Finite Group Databasebeta

← #11805239

Subgroups — #11805239

Order 1152.

1213 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
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4#10591716C211yesmaximal, characteristic
5#10591716C211yesmaximal, characteristic
6Dic3×#217C211yesmaximal, characteristic
7Dic3×#217C211yesmaximal, characteristic
8#10591272C212yesmaximal, complemented
9#10591268C212yesmaximal, complemented
10Dic3×Dic3⋊C4C212yesmaximal, complemented
11#10591201C212yesmaximal, complemented
12#82160—31nomaximal
13#73458—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2212yes—
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×Dic3⋊C4C418yescomplemented
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63658C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C22×C3×C4⋊C4—31no—
39C22×Dic3⋊C4D311yescharacteristic
40C3×C4×C22⋊C4—31no—
41#5212—31no—
42#5212—31no—
43#5212—31no—
44#5212—31no—
45#5212—61no—
46C4×#217—31no—
47C4×#217—31no—
48C4×#217D311yescharacteristic
49#4984—32no—
50#4980—32no—
51#4980—32no—
52Dic3×C4⋊C4—32no—
53#4942—31no—
54#4942—31no—
55Dic3×C22⋊C4—31no—
56Dic3×C22⋊C4—31no—
57#4933—32no—
58C4×Dic3⋊C4—32no—
59#4655—32no—
60#4647—32no—
61C24×C32C2311yescharacteristic
62C22×C32×C4—42no—
63C22×C32×C4C2×C414yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3—24no—
69C22×C3×Dic3—42no—
70C22×C3×Dic3C2×C414yes—
71C22×C3×Dic3C2×C414yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78#3757—22no—
79#3757—22no—
80C4⋊(C3⋊Dic3)—42no—
81C3×#217—22no—
82C3×#217Q814yes—
83C3×Dic3⋊C4C2×C414yes—
84C3×Dic3⋊C4C2×C414yes—
85C3×Dic3⋊C4C2×C414yes—
86C3×Dic3⋊C4C2×C414yes—
87C3×C4×Dic3—42no—
88Dic3⋊Dic3—24no—
89Dic3⋊Dic3—42no—
90Dic32—24no—
91Dic32—42no—
92#2345—91noSylow
93C23×C3×C4—21no—
94C23×C3×C4—31no—
95C23×C3×C4—31no—
96C23×C3×C4C2×D311yescharacteristic
97C23×C3×C4C2×D311yescharacteristic
98C23×Dic3C2×D311yescharacteristic
99C23×Dic3C2×D311yescharacteristic
100C2×C3×C4⋊C4—38no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C42—32no—
108C2×#217—31no—
109C2×#217—31no—
110C2×#217—31no—
111C2×#217—31no—
112C2×#217—61no—
113C2×#217—61no—
114C2×#217C2×D311yescharacteristic
115C2×#217C2×D311yescharacteristic
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—62no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4Dic318yescomplemented
124C2×Dic3⋊C4C2×D311yescharacteristic
125C2×Dic3⋊C4C2×D311yescharacteristic
126C2×Dic3⋊C4C2×D311yescharacteristic
127C2×Dic3⋊C4C2×D311yescharacteristic
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3C2×D312yes—
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—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—62no—
145C3⋊#95C2×D312yes—
146C23×C32—22no—
147C23×C32—22no—
148C23×C32C22×C412yes—
149C23×C32C2×Q812yes—
150C23×C32#4112yes—
151C23×C32C2411yescharacteristic
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—44no—
155C2×C32×C4C22×C412yes—
156C2×C32×C4C22×C412yes—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—28no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—44no—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3C2×Q814yes—
178C2×C3×Dic3#4114yes—
179C22×C4⋊C4—31no—
180#389—92no—
181#387—92no—
182#387—92no—
183#380—91no—
184#380—91no—
185#380—91no—
186C4×C4⋊C4—92no—
187C4×C22⋊C4—31no—
188C4×C22⋊C4—91no—
189C4×C22⋊C4—91no—
190C24×C3—21no—
191C24×C3C22×D311yescharacteristic
192C24×C3C22×D311yescharacteristic
193C22×C3×C4—24no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—31no—
197C22×C3×C4—34no—
198C22×C3×C4—31no—
199C22×C3×C4—32no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—34no—
203C22×C3×C4—32no—
204C22×C3×C4—42no—
205C22×C3×C4—42no—
206C22×C3×C4—44no—
207C22×C3×C4—64no—
208C22×C3×C4—122no—
209C22×C3×C4C4×D314yes—
210C22×C3×C4C2×Dic314yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—24no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—42no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3C2×Dic314yes—
224C22×Dic3C2×Dic314yes—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D311yescharacteristic
231C3×C4⋊C4—34no—
232C3×C4⋊C4—34no—
233C3×C4⋊C4—34no—
234C3×C4⋊C4—34no—
235C3×C22⋊C4—34no—
236C3×C22⋊C4—62no—
237C3×C42—122no—
238#217—22no—
239#217—62no—
240#217—62no—
241#217—62no—
242#217—62no—
243#217—122no—
244#217—122no—
245#217Dic614yes—
246C4⋊Dic3—64no—
247C4⋊Dic3—122no—
248C4⋊Dic3—122no—
249C4⋊Dic3—122no—
250C4⋊Dic3—124no—
251Dic3⋊C4—64no—
252Dic3⋊C4—122no—
253Dic3⋊C4C2×Dic314yes—
254Dic3⋊C4C2×Dic314yes—
255Dic3⋊C4C2×Dic314yes—
256Dic3⋊C4C2×Dic314yes—
257C4×Dic3—42no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—122no—
261C4×Dic3—122no—
262C22×C32—22no—
263C22×C32—22no—
264C22×C32—24no—
265C22×C32—24no—
266C22×C32C4×Q814yes—
267C22×C32C23×C411yescharacteristic
268C22×C32C22×Q811yescharacteristic
269C22×C32C2×#4111yescharacteristic
270C22×C32C2×#4112yes—
271C22×C32H(5,𝔽2)12yes—
272C32×C4—22no—
273C32×C4—22no—
274C3⋊Dic3—42no—
275C3⋊Dic3—42no—
276C3×Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—22no—
279C3×Dic3—24no—
280C3×Dic3—42no—
281C3×Dic3#11714yes—
282C23×C4—31no—
283C23×C4—31no—
284C23×C4D3211yescharacteristic
285C2×C4⋊C4—38no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—92no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—92no—
293C2×C22⋊C4—31no—
294C2×C22⋊C4—31no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—91no—
297C2×C42—32no—
298C2×C42—92no—
299C2×C42—92no—
300#95—32no—
301#95—92no—
302#95—92no—
303#95—92no—
304#95—92no—
305#95—92no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—21no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3C2×Dic612yes—
317C23×C3C2×C4×D312yes—
318C23×C3#23512yes—
319C23×C3D3×Q812yes—
320C23×C3#23912yes—
321C23×C3C22×Dic312yes—
322C23×C3C23×D311yescharacteristic
323C23×C3C23×D311yescharacteristic
324C2×C3×C4—24no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—32no—
332C2×C3×C4—34no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—34no—
337C2×C3×C4—42no—
338C2×C3×C4—44no—
339C2×C3×C4—44no—
340C2×C3×C4—48no—
341C2×C3×C4—68no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—124no—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4C22×Dic312yes—
354C2×C3×C4C22×Dic312yes—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—28no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—44no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380C2×Dic3—122no—
381C2×Dic3—122no—
382C2×Dic3—122no—
383C2×Dic3C2×Dic614yes—
384C2×Dic3#23514yes—
385C2×Dic3C22×Dic312yes—
386C2×Dic3C22×Dic312yes—
387C2×Dic3C22×Dic312yes—
388C2×Dic3C22×Dic312yes—
389C2×C32—24no—
390C2×C32C2×#11711yescharacteristic
391C2×C32C2×C4×Q811yescharacteristic
392C2×C32#51811yescharacteristic
393C2×C32#55312yes—
394C2×C32#55412yes—
395C24C2×D3211yescharacteristic
396C22×C4—31no—
397C22×C4—32no—
398C22×C4—31no—
399C22×C4—31no—
400C22×C4—31no—
401C22×C4—34no—
402C22×C4—34no—
403C22×C4—32no—
404C22×C4—42no—
405C22×C4—64no—
406C22×C4—92no—
407C22×C4—92no—
408C22×C4—122no—
409C22×C4D3×Dic314yes—
410C22×C4C2×D3211yescharacteristic
411C22×C4C2×D3211yescharacteristic
412C4⋊C4—34no—
413C4⋊C4—34no—
414C4⋊C4—34no—
415C4⋊C4—34no—
416C4⋊C4—184no—
417C4⋊C4—362no—
418C4⋊C4—362no—
419C22⋊C4—34no—
420C22⋊C4—62no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C42—122no—
424C42—184no—
425C42—362no—
426C22×C3—22no—
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—24no—
432C22×C3—24no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—24no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3C4×Dic614yes—
445C22×C3Q8×Dic314yes—
446C22×C3C22×Dic611yescharacteristic
447C22×C3C22×C4×D311yescharacteristic
448C22×C3C2×#23511yescharacteristic
449C22×C3C2×#23512yes—
450C22×C3#100412yes—
451C22×C3#100412yes—
452C22×C3C2×D3×Q811yescharacteristic
453C22×C3C2×#23911yescharacteristic
454C22×C3D3×#4112yes—
455C22×C3C23×Dic311yescharacteristic
456C3×C4—24no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—34no—
462C3×C4—42no—
463C3×C4—62no—
464C3×C4—62no—
465C3×C4—64no—
466C3×C4—62no—
467C3×C4—122no—
468Dic3—22no—
469Dic3—24no—
470Dic3—22no—
471Dic3—22no—
472Dic3—42no—
473Dic3—122no—
474Dic3—122no—
475Dic3—122no—
476Dic3—122no—
477Dic3—242no—
478Dic3—242no—
479Dic3#92614yes—
480C32#234511yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23D3×Dic612yes—
484C23#379912yes—
485C23C2×D3×Dic312yes—
486C23C22×D3211yescharacteristic
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—34no—
490C2×C4—32no—
491C2×C4—34no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—44no—
496C2×C4—68no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—124no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4C2×D3×Dic312yes—
513C2×C4C2×D3×Dic312yes—
514C2×C3—24no—
515C2×C3—24no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—22no—
519C2×C3—21no—
520C2×C3—22no—
521C2×C3—44no—
522C2×C3C2×C4×Dic611yescharacteristic
523C2×C3#548611yescharacteristic
524C2×C3#551112yes—
525C2×C3#551412yes—
526C2×C3D3×#11711yescharacteristic
527C2×C3#553912yes—
528C2×C3#554012yes—
529C2×C3C2×#92611yescharacteristic
530C2×C3#579811yescharacteristic
531C2×C3C2×Q8×Dic311yescharacteristic
532C22—22no—
533C22—24no—
534C22—22no—
535C22—24no—
536C22Dic3×Dic614yes—
537C22C2×D3×Dic611yescharacteristic
538C22C2×#379911yescharacteristic
539C22D3×#23512yes—
540C22C22×D3×Dic311yescharacteristic
541C22#6433012yes—
542C4—22no—
543C4—22no—
544C4—34no—
545C4—62no—
546C4—64no—
547C4—62no—
548C4—62no—
549C4—122no—
550C4—362no—
551C4—362no—
552C3—21no—
553C3#7345811yescharacteristic, complemented
554C3#8216011yescharacteristic, complemented
555C2—24no—
556C2C2×Dic3×Dic611yescharacteristic
557C2D3×#92611yescharacteristic
558C2#1059495112yes—
559C2#1059502812yes—
560C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #10591272C2semidirect
9. #10591268C2semidirect
10. Dic3×Dic3⋊C4C2semidirect
11. #10591201C2semidirect
22. C2×C3×Dic3⋊C4C4semidirect
123. C2×Dic3⋊C4Dic3semidirect
480. C32#2345semidirect
553. C3#73458semidirect
554. C3#82160semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
#105929112
C3×C4×#2172
#105917162
Dic3×#2172
#105912722
#105912682
Dic3×Dic3⋊C42
#105912012
#821603
#734583