Finite Group Databasebeta

← #11808680

Subgroups — #11808680

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×#63878C211yesmaximal, characteristic
3C3×#5231C211yesmaximal, characteristic
4C3×#5230C211yesmaximal, characteristic, complemented
5#10591368C212yesmaximal
6#10591351C212yesmaximal, complemented
7#10591319C212yesmaximal
8#10591317C211yesmaximal, characteristic
9#10591257C211yesmaximal, characteristic, complemented
10#10591241C212yesmaximal, complemented
11#10591226C211yesmaximal, characteristic, complemented
12#77170—31nomaximal
13#76778—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×D3×Dic3C2211yescharacteristic
16Q8×C3⋊Dic3—24no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2212yes—
19C2×C4×C3⋊Dic3C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×(C2×D3)⋊Dic3C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×Dic32C2211yescharacteristic
31C2×Dic32C2212yes—
32#63878—24no—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×Q8×Dic3—31no—
40C2×Q8×Dic3—31no—
41C2×Q8×Dic3—61no—
42C2×#892—31no—
43C2×#877—31no—
44C3×#395—31no—
45C3×#393—31no—
46#5231D311yescharacteristic
47#5230D311yescharacteristic, complemented
48#4994—32no—
49#4986—31no—
50Dic3×C4⋊C4—32no—
51#4949—31no—
52#4948—32no—
53Dic3×C22⋊C4—32no—
54#4677—31no—
55#4666—32no—
56#4661—32no—
57#4659—31no—
58#4657—32no—
59#4649—32no—
60#4649—31no—
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⋊Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C2×D3×Dic3—22no—
76C2×D3×Dic3—22no—
77C2×D3×Dic3Q814yescomplemented
78C4⋊(C3⋊Dic3)—22no—
79C4⋊(C3⋊Dic3)—24no—
80C4×C3⋊Dic3—24no—
81C4×C3⋊Dic3D414yes—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—24no—
84C3×Dic3⋊C4—22no—
85C3×Dic3⋊C4—24no—
86#3724—24no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—24no—
89(C2×D3)⋊Dic3—22no—
90(C2×D3)⋊Dic3—24no—
91Dic32—22no—
92Dic32—24no—
93#2396—91noSylow
94C22×C3×Q8—21no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C23×Dic3—31no—
98C22×C4×D3—31no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C22⋊C4—31no—
103C2×#217—32no—
104C2×#217—31no—
105Q8×Dic3—64no—
106Q8×Dic3—64no—
107Q8×Dic3—68no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4C2×D312yes—
111C2×(C2×D3)⋊C4C2×D311yescharacteristic
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—32no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—62no—
119C2×C4⋊Dic3—61no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4C2×D312yes—
125C2×Dic3⋊C4C2×D311yescharacteristic
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—61no—
135C2×C4×Dic3—62no—
136#892—64no—
137#877—64no—
138C3×#95—32no—
139C3×#95—31no—
140C3×#95—31no—
141C3×#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95C2×D311yescharacteristic
147C3⋊#95C2×D311yescharacteristic
148C3⋊#95C2×D312yes—
149C3⋊#95C2×D312yes—
150C23×C32C2411yescharacteristic
151C22×C3×D3—21no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—21no—
155C22×C3×D3C2×Q812yes—
156C32×Q8—28no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4C2×D412yes—
161C2×C32×C4#4114yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C2×D412yes—
167C2×C3⋊Dic3C2×D412yes—
168C2×C3⋊Dic3C2×Q812yes—
169C2×C3⋊Dic3#4112yes—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×Q812yes—
182C2×C3×Dic3#4114yes—
183D3×Dic3—28no—
184C2×C4×Q8—91no—
185C2×#117—91no—
186#400—91no—
187#399—91no—
188#398—92no—
189#396—92no—
190#395—31no—
191#393—31no—
192C4×C4⋊C4—91no—
193C4×C4⋊C4—92no—
194C4×C22⋊C4—92no—
195C24×C3—31no—
196C23×D3C22×D311yescharacteristic
197C2×C3×Q8—24no—
198C2×C3×Q8—28no—
199C2×C3×Q8—22no—
200C2×C3×Q8—22no—
201C2×C3×Q8—24no—
202C2×C3×Q8—24no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D312yes—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—34no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—62no—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D312yes—
231C2×C4×D3—34no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—64no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—64no—
238#217—62no—
239#217—64no—
240(C2×D3)⋊C4—22no—
241(C2×D3)⋊C4—24no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—62no—
245C4⋊Dic3—64no—
246C4⋊Dic3—64no—
247C4⋊Dic3—64no—
248C4⋊Dic3—68no—
249C4⋊Dic3—64no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252Dic3⋊C4—22no—
253Dic3⋊C4—24no—
254Dic3⋊C4—62no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258C4×Dic3—34no—
259C4×Dic3—34no—
260C4×Dic3—64no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C4×Dic3—68no—
268C22×C32C22×D411yescharacteristic
269C22×C32C22×Q811yescharacteristic
270C22×C32C2×#4112yes—
271C22×C32C2×#4112yes—
272C22×C32C2×#4111yescharacteristic
273C2×C3×D3—22no—
274C2×C3×D3—24no—
275C2×C3×D3—41no—
276C2×C3×D3—42no—
277C2×C3×D3—41no—
278C32×C4—22no—
279C32×C4—24no—
280C3⋊Dic3—22no—
281C3⋊Dic3—42no—
282C3⋊Dic3C22⋊Q814yes—
283C3×Dic3—22no—
284C3×Dic3—24no—
285C3×Dic3—41no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C22×Q8D3211yescharacteristic
289C23×C4—91no—
290C4×Q8—184no—
291#117—184no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—32no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—92no—
296C2×C4⋊C4—92no—
297C2×C4⋊C4—92no—
298C2×C4⋊C4—91no—
299C2×C22⋊C4—31no—
300C2×C22⋊C4—32no—
301C2×C22⋊C4—91no—
302C2×C22⋊C4—92no—
303C2×C42—91no—
304C2×C42—91no—
305C2×C42—92no—
306C2×C42—92no—
307#95—32no—
308#95—32no—
309#95—31no—
310#95—31no—
311#95—92no—
312#95—92no—
313C23×C3—21no—
314C23×C3—32no—
315C23×C3—61no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3—61no—
319C23×C3C23×D311yescharacteristic
320C23×C3C23×D311yescharacteristic
321C22×D3—21no—
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—21no—
325C22×D3D3×Q812yes—
326C3×Q8—216no—
327C3×Q8—28no—
328C3×Q8—28no—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—24no—
339C2×C3×C4—22no—
340C2×C3×C4—32no—
341C2×C3×C4—34no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4D3×D412yes—
354C2×C3×C4D3×D412yes—
355C2×C3×C4#23714yes—
356C2×C3×C4#23714yes—
357C2×Dic3—21no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—32no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—68no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—64no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—122no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3D3×Q812yes—
394C2×Dic3#23914yes—
395C4×D3—68no—
396C2×C32C2×C22⋊Q811yescharacteristic
397C2×C32#52511yescharacteristic
398C2×C32#52912yes—
399C2×C32#53211yescharacteristic
400C2×C32#53312yes—
401C3×D3—42no—
402C24—31no—
403C2×Q8—24no—
404C2×Q8—22no—
405C22×C4—31no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—94no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—92no—
414C22×C4—182no—
415C22×C4—182no—
416C22×C4C2×D3212yes—
417C22×C4C2×D3211yescharacteristic
418C4⋊C4—64no—
419C4⋊C4—62no—
420C4⋊C4—184no—
421C4⋊C4—184no—
422C4⋊C4—184no—
423C4⋊C4—182no—
424C4⋊C4—182no—
425C22⋊C4—64no—
426C22⋊C4—62no—
427C22⋊C4—184no—
428C22⋊C4—182no—
429C42—94no—
430C42—184no—
431C42—182no—
432C42—184no—
433C22×C3—21no—
434C22×C3—22no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—64no—
439C22×C3—62no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3—122no—
443C22×C3C2×D3×D411yescharacteristic
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C2×#23712yes—
446C22×C3C2×#23712yes—
447C22×C3C2×D3×Q811yescharacteristic
448C22×C3C2×D3×Q811yescharacteristic
449C22×C3C2×#23912yes—
450C22×C3D3×#4112yes—
451C22×C3D3×#4111yescharacteristic
452C22×C3D3×#4111yescharacteristic
453C2×D3—24no—
454C2×D3—22no—
455C2×D3—41no—
456C2×D3—42no—
457C2×D3—41no—
458C3×C4—28no—
459C3×C4—24no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—24no—
463C3×C4—24no—
464C3×C4—64no—
465C3×C4—62no—
466C3×C4—121no—
467C3×C4—121no—
468C3×C4—122no—
469Dic3—24no—
470Dic3—22no—
471Dic3—34no—
472Dic3—34no—
473Dic3—41no—
474Dic3—42no—
475Dic3—41no—
476Dic3—64no—
477Dic3—62no—
478Dic3—62no—
479Dic3—122no—
480Dic3—124no—
481Dic3—122no—
482Dic3—122no—
483C32#239611yescharacteristic, complemented, Sylow
484C23—32no—
485C23—62no—
486C23—61no—
487C23—62no—
488C23—61no—
489C23C22×D3211yescharacteristic
490Q8—28no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—32no—
495C2×C4—34no—
496C2×C4—62no—
497C2×C4—61no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—92no—
508C2×C4—92no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—188no—
512C2×C4—182no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4#380514yes—
517C2×C4#381112yes—
518C2×C3—21no—
519C2×C3—22no—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—122no—
524C2×C3#558611yescharacteristic
525C2×C3#558611yescharacteristic
526C2×C3#562212yes—
527C2×C3#562412yes—
528C2×C3D3×C22⋊Q811yescharacteristic
529C2×C3D3×C22⋊Q811yescharacteristic
530C2×C3#566811yescharacteristic
531C2×C3#568012yes—
532C2×C3#572511yescharacteristic
533C2×C3#572812yes—
534D3—42no—
535C22—64no—
536C22—62no—
537C22—121no—
538C22—122no—
539C22—121no—
540C22D32×Q811yescharacteristic
541C22D3×#23912yes—
542C22#6431911yescharacteristic
543C22C2×#380512yes—
544C22C2×#381111yescharacteristic
545C4—24no—
546C4—22no—
547C4—64no—
548C4—62no—
549C4—94no—
550C4—121no—
551C4—122no—
552C4—121no—
553C4—182no—
554C4—362no—
555C3—21no—
556C3#7677811yescharacteristic, complemented
557C3#7717011yescharacteristic, complemented
558C2—122no—
559C2#1059536311yescharacteristic
560C2#1059536812yes—
561C2#1059537712yes—
562C2#1059542911yescharacteristic
563C2#1059550111yescharacteristic
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×Q8×C3⋊Dic3C2semidirect
4. C3×#5230C2semidirect
6. #10591351C2semidirect
9. #10591257C2semidirect
10. #10591241C2semidirect
11. #10591226C2semidirect
47. #5230D3semidirect
77. C2×D3×Dic3Q8semidirect
483. C32#2396semidirect
556. C3#76778semidirect
557. C3#77170semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×#638782
C3×#52312
C3×#52302
#105913682
#105913512
#105913192
#105913172
#105912572
#105912412
#105912262
#771703
#767783