Finite Group Databasebeta

← #11857972

Subgroups — #11857972

Order 1152.

1989 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4#10591107C212yesmaximal, complemented
5#10591106C214yesmaximal, complemented
6#10591105C214yesmaximal, complemented
7#10591096C212yesmaximal, complemented
8#83768—31nomaximal
9#82213—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×#638—21no—
12C2×#3828—24no—
13C2×#3828—21no—
14C2×#3828—21no—
15C2×#3828C418yescomplemented
16C2×#3828C2212yes—
17C2×#3828C2212yes—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3—21no—
20C22×#634C2211yescharacteristic
21C2×C3×#217—21no—
22C3×#926—21no—
23C3×#926—21no—
24C3×#926C2212yes—
25C3×#926C2212yescomplemented
26C2×C3×C4⋊Dic3C2212yescomplemented
27C2×C3×C4×Dic3—21no—
28C2×C3×#208—24no—
29C2×C3×#208C2212yes—
30C2×C3×#208C2212yescomplemented
31C22×C3×C3⋊C8C2212yescomplemented
32#63567C2218yescomplemented
33#63564C2218yescomplemented
34C22×#235—31no—
35C22×#235—31no—
36C22×#235—61no—
37C22×C3×M16—31no—
38C2×C3×#117—31no—
39C2×#926D311yescharacteristic, complemented
40C22×#208D311yescharacteristic, complemented
41#5133—34no—
42#5131—32no—
43#5120—32no—
44#5113—34no—
45#5004—32no—
46#5002—34no—
47#5001—32no—
48#4966—34no—
49C24×C32D411yescharacteristic
50C23×C3⋊D3—21no—
51C22×C32×C4C2×C414yes—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D411yescharacteristic
55C22×C32×C4D414yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—28no—
60C2×#638—22no—
61C2×#638—22no—
62C22×C3⋊Dic3—21no—
63#3828—28no—
64#3828—28no—
65#3828—24no—
66#3828—24no—
67#3828C2×C418yes—
68#3828C2×C418yescomplemented
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)C2×C414yescomplemented
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C4×C3⋊D3—28no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×#634—21no—
77C2×#634—22no—
78C2×#634C2×C414yescomplemented
79C2×#634C2312yes—
80C22×C3×Dic3—22no—
81C3×#217—22no—
82C3×#217—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3C2314yes—
85C3×C4×Dic3—22no—
86C3×C4×Dic3—22no—
87C3×#208—24no—
88C3×#208—24no—
89C2×C3×C3⋊C8—24no—
90C2×C3×C3⋊C8C2314yes—
91#2896—91noSylow
92C23×C3×C4—21no—
93C23×C3×C4C2×D311yescharacteristic
94C23×C3×C4C2×D311yescharacteristic
95C22×#67—62no—
96C22×#67—61no—
97C22×#67—61no—
98C2×#235—38no—
99C2×#235—38no—
100C2×#235—32no—
101C2×#235—32no—
102C2×#235—32no—
103C2×#235—32no—
104C2×#235—68no—
105C2×#235—62no—
106C2×#235—62no—
107C2×#235—68no—
108C2×#235—62no—
109C2×#235—62no—
110C2×#235—64no—
111C2×#235—61no—
112C2×#235—61no—
113C2×#235—64no—
114C2×#235—61no—
115C2×#235—61no—
116C22×D12—31no—
117C22×D12—31no—
118C22×D12—61no—
119C22×C4×D3—62no—
120C22×C4×D3—61no—
121C22×C4×D3—61no—
122C22×Dic6—31no—
123C22×Dic6—31no—
124C22×Dic6—61no—
125C2×C3×M16—32no—
126C2×C3×M16—32no—
127C2×C3×M16—64no—
128C22×C3×C8—32no—
129C3×#117—32no—
130C3×#117—32no—
131C3×#117—61no—
132C3×#117—61no—
133C2×C3×C4⋊C4—32no—
134C2×C3×C22⋊C4—61no—
135C2×C3×C42—61no—
136C2×#217—21no—
137#926—21no—
138#926—21no—
139#926C2×D312yes—
140#926C2×D312yescomplemented
141C2×C4⋊Dic3C2×D312yescomplemented
142C2×C4×Dic3—21no—
143C2×#208—24no—
144C2×#208C2×D312yes—
145C2×#208C2×D312yescomplemented
146C22×C3⋊C8C2×D312yescomplemented
147#821—38no—
148#816—38no—
149#810—38no—
150#809—38no—
151C23×C32—42no—
152C23×C32C22⋊C414yes—
153C23×C32C2×D411yescharacteristic
154C23×C32C2×D411yescharacteristic
155C23×C32C2×D411yescharacteristic
156C22×C3⋊D3—24no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—44no—
159C2×C32×C4C22⋊C414yes—
160C2×C32×C4C22⋊C414yes—
161C2×C32×C4C22⋊C414yes—
162C2×C32×C4C22×C412yes—
163C2×C32×C4C22×C412yes—
164C2×C32×C4C22×C412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2411yescharacteristic
172#638—28no—
173#638—28no—
174C2×C3⋊Dic3—24no—
175C2×C3⋊Dic3—22no—
176C4⋊(C3⋊D3)—24no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)C22×C414yes—
179C4×C3⋊D3—28no—
180C4×C3⋊D3—28no—
181#634—24no—
182#634—22no—
183#634C22×C414yes—
184C2×C3×Dic3—24no—
185C2×C3×Dic3—44no—
186C3×C3⋊C8—24no—
187C22×#41—91no—
188C22×M16—31no—
189C2×#117—31no—
190#419—92no—
191#418—92no—
192#417—94no—
193#416—94no—
194C24×C3—21no—
195C24×C3D1211yescharacteristic
196C24×C3#6711yescharacteristic
197C23×D3—62no—
198C23×D3—61no—
199C23×D3—61no—
200C22×C3×C4—24no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—24no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—62no—
209C22×C3×C4C4×D314yes—
210C22×C3×C4C4×D314yes—
211C22×C3×C4D1211yescharacteristic
212C22×C3×C4D1211yescharacteristic
213C22×C3×C4D1211yescharacteristic
214C22×C3×C4D1214yes—
215C22×C3×C4#6711yescharacteristic
216C22×C3×C4#6711yescharacteristic
217C22×C3×C4#6711yescharacteristic
218C22×C3×C4#6714yes—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—616no—
226C2×#67—64no—
227C2×#67—64no—
228C2×#67—68no—
229C2×#67—68no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67—62no—
233C2×#67—62no—
234C22×Dic3—22no—
235C22×Dic3—62no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238#235—38no—
239#235—38no—
240#235—38no—
241#235—38no—
242#235—68no—
243#235—68no—
244#235—616no—
245#235—616no—
246#235—68no—
247#235—68no—
248#235—68no—
249#235—68no—
250#235—68no—
251#235—68no—
252#235—64no—
253#235—64no—
254#235—64no—
255#235—64no—
256C2×D12—34no—
257C2×D12—34no—
258C2×D12—32no—
259C2×D12—32no—
260C2×D12—64no—
261C2×D12—62no—
262C2×D12—64no—
263C2×D12—62no—
264C2×D12—61no—
265C2×D12—62no—
266C2×D12—61no—
267C2×D12—62no—
268C2×C4×D3—616no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—68no—
272C2×C4×D3—68no—
273C2×C4×D3—62no—
274C2×C4×D3—62no—
275C2×C4×D3—62no—
276C2×C4×D3—62no—
277C2×Dic6—34no—
278C2×Dic6—34no—
279C2×Dic6—32no—
280C2×Dic6—32no—
281C2×Dic6—64no—
282C2×Dic6—62no—
283C2×Dic6—62no—
284C2×Dic6—64no—
285C2×Dic6—61no—
286C2×Dic6—62no—
287C2×Dic6—61no—
288C2×Dic6—62no—
289C3×M16—64no—
290C3×M16—64no—
291C2×C3×C8—34no—
292C2×C3×C8—64no—
293C3×C4⋊C4—34no—
294C3×C4⋊C4—62no—
295C3×C22⋊C4—62no—
296C3×C22⋊C4—62no—
297C3×C42—62no—
298C3×C42—62no—
299#217—22no—
300#217—22no—
301C4⋊Dic3—22no—
302C4⋊Dic3C22×D314yes—
303C4×Dic3—22no—
304C4×Dic3—22no—
305#208—24no—
306#208—24no—
307C2×C3⋊C8—24no—
308C2×C3⋊C8C22×D314yes—
309C22×C32—22no—
310C22×C32—22no—
311C22×C32—22no—
312C22×C32—44no—
313C22×C32C2×C22⋊C412yes—
314C22×C32C2×C22⋊C412yes—
315C22×C32C2×C22⋊C412yes—
316C22×C32C22×D411yescharacteristic
317C2×C3⋊D3—24no—
318C2×C3⋊D3—48no—
319C2×C3⋊D3—44no—
320C32×C4C2×C22⋊C412yes—
321C32×C4C2×C22⋊C412yes—
322C32×C4C2×C22⋊C412yes—
323C32×C4C23×C411yescharacteristic
324C32×C4C22×D411yescharacteristic
325C3⋊Dic3—24no—
326C3×Dic3—44no—
327C2×#41—98no—
328C2×#41—92no—
329C2×#41—92no—
330C2×#41—184no—
331C2×#41—181no—
332C2×#41—181no—
333C22×Q8—91no—
334C22×D4—91no—
335C22×D4—181no—
336C23×C4—181no—
337C23×C4D3211yescharacteristic
338C2×M16—32no—
339C2×M16—32no—
340C2×M16—64no—
341C22×C8—32no—
342#117—32no—
343#117—32no—
344#117—61no—
345#117—61no—
346C2×C4⋊C4—32no—
347C2×C22⋊C4—61no—
348C2×C42—61no—
349#103—98no—
350#102—98no—
351C23×C3—24no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—44no—
358C23×C3(C2×D3)⋊C414yes—
359C23×C3(C2×D3)⋊C414yes—
360C23×C3C2×D1211yescharacteristic
361C23×C3C2×D1211yescharacteristic
362C23×C3C2×D1211yescharacteristic
363C23×C3C2×#6711yescharacteristic
364C23×C3C2×#6711yescharacteristic
365C23×C3C2×#6711yescharacteristic
366C22×D3—64no—
367C22×D3—68no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—128no—
373C22×D3—124no—
374C22×D3—124no—
375C2×C3×C4—21no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—64no—
389C2×C3×C4—124no—
390C2×C3×C4(C2×D3)⋊C414yes—
391C2×C3×C4(C2×D3)⋊C414yes—
392C2×C3×C4(C2×D3)⋊C414yes—
393C2×C3×C4(C2×D3)⋊C414yes—
394C2×C3×C4(C2×D3)⋊C414yes—
395C2×C3×C4(C2×D3)⋊C414yes—
396C2×C3×C4C2×C4×D312yes—
397C2×C3×C4C2×C4×D312yes—
398C2×C3×C4C2×C4×D312yes—
399C2×C3×C4C2×C4×D312yes—
400C2×C3×C4C2×C4×D312yes—
401C2×C3×C4C2×C4×D312yes—
402C2×C3×C4C2×D1211yescharacteristic
403C2×C3×C4C2×D1211yescharacteristic
404C2×C3×C4C2×D1212yes—
405C2×C3×C4C2×D1212yes—
406C2×C3×C4C2×D1212yes—
407C2×C3×C4C2×D1211yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C2×#6711yescharacteristic
410C2×C3×C4C2×#6712yes—
411C2×C3×C4C2×#6712yes—
412C2×C3×C4C2×#6712yes—
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416#67—616no—
417#67—616no—
418#67—68no—
419#67—68no—
420#67—68no—
421#67—68no—
422C2×Dic3—24no—
423C2×Dic3—44no—
424C2×Dic3—64no—
425C2×Dic3—68no—
426C2×Dic3—64no—
427C2×Dic3—64no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430D12—34no—
431D12—34no—
432D12—64no—
433D12—64no—
434D12—68no—
435D12—64no—
436D12—64no—
437D12—62no—
438D12—62no—
439C4×D3—616no—
440C4×D3—616no—
441C4×D3—68no—
442C4×D3—68no—
443C4×D3—68no—
444C4×D3—68no—
445Dic6—34no—
446Dic6—34no—
447Dic6—64no—
448Dic6—64no—
449Dic6—68no—
450Dic6—64no—
451Dic6—64no—
452Dic6—62no—
453Dic6—62no—
454C3×C8—64no—
455C3⋊C8—24no—
456C2×C32—22no—
457C2×C32—22no—
458C2×C32—22no—
459C2×C32C22×C22⋊C411yescharacteristic
460C2×C32#57512yes—
461C3⋊D3—44no—
462C24—181no—
463C24#62611yescharacteristic
464#41—98no—
465#41—98no—
466#41—188no—
467#41—188no—
468#41—184no—
469#41—184no—
470C2×Q8—92no—
471C2×Q8—94no—
472C2×Q8—181no—
473C2×Q8—182no—
474C2×D4—92no—
475C2×D4—94no—
476C2×D4—188no—
477C2×D4—182no—
478C2×D4—182no—
479C2×D4—182no—
480C2×D4—181no—
481C22×C4—62no—
482C22×C4—181no—
483C22×C4—188no—
484C22×C4—182no—
485C22×C4—182no—
486C22×C4#62414yes—
487C22×C4#62611yescharacteristic
488C22×C4#62611yescharacteristic
489C22×C4#62611yescharacteristic
490C22×C4#62614yes—
491C22×C4C2×D3211yescharacteristic
492C22×C4C2×D3211yescharacteristic
493C22×C4C2×D3211yescharacteristic
494M16—64no—
495M16—64no—
496C2×C8—34no—
497C2×C8—64no—
498C4⋊C4—34no—
499C4⋊C4—62no—
500C22⋊C4—62no—
501C22⋊C4—62no—
502C42—62no—
503C42—62no—
504C22×C3—24no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3—48no—
520C22×C3C2×(C2×D3)⋊C412yes—
521C22×C3C2×(C2×D3)⋊C412yes—
522C22×C3C2×(C2×D3)⋊C412yes—
523C22×C3C2×(C2×D3)⋊C412yes—
524C22×C3C2×(C2×D3)⋊C412yes—
525C22×C3C2×(C2×D3)⋊C412yes—
526C22×C3C22×D1211yescharacteristic
527C22×C3C22×#6711yescharacteristic
528C2×D3—68no—
529C2×D3—64no—
530C2×D3—64no—
531C2×D3—1216no—
532C2×D3—128no—
533C2×D3—128no—
534C2×D3—128no—
535C2×D3—124no—
536C2×D3—124no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—124no—
543C3×C4C2×(C2×D3)⋊C412yes—
544C3×C4C2×(C2×D3)⋊C412yes—
545C3×C4C2×(C2×D3)⋊C412yes—
546C3×C4C2×(C2×D3)⋊C412yes—
547C3×C4C2×(C2×D3)⋊C412yes—
548C3×C4C2×(C2×D3)⋊C412yes—
549C3×C4C22×C4×D311yescharacteristic
550C3×C4C22×C4×D311yescharacteristic
551C3×C4C22×D1211yescharacteristic
552C3×C4C22×#6711yescharacteristic
553Dic3—44no—
554Dic3—68no—
555Dic3—64no—
556Dic3—64no—
557C32#289611yescharacteristic, complemented, Sylow
558C23—42no—
559C23—182no—
560C23—184no—
561C23—364no—
562C23#372214yes—
563C23C2×#62611yescharacteristic
564C23C2×#62611yescharacteristic
565C23C2×#62611yescharacteristic
566Q8—94no—
567Q8—182no—
568Q8—184no—
569D4—94no—
570D4—188no—
571D4—188no—
572D4—182no—
573D4—184no—
574C2×C4—64no—
575C2×C4—124no—
576C2×C4—182no—
577C2×C4—184no—
578C2×C4—188no—
579C2×C4—188no—
580C2×C4#372214yes—
581C2×C4#372214yes—
582C2×C4#372214yes—
583C2×C4C2×#62412yes—
584C2×C4C2×#62412yes—
585C2×C4C2×#62412yes—
586C2×C4C2×#62612yes—
587C2×C4C2×#62612yes—
588C2×C4C2×#62612yes—
589C2×C4C2×#62611yescharacteristic
590C2×C4C2×#62611yescharacteristic
591C2×C4C2×#62611yescharacteristic
592C2×C4C22×D3211yescharacteristic
593C8—64no—
594C2×C3—24no—
595C2×C3—22no—
596C2×C3—22no—
597C2×C3—22no—
598C2×C3—22no—
599C2×C3—22no—
600C2×C3—22no—
601C2×C3—21no—
602C2×C3—22no—
603C2×C3—42no—
604C2×C3—42no—
605C2×C3#574812yes—
606C2×C3C22×(C2×D3)⋊C411yescharacteristic
607C2×C3C22×(C2×D3)⋊C411yescharacteristic
608C2×C3#582212yes—
609D3—128no—
610D3—124no—
611D3—124no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—44no—
616C22—184no—
617C22—368no—
618C22—364no—
619C22C2×#372212yes—
620C22C2×#372212yes—
621C22C2×#372212yes—
622C22C22×#62611yescharacteristic
623C4—124no—
624C4—184no—
625C4C2×#372212yes—
626C4C2×#372212yes—
627C4C2×#372212yes—
628C4C22×#62411yescharacteristic
629C4C22×#62611yescharacteristic
630C3—21no—
631C3#8221311yescharacteristic, complemented
632C3#8376811yescharacteristic, complemented
633C2—22no—
634C2—22no—
635C2—22no—
636C2—364no—
637C2#1059479512yes—
638C2C22×#372211yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
prime radicalC22×#3828C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C22×C3×#208C2semidirect
4. #10591107C2semidirect
5. #10591106C2semidirect
6. #10591105C2semidirect
7. #10591096C2semidirect
15. C2×#3828C4semidirect
25. C3×#926C22semidirect
26. C2×C3×C4⋊Dic3C22semidirect
30. C2×C3×#208C22semidirect
31. C22×C3×C3⋊C8C22semidirect
32. #63567C22semidirect
33. #63564C22semidirect
39. C2×#926D3semidirect
40. C22×#208D3semidirect
68. #3828C2×C4semidirect
71. C2×C4⋊(C3⋊D3)C2×C4semidirect
78. C2×#634C2×C4semidirect
140. #926C2×D3semidirect
141. C2×C4⋊Dic3C2×D3semidirect
145. C2×#208C2×D3semidirect
146. C22×C3⋊C8C2×D3semidirect
557. C32#2896semidirect
631. C3#82213semidirect
632. C3#83768semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×#9262
C22×C3×#2082
#105911072
#105911062
#105911052
#105910962
#837683
#822133