Finite Group Databasebeta

← #11808695

Subgroups — #11808695

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×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10591354C211yesmaximal, characteristic, complemented
5#10591342C212yesmaximal, complemented
6C4×Dic3⋊Dic3C212yesmaximal, complemented
7#10591322C211yesmaximal, characteristic
8#10591317C211yesmaximal, characteristic
9#10591308C212yesmaximal
10C4×(C2×D3)⋊Dic3C212yesmaximal
11#10591226C211yesmaximal, characteristic, complemented
12#82245—31nomaximal
13#73668—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750C2212yes—
19C2×C4×C3⋊Dic3C2212yes—
20C4×#634—24no—
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×#872—24no—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×#117—31no—
40C2×#872D311yescharacteristic
41C2×C4×Dic6—31no—
42C2×C4×Dic6—31no—
43C2×C4×Dic6—61no—
44C3×C4×C4⋊C4—31no—
45C4×#217—32no—
46#4994—32no—
47#4986—31no—
48#4982—32no—
49#4981—32no—
50#4979—31no—
51#4949—31no—
52#4948—32no—
53#4947—31no—
54C4×(C2×D3)⋊C4—32no—
55C4×C4⋊Dic3—32no—
56C4×C4⋊Dic3D311yescharacteristic, complemented
57C4×Dic3⋊C4—32no—
58#4677—31no—
59#4673—31no—
60#4659—31no—
61#4656—31no—
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×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3Q814yescomplemented
78C32×C42D414yes—
79C4⋊(C3⋊Dic3)—22no—
80#3750—24no—
81C4×C3⋊Dic3—24no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—24no—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4—22no—
87C3×C4×Dic3—22no—
88C3×C4×Dic3—24no—
89Dic3⋊Dic3—24no—
90Dic3⋊Dic3—24no—
91(C2×D3)⋊Dic3—24no—
92(C2×D3)⋊Dic3—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—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C42—21no—
106C2×C3×C42—31no—
107C2×C3×C42—32no—
108C2×C3×C42C2×D311yescharacteristic
109C2×C3×C42C2×D311yescharacteristic
110C2×#217—32no—
111C2×#217—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4C2×D311yescharacteristic
115C2×(C2×D3)⋊C4C2×D311yescharacteristic
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—61no—
121C2×C4⋊Dic3C2×D312yes—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—62no—
127C2×Dic3⋊C4C2×D311yescharacteristic
128C2×Dic3⋊C4C2×D311yescharacteristic
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—62no—
132C2×C4×Dic3C2×D312yes—
133C2×C4×Dic3C2×D311yescharacteristic
134#872—24no—
135C4×Dic6—68no—
136C4×Dic6—64no—
137C4×Dic6—64no—
138C3×#95—31no—
139C3×#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D311yescharacteristic
150C23×C32C2411yescharacteristic
151C22×C3×D3—21no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—21no—
155C22×C3×D3C2×Q812yes—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×Q812yes—
162C2×C32×C4#4112yes—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3#4114yes—
169#634—28no—
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—
183C3×C4×D3—28no—
184C2×C4×Q8—91no—
185C2×#117—31no—
186#400—91no—
187#399—91no—
188#398—92no—
189#396—92no—
190#395—91no—
191#393—91no—
192C4×C4⋊C4—31no—
193C4×C4⋊C4—92no—
194C4×C22⋊C4—92no—
195C24×C3—31no—
196C23×D3C22×D311yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—31no—
201C22×C3×C4—32no—
202C22×C3×C4—34no—
203C22×C3×C4—32no—
204C22×C3×C4—31no—
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×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D312yes—
225C2×C4×D3—22no—
226C2×C4×D3—22no—
227C2×C4×D3Dic614yescomplemented
228C2×Dic6—64no—
229C2×Dic6—64no—
230C2×Dic6—64no—
231C2×Dic6—68no—
232C2×Dic6—62no—
233C2×Dic6—62no—
234C3×C4⋊C4—64no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C42—24no—
240C3×C42—62no—
241C3×C42—64no—
242C3×C42D1214yes—
243C3×C42#6714yes—
244#217—64no—
245#217—64no—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—22no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250C4⋊Dic3—24no—
251C4⋊Dic3—64no—
252C4⋊Dic3—64no—
253C4⋊Dic3—64no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256Dic3⋊C4—22no—
257Dic3⋊C4—22no—
258Dic3⋊C4—64no—
259Dic3⋊C4—68no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263C4×Dic3—24no—
264C4×Dic3—22no—
265C4×Dic3—68no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268C22×C32C22×D411yescharacteristic
269C22×C32C22×Q811yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C32C2×#4112yes—
272C22×C32C2×#4112yes—
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—22no—
280C32×C4C22⋊Q814yes—
281C3⋊Dic3—24no—
282C3⋊Dic3—42no—
283C3×Dic3—22no—
284C3×Dic3—24no—
285C3×Dic3—41no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C22×Q8—91no—
289C23×C4—31no—
290C4×Q8—184no—
291#117—64no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—32no—
295C2×C4⋊C4—92no—
296C2×C4⋊C4—92no—
297C2×C4⋊C4—92no—
298C2×C4⋊C4—91no—
299C2×C22⋊C4—31no—
300C2×C22⋊C4—31no—
301C2×C22⋊C4—92no—
302C2×C22⋊C4—92no—
303C2×C42—31no—
304C2×C42—32no—
305C2×C42—92no—
306C2×C42D3211yescharacteristic
307#95—31no—
308#95—31no—
309#95—92no—
310#95—92no—
311#95—92no—
312#95—92no—
313C23×C3—21no—
314C23×C3—32no—
315C23×C3—61no—
316C23×C3—62no—
317C23×C3—61no—
318C23×C3—62no—
319C23×C3C23×D311yescharacteristic
320C23×C3C23×D311yescharacteristic
321C22×D3—21no—
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—21no—
325C22×D3C2×Dic612yes—
326C2×C3×C4—24no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—32no—
337C2×C3×C4—34no—
338C2×C3×C4—42no—
339C2×C3×C4—61no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4—68no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4C2×Dic612yes—
352C2×C3×C4C2×D1212yes—
353C2×C3×C4C2×D1212yes—
354C2×C3×C4C2×D1212yes—
355C2×C3×C4#23512yes—
356C2×C3×C4#23712yes—
357C2×C3×C4D3×Q812yes—
358C2×C3×C4C2×#6712yes—
359C2×C3×C4C2×#6712yes—
360C2×C3×C4C2×#6712yes—
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—122no—
389C2×Dic3—122no—
390C2×Dic3C2×Dic612yes—
391C2×Dic3#23514yes—
392C4×D3—28no—
393Dic6—616no—
394Dic6—68no—
395Dic6—68no—
396C2×C32C2×C22⋊Q811yescharacteristic
397C2×C32#52511yescharacteristic
398C2×C32#52912yes—
399C2×C32#53211yescharacteristic
400C2×C32#53312yes—
401C3×D3—42no—
402C24—31no—
403C2×Q8—184no—
404C2×Q8—182no—
405C22×C4—32no—
406C22×C4—31no—
407C22×C4—34no—
408C22×C4—32no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—62no—
412C22×C4—62no—
413C22×C4—92no—
414C22×C4—92no—
415C22×C4C2×D3211yescharacteristic
416C22×C4C2×D3211yescharacteristic
417C22×C4C2×D3211yescharacteristic
418C4⋊C4—64no—
419C4⋊C4—62no—
420C4⋊C4—62no—
421C4⋊C4—184no—
422C4⋊C4—184no—
423C4⋊C4—184no—
424C4⋊C4—182no—
425C22⋊C4—62no—
426C22⋊C4—62no—
427C22⋊C4—184no—
428C22⋊C4—184no—
429C42—64no—
430C42—62no—
431C42—184no—
432C42#62614yes—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—62no—
439C22×C3—64no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3—122no—
443C22×C3C22×Dic611yescharacteristic
444C22×C3C22×D1211yescharacteristic
445C22×C3C2×#23511yescharacteristic
446C22×C3C2×#23512yes—
447C22×C3C2×#23711yescharacteristic
448C22×C3C2×D3×Q811yescharacteristic
449C22×C3D3×#4112yes—
450C22×C3D3×#4112yes—
451C22×C3D3×#4112yes—
452C22×C3C22×#6711yescharacteristic
453C2×D3—24no—
454C2×D3—22no—
455C2×D3—42no—
456C2×D3—41no—
457C2×D3—41no—
458C3×C4—24no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—24no—
464C3×C4—42no—
465C3×C4—62no—
466C3×C4—64no—
467C3×C4—121no—
468C3×C4—121no—
469C3×C4—122no—
470C3×C4#89714yes—
471C3×C4#92414yes—
472Dic3—22no—
473Dic3—24no—
474Dic3—42no—
475Dic3—41no—
476Dic3—41no—
477Dic3—68no—
478Dic3—64no—
479Dic3—64no—
480Dic3—124no—
481Dic3—122no—
482Dic3—122no—
483C32#239611yescharacteristic, complemented, Sylow
484C23—32no—
485C23—61no—
486C23—62no—
487C23—62no—
488C23—61no—
489C23C22×D3211yescharacteristic
490Q8—188no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—32no—
494C2×C4—34no—
495C2×C4—62no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—61no—
499C2×C4—68no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—94no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4D3×Dic612yes—
514C2×C4#379512yes—
515C2×C4C2×#62612yes—
516C2×C4C2×#62612yes—
517C2×C4C2×#62612yes—
518C2×C3—21no—
519C2×C3—22no—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—122no—
524C2×C3#547711yescharacteristic
525C2×C3C2×#89711yescharacteristic
526C2×C3#551712yes—
527C2×C3#552411yescharacteristic
528C2×C3#552812yes—
529C2×C3#553812yes—
530C2×C3#557812yes—
531C2×C3C2×#92411yescharacteristic
532C2×C3#582811yescharacteristic
533C2×C3#583211yescharacteristic
534D3—42no—
535C22—62no—
536C22—64no—
537C22—122no—
538C22—121no—
539C22—121no—
540C22C2×D3×Dic611yescharacteristic
541C22C2×#379511yescharacteristic
542C22D3×#23512yes—
543C22#6430612yes—
544C22C22×#62611yescharacteristic
545C4—22no—
546C4—22no—
547C4—62no—
548C4—64no—
549C4—122no—
550C4—121no—
551C4—121no—
552C4—184no—
553C4—362no—
554C4#6385714yes—
555C3—21no—
556C3#7366811yescharacteristic, complemented
557C3#8224511yescharacteristic, complemented
558C2—122no—
559C2#1059391012yes—
560C2#1059392612yes—
561C2C2×#6385711yescharacteristic
562C2#1059502911yescharacteristic
563C2#1059503411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
4. #10591354C2semidirect
5. #10591342C2semidirect
6. C4×Dic3⋊Dic3C2semidirect
11. #10591226C2semidirect
56. C4×C4⋊Dic3D3semidirect
77. C2×C3×C4×D3Q8semidirect
227. C2×C4×D3Dic6semidirect
483. C32#2396semidirect
556. C3#73668semidirect
557. C3#82245semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×#8722
C3×C4×C4⋊Dic32
#105913542
#105913422
C4×Dic3⋊Dic32
#105913222
#105913172
#105913082
C4×(C2×D3)⋊Dic32
#105912262
#822453
#736683