Finite Group Databasebeta

← #11802158

Subgroups — #11802158

Order 1152.

1589 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C2×#63966C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic, complemented
4C3×#4946C211yesmaximal, characteristic, complemented
5C3×#4943C211yesmaximal, characteristic, complemented
6#10591711C211yesmaximal, characteristic
7#10591705C211yesmaximal, characteristic, complemented
8#10591260C212yesmaximal, complemented
9#10591258C212yesmaximal, complemented
10#10591251C212yesmaximal, complemented
11#10591241C212yesmaximal, complemented
12#74380—31nomaximal
13#74052—31nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64090—24no—
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27#63966C418yescomplemented
28C2×Dic3⋊Dic3C2212yes—
29C2×#3722C2212yes—
30C2×#3722C2212yes—
31C2×Dic32—24no—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34C2×Dic32C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×#929—31no—
41C22×C4×Dic3—31no—
42C22×C4×Dic3—31no—
43C2×#886—31no—
44C2×#67⋊C4—31no—
45C2×#67⋊C4—31no—
46C2×#67⋊C4—61no—
47C3×#385—31no—
48C3×#381—31no—
49#5213—31no—
50#4990—32no—
51Dic3×C4⋊C4—32no—
52#4958—31no—
53#4946D311yescharacteristic, complemented
54#4943D311yescharacteristic, complemented
55Dic3×C22⋊C4—31no—
56Dic3×C22⋊C4—31no—
57#4669—32no—
58#4666—32no—
59#4666—32no—
60#4654—32no—
61#4652—32no—
62#4649—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C2×#638—22no—
68C2×#638—22no—
69C2×#638C2×C414yes—
70C22×C3⋊Dic3—24no—
71C22×C3⋊Dic3D414yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—24no—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—22no—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—24no—
81C22×C3×Dic3C2×C414yescomplemented
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C32×C22⋊C4—22no—
87#3752—22no—
88#3750—22no—
89C4×C3⋊Dic3—22no—
90C3×#217—22no—
91C3×#217C2×C414yescomplemented
92C3×Dic3⋊C4—24no—
93Dic3⋊Dic3C2×C418yescomplemented
94#3722—24no—
95#3722C2×C418yescomplemented
96Dic32—24no—
97Dic32—24no—
98Dic32—24no—
99C4×#123—91noSylow
100C23×C3×C4—31no—
101C23×C3×C4—31no—
102C22×#67—31no—
103C22×#67—31no—
104C22×#67—61no—
105C23×Dic3—31no—
106C23×Dic3—31no—
107C23×Dic3—61no—
108C23×Dic3C2×D311yescharacteristic
109C23×Dic3C2×D311yescharacteristic
110C22×C4×D3—31no—
111C22×C4×D3—31no—
112C22×C4×D3—61no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4C2×D311yescharacteristic
118C2×C3×C22⋊C4C2×D311yescharacteristic
119C2×#217C2×D311yescharacteristic
120C2×#217C2×D311yescharacteristic
121#929—38no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—31no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—61no—
129C2×C4⋊Dic3—32no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—61no—
134C2×Dic3⋊C4C2×D312yes—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—61no—
144C2×C4×Dic3—64no—
145C2×C4×Dic3—64no—
146#886—38no—
147#67⋊C4—64no—
148#67⋊C4—64no—
149#67⋊C4—68no—
150C3×#95—32no—
151C3×#95—32no—
152C3×#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95C2×D312yes—
158C3⋊#95C2×D312yes—
159C3⋊#95C2×D312yes—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32C22×C412yes—
163C23×C32C2×D412yes—
164C23×C32#4112yes—
165C23×C32C2411yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3C22×C412yes—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175#638—28no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—28no—
180C2×C3⋊Dic3C22×C412yes—
181C2×C3⋊Dic3C2×D412yes—
182C2×C3⋊Dic3C2×D412yes—
183C2×C3⋊Dic3#4114yes—
184C4×C3⋊D3—44no—
185C2×C3×Dic3—28no—
186C2×C3×Dic3—28no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3C22×C414yes—
197C2×C3×Dic3C22×C414yes—
198C2×C3×Dic3#4114yes—
199C2×#123—91no—
200C2×C4×D4—91no—
201C22×C42—91no—
202#388—92no—
203#387—92no—
204#386—91no—
205#385—31no—
206#381—31no—
207C4×C4⋊C4—92no—
208C4×C22⋊C4—92no—
209C4×C22⋊C4—91no—
210C24×C3—21no—
211C24×C3C22×D311yescharacteristic
212C24×C3C22×D311yescharacteristic
213C23×D3—31no—
214C23×D3—31no—
215C23×D3—61no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—34no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—64no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4—62no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—34no—
232C2×#67—34no—
233C2×#67—64no—
234C2×#67—64no—
235C2×#67—64no—
236C2×#67—62no—
237C2×#67—62no—
238C2×#67—62no—
239C2×#67—62no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—24no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—34no—
247C22×Dic3—34no—
248C22×Dic3—31no—
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—31no—
252C22×Dic3—61no—
253C22×Dic3—61no—
254C22×Dic3—64no—
255C22×Dic3—61no—
256C22×Dic3—64no—
257C22×Dic3—64no—
258C22×Dic3—124no—
259C22×Dic3C4×D314yescomplemented
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D312yes—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3—64no—
267C2×C4×D3—64no—
268C2×C4×D3—64no—
269C2×C4×D3—124no—
270C3×C4⋊C4—64no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—22no—
273C3×C22⋊C4—22no—
274C3×C22⋊C4—34no—
275C3×C22⋊C4—62no—
276#217—22no—
277#217C4×D314yescomplemented
278(C2×D3)⋊C4—38no—
279(C2×D3)⋊C4—38no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—64no—
285C4⋊Dic3—38no—
286Dic3⋊C4—24no—
287Dic3⋊C4—38no—
288Dic3⋊C4—62no—
289Dic3⋊C4—62no—
290Dic3⋊C4—64no—
291C4×Dic3—64no—
292C4×Dic3—64no—
293C4×Dic3—64no—
294C4×Dic3—64no—
295C4×Dic3—64no—
296C4×Dic3—64no—
297C4×Dic3—62no—
298C4×Dic3—62no—
299C4×Dic3—64no—
300C22×C32—24no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—24no—
304C22×C32C4×D414yes—
305C22×C32C23×C411yescharacteristic
306C22×C32C22×D411yescharacteristic
307C22×C32C2×#4111yescharacteristic
308C22×C32C2×#4112yes—
309C22×C32C2×#4112yes—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—24no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—42no—
315C32×C4—41no—
316C32×C4—41no—
317C3⋊Dic3—22no—
318C3⋊Dic3—22no—
319C3⋊Dic3#12314yescomplemented
320C3×Dic3—24no—
321C3×Dic3—24no—
322C3×Dic3—24no—
323C3×Dic3—42no—
324C22×D4—91no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—91no—
328C23×C4—91no—
329#123—98no—
330C4×D4—184no—
331C2×C4⋊C4—32no—
332C2×C4⋊C4—92no—
333C2×C4⋊C4—91no—
334C2×C22⋊C4—31no—
335C2×C22⋊C4—31no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4—92no—
338C2×C22⋊C4—91no—
339C2×C22⋊C4D3211yescharacteristic
340C2×C42—92no—
341C2×C42—92no—
342C2×C42—92no—
343C2×C42—91no—
344C2×C42—184no—
345#95—32no—
346#95—32no—
347#95—32no—
348#95—92no—
349#95—92no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—21no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3C2×C4×D312yes—
361C23×C3C2×C4×D312yes—
362C23×C3D3×D412yes—
363C23×C3D3×D412yes—
364C23×C3#23712yes—
365C23×C3#23912yes—
366C23×C3C23×D311yescharacteristic
367C23×C3C23×D311yescharacteristic
368C22×D3—32no—
369C22×D3—32no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—61no—
374C22×D3—61no—
375C22×D3—62no—
376C22×D3—61no—
377C22×D3—61no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—122no—
382C22×D3—122no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—34no—
394C2×C3×C4—34no—
395C2×C3×C4—34no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—68no—
399C2×C3×C4—68no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409#67—616no—
410#67—68no—
411#67—68no—
412C2×Dic3—28no—
413C2×Dic3—28no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—34no—
426C2×Dic3—34no—
427C2×Dic3—32no—
428C2×Dic3—32no—
429C2×Dic3—32no—
430C2×Dic3—32no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—64no—
434C2×Dic3—62no—
435C2×Dic3—68no—
436C2×Dic3—68no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—61no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—128no—
446C2×Dic3—122no—
447C2×Dic3C2×C4×D314yes—
448C2×Dic3C2×C4×D314yes—
449C2×Dic3#23714yes—
450C4×D3—124no—
451C4×D3—124no—
452C4×D3—128no—
453C2×C32—24no—
454C2×C32C2×C4×D411yescharacteristic
455C2×C32C4×#4112yes—
456C2×C32C2×#12311yescharacteristic
457C2×C32#52511yescharacteristic
458C2×C32#52912yes—
459C3⋊D3—42no—
460C24—91no—
461C24C2×D3211yescharacteristic
462C2×D4—94no—
463C2×D4—182no—
464C2×D4—182no—
465C22×C4—32no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—34no—
469C22×C4—32no—
470C22×C4—64no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—91no—
475C22×C4—91no—
476C22×C4—91no—
477C22×C4—94no—
478C22×C4—182no—
479C22×C4—184no—
480C22×C4—184no—
481C22×C4C2×D3211yescharacteristic
482C22×C4C2×D3211yescharacteristic
483C4⋊C4—64no—
484C4⋊C4—98no—
485C4⋊C4—182no—
486C22⋊C4—22no—
487C22⋊C4—34no—
488C22⋊C4—62no—
489C22⋊C4—98no—
490C22⋊C4—182no—
491C22⋊C4—184no—
492C42—182no—
493C42—184no—
494C42—184no—
495C42—184no—
496C22×C3—24no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—22no—
503C22×C3—24no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—24no—
510C22×C3—42no—
511C22×C3—44no—
512C22×C3—42no—
513C22×C3—44no—
514C22×C3#67⋊C414yes—
515C22×C3#89314yes—
516C22×C3C22×C4×D311yescharacteristic
517C22×C3C22×C4×D311yescharacteristic
518C22×C3C2×D3×D411yescharacteristic
519C22×C3C2×D3×D411yescharacteristic
520C22×C3C2×#23711yescharacteristic
521C22×C3C2×#23712yes—
522C22×C3C2×#23911yescharacteristic
523C22×C3D3×#4112yes—
524C22×C3D3×#4112yes—
525C22×C3D3×#4112yes—
526C2×D3—64no—
527C2×D3—62no—
528C2×D3—62no—
529C2×D3—64no—
530C2×D3—64no—
531C2×D3—124no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—124no—
535C2×D3—122no—
536C2×D3—121no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—121no—
540C2×D3—122no—
541C3×C4—42no—
542C3×C4—42no—
543C3×C4—41no—
544C3×C4—41no—
545C3×C4—41no—
546C3×C4—41no—
547C3×C4—64no—
548C3×C4—64no—
549C3×C4—64no—
550C3×C4—122no—
551Dic3—24no—
552Dic3—24no—
553Dic3—24no—
554Dic3—34no—
555Dic3—34no—
556Dic3—42no—
557Dic3—64no—
558Dic3—64no—
559Dic3—62no—
560Dic3—62no—
561Dic3—62no—
562Dic3—62no—
563Dic3—122no—
564C32C4×#12311yescharacteristic, complemented, Sylow
565C23—22no—
566C23—22no—
567C23—92no—
568C23—181no—
569C23—182no—
570C23—182no—
571C23—181no—
572C23#379612yes—
573C23C4×D3212yes—
574C23#381112yes—
575C23C22×D3211yescharacteristic
576D4—188no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—34no—
582C2×C4—34no—
583C2×C4—34no—
584C2×C4—68no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—68no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—94no—
596C2×C4—92no—
597C2×C4—92no—
598C2×C4—92no—
599C2×C4—188no—
600C2×C4—181no—
601C2×C4—182no—
602C2×C4—181no—
603C2×C4—364no—
604C2×C3—24no—
605C2×C3—24no—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—22no—
610C2×C3—21no—
611C2×C3—44no—
612C2×C3C2×#67⋊C411yescharacteristic
613C2×C3C2×#89311yescharacteristic
614C2×C3#552212yes—
615C2×C3C4×#23712yes—
616C2×C3#558611yescharacteristic
617C2×C3#562412yes—
618C2×C3#564912yes—
619C2×C3D3×#12311yescharacteristic
620C2×C3D3×#12311yescharacteristic
621C2×C3#565611yescharacteristic
622D3—124no—
623D3—122no—
624D3—122no—
625C22—24no—
626C22—22no—
627C22—24no—
628C22—22no—
629C22—184no—
630C22—182no—
631C22—361no—
632C22—362no—
633C22—361no—
634C22#6388114yes—
635C22C2×#379611yescharacteristic
636C22C2×C4×D3211yescharacteristic
637C22D3×#23712yes—
638C22#6431212yes—
639C22C2×#381111yescharacteristic
640C4—41no—
641C4—41no—
642C4—64no—
643C4—64no—
644C4—64no—
645C4—94no—
646C4—122no—
647C4—182no—
648C4—182no—
649C3—21no—
650C3#7405211yescharacteristic, complemented
651C3#7438011yescharacteristic, complemented
652C2—24no—
653C2—362no—
654C2#1059404812yes—
655C2#1059414412yes—
656C2C2×#6388111yescharacteristic
657C2#1059516011yescharacteristic
658C2#1059516911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×Dic32C2semidirect
4. C3×#4946C2semidirect
5. C3×#4943C2semidirect
7. #10591705C2semidirect
8. #10591260C2semidirect
9. #10591258C2semidirect
10. #10591251C2semidirect
11. #10591241C2semidirect
27. #63966C4semidirect
53. #4946D3semidirect
54. #4943D3semidirect
81. C22×C3×Dic3C2×C4semidirect
91. C3×#217C2×C4semidirect
93. Dic3⋊Dic3C2×C4semidirect
95. #3722C2×C4semidirect
259. C22×Dic3C4×D3semidirect
277. #217C4×D3semidirect
319. C3⋊Dic3#123semidirect
564. C32C4×#123semidirect
650. C3#74052semidirect
651. C3#74380semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#639662
C22×Dic322
C3×#49462
C3×#49432
#105917112
#105917052
#105912602
#105912582
#105912512
#105912412
#743803
#740523