Finite Group Databasebeta

← #11805180

Subgroups — #11805180

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2C2×#63878C212yesmaximal
3C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
5C3×#4928C211yesmaximal, characteristic, complemented
6#10591362C212yesmaximal
7#10591352C211yesmaximal, characteristic, complemented
8#10591334C212yesmaximal, complemented
9#10591313C211yesmaximal, characteristic
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591253C212yesmaximal, complemented
12#76200—31nomaximal
13#73456—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2212yes—
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30D3×C4⋊Dic3C418yescomplemented
31#63878—28no—
32#63658C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C22×C4⋊Dic3—31no—
40C2×#892—32no—
41C2×D3×C4⋊C4—31no—
42C2×#877—32no—
43C3×#389—31no—
44C3×C4×C22⋊C4—31no—
45#5212—31no—
46#4987—31no—
47#4984—31no—
48#4978—32no—
49Dic3×C4⋊C4—31no—
50#4943—32no—
51C4×(C2×D3)⋊C4D311yescharacteristic
52C4×C4⋊Dic3—31no—
53C4×C4⋊Dic3—31no—
54C4×C4⋊Dic3—31no—
55C4×C4⋊Dic3—61no—
56#4928—31no—
57#4928D311yescharacteristic, complemented
58#4664—32no—
59#4655—32no—
60#4653—32no—
61#4653—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3C2×C414yes—
76C2×D3×Dic3—24no—
77C2×D3×Dic3—24no—
78C2×D3×Dic3C2×C418yes—
79C32×C42—22no—
80C4⋊(C3⋊Dic3)—22no—
81C4⋊(C3⋊Dic3)C2×C414yes—
82C4×C3⋊Dic3—24no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4D414yes—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3C2×C414yes—
87C3×Dic3⋊C4—24no—
88C3×C4×Dic3—22no—
89Dic3⋊Dic3—24no—
90Dic3⋊Dic3C2×C418yes—
91(C2×D3)⋊Dic3—24no—
92Dic32—24no—
93#2344—91noSylow
94C23×C3×C4—31no—
95C23×Dic3—32no—
96C22×C4×D3—32no—
97C22×C4×D3C2×D311yescharacteristic
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C42—21no—
104C2×C3×C42—31no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×#217—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4C2×D311yescharacteristic
110C2×(C2×D3)⋊C4C2×D311yescharacteristic
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—38no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4C2×D312yes—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—62no—
130C2×C4×Dic3C2×D311yescharacteristic
131#892—68no—
132D3×C4⋊C4—38no—
133#877—68no—
134C3×#95—31no—
135C3×#95—31no—
136C3×#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—62no—
146C3⋊#95C2×D312yes—
147C3⋊#95C2×D311yescharacteristic
148C3⋊#95C2×D311yescharacteristic
149C23×C32C2411yescharacteristic
150C22×C3×D3—21no—
151C22×C3×D3—21no—
152C22×C3×D3—21no—
153C22×C3×D3—21no—
154C22×C3×D3C22×C412yes—
155C22×C3×D3C2×D412yes—
156C22×C3×D3#4112yes—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4C22×C412yes—
163C2×C32×C4C2×D412yes—
164C2×C32×C4#4112yes—
165C2×C32×C4#4112yes—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C22×C414yes—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C22×C414yes—
186C2×C3×Dic3C2×D412yes—
187C3×C4×D3—28no—
188D3×Dic3—216no—
189C2×#117—92no—
190C22×C4⋊C4—91no—
191#389—31no—
192#389—91no—
193#387—92no—
194#387—92no—
195#381—92no—
196#380—91no—
197C4×C4⋊C4—91no—
198C4×C4⋊C4—91no—
199C4×C22⋊C4—31no—
200C24×C3—31no—
201C23×D3C22×D311yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—31no—
208C22×C3×C4—34no—
209C22×C3×C4—31no—
210C22×C3×C4—32no—
211C22×C3×C4—62no—
212C22×C3×C4—62no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—38no—
222C22×Dic3—32no—
223C22×Dic3—32no—
224C22×Dic3—62no—
225C22×Dic3—62no—
226C22×Dic3—64no—
227C22×Dic3—64no—
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D311yescharacteristic
233C2×C4×D3—22no—
234C2×C4×D3—22no—
235C2×C4×D3—38no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3C4×D314yes—
239C3×C4⋊C4—34no—
240C3×C4⋊C4—64no—
241C3×C4⋊C4—62no—
242C3×C22⋊C4—34no—
243C3×C22⋊C4—62no—
244C3×C42—24no—
245C3×C42—22no—
246C3×C42—22no—
247C3×C42—62no—
248#217—64no—
249(C2×D3)⋊C4—22no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4D1214yes—
252C4⋊Dic3—22no—
253C4⋊Dic3—34no—
254C4⋊Dic3—34no—
255C4⋊Dic3—38no—
256C4⋊Dic3—64no—
257C4⋊Dic3—64no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—64no—
261C4⋊Dic3C4×D314yes—
262Dic3⋊C4—24no—
263Dic3⋊C4—38no—
264Dic3⋊C4—64no—
265C4×Dic3—22no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C4×Dic3—124no—
271C22×C32C23×C411yescharacteristic
272C22×C32C22×D411yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C32C2×#4111yescharacteristic
276C22×C322−1+411yescharacteristic
277C22×C322−1+411yescharacteristic
278C2×C3×D3—22no—
279C2×C3×D3—22no—
280C2×C3×D3—22no—
281C2×C3×D3—22no—
282C2×C3×D3—22no—
283C2×C3×D3—22no—
284C2×C3×D3C4×D414yes—
285C32×C4—22no—
286C32×C4—41no—
287C32×C4#11714yescomplemented
288C3⋊Dic3—24no—
289C3⋊Dic3—42no—
290C3×Dic3—22no—
291C3×Dic3—24no—
292C3×Dic3—22no—
293C3×Dic3—42no—
294C3×Dic3—41no—
295C23×C4—31no—
296C23×C4—92no—
297#117—188no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—32no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—98no—
302C2×C4⋊C4—92no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—92no—
305C2×C4⋊C4—91no—
306C2×C22⋊C4—31no—
307C2×C22⋊C4—31no—
308C2×C22⋊C4—92no—
309C2×C42—31no—
310C2×C42—92no—
311C2×C42—92no—
312C2×C42D3211yescharacteristic
313#95—31no—
314#95—31no—
315#95—32no—
316#95—92no—
317#95—92no—
318#95—92no—
319#95—92no—
320C23×C3—21no—
321C23×C3—32no—
322C23×C3—32no—
323C23×C3—32no—
324C23×C3—61no—
325C23×C3—61no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3C23×D311yescharacteristic
329C23×C3C23×D311yescharacteristic
330C22×D3—21no—
331C22×D3—21no—
332C22×D3—21no—
333C22×D3—21no—
334C22×D3C2×C4×D312yes—
335C22×D3C2×D1212yes—
336C22×D3#23512yes—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—34no—
355C2×C3×C4—32no—
356C2×C3×C4—32no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—68no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—62no—
372C2×C3×C4C2×C4×D312yes—
373C2×C3×C4C2×C4×D312yes—
374C2×C3×C4C2×D1212yes—
375C2×C3×C4D3×D412yes—
376C2×C3×C4#23712yes—
377C2×C3×C4#23712yes—
378C2×C3×C4#23712yes—
379C2×C3×C4#23912yes—
380C2×Dic3—22no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—22no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—22no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—21no—
391C2×Dic3—22no—
392C2×Dic3—34no—
393C2×Dic3—34no—
394C2×Dic3—64no—
395C2×Dic3—616no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—64no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—122no—
408C2×Dic3—122no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3C2×C4×D312yes—
412C2×Dic3C2×C4×D314yes—
413C2×Dic3C2×D1212yes—
414C4×D3—28no—
415C4×D3—616no—
416C2×C32C2×#11711yescharacteristic
417C2×C32C2×C4×D411yescharacteristic
418C2×C32#51911yescharacteristic
419C2×C32#54711yescharacteristic
420C2×C32#54711yescharacteristic
421C2×C32#55211yescharacteristic
422C2×C32#55211yescharacteristic
423C3×D3—24no—
424C24—31no—
425C22×C4—31no—
426C22×C4—32no—
427C22×C4—31no—
428C22×C4—34no—
429C22×C4—31no—
430C22×C4—32no—
431C22×C4—62no—
432C22×C4—62no—
433C22×C4—98no—
434C22×C4—92no—
435C22×C4—92no—
436C22×C4—184no—
437C22×C4—184no—
438C22×C4C2×D3211yescharacteristic
439C22×C4C2×D3211yescharacteristic
440C22×C4C2×D3211yescharacteristic
441C4⋊C4—34no—
442C4⋊C4—64no—
443C4⋊C4—62no—
444C4⋊C4—98no—
445C4⋊C4—94no—
446C4⋊C4—184no—
447C4⋊C4—182no—
448C22⋊C4—34no—
449C22⋊C4—62no—
450C22⋊C4—184no—
451C42—22no—
452C42—62no—
453C42—184no—
454C42—184no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—34no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—62no—
466C22×C3—62no—
467C22×C3—62no—
468C22×C3—62no—
469C22×C3C22×C4×D311yescharacteristic
470C22×C3C22×C4×D311yescharacteristic
471C22×C3C22×D1211yescharacteristic
472C22×C3C2×#23511yescharacteristic
473C22×C3C2×D3×D411yescharacteristic
474C22×C3C2×#23711yescharacteristic
475C22×C3C2×#23711yescharacteristic
476C22×C3C2×#23711yescharacteristic
477C22×C3C2×#23911yescharacteristic
478C22×C3#100711yescharacteristic
479C22×C3D3×#4111yescharacteristic
480C22×C3#101011yescharacteristic
481C22×C3#101011yescharacteristic
482C22×C3#101011yescharacteristic
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—22no—
488C2×D3—22no—
489C2×D3C4×D1214yes—
490C3×C4—24no—
491C3×C4—22no—
492C3×C4—22no—
493C3×C4—24no—
494C3×C4—42no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—62no—
498C3×C4—64no—
499C3×C4—62no—
500C3×C4—121no—
501C3×C4—122no—
502C3×C4#87714yescomplemented
503C3×C4#89214yescomplemented
504Dic3—22no—
505Dic3—24no—
506Dic3—22no—
507Dic3—41no—
508Dic3—42no—
509Dic3—64no—
510Dic3—64no—
511Dic3—124no—
512Dic3—124no—
513Dic3—122no—
514Dic3—122no—
515C32#234411yescharacteristic, complemented, Sylow
516C23—32no—
517C23—32no—
518C23—32no—
519C23—61no—
520C23—61no—
521C23—61no—
522C23—61no—
523C23C22×D3211yescharacteristic
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—34no—
530C2×C4—32no—
531C2×C4—32no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—61no—
538C2×C4—68no—
539C2×C4—61no—
540C2×C4—62no—
541C2×C4—61no—
542C2×C4—62no—
543C2×C4—61no—
544C2×C4—62no—
545C2×C4—94no—
546C2×C4—1816no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4—182no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4#379612yes—
553C2×C4C4×D3212yes—
554C2×C4D3×D1212yes—
555C2×C4#380512yes—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—64no—
564C2×C3C2×C4×D1211yescharacteristic
565C2×C3C2×#87711yescharacteristic
566C2×C3C2×#89211yescharacteristic
567C2×C3#551611yescharacteristic
568C2×C3#554111yescharacteristic
569C2×C3#554111yescharacteristic
570C2×C3C4×D3×D411yescharacteristic
571C2×C3#555511yescharacteristic
572C2×C3#555511yescharacteristic
573C2×C3#557211yescharacteristic
574C2×C3#561111yescharacteristic
575C2×C3#563911yescharacteristic
576C2×C3#569411yescharacteristic
577C2×C3#572611yescharacteristic
578D3—24no—
579C22—34no—
580C22—62no—
581C22—62no—
582C22—62no—
583C22—62no—
584C22—62no—
585C22—62no—
586C22C2×#379611yescharacteristic
587C22#6429711yescharacteristic
588C22#6429811yescharacteristic
589C22C2×C4×D3211yescharacteristic
590C22C2×D3×D1211yescharacteristic
591C22D3×#23511yescharacteristic
592C22C2×#380511yescharacteristic
593C4—22no—
594C4—41no—
595C4—62no—
596C4—62no—
597C4—64no—
598C4—122no—
599C4—121no—
600C4—184no—
601C4—362no—
602C4#6387814yescomplemented
603C3—21no—
604C3#7345611yescharacteristic, complemented
605C3#7620011yescharacteristic, complemented
606C2—64no—
607C2#1059388511yescharacteristic
608C2#1059389611yescharacteristic
609C2#1059392011yescharacteristic
610C2C4×D3×D1211yescharacteristic
611C2C2×#6387811yescharacteristic
612C2#1059490711yescharacteristic
613C2#1059494211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2344
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C4×C4⋊(C3⋊Dic3)C2semidirect
5. C3×#4928C2semidirect
7. #10591352C2semidirect
8. #10591334C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591253C2semidirect
30. D3×C4⋊Dic3C4semidirect
57. #4928D3semidirect
287. C32×C4#117semidirect
502. C3×C4#877semidirect
503. C3×C4#892semidirect
515. C32#2344semidirect
602. C4#63878semidirect
604. C3#73456semidirect
605. C3#76200semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
C2×#638782
C4×C4⋊(C3⋊Dic3)2
C3×C4×(C2×D3)⋊C42
C3×#49282
#105913622
#105913522
#105913342
#105913132
Dic3×C4⋊Dic32
#105912532
#762003
#734563