Finite Group Databasebeta

← #11792565

Subgroups — #11792565

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63911C211yesmaximal, characteristic
2C22×#3717C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic, complemented
5C3×#4973C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70210—31nomaximal
9#69688—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#626—22no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18#63911—22no—
19#63911—22no—
20C2×#3717—22no—
21C2×#3717—22no—
22C2×#3717—22no—
23C2×#3715—22no—
24C2×#3715—22no—
25C2×#3715—22no—
26#63636—22no—
27C3×C3⋊#95—22no—
28C3×#809—22no—
29C22×#215—31no—
30C22×#215—31no—
31C2×#940—31no—
32C22×#214—31no—
33C22×#204—31no—
34C2×#874—31no—
35C2×C3×#102—31no—
36C3×#391—31no—
37#4973D311yescharacteristic, complemented
38C2×#809—31no—
39C2×#809—31no—
40C2×#809—61no—
41C2×#809D311yescharacteristic, complemented
42#4550—31no—
43#4524—31no—
44C23×C3⋊D3—21no—
45C23×C3×D3—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)D412yes—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
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×Dic6D412yescomplemented
68C2×#626—28no—
69C2×#626—44no—
70C2×#626—44no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)D412yescomplemented
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8D412yescomplemented
81#3717—28no—
82#3715—28no—
83#2014—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—31no—
86C22×#67—62no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×D12—62no—
91C22×D12C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C22×C3×C8—31no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C42—31no—
98C2×#215—62no—
99C2×#215—62no—
100C2×#215—62no—
101C2×#215—62no—
102C2×#215—62no—
103C2×#215—62no—
104#940—62no—
105#940—62no—
106C2×#214—62no—
107C2×#214—62no—
108C2×#214—62no—
109C2×C4×Dic3C2×D311yescharacteristic
110C22×C3⋊C8—31no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—61no—
113C22×C3⋊C8C2×D311yescharacteristic
114C2×#204—62no—
115C2×#204—62no—
116C2×#204—62no—
117#874—62no—
118#874—62no—
119C3×#102—62no—
120C3×#95—62no—
121C3⋊#95—22no—
122#809—22no—
123#809—62no—
124#809—62no—
125#809—64no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C22×C3×D3—22no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C2×C32×C4—41no—
138C2×C32×C4—42no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—41no—
148C4⋊(C3⋊D3)—41no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3SD1614yescomplemented
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—41no—
158C3×D12—41no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×Dic6—41no—
162C3×Dic6—41no—
163#626—416no—
164C3⋊(C3⋊C8)—22no—
165C3×C3⋊C8—22no—
166C22×SD16—91no—
167C22×SD16—91no—
168C2×#127—91no—
169C2×#102—31no—
170C2×#102—91no—
171#391—31no—
172#336—91no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—121no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×D4—32no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—32no—
194C22×C3×C4—41no—
195C22×C3×C4—61no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—68no—
199C2×#67—124no—
200C2×#67—124no—
201C22×Dic3—21no—
202C22×Dic3#6712yes—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—68no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—121no—
225C2×D12—121no—
226C2×D12—121no—
227C2×D12—124no—
228C2×D12—124no—
229C2×D12D1212yes—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6D1212yescomplemented
236C2×C3×C8—32no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—41no—
245C3×C42—61no—
246C3×C42—61no—
247#215—68no—
248#215—68no—
249#214—68no—
250C4×Dic3—21no—
251C4×Dic3—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—121no—
262C2×C3⋊C8—121no—
263C2×C3⋊C8#6712yescomplemented
264#204—68no—
265C22×C32#12011yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32#12711yescharacteristic
268C22×C32C2×SD1612yes—
269C22×C32AGL(1,ℤ/8)12yes—
270C2×C3⋊D3—42no—
271C2×C3⋊D3—44no—
272C2×C3⋊D3—82no—
273C2×C3⋊D3—81no—
274C2×C3⋊D3—81no—
275C2×C3×D3—42no—
276C2×C3×D3—44no—
277C2×C3×D3—82no—
278C2×C3×D3—81no—
279C2×C3×D3—81no—
280C32×C4—81no—
281C32×C4#12011yescharacteristic
282C32×C4#12011yescharacteristic
283C32×C4#12111yescharacteristic
284C32×C4#12111yescharacteristic
285C3×Dic3—24no—
286C3×Dic3—42no—
287C22×Q8—31no—
288C22×D4—31no—
289C22×D4—91no—
290C22×D4—182no—
291C2×SD16—182no—
292C2×SD16—182no—
293C2×SD16—182no—
294C2×SD16—182no—
295C2×SD16—182no—
296C2×SD16—182no—
297C22×C8—31no—
298C22×C8—91no—
299#127—182no—
300#127—182no—
301C2×C4⋊C4D3211yescharacteristic
302C2×C42—31no—
303#102—62no—
304#102—182no—
305#95—62no—
306C23×C3—21no—
307C23×C3—62no—
308C23×C3—121no—
309C23×C3—121no—
310C23×C3—122no—
311C23×C3—122no—
312C23×C3D3×D411yescharacteristic
313C23×C3C2×#6711yescharacteristic
314C22×D3—22no—
315C22×D3—41no—
316C22×D3—42no—
317C22×D3—42no—
318C22×D3—41no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—122no—
324C22×D3—121no—
325C22×D3—122no—
326C22×D3—122no—
327C22×D3—121no—
328C22×D3—121no—
329C22×D3—121no—
330C22×D3—122no—
331C22×D3—122no—
332C22×D3—242no—
333C22×D3—242no—
334C3×Q8—62no—
335C3×Q8—62no—
336C3×Q8—121no—
337C3×Q8—121no—
338C3×D4—62no—
339C3×D4—62no—
340C3×D4—121no—
341C3×D4—121no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—34no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—42no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—82no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4C2×D1211yescharacteristic
361C2×C3×C4C2×D1211yescharacteristic
362C2×C3×C4#23511yescharacteristic
363C2×C3×C4#23511yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372#67—1216no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—41no—
377C2×Dic3—41no—
378C2×Dic3#21514yescomplemented
379D12—22no—
380D12—22no—
381D12—41no—
382D12—41no—
383D12—64no—
384D12—62no—
385D12—62no—
386D12—62no—
387D12—62no—
388D12—122no—
389D12—122no—
390D12—122no—
391D12—1216no—
392D12—121no—
393D12—121no—
394D12—121no—
395D12—121no—
396Dic6—22no—
397Dic6—22no—
398Dic6—41no—
399Dic6—41no—
400C3×C8—62no—
401C3⋊C8—22no—
402C3⋊C8—62no—
403C3⋊C8—62no—
404C3⋊C8—122no—
405C2×C32#39211yescharacteristic
406C2×C32#45012yes—
407C2×C32#46012yes—
408C2×C32#49211yescharacteristic
409C2×C32#49611yescharacteristic
410C3⋊D3—82no—
411C3×D3—82no—
412C24—61no—
413C24—181no—
414C2×Q8—32no—
415C2×Q8—61no—
416C2×Q8—61no—
417C2×Q8—61no—
418C2×Q8—61no—
419C2×Q8—61no—
420C2×D4—32no—
421C2×D4—61no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—92no—
427C2×D4—188no—
428C2×D4—181no—
429C2×D4—181no—
430C2×D4—181no—
431C2×D4—181no—
432C2×D4—181no—
433C2×D4—364no—
434C2×D4—364no—
435C22×C4—21no—
436C22×C4—32no—
437C22×C4—61no—
438C22×C4C2×D3211yescharacteristic
439SD16—188no—
440SD16—188no—
441C2×C8—32no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—92no—
445C2×C8—181no—
446C2×C8—181no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C42—61no—
450C42—61no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—122no—
457C22×C3—124no—
458C22×C3—242no—
459C22×C3—241no—
460C22×C3—241no—
461C22×C3#88211yescharacteristic
462C22×C3#88411yescharacteristic
463C22×C3#91112yes—
464C22×C3D3×SD1612yes—
465C22×C3#93011yescharacteristic
466C22×C3#93711yescharacteristic
467C22×C3#94011yescharacteristic
468C22×C3#94011yescharacteristic
469C22×C3C2×#21512yes—
470C22×C3#94912yes—
471C2×D3—42no—
472C2×D3—44no—
473C2×D3—81no—
474C2×D3—81no—
475C2×D3—82no—
476C2×D3—124no—
477C2×D3—122no—
478C2×D3—122no—
479C2×D3—124no—
480C2×D3—124no—
481C2×D3—244no—
482C2×D3—244no—
483C2×D3—242no—
484C2×D3—242no—
485C2×D3—241no—
486C2×D3—241no—
487C2×D3—242no—
488C2×D3—242no—
489C2×D3—241no—
490C2×D3—241no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—64no—
496C3×C4—82no—
497C3×C4—81no—
498C3×C4—81no—
499C3×C4—122no—
500C3×C4#88211yescharacteristic
501C3×C4#88211yescharacteristic
502C3×C4#88211yescharacteristic
503C3×C4#88411yescharacteristic
504C3×C4#88411yescharacteristic
505C3×C4#88411yescharacteristic
506C3×C4#93011yescharacteristic
507C3×C4#93711yescharacteristic
508Dic3—24no—
509Dic3—42no—
510C32#201411yescharacteristic, complemented, Sylow
511C23—62no—
512C23—121no—
513C23—122no—
514C23—122no—
515C23—121no—
516C23—182no—
517C23—361no—
518C23—362no—
519C23—362no—
520C23—361no—
521C23D3×#6711yescharacteristic
522Q8—62no—
523Q8—62no—
524Q8—121no—
525Q8—121no—
526D4—62no—
527D4—62no—
528D4—121no—
529D4—121no—
530D4—182no—
531D4—182no—
532D4—3616no—
533D4—361no—
534D4—361no—
535C2×C4—34no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4#379811yescharacteristic
544C2×C4D3×D1211yescharacteristic
545C2×C4D3×D1211yescharacteristic
546C2×C4#380211yescharacteristic
547C2×C4D3×#6711yescharacteristic
548C2×C4#381111yescharacteristic
549C8—62no—
550C8—182no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—22no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—242no—
557C2×C3#476212yes—
558C2×C3#477612yes—
559C2×C3#496011yescharacteristic
560C2×C3#496011yescharacteristic
561C2×C3#502712yes—
562C2×C3#504612yes—
563C2×C3#505811yescharacteristic
564C2×C3#508511yescharacteristic
565C2×C3#515411yescharacteristic
566C2×C3#517511yescharacteristic
567D3—82no—
568D3—244no—
569D3—242no—
570D3—242no—
571C22—124no—
572C22—122no—
573C22—242no—
574C22—241no—
575C22—241no—
576C22—364no—
577C22—362no—
578C22—722no—
579C22—721no—
580C22—721no—
581C22#6390611yescharacteristic
582C22#6392211yescharacteristic
583C22#6392512yes—
584C22D3×#21512yes—
585C22#6397911yescharacteristic
586C4—64no—
587C4—81no—
588C4—122no—
589C4#6390611yescharacteristic
590C4#6391211yescharacteristic
591C4#6392211yescharacteristic
592C4#6392311yescharacteristic
593C3—21no—
594C3#6968811yescharacteristic, complemented
595C3#7021011yescharacteristic, complemented
596C2—242no—
597C2—722no—
598C2#1059054912yes—
599C2#1059059612yes—
600C2#1059139311yescharacteristic
601C2#1059148311yescharacteristic
602C2#1059161811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2014
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#3717C2semidirect
3. C22×#3715C2semidirect
4. C2×#63636C2semidirect
5. C3×#4973C2semidirect
6. C2×C3×#809C2semidirect
7. #10589155C2semidirect
37. #4973D3semidirect
41. C2×#809D3semidirect
67. C2×C3×Dic6D4semidirect
75. C2×C3⋊(C3⋊C8)D4semidirect
80. C2×C3×C3⋊C8D4semidirect
154. C2×C3×Dic3SD16semidirect
235. C2×Dic6D12semidirect
263. C2×C3⋊C8#67semidirect
378. C2×Dic3#215semidirect
510. C32#2014semidirect
594. C3#69688semidirect
595. C3#70210semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
C22×#37172
C22×#37152
C2×#636362
C3×#49732
C2×C3×#8092
#105891552
#702103
#696883