—91no—
312#95—91no—
313C23×C3—24no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—22no—
324C23×C3—32no—
325C23×C3—42no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3C2×C4×D312yes—
333C23×C3C22×Dic312yes—
334C23×C3C23×D311yescharacteristic
335C23×C3C23×D311yescharacteristic
336C22×D3—21no—
337C22×D3—21no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3C22×Dic312yes—
341C3×D4—68no—
342C2×C3×C4—24no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—42no—
355C2×C3×C4—44no—
356C2×C3×C4—44no—
357C2×C3×C4—48no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—124no—
367C2×C3×C4C2×C4×D312yes—
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4C22×Dic312yes—
370C2×C3×C4C22×Dic312yes—
371#67—28no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—34no—
381C2×Dic3—34no—
382C2×Dic3—64no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—64no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—122no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3#23512yes—
399C2×Dic3#23512yes—
400C2×Dic3C22×Dic312yes—
401C2×Dic3C22×Dic312yes—
402C2×Dic3C22×Dic312yes—
403C4×D3—44no—
404C2×C32—42no—
405C2×C32C2×#11711yescharacteristic
406C2×C32C4×#4111yescharacteristic
407C2×C32#51811yescharacteristic
408C2×C32#55312yes—
409C2×C32#55912yes—
410C3×D3—42no—
411C24—31no—
412C24C2×D3211yescharacteristic
413C2×D4—34no—
414C2×D4—62no—
415C2×D4—62no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—34no—
420C22×C4—32no—
421C22×C4—32no—
422C22×C4—42no—
423C22×C4—92no—
424C22×C4—92no—
425C22×C4—122no—
426C22×C4D3×Dic314yes—
427C22×C4C2×D3211yescharacteristic
428C22×C4C2×D3211yescharacteristic
429C4⋊C4—34no—
430C4⋊C4—184no—
431C4⋊C4—184no—
432C22⋊C4—34no—
433C22⋊C4—34no—
434C22⋊C4—122no—
435C22⋊C4—184no—
436C22⋊C4—184no—
437C22⋊C4—362no—
438C42—34no—
439C42—184no—
440C42—362no—
441C42—362no—
442C22×C3—24no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—22no—
452C22×C3—21no—
453C22×C3—22no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—44no—
457C22×C3—44no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3C22×C4×D311yescharacteristic
468C22×C3C2×#23511yescharacteristic
469C22×C3C2×#23511yescharacteristic
470C22×C3#100412yes—
471C22×C3#100412yes—
472C22×C3D3×#4111yescharacteristic
473C22×C3D3×#4111yescharacteristic
474C22×C3D3×#4112yes—
475C22×C3D3×#4112yes—
476C22×C3C23×Dic311yescharacteristic
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—42no—
481C2×D3—42no—
482C3×C4—24no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4—34no—
488C3×C4—42no—
489C3×C4—62no—
490C3×C4—62no—
491C3×C4—122no—
492C3×C4—122no—
493Dic3—22no—
494Dic3—22no—
495Dic3—42no—
496Dic3—42no—
497Dic3—64no—
498Dic3—64no—
499Dic3—124no—
500Dic3—124no—
501Dic3—122no—
502Dic3—122no—
503Dic3#92614yes—
504C32#235711yescharacteristic, complemented, Sylow
505C23—21no—
506C23—21no—
507C23—22no—
508C23—22no—
509C23—32no—
510C23—61no—
511C23—61no—
512C23—62no—
513C23—62no—
514C23C2×D3×Dic312yes—
515C23C22×D3211yescharacteristic
516D4—68no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—32no—
523C2×C4—32no—
524C2×C4—44no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—94no—
534C2×C4—124no—
535C2×C4—182no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4C2×D3×Dic312yes—
541C2×C4C2×D3×Dic312yes—
542C2×C3—21no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—22no—
547C2×C3—44no—
548C2×C3—42no—
549C2×C3—42no—
550C2×C3—122no—
551C2×C3#548611yescharacteristic
552C2×C3D3×#11711yescharacteristic
553C2×C3#552211yescharacteristic
554C2×C3#555812yes—
555C2×C3#555912yes—
556C2×C3#566112yes—
557C2×C3#566412yes—
558C2×C3C2×#92611yescharacteristic
559C2×C3#579811yescharacteristic
560C2×C3Dic3×#4111yescharacteristic
561D3—42no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—42no—
566C22—42no—
567C22—62no—
568C22—62no—
569C22—62no—
570C22—122no—
571C22—122no—
572C22D3×#23511yescharacteristic
573C22D3×#23511yescharacteristic
574C22#6430612yes—
575C22C22×D3×Dic311yescharacteristic
576C22#6433012yes—
577C4—22no—
578C4—22no—
579C4—34no—
580C4—62no—
581C4—62no—
582C4—122no—
583C4—122no—
584C4—184no—
585C4—362no—
586C3—21no—
587C3#7406111yescharacteristic, complemented
588C3#8233811yescharacteristic, complemented
589C2—42no—
590C2—122no—
591C2D3×#92611yescharacteristic
592C2#1059495712yes—
593C2#1059495811yescharacteristic
594C2#1059502512yes—
595C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C4×#3757C2semidirect
3. C3×#5211C2semidirect
5. #10591701C2semidirect
6. #10591294C2semidirect
7. #10591286C2semidirect
8. #10591242C2semidirect
9. #10591241C2semidirect
10. #10591237C2semidirect
11. #10591206C2semidirect
21. C3×C4×#67C4semidirect
43. #5211D3semidirect
113. C4×#67Dic3semidirect
504. C32#2357semidirect
587. C3#74061semidirect
588. C3#82338semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C4×#37572
C3×#52112
#105917072
#105917012
#105912942
#105912862
#105912422
#105912412
#105912372
#105912062
#823383
#740613