Finite Group Databasebeta

← #11801154

Subgroups — #11801154

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Dic3C211yesmaximal, characteristic
2#10592631C211yesmaximal, characteristic, complemented
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10591366C212yesmaximal
6#10591362C212yesmaximal
7C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic
9#10591248C212yesmaximal, complemented
10#10591245C212yesmaximal, complemented
11#10591222C211yesmaximal, characteristic, complemented
12#73752—31nomaximal
13#73437—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×D3×Dic3C2211yescharacteristic
16C22×D3×Dic3C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×Dic32C2211yescharacteristic
28C2×Dic32C2211yescharacteristic
29C4×D3×Dic3C418yescomplemented
30#63658C2212yes—
31#63658C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C22×C4×Dic3—31no—
39C2×C42×D3—31no—
40C3×C4×C4⋊C4—31no—
41C3×C4×C22⋊C4—31no—
42C4×#217—31no—
43#4987—32no—
44#4977—32no—
45#4943—32no—
46#4942—32no—
47C4×(C2×D3)⋊C4—31no—
48C4×(C2×D3)⋊C4D311yescharacteristic
49C4×C4⋊Dic3—31no—
50#4932—31no—
51#4932—31no—
52#4932—31no—
53#4932—31no—
54#4932—61no—
55C4×Dic3⋊C4—31no—
56C4×Dic3⋊C4D311yescharacteristic, complemented
57#4664—32no—
58#4651—32no—
59#4651—32no—
60#4650—32no—
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3C2×C414yes—
75C2×D3×Dic3—24no—
76C2×D3×Dic3—24no—
77C2×D3×Dic3C2×C414yes—
78C2×D3×Dic3C2×C414yes—
79C32×C42—22no—
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3C2×C414yes—
82C3×(C2×D3)⋊C4—24no—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3—22no—
86C3×C4×Dic3C2×C414yes—
87Dic3⋊Dic3—24no—
88(C2×D3)⋊Dic3—24no—
89Dic32C2×C414yes—
90Dic32C2×C414yes—
91#2283—91noSylow
92C23×C3×C4—31no—
93C23×Dic3—31no—
94C23×Dic3—31no—
95C22×C4×D3—31no—
96C22×C4×D3—31no—
97C22×C4×D3C2×D311yescharacteristic
98C2×C3×C4⋊C4—32no—
99C2×C3×C22⋊C4—32no—
100C2×C3×C42—21no—
101C2×C3×C42—31no—
102C2×C3×C42—31no—
103C2×C3×C42—31no—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C2×D311yescharacteristic
106C2×#217—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4C2×D312yes—
109C2×C4⋊Dic3—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4C2×D312yes—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—38no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—61no—
122C2×C4×Dic3—61no—
123C2×C4×Dic3C2×D311yescharacteristic
124C2×C4×Dic3C2×D311yescharacteristic
125C2×C4×Dic3C2×D311yescharacteristic
126C42×D3—38no—
127C3×#95—32no—
128C3×#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—62no—
142C3⋊#95—62no—
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—21no—
148C22×C3×D3—21no—
149C22×C3×D3C22×C412yes—
150C22×C3×D3#4114yes—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4#4112yes—
156C2×C32×C4#4112yes—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3C22×C412yes—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3#4114yes—
177C3×C4×D3—28no—
178D3×Dic3—28no—
179D3×Dic3—28no—
180C22×C42—91no—
181#383—92no—
182#382—92no—
183#381—92no—
184#380—92no—
185C4×C4⋊C4—31no—
186C4×C4⋊C4—91no—
187C4×C22⋊C4—31no—
188C4×C22⋊C4—91no—
189#376—91no—
190#376—91no—
191C24×C3—31no—
192C23×D3C22×D311yescharacteristic
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—34no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4—62no—
202C22×C3×C4—62no—
203C22×C3×C4C22×D312yes—
204C22×C3×C4C22×D312yes—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—34no—
212C22×Dic3—34no—
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3—62no—
218C22×Dic3—64no—
219C22×Dic3—64no—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D311yescharacteristic
225C2×C4×D3—22no—
226C2×C4×D3—22no—
227C2×C4×D3—34no—
228C2×C4×D3—34no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3C4×D314yes—
232C3×C4⋊C4—64no—
233C3×C22⋊C4—64no—
234C3×C42—24no—
235C3×C42—22no—
236C3×C42—22no—
237C3×C42—34no—
238C3×C42—62no—
239C3×C42—62no—
240#217—64no—
241(C2×D3)⋊C4—24no—
242(C2×D3)⋊C4—64no—
243C4⋊Dic3—64no—
244Dic3⋊C4—24no—
245Dic3⋊C4—64no—
246C4×Dic3—22no—
247C4×Dic3—22no—
248C4×Dic3—34no—
249C4×Dic3—34no—
250C4×Dic3—34no—
251C4×Dic3—34no—
252C4×Dic3—34no—
253C4×Dic3—34no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3C4×D314yes—
259C22×C32C23×C411yescharacteristic
260C22×C32C2×#4112yes—
261C22×C32C2×#4112yes—
262C22×C32C2×#4111yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C2×C3×D3—22no—
265C2×C3×D3—22no—
266C2×C3×D3—24no—
267C2×C3×D3—24no—
268C2×C3×D3#11714yes—
269C32×C4—42no—
270C32×C4#11714yes—
271C3⋊Dic3—22no—
272C3⋊Dic3—22no—
273C3⋊Dic3—42no—
274C3×Dic3—22no—
275C3×Dic3—22no—
276C3×Dic3—42no—
277C3×Dic3—42no—
278C3×Dic3#11714yes—
279C23×C4—31no—
280C23×C4—91no—
281C23×C4—91no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—92no—
284C2×C22⋊C4—32no—
285C2×C22⋊C4—92no—
286C2×C42—31no—
287C2×C42—31no—
288C2×C42—31no—
289C2×C42—98no—
290C2×C42—91no—
291C2×C42—91no—
292C2×C42—91no—
293C2×C42—91no—
294C2×C42D3211yescharacteristic
295#95—32no—
296#95—32no—
297#95—92no—
298#95—92no—
299#95—92no—
300#95—92no—
301#95—92no—
302#95—92no—
303C23×C3—21no—
304C23×C3—32no—
305C23×C3—34no—
306C23×C3—62no—
307C23×C3—61no—
308C23×C3—61no—
309C23×C3C23×D311yescharacteristic
310C23×C3C23×D311yescharacteristic
311C22×D3—21no—
312C22×D3—21no—
313C22×D3—22no—
314C22×D3C2×C4×D312yes—
315C22×D3#23514yes—
316C2×C3×C4—24no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—32no—
327C2×C3×C4—34no—
328C2×C3×C4—32no—
329C2×C3×C4—32no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—62no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—68no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4C2×C4×D312yes—
343C2×C3×C4C2×C4×D312yes—
344C2×C3×C4#23712yes—
345C2×C3×C4#23712yes—
346C2×C3×C4#23712yes—
347C2×C3×C4#23912yes—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—68no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—68no—
369C2×Dic3—64no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380C2×Dic3C2×C4×D312yes—
381C2×Dic3C2×C4×D312yes—
382C2×Dic3C2×C4×D312yes—
383C2×Dic3#23514yes—
384C4×D3—28no—
385C4×D3—68no—
386C4×D3—68no—
387C2×C32C2×#11711yescharacteristic
388C2×C32C2×#11711yescharacteristic
389C2×C32C2×#11711yescharacteristic
390C2×C32#52912yes—
391C2×C32#52912yes—
392C3×D3—24no—
393C24—31no—
394C22×C4—31no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—34no—
398C22×C4—32no—
399C22×C4—32no—
400C22×C4—62no—
401C22×C4—62no—
402C22×C4—94no—
403C22×C4—94no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—92no—
407C22×C4—184no—
408C22×C4—184no—
409C22×C4C2×D3212yes—
410C22×C4C2×D3211yescharacteristic
411C4⋊C4—64no—
412C4⋊C4—184no—
413C22⋊C4—64no—
414C22⋊C4—184no—
415C42—22no—
416C42—34no—
417C42—62no—
418C42—62no—
419C42—94no—
420C42—94no—
421C42—94no—
422C42—182no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—34no—
429C22×C3—62no—
430C22×C3—62no—
431C22×C3—64no—
432C22×C3—64no—
433C22×C3C22×C4×D311yescharacteristic
434C22×C3C22×C4×D311yescharacteristic
435C22×C3C2×#23512yes—
436C22×C3C2×#23512yes—
437C22×C3C2×#23711yescharacteristic
438C22×C3C2×#23711yescharacteristic
439C22×C3C2×#23711yescharacteristic
440C22×C3C2×#23911yescharacteristic
441C22×C3D3×#4112yes—
442C22×C3D3×#4112yes—
443C2×D3—22no—
444C2×D3—22no—
445C2×D3—24no—
446C2×D3—24no—
447C2×D3#87214yes—
448C3×C4—24no—
449C3×C4—34no—
450C3×C4—44no—
451C3×C4—42no—
452C3×C4—42no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—122no—
456C3×C4—122no—
457C3×C4#87714yes—
458C3×C4#89214yes—
459Dic3—22no—
460Dic3—22no—
461Dic3—42no—
462Dic3—42no—
463Dic3—62no—
464Dic3—62no—
465Dic3—62no—
466Dic3—62no—
467Dic3—122no—
468Dic3—122no—
469Dic3—124no—
470Dic3—122no—
471Dic3—122no—
472Dic3#87214yes—
473C32#228311yescharacteristic, complemented, Sylow
474C23—32no—
475C23—34no—
476C23—61no—
477C23—62no—
478C23—61no—
479C23C22×D3211yescharacteristic
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—32no—
484C2×C4—34no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—61no—
490C2×C4—68no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—92no—
498C2×C4—92no—
499C2×C4—188no—
500C2×C4—188no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4#379612yes—
507C2×C4C4×D3212yes—
508C2×C4#380512yes—
509C2×C3—21no—
510C2×C3—22no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—64no—
515C2×C3C2×#87211yescharacteristic
516C2×C3C2×#87211yescharacteristic
517C2×C3C2×#87711yescharacteristic
518C2×C3C2×#89211yescharacteristic
519C2×C3D3×#11711yescharacteristic
520C2×C3D3×#11711yescharacteristic
521C2×C3#553812yes—
522C2×C3#553812yes—
523C2×C3#555712yes—
524C2×C3#558012yes—
525D3—24no—
526C22—34no—
527C22—62no—
528C22—64no—
529C22—64no—
530C22—62no—
531C22C2×#379611yescharacteristic
532C22C2×C4×D3211yescharacteristic
533C22D3×#23512yes—
534C22D3×#23512yes—
535C22C2×#380511yescharacteristic
536C4—34no—
537C4—42no—
538C4—62no—
539C4—62no—
540C4—122no—
541C4—122no—
542C4—182no—
543C4—182no—
544C4—362no—
545C4#6387814yes—
546C3—21no—
547C3#7343711yescharacteristic, complemented
548C3#7375211yescharacteristic, complemented
549C2—64no—
550C2#1059391112yes—
551C2D3×#87211yescharacteristic
552C2D3×#87211yescharacteristic
553C2C2×#6387811yescharacteristic
554C2#1059493412yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2283
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592631C2semidirect
4. C3×C4×Dic3⋊C4C2semidirect
7. C4×Dic3⋊Dic3C2semidirect
9. #10591248C2semidirect
10. #10591245C2semidirect
11. #10591222C2semidirect
29. C4×D3×Dic3C4semidirect
56. C4×Dic3⋊C4D3semidirect
473. C32#2283semidirect
547. C3#73437semidirect
548. C3#73752semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×Dic32
#105926312
C3×C4×(C2×D3)⋊C42
C3×C4×Dic3⋊C42
#105913662
#105913622
C4×Dic3⋊Dic32
C4×(C2×D3)⋊Dic32
#105912482
#105912452
#105912222
#737523
#734373