Finite Group Databasebeta

← #11802934

Subgroups — #11802934

Order 1152.

1285 conjugacy classes of subgroups.

The subgroup lattice has 631 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C2×#63855C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic
4#10592683C211yesmaximal, characteristic, complemented
5C3×#4984C211yesmaximal, characteristic, complemented
6#10591357C211yesmaximal, characteristic, complemented
7#10591352C211yesmaximal, characteristic, complemented
8#10591313C212yesmaximal
9#10591295C212yesmaximal
10#10591268C212yesmaximal, complemented
11#10591265C212yesmaximal, complemented
12#82156—31nomaximal
13#76195—31nomaximal
14C22×C3×C4×D3C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×D3×C4⋊C4C418yescomplemented
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×Dic32C2212yes—
34#63855—24no—
35#63841—24no—
36#63658C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C22×C3×C4⋊C4—31no—
41C2×#926—31no—
42C2×#926—31no—
43C2×#892—31no—
44C2×D3×C4⋊C4D311yescharacteristic
45C2×#872—31no—
46C3×#389—31no—
47#5212—32no—
48#5212—32no—
49#4987—32no—
50#4984—31no—
51#4984—31no—
52#4984—32no—
53#4984—31no—
54#4984—31no—
55#4984—32no—
56#4984—61no—
57#4984D311yescharacteristic, complemented
58#4976—32no—
59#4972—31no—
60#4928—31no—
61#4667—32no—
62#4647—32no—
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×C4×D3—42no—
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3C2×C418yes—
77C2×C3×C4×D3C2×C414yes—
78C2×C3×C4×D3D414yes—
79C2×C3×C4×D3Q814yes—
80C32×C4⋊C4C2×C414yes—
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)—42no—
83C4×C3⋊Dic3—22no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3—42no—
86C3×C4⋊Dic3C2×C414yes—
87C3×Dic3⋊C4C2×C418yes—
88C3×C4×Dic3—22no—
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—42no—
92Dic3⋊Dic3—42no—
93(C2×D3)⋊Dic3—24no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—24no—
97#2316—91noSylow
98C23×C3×C4—31no—
99C23×C3×C4—32no—
100C22×C4×D3C2×D312yes—
101C22×C4×D3C2×D311yescharacteristic
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—38no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C2×D311yescharacteristic
110C2×C3×C42—31no—
111C2×#217—31no—
112C2×#217—32no—
113C2×#217—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—31no—
117#926—64no—
118#926—64no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3—62no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×C4⋊Dic3C2×D312yes—
131C2×C4⋊Dic3C2×D311yescharacteristic
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—31no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4C2×D312yes—
137C2×C4×Dic3—31no—
138C2×C4×Dic3—31no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—61no—
142C2×C4×Dic3C2×D311yescharacteristic
143#892—64no—
144D3×C4⋊C4Dic318yescomplemented
145#872—64no—
146C3×#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—62no—
154C3⋊#95C2×D312yes—
155C23×C32C2411yescharacteristic
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—21no—
160C22×C3×D3C22×C412yes—
161C22×C3×D3C2×D412yes—
162C22×C3×D3C2×Q812yes—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C22×C414yes—
166C2×C32×C4C22×C412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×Q812yes—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3C22×C414yes—
190C2×C3×Dic3C22×C412yes—
191C2×C3×Dic3C2×D412yes—
192C2×C3×Dic3C2×Q812yes—
193C3×C4×D3—48no—
194C3×C4×D3C4⋊C4116yescomplemented
195C2×#117—91no—
196C2×#117—91no—
197C22×C4⋊C4—31no—
198#389—31no—
199#389—92no—
200#389—91no—
201#389—91no—
202#389—92no—
203#389—91no—
204#380—92no—
205#380—92no—
206C24×C3—31no—
207C23×D3C22×D311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—31no—
211C22×C3×C4—34no—
212C22×C3×C4—34no—
213C22×C3×C4—34no—
214C22×C3×C4—32no—
215C22×C3×C4—38no—
216C22×C3×C4—31no—
217C22×C3×C4—32no—
218C22×C3×C4—31no—
219C22×C3×C4—122no—
220C22×C3×C4—122no—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—32no—
228C22×Dic3—31no—
229C22×Dic3—32no—
230C22×Dic3—31no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3—62no—
234C22×Dic3C22×D311yescharacteristic
235C22×Dic3C22×D312yes—
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D311yescharacteristic
239C2×C4×D3—42no—
240C2×C4×D3—42no—
241C2×C4×D3Dic614yes—
242C2×C4×D3D1214yes—
243C2×C4×D3C2×Dic318yes—
244C2×C4×D3C2×Dic314yes—
245C3×C4⋊C4—24no—
246C3×C4⋊C4—38no—
247C3×C4⋊C4—34no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—122no—
250C3×C4⋊C4C4×D314yes—
251C3×C4⋊C4C2×Dic314yes—
252C3×C42—62no—
253#217—62no—
254#217—62no—
255#217—64no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—64no—
259C4⋊Dic3—22no—
260C4⋊Dic3—42no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—62no—
264C4⋊Dic3—62no—
265C4⋊Dic3—122no—
266C4⋊Dic3—122no—
267C4⋊Dic3—122no—
268C4⋊Dic3—122no—
269C4⋊Dic3—122no—
270C4⋊Dic3—124no—
271C4⋊Dic3C2×Dic314yes—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—122no—
275Dic3⋊C4—122no—
276Dic3⋊C4C2×Dic318yes—
277C4×Dic3—22no—
278C4×Dic3—64no—
279C4×Dic3—62no—
280C4×Dic3—62no—
281C4×Dic3—64no—
282C4×Dic3—122no—
283C22×C32C23×C411yescharacteristic
284C22×C32C22×D411yescharacteristic
285C22×C32C22×Q811yescharacteristic
286C22×C32H(5,𝔽2)11yescharacteristic
287C22×C32H(5,𝔽2)11yescharacteristic
288C22×C322−1+411yescharacteristic
289C22×C322−1+411yescharacteristic
290C2×C3×D3—22no—
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—22no—
296C2×C3×D3C2×C4⋊C414yes—
297C32×C4—24no—
298C32×C4C2×C4⋊C414yes—
299C3⋊Dic3—41no—
300C3⋊Dic3—41no—
301C3⋊Dic3—42no—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C3×Dic3—41no—
306C3×Dic3C2×C4⋊C414yes—
307C23×C4—31no—
308C23×C4—32no—
309#117—184no—
310#117—184no—
311C2×C4⋊C4—32no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—38no—
314C2×C4⋊C4—31no—
315C2×C4⋊C4—32no—
316C2×C4⋊C4—91no—
317C2×C4⋊C4—91no—
318C2×C4⋊C4—91no—
319C2×C4⋊C4—92no—
320C2×C4⋊C4—92no—
321C2×C4⋊C4—92no—
322C2×C4⋊C4D3211yescharacteristic
323C2×C22⋊C4—91no—
324C2×C22⋊C4—92no—
325C2×C22⋊C4—91no—
326C2×C42—31no—
327C2×C42—92no—
328C2×C42—91no—
329#95—32no—
330#95—92no—
331#95—92no—
332#95—92no—
333C23×C3—21no—
334C23×C3—32no—
335C23×C3—32no—
336C23×C3—32no—
337C23×C3—61no—
338C23×C3—61no—
339C23×C3—61no—
340C23×C3—61no—
341C23×C3C23×D311yescharacteristic
342C23×C3C23×D311yescharacteristic
343C22×D3—21no—
344C22×D3—21no—
345C22×D3—21no—
346C22×D3—21no—
347C22×D3C2×Dic612yes—
348C22×D3C2×D1212yes—
349C22×D3C22×Dic312yes—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—24no—
358C2×C3×C4—32no—
359C2×C3×C4—32no—
360C2×C3×C4—32no—
361C2×C3×C4—316no—
362C2×C3×C4—34no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—62no—
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×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—128no—
377C2×C3×C4C2×Dic612yes—
378C2×C3×C4C2×C4×D314yes—
379C2×C3×C4C2×C4×D312yes—
380C2×C3×C4C2×D1212yes—
381C2×C3×C4D3×D412yes—
382C2×C3×C4D3×Q812yes—
383C2×C3×C4C22×Dic314yes—
384C2×C3×C4C22×Dic312yes—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—21no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—62no—
401C2×Dic3—61no—
402C2×Dic3—62no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—62no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—62no—
411C2×Dic3—61no—
412C2×Dic3—62no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—61no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C2×Dic3—122no—
421C2×Dic3—122no—
422C2×Dic3—122no—
423C2×Dic3C2×Dic612yes—
424C2×Dic3C2×D1212yes—
425C2×Dic3C22×Dic314yes—
426C2×Dic3C22×Dic312yes—
427C4×D3—48no—
428C4×D3C4⋊Dic3116yescomplemented
429C2×C32C22×C4⋊C411yescharacteristic
430C2×C32#51811yescharacteristic
431C2×C32#51911yescharacteristic
432C2×C32#53711yescharacteristic
433C2×C32#53711yescharacteristic
434C2×C32#54411yescharacteristic
435C2×C32#54411yescharacteristic
436C3×D3—24no—
437C24—31no—
438C22×C4—31no—
439C22×C4—34no—
440C22×C4—34no—
441C22×C4—34no—
442C22×C4—32no—
443C22×C4—38no—
444C22×C4—31no—
445C22×C4—32no—
446C22×C4—31no—
447C22×C4—91no—
448C22×C4—91no—
449C22×C4—92no—
450C22×C4—122no—
451C22×C4—122no—
452C22×C4C2×D3212yes—
453C22×C4C2×D3211yescharacteristic
454C4⋊C4—38no—
455C4⋊C4—34no—
456C4⋊C4—62no—
457C4⋊C4—122no—
458C4⋊C4—182no—
459C4⋊C4—182no—
460C4⋊C4—182no—
461C4⋊C4—362no—
462C4⋊C4—362no—
463C4⋊C4—362no—
464C4⋊C4D3×Dic314yes—
465C22⋊C4—182no—
466C22⋊C4—182no—
467C22⋊C4—184no—
468C42—62no—
469C42—184no—
470C42—182no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—34no—
479C22×C3—62no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—62no—
483C22×C3—62no—
484C22×C3—62no—
485C22×C3C22×Dic611yescharacteristic
486C22×C3C22×C4×D311yescharacteristic
487C22×C3C22×D1211yescharacteristic
488C22×C3C2×D3×D411yescharacteristic
489C22×C3#100411yescharacteristic
490C22×C3#100411yescharacteristic
491C22×C3#100411yescharacteristic
492C22×C3C2×D3×Q811yescharacteristic
493C22×C3#100711yescharacteristic
494C22×C3#100711yescharacteristic
495C22×C3#100711yescharacteristic
496C22×C3#100911yescharacteristic
497C22×C3#101011yescharacteristic
498C22×C3C23×Dic311yescharacteristic
499C2×D3—22no—
500C2×D3—22no—
501C2×D3—22no—
502C2×D3—22no—
503C2×D3—22no—
504C2×D3—22no—
505C2×D3C2×C4⋊Dic314yes—
506C3×C4—24no—
507C3×C4—24no—
508C3×C4—24no—
509C3×C4—34no—
510C3×C4—44no—
511C3×C4—64no—
512C3×C4—122no—
513C3×C4—121no—
514C3×C4—121no—
515C3×C4D3×C4⋊C414yes—
516C3×C4C2×C4⋊Dic314yes—
517Dic3—24no—
518Dic3—41no—
519Dic3—42no—
520Dic3—41no—
521Dic3—122no—
522Dic3—122no—
523Dic3—121no—
524Dic3—121no—
525Dic3—122no—
526Dic3—121no—
527Dic3—121no—
528Dic3—122no—
529Dic3—242no—
530Dic3C2×C4⋊Dic314yes—
531C32#231611yescharacteristic, complemented, Sylow
532C23—32no—
533C23—32no—
534C23—32no—
535C23—61no—
536C23—61no—
537C23—61no—
538C23—61no—
539C23C22×D3211yescharacteristic
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—32no—
543C2×C4—32no—
544C2×C4—32no—
545C2×C4—316no—
546C2×C4—34no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—61no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—128no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—182no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—182no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—182no—
568C2×C4D3×Dic612yes—
569C2×C4D3×D1212yes—
570C2×C4C2×D3×Dic314yes—
571C2×C4C2×D3×Dic312yes—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—64no—
580C2×C3#550011yescharacteristic
581C2×C3#550011yescharacteristic
582C2×C3C2×D3×C4⋊C411yescharacteristic
583C2×C3#551011yescharacteristic
584C2×C3#551011yescharacteristic
585C2×C3#554511yescharacteristic
586C2×C3#557211yescharacteristic
587C2×C3#560811yescharacteristic
588C2×C3#562911yescharacteristic
589C2×C3#568911yescharacteristic
590C2×C3#572911yescharacteristic
591C2×C3C22×C4⋊Dic311yescharacteristic
592C2×C3#579811yescharacteristic
593C2×C3#581211yescharacteristic
594D3—24no—
595C22—34no—
596C22—62no—
597C22—62no—
598C22—62no—
599C22—62no—
600C22—62no—
601C22—62no—
602C22C2×D3×Dic611yescharacteristic
603C22C2×D3×D1211yescharacteristic
604C22#6431311yescharacteristic
605C22#6431411yescharacteristic
606C22#6431511yescharacteristic
607C22#6431611yescharacteristic
608C22C22×D3×Dic311yescharacteristic
609C4—24no—
610C4—34no—
611C4—64no—
612C4—121no—
613C4—122no—
614C4—121no—
615C4—361no—
616C4—361no—
617C4—362no—
618C4D3×C4⋊Dic314yes—
619C3—21no—
620C3#7619511yescharacteristic, complemented
621C3#8215611yescharacteristic, complemented
622C2—64no—
623C2#1059434211yescharacteristic
624C2#1059434411yescharacteristic
625C2#1059452211yescharacteristic
626C2#1059452311yescharacteristic
627C2C2×D3×C4⋊Dic311yescharacteristic
628C2#1059521511yescharacteristic
629C2#1059534711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2316
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10592683C2semidirect
5. C3×#4984C2semidirect
6. #10591357C2semidirect
7. #10591352C2semidirect
10. #10591268C2semidirect
11. #10591265C2semidirect
25. C3×D3×C4⋊C4C4semidirect
57. #4984D3semidirect
144. D3×C4⋊C4Dic3semidirect
194. C3×C4×D3C4⋊C4semidirect
428. C4×D3C4⋊Dic3semidirect
531. C32#2316semidirect
620. C3#76195semidirect
621. C3#82156semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×#638552
C2×#638412
#105926832
C3×#49842
#105913572
#105913522
#105913132
#105912952
#105912682
#105912652
#821563
#761953