Finite Group Databasebeta

← #11791459

Subgroups — #11791459

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63911C211yesmaximal, characteristic
2C2×#63636C211yesmaximal, characteristic, complemented
3C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#70161—31nomaximal
9#69487—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#626—21no—
13C22×#626—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3—21no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20#63911—22no—
21#63911C414yescomplemented
22#63636—22no—
23C3×C3⋊#95—21no—
24C3×#809—22no—
25Dic3⋊(C3⋊C8)—22no—
26#63564—22no—
27#63562—22no—
28C2×#940—31no—
29C2×#874—31no—
30C2×C3×#102—31no—
31C3×C4×C4⋊C4—31no—
32C2×#832—31no—
33C2×#821—31no—
34C2×Dic3⋊C8—31no—
35Dic3×C4⋊C4D311yescharacteristic, complemented
36C2×#809—31no—
37C2×#809—31no—
38C2×#809—31no—
39C2×#809—31no—
40C2×#809—61no—
41C2×#809D311yescharacteristic, complemented
42C2×C4⋊(C3⋊C8)—31no—
43C23×C3⋊D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)C2×C412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C2×#626—24no—
63C2×#626—24no—
64C2×#626—42no—
65C2×#626—42no—
66C2×#626—42no—
67C2×#626—42no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4D412yescomplemented
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3D412yescomplemented
75C3×C4×Dic3—42no—
76C3×C4×Dic3C2×C412yes—
77C3×C4×Dic3D412yes—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81#1982—91noSylow
82C22×C3×D4—31no—
83C22×#67—61no—
84C22×#67—61no—
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C22×D12—61no—
89C22×D12—61no—
90C22×D12C2×D311yescharacteristic
91C22×C3×C8—31no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C42—31no—
97C2×C3×C42—61no—
98#940—34no—
99#940—62no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4×Dic3—21no—
102C2×C4×Dic3C2×D311yescharacteristic
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106C22×C3⋊C8C2×D311yescharacteristic
107#874—34no—
108#874—62no—
109C3×#102—62no—
110C3×#95—61no—
111#832—62no—
112C3⋊#95—21no—
113#821—62no—
114Dic3⋊C8—62no—
115#809—22no—
116#809—62no—
117#809—64no—
118#809—62no—
119#809—62no—
120#809—62no—
121C4⋊(C3⋊C8)—62no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3×D3—22no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C2×C32×C4—22no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—41no—
149C4⋊(C3⋊D3)—41no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3C22⋊C412yes—
156C2×C3×Dic3C22⋊C412yes—
157C2×C3×Dic3D812yes—
158C2×C3×Dic3SD1612yes—
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—41no—
162C3×D12—41no—
163#626—48no—
164#626—48no—
165C3⋊(C3⋊C8)—41no—
166C3×C3⋊C8—41no—
167C2×#127—91no—
168C2×C4⋊C8—91no—
169C2×#102—31no—
170C2×#102—91no—
171C2×#102—91no—
172C2×#102—91no—
173C4×C4⋊C4—31no—
174C24×C3—61no—
175C23×D3—21no—
176C23×D3—61no—
177C23×D3—61no—
178C23×D3—121no—
179C2×C3×D4—32no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—41no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—64no—
195C2×#67—64no—
196C2×#67—122no—
197C2×#67—122no—
198C2×#67—122no—
199C2×#67—122no—
200C22×Dic3—21no—
201C22×Dic3#6711yescharacteristic
202C22×Dic3#6711yescharacteristic
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—64no—
222C2×D12—64no—
223C2×D12—61no—
224C2×D12—61no—
225C2×D12—121no—
226C2×D12—121no—
227C2×D12—121no—
228C2×D12—122no—
229C2×D12—122no—
230C2×D12—122no—
231C2×D12—122no—
232C2×D12C4×D312yes—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4D1212yescomplemented
243C3×C4⋊C4#6712yescomplemented
244C3×C42—32no—
245C3×C42—32no—
246C3×C42—122no—
247C4⋊Dic3—21no—
248C4⋊Dic3D1212yescomplemented
249C4×Dic3—42no—
250C4×Dic3C4×D312yes—
251C4×Dic3D1212yes—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—121no—
263C2×C3⋊C8—121no—
264C22×C32C2×C22⋊C411yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32C2×D811yescharacteristic
268C22×C32C2×SD1611yescharacteristic
269C22×C32AGL(1,ℤ/8)11yescharacteristic
270C22×C32AGL(1,ℤ/8)11yescharacteristic
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—81no—
275C2×C3⋊D3—81no—
276C2×C3⋊D3—81no—
277C2×C3⋊D3—81no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3—81no—
282C2×C3×D3—81no—
283C2×C3×D3—81no—
284C2×C3×D3—81no—
285C32×C4—42no—
286C32×C4C4×D411yescharacteristic
287C32×C4C4×D411yescharacteristic
288C32×C4#12411yescharacteristic
289C32×C4#12711yescharacteristic
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3#10214yescomplemented
293C22×D4—31no—
294C22×D4—91no—
295C22×D4—181no—
296C22×D4—181no—
297C22×C8—31no—
298C22×C8—91no—
299#127—94no—
300#127—182no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4D3211yescharacteristic
303C2×C42—31no—
304C2×C42—61no—
305C4⋊C8—182no—
306#102—62no—
307#102—182no—
308#102—182no—
309#102—182no—
310#95—61no—
311C23×C3—21no—
312C23×C3—62no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3—121no—
319C23×C3D3×D411yescharacteristic
320C23×C3C2×#6711yescharacteristic
321C22×D3—22no—
322C22×D3—41no—
323C22×D3—41no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—122no—
331C22×D3—122no—
332C22×D3—122no—
333C22×D3—121no—
334C22×D3—121no—
335C22×D3—121no—
336C22×D3—121no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—121no—
340C22×D3—121no—
341C22×D3—121no—
342C22×D3—121no—
343C22×D3—121no—
344C22×D3—121no—
345C22×D3—241no—
346C22×D3—241no—
347C22×D3—241no—
348C22×D3—241no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—121no—
352C3×D4—121no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—32no—
365C2×C3×C4—42no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—81no—
374C2×C3×C4—81no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4C2×C4×D311yescharacteristic
378C2×C3×C4C2×C4×D311yescharacteristic
379C2×C3×C4C2×D1211yescharacteristic
380C2×C3×C4C2×D1211yescharacteristic
381C2×C3×C4C2×D1211yescharacteristic
382C2×C3×C4#23511yescharacteristic
383C2×C3×C4#23511yescharacteristic
384C2×C3×C4#23511yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4#23711yescharacteristic
388C2×C3×C4C2×#6711yescharacteristic
389#67—128no—
390#67—128no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—41no—
395C2×Dic3—41no—
396C2×Dic3(C2×D3)⋊C412yes—
397C2×Dic3(C2×D3)⋊C412yes—
398C2×Dic3#21312yes—
399C2×Dic3#21512yes—
400D12—22no—
401D12—22no—
402D12—41no—
403D12—41no—
404D12—64no—
405D12—62no—
406D12—62no—
407D12—62no—
408D12—62no—
409D12—122no—
410D12—122no—
411D12—122no—
412D12—128no—
413D12—128no—
414D12—121no—
415D12—121no—
416D12—121no—
417D12—121no—
418C3×C8—121no—
419C3⋊C8—41no—
420C3⋊C8—122no—
421C3⋊C8—121no—
422C3⋊C8—121no—
423C2×C32#39011yescharacteristic
424C2×C32C2×#10211yescharacteristic
425C2×C32#41811yescharacteristic
426C2×C32#45911yescharacteristic
427C2×C32#45911yescharacteristic
428C2×C32#46011yescharacteristic
429C2×C32#46011yescharacteristic
430C3⋊D3—82no—
431C3×D3—82no—
432C24—61no—
433C24—181no—
434C2×D4—32no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—61no—
440C2×D4—92no—
441C2×D4—184no—
442C2×D4—184no—
443C2×D4—181no—
444C2×D4—181no—
445C2×D4—181no—
446C2×D4—181no—
447C2×D4—181no—
448C2×D4—362no—
449C2×D4—362no—
450C2×D4—362no—
451C2×D4—362no—
452C22×C4—21no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—61no—
456C22×C4C2×D3211yescharacteristic
457C2×C8—61no—
458C2×C8—61no—
459C2×C8—61no—
460C2×C8—181no—
461C2×C8—181no—
462C2×C8—181no—
463C4⋊C4—21no—
464C4⋊C4—32no—
465C4⋊C4—61no—
466C4⋊C4#62612yescomplemented
467C42—32no—
468C42—32no—
469C42—122no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3—241no—
481C22×C3—241no—
482C22×C3—241no—
483C22×C3—241no—
484C22×C3D3×C22⋊C411yescharacteristic
485C22×C3#88411yescharacteristic
486C22×C3D3×D811yescharacteristic
487C22×C3#91111yescharacteristic
488C22×C3D3×SD1611yescharacteristic
489C22×C3#91411yescharacteristic
490C22×C3C2×(C2×D3)⋊C411yescharacteristic
491C22×C3#93011yescharacteristic
492C22×C3#93011yescharacteristic
493C22×C3C2×#21311yescharacteristic
494C22×C3#93911yescharacteristic
495C22×C3C2×#21511yescharacteristic
496C22×C3#94911yescharacteristic
497C22×C3#94911yescharacteristic
498C2×D3—42no—
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—81no—
502C2×D3—81no—
503C2×D3—81no—
504C2×D3—81no—
505C2×D3—124no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—242no—
513C2×D3—242no—
514C2×D3—242no—
515C2×D3—242no—
516C2×D3—242no—
517C2×D3—242no—
518C2×D3—241no—
519C2×D3—241no—
520C2×D3—241no—
521C2×D3—241no—
522C2×D3—241no—
523C2×D3—241no—
524C2×D3—241no—
525C2×D3—241no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—34no—
531C3×C4—42no—
532C3×C4—42no—
533C3×C4—62no—
534C3×C4—82no—
535C3×C4—122no—
536C3×C4C4×D1211yescharacteristic
537C3×C4C4×D1211yescharacteristic
538C3×C4#87411yescharacteristic
539C3×C4#87511yescharacteristic
540C3×C4#67⋊C411yescharacteristic
541C3×C4#88511yescharacteristic
542C3×C4C4×#6711yescharacteristic
543C3×C4#94011yescharacteristic
544Dic3—22no—
545Dic3—42no—
546Dic3#80914yescomplemented
547C32#198211yescharacteristic, complemented, Sylow
548C23—62no—
549C23—121no—
550C23—121no—
551C23—121no—
552C23—121no—
553C23—121no—
554C23—121no—
555C23—182no—
556C23—361no—
557C23—361no—
558C23—361no—
559C23—361no—
560C23—361no—
561C23—361no—
562C23D3×#6711yescharacteristic
563D4—62no—
564D4—62no—
565D4—121no—
566D4—121no—
567D4—182no—
568D4—182no—
569D4—368no—
570D4—368no—
571D4—361no—
572D4—361no—
573C2×C4—22no—
574C2×C4—32no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—61no—
581C2×C4—61no—
582C2×C4—62no—
583C2×C4—121no—
584C2×C4—121no—
585C2×C4#379811yescharacteristic
586C2×C4C4×D3211yescharacteristic
587C2×C4D3×D1211yescharacteristic
588C2×C4D3×D1211yescharacteristic
589C2×C4#380411yescharacteristic
590C2×C4C2×#62611yescharacteristic
591C8—121no—
592C8—361no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—242no—
601C2×C3#476211yescharacteristic
602C2×C3D3×#10211yescharacteristic
603C2×C3#477011yescharacteristic
604C2×C3#478611yescharacteristic
605C2×C3#493911yescharacteristic
606C2×C3#495711yescharacteristic
607C2×C3C2×#80911yescharacteristic
608C2×C3#500111yescharacteristic
609C2×C3#501511yescharacteristic
610C2×C3#501511yescharacteristic
611C2×C3#502711yescharacteristic
612C2×C3#502711yescharacteristic
613C2×C3#515011yescharacteristic
614C2×C3#516311yescharacteristic
615D3—82no—
616D3—244no—
617D3—242no—
618D3—242no—
619C22—122no—
620C22—122no—
621C22—122no—
622C22—241no—
623C22—241no—
624C22—241no—
625C22—241no—
626C22—362no—
627C22—362no—
628C22—362no—
629C22—721no—
630C22—721no—
631C22—721no—
632C22—721no—
633C22#6390611yescharacteristic
634C22D3×(C2×D3)⋊C411yescharacteristic
635C22D3×#21311yescharacteristic
636C22#6392511yescharacteristic
637C22D3×#21511yescharacteristic
638C22#6393911yescharacteristic
639C22#6397811yescharacteristic
640C4—34no—
641C4—42no—
642C4—62no—
643C4—122no—
644C4#6385211yescharacteristic
645C4#6388011yescharacteristic
646C4C4×#62611yescharacteristic
647C4#6391111yescharacteristic
648C3—21no—
649C3#6948711yescharacteristic, complemented
650C3#7016111yescharacteristic, complemented
651C2—242no—
652C2—722no—
653C2#1059054711yescharacteristic
654C2#1059054911yescharacteristic
655C2D3×#80911yescharacteristic
656C2#1059059211yescharacteristic
657C2#1059138311yescharacteristic
658C2#1059148111yescharacteristic
659C2#1059161711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1982
LCSG ▷ C2×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. C2×#63636C2semidirect
3. C3×Dic3×C4⋊C4C2semidirect
4. C2×C3×#809C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63564C2semidirect
7. C2×#63562C2semidirect
21. #63911C4semidirect
35. Dic3×C4⋊C4D3semidirect
41. C2×#809D3semidirect
69. C32×C4⋊C4D4semidirect
74. C3×C4⋊Dic3D4semidirect
242. C3×C4⋊C4D12semidirect
243. C3×C4⋊C4#67semidirect
248. C4⋊Dic3D12semidirect
292. C3×Dic3#102semidirect
466. C4⋊C4#626semidirect
546. Dic3#809semidirect
547. C32#1982semidirect
649. C3#69487semidirect
650. C3#70161semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
C2×#636362
C3×Dic3×C4⋊C42
C2×C3×#8092
C2×Dic3⋊(C3⋊C8)2
C2×#635642
C2×#635622
#701613
#694873