Finite Group Databasebeta

← #11793170

Subgroups — #11793170

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C2×#63657C211yesmaximal, characteristic, complemented
3C3×#5212C211yesmaximal, characteristic, complemented
4C2×#63576C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71679—31nomaximal
9#69523—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×D12C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#217—21no—
16C3×#930—22no—
17C3×#930—22no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22#63657—22no—
23C3×C3⋊#95—21no—
24#63576—22no—
25#63562—22no—
26#63562—22no—
27C2×C3×#121—31no—
28C2×#930D311yescharacteristic
29C3×#380—31no—
30C2×#832—31no—
31C2×#832—31no—
32#5212D311yescharacteristic, complemented
33C2×#830—31no—
34C2×#830—31no—
35C2×#830—61no—
36C2×#809—31no—
37C2×#809—31no—
38C2×#807—31no—
39C2×#807—31no—
40#4529—31no—
41#4529—31no—
42C24×C32D411yescharacteristic
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C2×C3×#67—24no—
53C2×C3×#67—42no—
54C2×C3×#67—42no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12D412yes—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)D412yescomplemented
70C3×#217—42no—
71C3×(C2×D3)⋊C4—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3D412yes—
78#2033—91noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—21no—
82C23×C3×C4C2×D311yescharacteristic
83C23×C3×C4C2×D311yescharacteristic
84C22×#67—21no—
85C22×D12C2×D311yescharacteristic
86C3×#121—62no—
87C3×#121—62no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C22⋊C4—61no—
92C2×C3×C22⋊C4—61no—
93C2×#217—21no—
94#930—22no—
95#930—22no—
96C2×(C2×D3)⋊C4—21no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—31no—
104C22×C3⋊C8—61no—
105C22×C3⋊C8—61no—
106C3×#95—61no—
107#832—62no—
108#832—62no—
109C3⋊#95—21no—
110#830—62no—
111#830—62no—
112#830—64no—
113#809—62no—
114#809—62no—
115#807—62no—
116#807—62no—
117C23×C32—21no—
118C23×C32—21no—
119C23×C32—21no—
120C23×C32—21no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32D812yes—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C3×#67—48no—
146C2×C3×Dic3—22no—
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×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—41no—
158C3×D12—41no—
159C3⋊(C3⋊C8)—22no—
160C3⋊(C3⋊C8)—41no—
161C2×#121—31no—
162C2×#107—91no—
163C2×#102—91no—
164C2×#102—91no—
165C2×C22⋊C8—91no—
166#380—31no—
167#340—91no—
168C24×C3—21no—
169C24×C3—61no—
170C24×C3#6711yescharacteristic
171C24×C3#6711yescharacteristic
172C23×D3—21no—
173C2×C3×D4—32no—
174C2×C3×D4—64no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—122no—
181C2×C3×D4—122no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—41no—
199C22×C3×C4—41no—
200C22×C3×C4—41no—
201C22×C3×C4—41no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4#6711yescharacteristic
206C22×C3×C4#6711yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C2×#67—24no—
210C2×#67—42no—
211C2×#67—42no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12#6712yes—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C22⋊C4—64no—
228C3×C22⋊C4—122no—
229#217—42no—
230(C2×D3)⋊C4—24no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—21no—
236C4⋊Dic3#6712yes—
237C2×C3⋊C8—32no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—62no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—121no—
252C2×C3⋊C8—121no—
253C2×C3⋊C8—121no—
254C2×C3⋊C8—121no—
255C22×C32—22no—
256C22×C32—22no—
257C22×C32—22no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32#12011yescharacteristic
263C22×C32#12111yescharacteristic
264C22×C32#12311yescharacteristic
265C22×C32C2×D811yescharacteristic
266C22×C32#13511yescharacteristic
267C22×C32AGL(1,ℤ/8)11yescharacteristic
268C22×C32#13711yescharacteristic
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—81no—
273C2×C3×D3—81no—
274C2×C3×D3—81no—
275C2×C3×D3—81no—
276C32×C4—41no—
277C32×C4#12111yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12311yescharacteristic
280C32×C4#12411yescharacteristic
281C3×Dic3—42no—
282C3×Dic3—81no—
283C3×Dic3—81no—
284C22×D4—31no—
285C22×D4—61no—
286C23×C4D3211yescharacteristic
287C22×C8—91no—
288C22×C8—91no—
289#121—62no—
290#121—62no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C22⋊C4—61no—
295C2×C22⋊C4—61no—
296#107—182no—
297#102—182no—
298#102—182no—
299C22⋊C8—182no—
300#95—61no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—62no—
322C23×C3—121no—
323C23×C3—121no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3—121no—
327C23×C3—121no—
328C23×C3#21312yes—
329C23×C3#21312yes—
330C23×C3C2×#6711yescharacteristic
331C23×C3C2×#6711yescharacteristic
332C22×D3—22no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—41no—
337C22×D3—41no—
338C22×D3—41no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—128no—
342C3×D4—121no—
343C3×D4—121no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—62no—
372C2×C3×C4—121no—
373C2×C3×C4—121no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4#23511yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4#23711yescharacteristic
387C2×C3×C4#23711yescharacteristic
388C2×C3×C4#23711yescharacteristic
389C2×C3×C4#23711yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392#67—48no—
393C2×Dic3—22no—
394C2×Dic3—41no—
395C2×Dic3—41no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—41no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C2×Dic3—41no—
402D12—22no—
403D12—22no—
404D12—41no—
405D12—41no—
406C3⋊C8—62no—
407C3⋊C8—62no—
408C3⋊C8—122no—
409C3⋊C8—122no—
410C3⋊C8—121no—
411C3⋊C8—121no—
412C2×C32—42no—
413C2×C32#39411yescharacteristic
414C2×C32#44711yescharacteristic
415C2×C32#45211yescharacteristic
416C2×C32#46611yescharacteristic
417C2×C32#46811yescharacteristic
418C2×C32#48011yescharacteristic
419C2×C32#48211yescharacteristic
420C3×D3—82no—
421C24—61no—
422C24#62511yescharacteristic
423C2×D4—32no—
424C2×D4—64no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—122no—
431C2×D4—122no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4#62511yescharacteristic
442C22×C4C2×D3211yescharacteristic
443C2×C8—92no—
444C2×C8—181no—
445C2×C8—181no—
446C2×C8—181no—
447C2×C8—181no—
448C2×C8—181no—
449C4⋊C4—32no—
450C4⋊C4—61no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C22⋊C4—64no—
456C22⋊C4—122no—
457C22×C3—24no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—122no—
488C22×C3—241no—
489C22×C3—241no—
490C22×C3—241no—
491C22×C3—241no—
492C22×C3#92911yescharacteristic
493C22×C3C2×#21311yescharacteristic
494C22×C3C2×#21311yescharacteristic
495C22×C3#93211yescharacteristic
496C22×C3#93511yescharacteristic
497C22×C3#93711yescharacteristic
498C22×C3#93911yescharacteristic
499C22×C3#93911yescharacteristic
500C22×C3#94211yescharacteristic
501C22×C3#94911yescharacteristic
502C22×C3#95011yescharacteristic
503C22×C3#95011yescharacteristic
504C22×C3#95111yescharacteristic
505C22×C3#95311yescharacteristic
506C2×D3—42no—
507C2×D3—42no—
508C2×D3—42no—
509C2×D3—81no—
510C2×D3—81no—
511C2×D3—81no—
512C2×D3—81no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—42no—
518C3×C4—41no—
519C3×C4—41no—
520C3×C4—122no—
521C3×C4—241no—
522C3×C4—241no—
523C3×C4#88311yescharacteristic
524C3×C4#88411yescharacteristic
525C3×C4#88411yescharacteristic
526C3×C4#88511yescharacteristic
527C3×C4#93511yescharacteristic
528C3×C4#93611yescharacteristic
529C3×C4#93811yescharacteristic
530C3×C4#93911yescharacteristic
531Dic3—42no—
532Dic3—81no—
533Dic3—81no—
534C32#203311yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—62no—
542C23—121no—
543C23—121no—
544C23—121no—
545C23—121no—
546C23—121no—
547C23—121no—
548C23#371312yes—
549C23C2×#62511yescharacteristic
550D4—62no—
551D4—62no—
552D4—128no—
553D4—121no—
554D4—121no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—62no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—121no—
567C2×C4—121no—
568C2×C4—121no—
569C2×C4—121no—
570C2×C4—121no—
571C2×C4#380411yescharacteristic
572C2×C4#380411yescharacteristic
573C2×C4#380511yescharacteristic
574C2×C4D3×#6711yescharacteristic
575C2×C4D3×#6711yescharacteristic
576C2×C4#381111yescharacteristic
577C8—182no—
578C8—361no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—44no—
587C2×C3—42no—
588C2×C3—42no—
589C2×C3—242no—
590C2×C3#495911yescharacteristic
591C2×C3#496711yescharacteristic
592C2×C3#500311yescharacteristic
593C2×C3#503311yescharacteristic
594C2×C3#503511yescharacteristic
595C2×C3#503611yescharacteristic
596C2×C3#503811yescharacteristic
597C2×C3#503811yescharacteristic
598C2×C3#504211yescharacteristic
599C2×C3#504711yescharacteristic
600C2×C3#504911yescharacteristic
601C2×C3#521711yescharacteristic
602C2×C3#522211yescharacteristic
603C2×C3#523911yescharacteristic
604D3—82no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—122no—
613C22—122no—
614C22—122no—
615C22—241no—
616C22—241no—
617C22—241no—
618C22—241no—
619C22C2×#371311yescharacteristic
620C22#6382211yescharacteristic
621C22#6382311yescharacteristic
622C22#6382711yescharacteristic
623C22#6396111yescharacteristic
624C22#6397611yescharacteristic
625C22#6398011yescharacteristic
626C4—41no—
627C4—122no—
628C4—241no—
629C4—241no—
630C4#6395811yescharacteristic
631C4#6395911yescharacteristic
632C4#6396911yescharacteristic
633C4#6397111yescharacteristic
634C3—21no—
635C3#6952311yescharacteristic, complemented
636C3#7167911yescharacteristic, complemented
637C2—42no—
638C2—242no—
639C2#1059108911yescharacteristic
640C2#1059109011yescharacteristic
641C2#1059116011yescharacteristic
642C2#1059116611yescharacteristic
643C2#1059117011yescharacteristic
644C2#1059118011yescharacteristic
645C2#1059170811yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32#2033
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63657C2semidirect
3. C3×#5212C2semidirect
4. C2×#63576C2semidirect
5. C2×#63562C2semidirect
6. C2×#63562C2semidirect
7. #10589163C2semidirect
32. #5212D3semidirect
69. C2×C3⋊(C3⋊C8)D4semidirect
534. C32#2033semidirect
635. C3#69523semidirect
636. C3#71679semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C2×#636572
C3×#52122
C2×#635762
C2×#635622
#105891632
#716793
#695233