Finite Group Databasebeta

← #11792561

Subgroups — #11792561

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic
3C22×#3715C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5#10591221C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#72056—31nomaximal
9#70210—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#625—22no—
14C22×C32×C8C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#204—22no—
19C2×C3×#204—22no—
20C2×C3×#204—22no—
21#63914—22no—
22#63914—22no—
23C2×#3715—22no—
24C2×#3715—22no—
25C2×#3715—22no—
26C3×#821—22no—
27#63579—22no—
28#63562—22no—
29C22×C3×SD16—31no—
30C22×#215—31no—
31C2×#940—31no—
32C2×#940—31no—
33C22×#214—31no—
34C22×#204D311yescharacteristic, complemented
35C2×C3×#102—31no—
36#5229—31no—
37C2×#832—31no—
38C2×#821D311yescharacteristic, complemented
39#4973—31no—
40C2×#809—31no—
41#4550—31no—
42#4550—31no—
43#4550—61no—
44C23×C3×D3—21no—
45C23×C3×D3—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D412yes—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
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×Dic6D412yescomplemented
68C2×#625—28no—
69C2×#625—44no—
70C2×#625—44no—
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73C2×C32×C8D412yescomplemented
74C4×C3⋊Dic3—21no—
75C4×C3⋊Dic3—21no—
76C2×C3⋊(C3⋊C8)—21no—
77C2×C3⋊(C3⋊C8)—21no—
78C2×C3⋊(C3⋊C8)D412yescomplemented
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×#204—28no—
82#3715—28no—
83#2014—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—31no—
86C22×C3×D4—31no—
87C22×#67—62no—
88C22×#67—62no—
89C22×D12C2×D311yescharacteristic
90C22×D12C2×D311yescharacteristic
91C22×Dic6C2×D311yescharacteristic
92C2×C3×SD16—62no—
93C2×C3×SD16—62no—
94C2×C3×SD16—62no—
95C22×C3×C8—21no—
96C22×C3×C8C2×D311yescharacteristic
97C22×C3×C8C2×D311yescharacteristic
98C2×C3×C4⋊C4—31no—
99C2×#215—62no—
100C2×#215—62no—
101C2×#215—62no—
102#940—62no—
103#940—62no—
104#940—62no—
105#940—62no—
106C2×#214—62no—
107C2×#214—62no—
108C2×#214—62no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4×Dic3—31no—
111C2×C4×Dic3—31no—
112C2×C4×Dic3—61no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—31no—
115C22×C3⋊C8—61no—
116C2×#204—22no—
117C2×#204—22no—
118C2×#204—22no—
119C3×#102—62no—
120#832—62no—
121C3⋊#95—62no—
122C3⋊#95—62no—
123#821—22no—
124#809—62no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—42no—
133C22×C3×D3—42no—
134C22×C3×D3—42no—
135C22×C3×D3—42no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3SD1614yescomplemented
145C2×C3×Dic3—22no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—42no—
150C3×D12—22no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—22no—
154C3×D12—41no—
155C3×D12—41no—
156C3×D12—41no—
157C3×D12—41no—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—41no—
161C3×Dic6—41no—
162#625—416no—
163C32×C8—22no—
164C3⋊(C3⋊C8)—22no—
165C22×SD16—31no—
166C22×SD16—91no—
167C2×#127—91no—
168C2×#102—31no—
169C2×#102—91no—
170#391—91no—
171#336—91no—
172C24×C3—61no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—21no—
176C2×C3×Q8—32no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×D4—32no—
183C2×C3×D4—32no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C22×C3×C4—21no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—68no—
200C2×#67—68no—
201C2×#67—124no—
202C2×#67—124no—
203C2×#67—124no—
204C2×#67—124no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—62no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12D1212yes—
221C2×D12#6712yes—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6#6712yescomplemented
228C3×SD16—68no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—22no—
234C2×C3×C8—41no—
235C2×C3×C8—41no—
236C2×C3×C8#6712yescomplemented
237C2×C3×C8#6712yescomplemented
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240#215—68no—
241#214—68no—
242C4⋊Dic3—21no—
243C4⋊Dic3—21no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249C4×Dic3—121no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—121no—
258C2×C3⋊C8—121no—
259#204—28no—
260C22×C32#12011yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32#12711yescharacteristic
263C22×C32C2×SD1612yes—
264C22×C32AGL(1,ℤ/8)12yes—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—44no—
268C2×C3×D3—44no—
269C2×C3×D3—82no—
270C2×C3×D3—82no—
271C2×C3×D3—81no—
272C2×C3×D3—81no—
273C2×C3×D3—81no—
274C2×C3×D3—81no—
275C32×C4#12011yescharacteristic
276C32×C4#12011yescharacteristic
277C32×C4#12111yescharacteristic
278C32×C4#12111yescharacteristic
279C3⋊Dic3—24no—
280C3×Dic3—42no—
281C3×Dic3—81no—
282C22×Q8—31no—
283C22×D4—31no—
284C22×D4—31no—
285C22×D4—182no—
286C2×SD16—62no—
287C2×SD16—62no—
288C2×SD16—62no—
289C2×SD16—182no—
290C2×SD16—182no—
291C2×SD16—182no—
292C22×C8—91no—
293C22×C8D3211yescharacteristic
294#127—182no—
295#127—182no—
296C2×C4⋊C4—31no—
297C2×C42—91no—
298#102—62no—
299#102—182no—
300#95—182no—
301C23×C3—21no—
302C23×C3—62no—
303C23×C3—62no—
304C23×C3—121no—
305C23×C3—122no—
306C23×C3—122no—
307C23×C3—122no—
308C23×C3—122no—
309C23×C3—121no—
310C23×C3—121no—
311C23×C3—121no—
312C23×C3D3×D411yescharacteristic
313C23×C3D3×D411yescharacteristic
314C22×D3—22no—
315C22×D3—22no—
316C22×D3—41no—
317C22×D3—42no—
318C22×D3—42no—
319C22×D3—42no—
320C22×D3—42no—
321C22×D3—41no—
322C22×D3—41no—
323C22×D3—41no—
324C3×Q8—62no—
325C3×Q8—62no—
326C3×Q8—121no—
327C3×Q8—121no—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—62no—
331C3×D4—62no—
332C3×D4—121no—
333C3×D4—121no—
334C3×D4—121no—
335C3×D4—121no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—62no—
343C2×C3×C4—121no—
344C2×C3×C4—121no—
345C2×C3×C4—122no—
346C2×C3×C4—121no—
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359#67—1216no—
360#67—1216no—
361C2×Dic3—22no—
362C2×Dic3—34no—
363C2×Dic3—34no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—42no—
367C2×Dic3—41no—
368C2×Dic3—64no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—122no—
374C2×Dic3—122no—
375D12—22no—
376D12—22no—
377D12—22no—
378D12—22no—
379D12—41no—
380D12—41no—
381D12—41no—
382D12—41no—
383Dic6—22no—
384Dic6—22no—
385Dic6—41no—
386Dic6—41no—
387C3×C8—22no—
388C3×C8—22no—
389C3×C8—42no—
390C3⋊C8—62no—
391C3⋊C8—62no—
392C3⋊C8—122no—
393C2×C32#39211yescharacteristic
394C2×C32#45012yes—
395C2×C32#46012yes—
396C2×C32#49211yescharacteristic
397C2×C32#49611yescharacteristic
398C3×D3—82no—
399C3×D3—82no—
400C24—61no—
401C24—61no—
402C2×Q8—32no—
403C2×Q8—61no—
404C2×Q8—61no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×D4—32no—
409C2×D4—32no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—61no—
415C2×D4—61no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—188no—
421C2×D4—364no—
422C2×D4—364no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—92no—
426C22×C4C2×D3211yescharacteristic
427SD16—68no—
428SD16—188no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—92no—
432C2×C8—181no—
433C2×C8—181no—
434C2×C8#62512yescomplemented
435C4⋊C4—61no—
436C4⋊C4—61no—
437C42—181no—
438C42—181no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—124no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3—124no—
448C22×C3—241no—
449C22×C3—242no—
450C22×C3—241no—
451C22×C3—241no—
452C22×C3—241no—
453C22×C3—242no—
454C22×C3#88211yescharacteristic
455C22×C3#88411yescharacteristic
456C22×C3#91112yes—
457C22×C3D3×SD1612yes—
458C22×C3D3×SD1612yes—
459C22×C3#91412yes—
460C22×C3#93711yescharacteristic
461C22×C3#93911yescharacteristic
462C22×C3#94011yescharacteristic
463C22×C3#94011yescharacteristic
464C2×D3—44no—
465C2×D3—42no—
466C2×D3—42no—
467C2×D3—44no—
468C2×D3—81no—
469C2×D3—82no—
470C2×D3—81no—
471C2×D3—81no—
472C2×D3—81no—
473C2×D3—82no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—122no—
479C3×C4—241no—
480C3×C4#88211yescharacteristic
481C3×C4#88411yescharacteristic
482C3×C4#93011yescharacteristic
483C3×C4#93711yescharacteristic
484C3×C4#93711yescharacteristic
485C3×C4#93811yescharacteristic
486C3×C4#93911yescharacteristic
487C3×C4#95311yescharacteristic
488Dic3—42no—
489Dic3—64no—
490Dic3—64no—
491Dic3—81no—
492Dic3—124no—
493C32#201411yescharacteristic, complemented, Sylow
494C23—62no—
495C23—62no—
496C23—122no—
497C23—122no—
498C23—122no—
499C23—122no—
500C23—121no—
501C23—121no—
502C23—121no—
503C23—121no—
504C23#380211yescharacteristic
505Q8—62no—
506Q8—62no—
507Q8—121no—
508Q8—121no—
509D4—62no—
510D4—62no—
511D4—62no—
512D4—62no—
513D4—121no—
514D4—121no—
515D4—121no—
516D4—121no—
517D4—3616no—
518C2×C4—62no—
519C2×C4—94no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4—122no—
523C2×C4—121no—
524C2×C4—182no—
525C2×C4—182no—
526C2×C4#379511yescharacteristic
527C2×C4D3×D1211yescharacteristic
528C2×C4#380211yescharacteristic
529C2×C4C2×#62511yescharacteristic
530C2×C4D3×#6711yescharacteristic
531C2×C4D3×#6711yescharacteristic
532C8—22no—
533C8—182no—
534C2×C3—22no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—22no—
539C2×C3—242no—
540C2×C3—242no—
541C2×C3#476212yes—
542C2×C3#477612yes—
543C2×C3#496011yescharacteristic
544C2×C3#515411yescharacteristic
545C2×C3#516312yes—
546C2×C3#516912yes—
547C2×C3#517511yescharacteristic
548C2×C3#517511yescharacteristic
549C2×C3#517611yescharacteristic
550C2×C3#522311yescharacteristic
551D3—82no—
552D3—82no—
553C22—122no—
554C22—122no—
555C22—124no—
556C22—124no—
557C22—242no—
558C22—242no—
559C22—241no—
560C22—241no—
561C22—241no—
562C22—241no—
563C22#6379612yes—
564C22#6379812yes—
565C22#6388511yescharacteristic
566C22#6391411yescharacteristic
567C22#6392211yescharacteristic
568C4—122no—
569C4—184no—
570C4—241no—
571C4#6388511yescharacteristic
572C4#6390811yescharacteristic
573C4#6392211yescharacteristic
574C4#6397611yescharacteristic
575C3—21no—
576C3#7021011yescharacteristic, complemented
577C3#7205611yescharacteristic, complemented
578C2—242no—
579C2—242no—
580C2#1059087612yes—
581C2#1059088411yescharacteristic
582C2#1059088711yescharacteristic
583C2#1059094312yes—
584C2#1059138911yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63914C2
hypercenterC22×C8D32
hypocenterC32#2014
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#204C2semidirect
3. C22×#3715C2semidirect
4. C2×C3×#821C2semidirect
5. #10591221C2semidirect
6. C2×#63562C2semidirect
7. #10589416C2semidirect
34. C22×#204D3semidirect
38. C2×#821D3semidirect
67. C2×C3×Dic6D4semidirect
73. C2×C32×C8D4semidirect
78. C2×C3⋊(C3⋊C8)D4semidirect
144. C2×C3⋊Dic3SD16semidirect
227. C2×Dic6#67semidirect
236. C2×C3×C8#67semidirect
237. C2×C3×C8#67semidirect
434. C2×C8#625semidirect
493. C32#2014semidirect
576. C3#70210semidirect
577. C3#72056semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#639142
C22×#37152
C2×C3×#8212
#105912212
C2×#635622
#105894162
#720563
#702103