Finite Group Databasebeta

← #11808668

Subgroups — #11808668

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×#877C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3#10592646C211yesmaximal, characteristic
4C3×#4949C211yesmaximal, characteristic
5Dic3×#217C212yesmaximal
6#10591691C212yesmaximal
7#10591354C211yesmaximal, characteristic, complemented
8#10591242C211yesmaximal, characteristic, complemented
9Dic3×Dic3⋊C4C212yesmaximal, complemented
10#10591225C211yesmaximal, characteristic, complemented
11#10591200C212yesmaximal, complemented
12#82245—31nomaximal
13#78018—31nomaximal
14C22×#634C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C2×C32×C22⋊C4C2211yescharacteristic
17C2×#3757C2212yes—
18C2×C3×#217C2212yes—
19C2×C3×#217C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#877—24no—
27C2×#3724C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63844—24no—
33#63658C2212yes—
34#63658C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×#117—31no—
40C2×#887—31no—
41C2×#877D311yescharacteristic
42C2×C4×Dic6—31no—
43C3×#399—31no—
44C4×#217—32no—
45#4986—31no—
46#4985—31no—
47#4983—32no—
48#4982—32no—
49#4979—31no—
50Dic3×C4⋊C4—32no—
51#4949D311yescharacteristic
52#4948—32no—
53#4948—32no—
54#4947—31no—
55#4947—31no—
56#4947—61no—
57Dic3×C22⋊C4—32no—
58C4×C4⋊Dic3—31no—
59C4×Dic3⋊C4—32no—
60#4656—31no—
61#4649—31no—
62C24×C32C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2312yes—
67C2×#634—22no—
68C2×#634—24no—
69C22×C3×Dic3—22no—
70C22×C3×Dic3—22no—
71C22×C3×Dic3Q814yescomplemented
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C32×C22⋊C4—22no—
79#3757—24no—
80C3×#217—22no—
81C3×#217—24no—
82C3×C4⋊Dic3—22no—
83C3×Dic3⋊C4—22no—
84C3×Dic3⋊C4—22no—
85C3×Dic3⋊C4—24no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3D414yes—
88#3724—24no—
89Dic3⋊Dic3—24no—
90Dic3⋊Dic3—24no—
91Dic32—24no—
92Dic32—24no—
93#2396—91noSylow
94C23×C3×C4—31no—
95C23×Dic3C2×D311yescharacteristic
96C22×Dic6—31no—
97C22×Dic6—31no—
98C22×Dic6—61no—
99C3×#117—64no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4C2×D311yescharacteristic
108C2×C3×C22⋊C4C2×D311yescharacteristic
109C2×C3×C42—31no—
110C2×C3×C42—31no—
111C2×#217—32no—
112C2×#217—32no—
113C2×#217—62no—
114C2×#217C2×D311yescharacteristic
115C2×#217C2×D312yes—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4C2×D311yescharacteristic
124C2×Dic3⋊C4C2×D312yes—
125C2×Dic3⋊C4C2×D311yescharacteristic
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#887—64no—
133#877—24no—
134C4×Dic6—64no—
135C3×#95—31no—
136C3⋊#95—31no—
137C3⋊#95—32no—
138C3⋊#95—31no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—62no—
147C3⋊#95—61no—
148C3⋊#95C2×D311yescharacteristic
149C23×C32—21no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32—21no—
153C23×C32C2×Q812yes—
154C23×C32C2411yescharacteristic
155C2×C32×C4—22no—
156C2×C32×C4—21no—
157C2×C32×C4—22no—
158C2×C32×C4C2×D412yes—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3#4114yes—
165#634—28no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—28no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×Q812yes—
180C2×C3×Dic3C2×Q812yes—
181C2×C3×Dic3#4112yes—
182C2×C3×Dic3#4114yes—
183C2×C4×Q8—91no—
184C2×#117—31no—
185#400—91no—
186#399—31no—
187#398—92no—
188#396—92no—
189#395—91no—
190#393—91no—
191C4×C4⋊C4—91no—
192C4×C4⋊C4—92no—
193C4×C22⋊C4—92no—
194C24×C3—21no—
195C24×C3C22×D311yescharacteristic
196C24×C3C22×D311yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—34no—
201C22×C3×C4—31no—
202C22×C3×C4—32no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—31no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3Dic614yescomplemented
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D311yescharacteristic
226C22×Dic3C22×D311yescharacteristic
227C2×Dic6—64no—
228C2×Dic6—64no—
229C2×Dic6—62no—
230C2×Dic6—62no—
231C2×Dic6—124no—
232C2×Dic6—122no—
233C3×C4⋊C4—64no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C22⋊C4—22no—
238C3×C22⋊C4—22no—
239C3×C22⋊C4—42no—
240C3×C22⋊C4—64no—
241C3×C22⋊C4—62no—
242C3×C42—34no—
243C3×C42—62no—
244#217—24no—
245#217—22no—
246#217—64no—
247#217—64no—
248#217—124no—
249C4⋊Dic3—22no—
250C4⋊Dic3—64no—
251C4⋊Dic3—64no—
252Dic3⋊C4—22no—
253Dic3⋊C4—24no—
254Dic3⋊C4—22no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259C4×Dic3—22no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3#6714yes—
265C22×C32—22no—
266C22×C32—24no—
267C22×C32—41no—
268C22×C32—42no—
269C22×C32—41no—
270C22×C32C22×D411yescharacteristic
271C22×C32C22×Q811yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4112yes—
274C22×C32C2×#4112yes—
275C32×C4—22no—
276C32×C4—41no—
277C3⋊Dic3—24no—
278C3⋊Dic3—42no—
279C3×Dic3—22no—
280C3×Dic3—24no—
281C3×Dic3—22no—
282C3×Dic3—41no—
283C3×Dic3—42no—
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—31no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—92no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—32no—
298C2×C22⋊C4—92no—
299C2×C22⋊C4D3211yescharacteristic
300C2×C42—31no—
301C2×C42—31no—
302C2×C42—92no—
303C2×C42—92no—
304#95—31no—
305#95—92no—
306#95—92no—
307#95—92no—
308#95—92no—
309#95—91no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—22no—
320C23×C3—42no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—42no—
324C23×C3C2×Dic612yes—
325C23×C3D3×Q812yes—
326C23×C3C23×D311yescharacteristic
327C23×C3C23×D311yescharacteristic
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—34no—
341C2×C3×C4—42no—
342C2×C3×C4—41no—
343C2×C3×C4—42no—
344C2×C3×C4—68no—
345C2×C3×C4—62no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4D3×D412yes—
356C2×C3×C4C2×#6712yes—
357C2×Dic3—21no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3—28no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—34no—
369C2×Dic3—34no—
370C2×Dic3—64no—
371C2×Dic3—62no—
372C2×Dic3—62no—
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×Dic3—122no—
386C2×Dic3C2×Dic612yes—
387C2×Dic3C2×Dic612yes—
388C2×Dic3#23512yes—
389C2×Dic3#23714yes—
390C2×Dic3C2×#6712yes—
391C2×Dic3C2×#6712yes—
392Dic6—68no—
393Dic6—68no—
394Dic6—128no—
395C2×C32—42no—
396C2×C32C2×C22⋊Q811yescharacteristic
397C2×C32#52511yescharacteristic
398C2×C32#52912yes—
399C2×C32#53211yescharacteristic
400C2×C32#53312yes—
401C24C2×D3211yescharacteristic
402C2×Q8—184no—
403C2×Q8—182no—
404C22×C4—31no—
405C22×C4—32no—
406C22×C4—31no—
407C22×C4—31no—
408C22×C4—34no—
409C22×C4—31no—
410C22×C4—32no—
411C22×C4—62no—
412C22×C4—62no—
413C22×C4—92no—
414C22×C4—92no—
415C22×C4C2×D3211yescharacteristic
416C22×C4C2×D3211yescharacteristic
417C4⋊C4—62no—
418C4⋊C4—64no—
419C4⋊C4—62no—
420C4⋊C4—62no—
421C4⋊C4—184no—
422C4⋊C4—184no—
423C4⋊C4—184no—
424C22⋊C4—22no—
425C22⋊C4—62no—
426C22⋊C4—64no—
427C22⋊C4—184no—
428C42—34no—
429C42—62no—
430C42—184no—
431C42—184no—
432C22×C3—24no—
433C22×C3—22no—
434C22×C3—24no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—42no—
442C22×C3—44no—
443C22×C3—42no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—42no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—82no—
450C22×C3—81no—
451C22×C3—81no—
452C22×C3C22×Dic611yescharacteristic
453C22×C3C2×#23511yescharacteristic
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C2×#23712yes—
456C22×C3C2×D3×Q811yescharacteristic
457C22×C3D3×#4111yescharacteristic
458C22×C3D3×#4112yes—
459C22×C3D3×#4112yes—
460C22×C3D3×#4112yes—
461C22×C3C22×#6711yescharacteristic
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—34no—
465C3×C4—42no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—62no—
469C3×C4—64no—
470C3×C4—62no—
471C3×C4—81no—
472C3×C4—121no—
473C3×C4—122no—
474Dic3—24no—
475Dic3—22no—
476Dic3—22no—
477Dic3—42no—
478Dic3—41no—
479Dic3—64no—
480Dic3—64no—
481Dic3—124no—
482Dic3—122no—
483Dic3—122no—
484Dic3—242no—
485Dic3#92414yes—
486C32#239611yescharacteristic, complemented, Sylow
487C23—21no—
488C23—22no—
489C23—22no—
490C23—21no—
491C23D3×Dic612yes—
492C23C22×D3211yescharacteristic
493Q8—188no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—32no—
501C2×C4—34no—
502C2×C4—32no—
503C2×C4—68no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—61no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—61no—
513C2×C4—62no—
514C2×C4—94no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—182no—
519C2×C4—182no—
520C2×C4D3×#6712yes—
521C2×C3—22no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—22no—
526C2×C3—42no—
527C2×C3—42no—
528C2×C3—82no—
529C2×C3#551712yes—
530C2×C3#552812yes—
531C2×C3#562212yes—
532C2×C3D3×C22⋊Q811yescharacteristic
533C2×C3#564912yes—
534C2×C3#565611yescharacteristic
535C2×C3#571611yescharacteristic
536C2×C3C2×#92411yescharacteristic
537C2×C3#582811yescharacteristic
538C2×C3#583211yescharacteristic
539C22—22no—
540C22—24no—
541C22—42no—
542C22—41no—
543C22—41no—
544C22C2×D3×Dic611yescharacteristic
545C22D3×#23511yescharacteristic
546C22D3×#23712yes—
547C22#6431212yes—
548C22C2×D3×#6711yescharacteristic
549C4—22no—
550C4—34no—
551C4—41no—
552C4—64no—
553C4—62no—
554C4—62no—
555C4—122no—
556C4—121no—
557C4—184no—
558C4—362no—
559C3—21no—
560C3#7801811yescharacteristic, complemented
561C3#8224511yescharacteristic, complemented
562C2—42no—
563C2#1059402912yes—
564C2#1059408812yes—
565C2D3×#92411yescharacteristic
566C2#1059515211yescharacteristic
567C2#1059515911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
7. #10591354C2semidirect
8. #10591242C2semidirect
9. Dic3×Dic3⋊C4C2semidirect
10. #10591225C2semidirect
11. #10591200C2semidirect
71. C22×C3×Dic3Q8semidirect
220. C22×Dic3Dic6semidirect
486. C32#2396semidirect
560. C3#78018semidirect
561. C3#82245semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
C2×#638442
#105926462
C3×#49492
Dic3×#2172
#105916912
#105913542
#105912422
Dic3×Dic3⋊C42
#105912252
#105912002
#822453
#780183