Finite Group Databasebeta

← #11794056

Subgroups — #11794056

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic
2C3×#5229C211yesmaximal, characteristic, complemented
3C2×C3×#835C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7#10589163C211yesmaximal, characteristic, complemented
8#70280—31nomaximal
9#69680—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×#3755—22no—
13C2×#3755—22no—
14C2×#3755—22no—
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3722—21no—
21C2×#3722—21no—
22C3×#835—22no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25Dic3⋊(C3⋊C8)—22no—
26#63564—22no—
27C22×#215—31no—
28C22×#215—31no—
29C22×#215—61no—
30C2×C3×#103—31no—
31C3×#391—31no—
32#5229D311yescharacteristic, complemented
33C2×#835D311yescharacteristic, complemented
34C2×#821—31no—
35C2×Dic3⋊C8—31no—
36#4988—31no—
37C2×#809—31no—
38#4939—31no—
39C2×C4⋊(C3⋊C8)—31no—
40#4529—31no—
41#4529—31no—
42C23×C3⋊D3—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8D412yes—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)D412yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61#3755—28no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)D412yes—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74#3722—42no—
75#3722—42no—
76#2055—91noSylow
77C22×C3×Q8—21no—
78C22×C3×Q8C2×D311yescharacteristic
79C22×C3×Q8C2×D311yescharacteristic
80C22×D12—31no—
81C22×D12—31no—
82C22×D12—61no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C42—31no—
87C2×#215—62no—
88C2×#215—62no—
89C2×#215—62no—
90C2×#215—62no—
91C2×#215—64no—
92C2×#215—64no—
93C2×#215—64no—
94C2×#215—62no—
95C2×#215—62no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4×Dic3C2×D311yescharacteristic
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106C22×C3⋊C8C2×D311yescharacteristic
107C3×#103—62no—
108C3×#95—61no—
109C3×#95—61no—
110#835—22no—
111C3⋊#95—21no—
112C3⋊#95—21no—
113#821—62no—
114Dic3⋊C8—62no—
115#809—62no—
116C4⋊(C3⋊C8)—62no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—22no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C32×Q8—22no—
126C32×Q8—22no—
127C32×Q8—41no—
128C32×Q8—41no—
129C2×C32×C4—22no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—41no—
141C4⋊(C3⋊D3)—41no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3SD1612yescomplemented
154C3⋊(C3⋊C8)—22no—
155C3×C3⋊C8—41no—
156C22×SD16—91no—
157C2×C4⋊C8—91no—
158C2×#103—31no—
159C2×#102—91no—
160#391—31no—
161#390—91no—
162#340—91no—
163C23×D3—61no—
164C23×D3—61no—
165C23×D3—121no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8—21no—
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—22no—
179C2×C3×Q8—41no—
180C2×C3×Q8—41no—
181C2×C3×Q8—41no—
182C2×C3×Q8D1212yes—
183C2×C3×Q8#6712yes—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—41no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3#6711yescharacteristic
197C22×Dic3#6711yescharacteristic
198C2×D12—32no—
199C2×D12—32no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—121no—
214C2×D12—121no—
215C2×D12—121no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C2×C3×C8—61no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C42—61no—
224C3×C42—61no—
225#215—616no—
226#215—68no—
227#215—68no—
228(C2×D3)⋊C4—122no—
229(C2×D3)⋊C4—122no—
230(C2×D3)⋊C4—122no—
231(C2×D3)⋊C4—122no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—21no—
236C4×Dic3—21no—
237C4×Dic3—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C22×C32#12111yescharacteristic
251C22×C32#12111yescharacteristic
252C22×C32#12111yescharacteristic
253C22×C32C2×SD1611yescharacteristic
254C22×C32#13511yescharacteristic
255C22×C32AGL(1,ℤ/8)11yescharacteristic
256C22×C32#13711yescharacteristic
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—81no—
261C2×C3⋊D3—81no—
262C2×C3⋊D3—81no—
263C2×C3⋊D3—81no—
264C32×C4—42no—
265C32×C4#12011yescharacteristic
266C32×C4#12311yescharacteristic
267C32×C4#12311yescharacteristic
268C32×C4#12411yescharacteristic
269C3×Dic3—22no—
270C3×Dic3—41no—
271C3×Dic3—81no—
272C3×Dic3—81no—
273C22×Q8D3211yescharacteristic
274C22×D4—91no—
275C2×SD16—182no—
276C2×SD16—182no—
277C2×SD16—182no—
278C22×C8—31no—
279C22×C8—91no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C22⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C42—31no—
285C4⋊C8—182no—
286#103—62no—
287#102—182no—
288#95—61no—
289#95—61no—
290C23×C3—21no—
291C23×C3D3×D411yescharacteristic
292C23×C3C2×#6711yescharacteristic
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3—122no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—121no—
306C22×D3—121no—
307C22×D3—121no—
308C22×D3—121no—
309C22×D3—121no—
310C22×D3—241no—
311C22×D3—241no—
312C22×D3—241no—
313C22×D3—241no—
314C3×Q8—24no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—42no—
320C3×Q8—42no—
321C3×Q8—42no—
322C3×Q8—41no—
323C3×Q8—41no—
324C3×Q8—41no—
325C3×Q8—41no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—32no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4#23511yescharacteristic
355C2×C3×C4#23511yescharacteristic
356C2×C3×C4#23511yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376C2×Dic3#21512yescomplemented
377D12—64no—
378D12—62no—
379D12—62no—
380D12—62no—
381D12—62no—
382D12—122no—
383D12—122no—
384D12—122no—
385D12—121no—
386D12—121no—
387D12—121no—
388D12—121no—
389C3×C8—121no—
390C3⋊C8—41no—
391C3⋊C8—64no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C2×C32#39411yescharacteristic
395C2×C32#46011yescharacteristic
396C2×C32#46111yescharacteristic
397C2×C32#46311yescharacteristic
398C2×C32#46411yescharacteristic
399C2×C32#46511yescharacteristic
400C2×C32#46811yescharacteristic
401C3⋊D3—82no—
402C24—181no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8#62612yes—
409C2×D4—92no—
410C2×D4—181no—
411C2×D4—181no—
412C2×D4—181no—
413C2×D4—181no—
414C2×D4—181no—
415C22×C4—21no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4C2×D3211yescharacteristic
421SD16—188no—
422C2×C8—61no—
423C2×C8—61no—
424C2×C8—61no—
425C2×C8—92no—
426C2×C8—181no—
427C2×C8—181no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4—61no—
432C22⋊C4—362no—
433C22⋊C4—362no—
434C42—61no—
435C42—61no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3#88411yescharacteristic
444C22×C3#88411yescharacteristic
445C22×C3D3×SD1611yescharacteristic
446C22×C3#91411yescharacteristic
447C22×C3#91811yescharacteristic
448C22×C3#91911yescharacteristic
449C22×C3#93011yescharacteristic
450C22×C3#93811yescharacteristic
451C22×C3#93911yescharacteristic
452C22×C3#93911yescharacteristic
453C22×C3C2×#21511yescharacteristic
454C22×C3#94211yescharacteristic
455C22×C3#94911yescharacteristic
456C22×C3#95011yescharacteristic
457C2×D3—124no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—242no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—242no—
468C2×D3—242no—
469C2×D3—242no—
470C2×D3—241no—
471C2×D3—241no—
472C2×D3—241no—
473C2×D3—241no—
474C2×D3—241no—
475C2×D3—241no—
476C2×D3—241no—
477C2×D3—241no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—44no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—62no—
486C3×C4—121no—
487C3×C4—241no—
488C3×C4—241no—
489C3×C4#88211yescharacteristic
490C3×C4#88311yescharacteristic
491C3×C4#88311yescharacteristic
492C3×C4#88511yescharacteristic
493C3×C4#88511yescharacteristic
494C3×C4#88611yescharacteristic
495C3×C4#92911yescharacteristic
496C3×C4#93711yescharacteristic
497Dic3—22no—
498Dic3—41no—
499Dic3—81no—
500Dic3—81no—
501C32#205511yescharacteristic, complemented, Sylow
502C23—182no—
503C23—361no—
504C23—361no—
505C23—361no—
506C23—361no—
507C23—361no—
508C23—361no—
509C23D3×#6711yescharacteristic
510Q8—22no—
511Q8—22no—
512Q8—41no—
513Q8—41no—
514D4—182no—
515D4—182no—
516D4—361no—
517D4—361no—
518C2×C4—22no—
519C2×C4—32no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4#380411yescharacteristic
534C2×C4#380411yescharacteristic
535C2×C4#380411yescharacteristic
536C2×C4C2×#62611yescharacteristic
537C2×C4#381111yescharacteristic
538C2×C4#381111yescharacteristic
539C8—121no—
540C8—182no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3#480711yescharacteristic
549C2×C3#481211yescharacteristic
550C2×C3#481811yescharacteristic
551C2×C3#481911yescharacteristic
552C2×C3#495911yescharacteristic
553C2×C3#496111yescharacteristic
554C2×C3#502711yescharacteristic
555C2×C3#502811yescharacteristic
556C2×C3#504811yescharacteristic
557C2×C3#504911yescharacteristic
558C2×C3#505711yescharacteristic
559C2×C3#508311yescharacteristic
560C2×C3#516311yescharacteristic
561C2×C3#518511yescharacteristic
562D3—244no—
563D3—242no—
564D3—242no—
565C22—362no—
566C22—362no—
567C22—362no—
568C22—721no—
569C22—721no—
570C22—721no—
571C22—721no—
572C22D3×#21511yescharacteristic
573C22#6393911yescharacteristic
574C22#6394811yescharacteristic
575C22#6394911yescharacteristic
576C22#6395811yescharacteristic
577C22#6397111yescharacteristic
578C22#6397811yescharacteristic
579C4—42no—
580C4—62no—
581C4—121no—
582C4—241no—
583C4—241no—
584C4#6395311yescharacteristic
585C4#6396611yescharacteristic
586C4#6397511yescharacteristic
587C4#6398111yescharacteristic
588C3—21no—
589C3#6968011yescharacteristic, complemented
590C3#7028011yescharacteristic, complemented
591C2—722no—
592C2#1059156511yescharacteristic
593C2#1059156811yescharacteristic
594C2#1059158511yescharacteristic
595C2#1059158911yescharacteristic
596C2#1059160711yescharacteristic
597C2#1059161711yescharacteristic
598C2#1059171211yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q8D32
hypocenterC32#2055
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
2. C3×#5229C2semidirect
3. C2×C3×#835C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
7. #10589163C2semidirect
32. #5229D3semidirect
33. C2×#835D3semidirect
153. C2×C3×Dic3SD16semidirect
376. C2×Dic3#215semidirect
501. C32#2055semidirect
589. C3#69680semidirect
590. C3#70280semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C3×#52292
C2×C3×#8352
#105913202
C2×Dic3⋊(C3⋊C8)2
C2×#635642
#105891632
#702803
#696803