Finite Group Databasebeta

← #11808716

Subgroups — #11808716

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3#10592678C211yesmaximal, characteristic, complemented
4C3×#4986C211yesmaximal, characteristic, complemented
5#10591345C212yesmaximal, complemented
6#10591324C211yesmaximal, characteristic
7#10591322C211yesmaximal, characteristic
8#10591309C212yesmaximal
9#10591243C212yesmaximal, complemented
10#10591242C211yesmaximal, characteristic, complemented
11#10591237C212yesmaximal
12#82245—31nomaximal
13#78130—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C3×(C2×D3)⋊C4C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#892—24no—
25C2×#3724C2212yes—
26C2×#3724C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63844—24no—
33#63658C2212yes—
34#63658C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39C2×C3×#117—31no—
40C2×#892D311yescharacteristic
41C2×#887—31no—
42C2×C4×Dic6—31no—
43C3×#400—31no—
44C4×#217—32no—
45#4993—31no—
46#4986D311yescharacteristic, complemented
47#4982—32no—
48#4979—31no—
49#4979—31no—
50#4979—61no—
51#4949—31no—
52#4948—32no—
53#4947—31no—
54C4×C4⋊Dic3—31no—
55C4×Dic3⋊C4—32no—
56#4676—32no—
57#4673—31no—
58#4666—32no—
59#4657—32no—
60#4649—31no—
61#4649—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C2×#634—22no—
69C2×#634—24no—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3Q814yescomplemented
78C32×C4⋊C4—22no—
79#3750—24no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3D414yes—
86#3724—24no—
87#3724—24no—
88Dic3⋊Dic3—24no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91Dic32—24no—
92Dic32—24no—
93#2396—91noSylow
94C23×C3×C4—31no—
95C22×C4×D3C2×D311yescharacteristic
96C22×Dic6—31no—
97C22×Dic6—31no—
98C22×Dic6—61no—
99C3×#117—64no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4C2×D311yescharacteristic
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C42—31no—
108C2×C3×C42—31no—
109C2×#217—32no—
110C2×#217—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⋊Dic3C2×D311yescharacteristic
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—62no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3C2×D311yescharacteristic
131C2×C4×Dic3C2×D311yescharacteristic
132#892—24no—
133#887—64no—
134C4×Dic6—64no—
135C3×#95—31no—
136C3×#95—32no—
137C3×#95—32no—
138C3⋊#95—31no—
139C3⋊#95—32no—
140C3⋊#95—31no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—62no—
145C3⋊#95—61no—
146C3⋊#95C2×D312yes—
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—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—22no—
158C2×C32×C4—21no—
159C2×C32×C4—22no—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×Q812yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3#4114yes—
167C2×C3⋊Dic3#4114yes—
168#634—28no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
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×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×Q812yes—
181C2×C3×Dic3#4112yes—
182C3×C4×D3—28no—
183C2×C4×Q8—91no—
184C2×#117—31no—
185#400—31no—
186#399—91no—
187#398—92no—
188#396—92no—
189#395—91no—
190#393—91no—
191C4×C4⋊C4—92no—
192C4×C4⋊C4—91no—
193C4×C22⋊C4—92no—
194C24×C3—31no—
195C23×D3C22×D311yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—34no—
202C22×C3×C4—31no—
203C22×C3×C4—32no—
204C22×C3×C4—32no—
205C22×C3×C4—62no—
206C22×C3×C4—62no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3C22×D311yescharacteristic
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C2×C4×D3—22no—
225C2×C4×D3—22no—
226C2×C4×D3Dic614yescomplemented
227C2×Dic6—64no—
228C2×Dic6—64no—
229C2×Dic6—62no—
230C2×Dic6—62no—
231C2×Dic6—124no—
232C2×Dic6—122no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—42no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—62no—
240C3×C42—34no—
241C3×C42—62no—
242#217—64no—
243#217—64no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—22no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248C4⋊Dic3—22no—
249C4⋊Dic3—22no—
250C4⋊Dic3—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—124no—
259C4×Dic3—22no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3#6714yes—
265C22×C32C22×D411yescharacteristic
266C22×C32C22×Q811yescharacteristic
267C22×C32C2×#4111yescharacteristic
268C22×C32C2×#4112yes—
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—22no—
277C32×C4—41no—
278C3⋊Dic3—24no—
279C3⋊Dic3—24no—
280C3×Dic3—22no—
281C3×Dic3—42no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C3×Dic3C22⋊Q814yes—
285C22×Q8—91no—
286C23×C4—31no—
287C4×Q8—184no—
288#117—64no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—92no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4D3211yescharacteristic
296C2×C22⋊C4—31no—
297C2×C22⋊C4—31no—
298C2×C22⋊C4—92no—
299C2×C22⋊C4—92no—
300C2×C42—31no—
301C2×C42—31no—
302C2×C42—92no—
303C2×C42—92no—
304#95—32no—
305#95—31no—
306#95—32no—
307#95—92no—
308#95—92no—
309#95—91no—
310C23×C3—21no—
311C23×C3—32no—
312C23×C3—61no—
313C23×C3—62no—
314C23×C3—62no—
315C23×C3—61no—
316C23×C3C23×D311yescharacteristic
317C23×C3C23×D311yescharacteristic
318C22×D3—21no—
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—21no—
322C22×D3C2×Dic612yes—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—41no—
340C2×C3×C4—42no—
341C2×C3×C4—41no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—68no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
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×C4—62no—
354C2×C3×C4C2×Dic612yes—
355C2×C3×C4D3×D412yes—
356C2×C3×C4D3×Q812yes—
357C2×C3×C4C2×#6712yes—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—21no—
367C2×Dic3—34no—
368C2×Dic3—34no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—122no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3C2×Dic612yes—
386C2×Dic3#23512yes—
387C2×Dic3C2×#6712yes—
388C2×Dic3C2×#6712yes—
389C4×D3—28no—
390Dic6—68no—
391Dic6—68no—
392Dic6—128no—
393C2×C32C2×C22⋊Q811yescharacteristic
394C2×C32#52511yescharacteristic
395C2×C32#52912yes—
396C2×C32#53211yescharacteristic
397C2×C32#53312yes—
398C3×D3—42no—
399C24—31no—
400C2×Q8—184no—
401C2×Q8—182no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—34no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—31no—
408C22×C4—62no—
409C22×C4—62no—
410C22×C4—92no—
411C22×C4—92no—
412C22×C4C2×D3211yescharacteristic
413C22×C4C2×D3211yescharacteristic
414C22×C4C2×D3211yescharacteristic
415C4⋊C4—22no—
416C4⋊C4—62no—
417C4⋊C4—62no—
418C4⋊C4—184no—
419C4⋊C4—184no—
420C4⋊C4—184no—
421C4⋊C4—184no—
422C22⋊C4—62no—
423C22⋊C4—62no—
424C22⋊C4—184no—
425C22⋊C4—184no—
426C42—34no—
427C42—62no—
428C42—184no—
429C42—184no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—64no—
436C22×C3—62no—
437C22×C3—121no—
438C22×C3—121no—
439C22×C3—122no—
440C22×C3C22×Dic611yescharacteristic
441C22×C3C2×#23511yescharacteristic
442C22×C3C2×D3×D411yescharacteristic
443C22×C3C2×D3×Q811yescharacteristic
444C22×C3D3×#4111yescharacteristic
445C22×C3D3×#4112yes—
446C22×C3D3×#4112yes—
447C22×C3D3×#4112yes—
448C22×C3D3×#4112yes—
449C22×C3C22×#6711yescharacteristic
450C2×D3—24no—
451C2×D3—22no—
452C2×D3—42no—
453C2×D3—41no—
454C2×D3—41no—
455C3×C4—22no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—34no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—62no—
465C3×C4—81no—
466C3×C4—121no—
467C3×C4—122no—
468C3×C4—122no—
469Dic3—22no—
470Dic3—42no—
471Dic3—42no—
472Dic3—41no—
473Dic3—64no—
474Dic3—64no—
475Dic3—64no—
476Dic3—64no—
477Dic3—124no—
478Dic3—124no—
479Dic3#92414yes—
480C32#239611yescharacteristic, complemented, Sylow
481C23—32no—
482C23—61no—
483C23—62no—
484C23—62no—
485C23—61no—
486C23C22×D3211yescharacteristic
487Q8—188no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—68no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—62no—
507C2×C4—94no—
508C2×C4—94no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4D3×Dic612yes—
514C2×C4D3×#6712yes—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—22no—
519C2×C3—22no—
520C2×C3—122no—
521C2×C3#551712yes—
522C2×C3#552812yes—
523C2×C3D3×C22⋊Q811yescharacteristic
524C2×C3#565611yescharacteristic
525C2×C3#566811yescharacteristic
526C2×C3#568812yes—
527C2×C3#570612yes—
528C2×C3C2×#92411yescharacteristic
529C2×C3#582811yescharacteristic
530C2×C3#583211yescharacteristic
531D3—42no—
532C22—62no—
533C22—64no—
534C22—121no—
535C22—121no—
536C22—122no—
537C22C2×D3×Dic611yescharacteristic
538C22D3×#23511yescharacteristic
539C22#6431212yes—
540C22#6431912yes—
541C22C2×D3×#6711yescharacteristic
542C4—22no—
543C4—22no—
544C4—34no—
545C4—41no—
546C4—62no—
547C4—122no—
548C4—121no—
549C4—122no—
550C4—184no—
551C4—184no—
552C3—21no—
553C3#7813011yescharacteristic, complemented
554C3#8224511yescharacteristic, complemented
555C2—122no—
556C2#1059441712yes—
557C2#1059447712yes—
558C2D3×#92411yescharacteristic
559C2#1059515911yescharacteristic
560C2#1059535911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
3. #10592678C2semidirect
4. C3×#4986C2semidirect
5. #10591345C2semidirect
9. #10591243C2semidirect
10. #10591242C2semidirect
46. #4986D3semidirect
77. C2×C3×C4×D3Q8semidirect
226. C2×C4×D3Dic6semidirect
480. C32#2396semidirect
553. C3#78130semidirect
554. C3#82245semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×#638442
#105926782
C3×#49862
#105913452
#105913242
#105913222
#105913092
#105912432
#105912422
#105912372
#822453
#781303