Finite Group Databasebeta

← #11808679

Subgroups — #11808679

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×#63836C211yesmaximal, characteristic
3#10592930C211yesmaximal, characteristic
4C3×#5230C211yesmaximal, characteristic, complemented
5#10591350C211yesmaximal, characteristic
6#10591348C212yesmaximal, complemented
7#10591311C212yesmaximal
8#10591242C211yesmaximal, characteristic, complemented
9Dic3×Dic3⋊C4C212yesmaximal, complemented
10#10591233C212yesmaximal
11#10591225C211yesmaximal, characteristic, complemented
12#82491—31nomaximal
13#77170—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×#624C2211yescharacteristic
16C2×#3752C2212yes—
17C2×#3752C2211yescharacteristic
18C3×Q8×Dic3—24no—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×#3722C2212yes—
29C2×#3722C2211yescharacteristic
30C2×Dic32C2212yes—
31C2×Dic32C2211yescharacteristic
32#63836—24no—
33#63658C2212yes—
34#63658C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×Q8—31no—
40C2×Q8×Dic3D311yescharacteristic, complemented
41C2×#892—31no—
42C2×#872—31no—
43C3×#395—31no—
44#5231—31no—
45#5231—31no—
46#5231—61no—
47#5230D311yescharacteristic, complemented
48#4994—32no—
49#4994—32no—
50#4993—31no—
51#4986—31no—
52#4985—31no—
53#4982—32no—
54Dic3×C4⋊C4—32no—
55C4×(C2×D3)⋊C4—32no—
56C4×C4⋊Dic3—31no—
57C4×Dic3⋊C4—32no—
58#4677—31no—
59#4666—32no—
60#4661—32no—
61#4649—31no—
62C23×C3⋊D3C2311yescharacteristic
63C2×C32×Q8—22no—
64C2×C32×Q8—24no—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C2×#624—22no—
76C2×#624—22no—
77C2×#624Q814yescomplemented
78#3752—22no—
79#3752—24no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3—24no—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3—24no—
85C3×C4×Dic3D414yes—
86Dic3⋊Dic3—22no—
87Dic3⋊Dic3—24no—
88Dic3⋊Dic3—24no—
89#3722—22no—
90#3722—24no—
91Dic32—22no—
92Dic32—24no—
93#2396—91noSylow
94C22×C3×Q8—21no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C22×C4×D3—31no—
98C22×C4×D3—31no—
99C3×C4×Q8—64no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C42—31no—
105C2×C3×C42—32no—
106Q8×Dic3—24no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—31no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—61no—
116C2×(C2×D3)⋊C4—62no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3C2×D312yes—
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4C2×D312yes—
126C2×Dic3⋊C4C2×D311yescharacteristic
127C2×C4×Dic3—32no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3C2×D312yes—
132C2×C4×Dic3C2×D311yescharacteristic
133#892—64no—
134#872—64no—
135C3×#95—31no—
136C3×#95—32no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—31no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—62no—
146C3⋊#95—61no—
147C3⋊#95C2×D311yescharacteristic
148C3⋊#95C2×D312yes—
149C23×C32C2411yescharacteristic
150C22×C3⋊D3—21no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3C2×Q812yes—
155C32×Q8—28no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4#4114yes—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
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×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×Q812yes—
179C2×C3×Dic3C2×Q812yes—
180C2×C3×Dic3#4114yes—
181C2×C3×Dic3#4112yes—
182#624—28no—
183C2×C4×Q8—31no—
184C2×#117—91no—
185#400—91no—
186#399—91no—
187#398—92no—
188#396—92no—
189#395—31no—
190#393—91no—
191C4×C4⋊C4—91no—
192C4×C4⋊C4—92no—
193C4×C22⋊C4—92no—
194C23×D3—31no—
195C23×D3—31no—
196C23×D3—61no—
197C2×C3×Q8—24no—
198C2×C3×Q8—22no—
199C2×C3×Q8—24no—
200C2×C3×Q8—22no—
201C2×C3×Q8—44no—
202C2×C3×Q8—42no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—32no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—32no—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—62no—
220C22×Dic3—61no—
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D311yescharacteristic
226C22×Dic3C22×D311yescharacteristic
227C2×C4×D3—34no—
228C2×C4×D3—34no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×C4×D3—62no—
233C3×C4⋊C4—64no—
234C3×C4⋊C4—64no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C42—34no—
238C3×C42—64no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—124no—
248(C2×D3)⋊C4—122no—
249C4⋊Dic3—22no—
250C4⋊Dic3—24no—
251C4⋊Dic3—64no—
252C4⋊Dic3—64no—
253C4⋊Dic3—62no—
254Dic3⋊C4—22no—
255Dic3⋊C4—24no—
256Dic3⋊C4—62no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259C4×Dic3—24no—
260C4×Dic3—62no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—62no—
264C4×Dic3#6714yes—
265C22×C32C22×D411yescharacteristic
266C22×C32C22×Q811yescharacteristic
267C22×C32C2×#4112yes—
268C22×C32C2×#4111yescharacteristic
269C22×C32C2×#4112yes—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—24no—
272C2×C3⋊D3—41no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—41no—
275C32×C4—22no—
276C32×C4—24no—
277C3⋊Dic3—42no—
278C3⋊Dic3—41no—
279C3×Dic3—22no—
280C3×Dic3—24no—
281C3×Dic3—22no—
282C3×Dic3—41no—
283C3×Dic3—42no—
284C3×Dic3C22⋊Q814yes—
285C22×Q8D3211yescharacteristic
286C23×C4—91no—
287C4×Q8—64no—
288#117—184no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—91no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—92no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—91no—
299C2×C22⋊C4—92no—
300C2×C42—31no—
301C2×C42—32no—
302C2×C42—91no—
303C2×C42—92no—
304#95—32no—
305#95—31no—
306#95—92no—
307#95—92no—
308#95—92no—
309#95—91no—
310C23×C3—21no—
311C23×C3C23×D311yescharacteristic
312C23×C3C23×D311yescharacteristic
313C22×D3—32no—
314C22×D3—32no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—61no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—61no—
321C22×D3—62no—
322C22×D3—61no—
323C22×D3—61no—
324C22×D3—122no—
325C22×D3—121no—
326C22×D3—122no—
327C22×D3—121no—
328C3×Q8—28no—
329C3×Q8—28no—
330C3×Q8—48no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—24no—
338C2×C3×C4—22no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—34no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—61no—
358C2×C3×C4#23514yes—
359C2×C3×C4D3×D412yes—
360C2×C3×C4#23714yes—
361C2×C3×C4C2×#6712yes—
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—62no—
373C2×Dic3—61no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—61no—
382C2×Dic3—122no—
383C2×Dic3—121no—
384C2×Dic3—122no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3D3×Q812yes—
388C2×Dic3D3×Q812yes—
389C2×Dic3#23914yes—
390C2×Dic3#23912yes—
391C2×Dic3C2×#6712yes—
392C2×Dic3C2×#6712yes—
393C4×D3—68no—
394C4×D3—68no—
395C2×C32C2×C22⋊Q811yescharacteristic
396C2×C32#52511yescharacteristic
397C2×C32#52912yes—
398C2×C32#53211yescharacteristic
399C2×C32#53312yes—
400C3⋊D3—42no—
401C24—91no—
402C2×Q8—24no—
403C2×Q8—22no—
404C22×C4—31no—
405C22×C4—31no—
406C22×C4—32no—
407C22×C4—31no—
408C22×C4—32no—
409C22×C4—31no—
410C22×C4—94no—
411C22×C4—92no—
412C22×C4—91no—
413C22×C4—182no—
414C22×C4—182no—
415C22×C4C2×D3212yes—
416C22×C4C2×D3211yescharacteristic
417C4⋊C4—64no—
418C4⋊C4—64no—
419C4⋊C4—62no—
420C4⋊C4—62no—
421C4⋊C4—182no—
422C4⋊C4—184no—
423C4⋊C4—184no—
424C22⋊C4—182no—
425C22⋊C4—184no—
426C22⋊C4—184no—
427C22⋊C4—182no—
428C42—34no—
429C42—64no—
430C42—182no—
431C42—184no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3C2×#23512yes—
438C22×C3C2×D3×D411yescharacteristic
439C22×C3C2×#23712yes—
440C22×C3C2×D3×Q811yescharacteristic
441C22×C3C2×D3×Q811yescharacteristic
442C22×C3C2×#23912yes—
443C22×C3C2×#23911yescharacteristic
444C22×C3D3×#4112yes—
445C22×C3D3×#4111yescharacteristic
446C22×C3C22×#6711yescharacteristic
447C2×D3—64no—
448C2×D3—62no—
449C2×D3—64no—
450C2×D3—62no—
451C2×D3—124no—
452C2×D3—122no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—122no—
457C2×D3—121no—
458C2×D3—122no—
459C2×D3—241no—
460C2×D3—242no—
461C2×D3—241no—
462C3×C4—24no—
463C3×C4—22no—
464C3×C4—22no—
465C3×C4—24no—
466C3×C4—34no—
467C3×C4—44no—
468C3×C4—42no—
469C3×C4—62no—
470C3×C4—62no—
471C3×C4—64no—
472C3×C4—122no—
473C3×C4—121no—
474Dic3—22no—
475Dic3—24no—
476Dic3—22no—
477Dic3—42no—
478Dic3—41no—
479Dic3—121no—
480Dic3—121no—
481Dic3—122no—
482Dic3—122no—
483Dic3—241no—
484Dic3—242no—
485Dic3#94614yes—
486C32#239611yescharacteristic, complemented, Sylow
487C23—92no—
488C23—182no—
489C23—181no—
490C23—182no—
491C23—181no—
492C23C22×D3211yescharacteristic
493Q8—28no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—32no—
501C2×C4—34no—
502C2×C4—32no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—62no—
507C2×C4—61no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—61no—
513C2×C4—188no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—181no—
519C2×C4#380414yes—
520C2×C4D3×#6712yes—
521C2×C3—21no—
522C2×C3—22no—
523C2×C3—22no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3#557812yes—
527C2×C3#558012yes—
528C2×C3#558611yescharacteristic
529C2×C3#562412yes—
530C2×C3D3×C22⋊Q811yescharacteristic
531C2×C3#572511yescharacteristic
532C2×C3#572812yes—
533C2×C3#579111yescharacteristic
534C2×C3C2×#94611yescharacteristic
535C2×C3#583211yescharacteristic
536D3—122no—
537D3—122no—
538D3—242no—
539C22—184no—
540C22—182no—
541C22—361no—
542C22—362no—
543C22—361no—
544C22D32×Q811yescharacteristic
545C22D3×#23912yes—
546C22D3×#23911yescharacteristic
547C22C2×#380412yes—
548C22C2×D3×#6711yescharacteristic
549C4—24no—
550C4—22no—
551C4—34no—
552C4—62no—
553C4—64no—
554C4—62no—
555C4—122no—
556C4—121no—
557C4—361no—
558C4—362no—
559C3—21no—
560C3#7717011yescharacteristic, complemented
561C3#8249111yescharacteristic, complemented
562C2—362no—
563C2#1059536011yescharacteristic
564C2#1059537412yes—
565C2#1059537612yes—
566C2D3×#94611yescharacteristic
567C2#1059549811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
prime radicalC23×C3⋊D3C23
hypercenterC22×Q8D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic3C2semidirect
4. C3×#5230C2semidirect
6. #10591348C2semidirect
8. #10591242C2semidirect
9. Dic3×Dic3⋊C4C2semidirect
11. #10591225C2semidirect
40. C2×Q8×Dic3D3semidirect
47. #5230D3semidirect
77. C2×#624Q8semidirect
486. C32#2396semidirect
560. C3#77170semidirect
561. C3#82491semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C2×#638362
#105929302
C3×#52302
#105913502
#105913482
#105913112
#105912422
Dic3×Dic3⋊C42
#105912332
#105912252
#824913
#771703