Finite Group Databasebeta

← #11792595

Subgroups — #11792595

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#216C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×#63863C211yesmaximal, characteristic
4#10592928C211yesmaximal, characteristic, complemented
5C2×#63566C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7#10589156C211yesmaximal, characteristic, complemented
8#72072—31nomaximal
9#72058—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×#216—22no—
16C2×C3×#216—22no—
17C2×C3×#216—22no—
18C2×C3×#215—22no—
19C2×C3×#215—22no—
20C2×C3×#215—22no—
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—22no—
24#63863—22no—
25#63863—22no—
26#63658—22no—
27#63566—22no—
28#63563—22no—
29C22×C3×Q16—31no—
30C22×C3×SD16—31no—
31C2×#947—31no—
32C22×#216D311yescharacteristic, complemented
33C22×#215D311yescharacteristic
34C2×#936—31no—
35#5229—31no—
36#5229—31no—
37#5229—61no—
38C2×#835—31no—
39C2×#832—31no—
40C2×#821—31no—
41C2×#816—31no—
42#4550—31no—
43#4550—31no—
44C23×C3×D3—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8D412yes—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3D412yes—
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12D412yes—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yes—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C4×C3⋊Dic3—21no—
71C4×C3⋊Dic3—21no—
72C3×#216—28no—
73C3×#215—28no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8D412yes—
79C2×C3×C3⋊C8D412yes—
80(C2×D3)⋊Dic3—28no—
81#2015—91noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8—31no—
84C22×C3×Q8C2×D311yescharacteristic
85C22×C3×Q8C2×D311yescharacteristic
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C2×C3×Q16—62no—
90C2×C3×Q16—62no—
91C2×C3×Q16—62no—
92C2×C3×SD16—62no—
93C2×C3×SD16—62no—
94C2×C3×SD16—62no—
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C2×#217—62no—
98#947—62no—
99#947—62no—
100C2×#216—22no—
101C2×#216—22no—
102C2×#216—22no—
103C2×#215—22no—
104C2×#215—22no—
105C2×#215—22no—
106#936—62no—
107#936—62no—
108C2×(C2×D3)⋊C4—62no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—61no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊C8C2×D311yescharacteristic
117#835—62no—
118#832—62no—
119C3⋊#95—62no—
120C3⋊#95—62no—
121C3⋊#95—64no—
122#821—62no—
123#816—62no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—42no—
129C22×C3×D3—42no—
130C32×Q8—22no—
131C32×Q8—22no—
132C32×Q8—41no—
133C32×Q8—41no—
134C2×C32×C4—22no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—42no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—41no—
154C3×D12—41no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—41no—
158C3×Dic6—41no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—22no—
161C22×Q16—31no—
162C22×SD16—31no—
163C2×#124—91no—
164C2×#103—91no—
165C2×#102—91no—
166#391—91no—
167#336—91no—
168C24×C3—61no—
169C23×D3—21no—
170C2×C3×Q8—22no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—21no—
181C2×C3×Q8—22no—
182C2×C3×Q8—32no—
183C2×C3×Q8—41no—
184C2×C3×Q8—41no—
185C2×C3×Q8—41no—
186C2×C3×Q8—41no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×Q8#6712yes—
193C2×C3×Q8#6712yes—
194C2×C3×D4—32no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C2×C3×D4—61no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×Dic3—21no—
208C22×Dic3—32no—
209C22×Dic3—32no—
210C22×Dic3—62no—
211C22×Dic3—62no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12#6712yes—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6#6712yes—
226C3×Q16—68no—
227C3×SD16—68no—
228C2×C3×C8—32no—
229C2×C3×C8—32no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234#217—68no—
235#216—28no—
236#215—28no—
237(C2×D3)⋊C4—68no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—121no—
243C4⋊Dic3—121no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249C4×Dic3—121no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8#6712yes—
255C2×C3⋊C8#6712yes—
256C22×C32#12011yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32#12711yescharacteristic
259C22×C32#13512yes—
260C22×C32#13712yes—
261C2×C3×D3—42no—
262C2×C3×D3—44no—
263C2×C3×D3—82no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C32×C4—42no—
267C32×C4#12011yescharacteristic
268C32×C4#12011yescharacteristic
269C32×C4#12111yescharacteristic
270C32×C4#12111yescharacteristic
271C3⋊Dic3—42no—
272C3⋊Dic3—81no—
273C3×Dic3—42no—
274C22×Q8—31no—
275C22×Q8D3211yescharacteristic
276C22×D4—31no—
277C2×Q16—62no—
278C2×Q16—62no—
279C2×Q16—62no—
280C2×SD16—62no—
281C2×SD16—62no—
282C2×SD16—62no—
283C22×C8—31no—
284C22×C8—31no—
285#124—182no—
286#124—182no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—182no—
289C2×C42—91no—
290#103—182no—
291#102—182no—
292#95—182no—
293C23×C3—21no—
294C23×C3—62no—
295C23×C3—122no—
296C23×C3—122no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3D3×D411yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—22no—
302C22×D3—42no—
303C22×D3—42no—
304C22×D3—41no—
305C22×D3—41no—
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—22no—
309C3×Q8—22no—
310C3×Q8—42no—
311C3×Q8—42no—
312C3×Q8—42no—
313C3×Q8—42no—
314C3×Q8—41no—
315C3×Q8—41no—
316C3×Q8—41no—
317C3×Q8—41no—
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—121no—
321C3×Q8—121no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—24no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—62no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4#23711yescharacteristic
349C2×C3×C4#23711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×Dic3—22no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—64no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—122no—
367C2×Dic3—122no—
368C2×Dic3—122no—
369C2×Dic3—124no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374D12—22no—
375D12—22no—
376D12—41no—
377D12—41no—
378Dic6—22no—
379Dic6—22no—
380Dic6—41no—
381Dic6—41no—
382C3×C8—62no—
383C3×C8—62no—
384C3⋊C8—22no—
385C3⋊C8—22no—
386C2×C32#39211yescharacteristic
387C2×C32#45212yes—
388C2×C32#46412yes—
389C2×C32#49511yescharacteristic
390C2×C32#49711yescharacteristic
391C3×D3—82no—
392C24—61no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—32no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8#62512yes—
405C2×D4—32no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—61no—
411C22×C4—21no—
412C22×C4—61no—
413C22×C4—92no—
414C22×C4—181no—
415C22×C4C2×D3211yescharacteristic
416Q16—68no—
417SD16—68no—
418C2×C8—32no—
419C2×C8—32no—
420C2×C8—61no—
421C2×C8—61no—
422C2×C8—61no—
423C2×C8—61no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C22⋊C4—188no—
427C42—181no—
428C42—181no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—124no—
435C22×C3—122no—
436C22×C3—242no—
437C22×C3—241no—
438C22×C3—241no—
439C22×C3#91512yes—
440C22×C3#91612yes—
441C22×C3#91812yes—
442C22×C3#91912yes—
443C22×C3#93711yescharacteristic
444C22×C3#93711yescharacteristic
445C22×C3#93911yescharacteristic
446C22×C3#93911yescharacteristic
447C22×C3#94011yescharacteristic
448C22×C3#94011yescharacteristic
449C2×D3—44no—
450C2×D3—42no—
451C2×D3—82no—
452C2×D3—81no—
453C2×D3—81no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—44no—
459C3×C4—42no—
460C3×C4—42no—
461C3×C4—122no—
462C3×C4#93711yescharacteristic
463C3×C4#93711yescharacteristic
464C3×C4#93811yescharacteristic
465C3×C4#93811yescharacteristic
466C3×C4#93911yescharacteristic
467C3×C4#93911yescharacteristic
468C3×C4#95311yescharacteristic
469C3×C4#95311yescharacteristic
470Dic3—42no—
471Dic3—124no—
472Dic3—122no—
473Dic3—122no—
474Dic3—242no—
475Dic3—241no—
476Dic3—241no—
477C32#201511yescharacteristic, complemented, Sylow
478C23—62no—
479C23—122no—
480C23—122no—
481C23—121no—
482C23—121no—
483C23#381111yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—41no—
487Q8—41no—
488Q8—62no—
489Q8—62no—
490Q8—121no—
491Q8—121no—
492D4—62no—
493D4—62no—
494D4—121no—
495D4—121no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—62no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—362no—
506C2×C4—361no—
507C2×C4#380511yescharacteristic
508C2×C4C2×#62511yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4D3×#6711yescharacteristic
513C8—62no—
514C8—62no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—22no—
518C2×C3—22no—
519C2×C3—21no—
520C2×C3—242no—
521C2×C3#516612yes—
522C2×C3#516711yescharacteristic
523C2×C3#516811yescharacteristic
524C2×C3#517312yes—
525C2×C3#518512yes—
526C2×C3#518712yes—
527C2×C3#519011yescharacteristic
528C2×C3#519111yescharacteristic
529C2×C3#522311yescharacteristic
530C2×C3#522311yescharacteristic
531D3—82no—
532C22—124no—
533C22—122no—
534C22—241no—
535C22—241no—
536C22—242no—
537C22#6395012yes—
538C22#6395112yes—
539C22#6397911yescharacteristic
540C22#6398011yescharacteristic
541C22#6398311yescharacteristic
542C4—42no—
543C4—122no—
544C4—362no—
545C4—721no—
546C4#6397011yescharacteristic
547C4#6397011yescharacteristic
548C4#6397611yescharacteristic
549C4#6397611yescharacteristic
550C3—21no—
551C3#7205811yescharacteristic, complemented
552C3#7207211yescharacteristic, complemented
553C2—242no—
554C2#1059161011yescharacteristic
555C2#1059161111yescharacteristic
556C2#1059161212yes—
557C2#1059165612yes—
558C2#1059172311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#216C2semidirect
4. #10592928C2semidirect
5. C2×#63566C2semidirect
7. #10589156C2semidirect
32. C22×#216D3semidirect
477. C32#2015semidirect
551. C3#72058semidirect
552. C3#72072semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2162
C22×C3×#2152
C2×#638632
#105929282
C2×#635662
C2×#635632
#105891562
#720723
#720583