Finite Group Databasebeta

← #11805248

Subgroups — #11805248

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C4×#3752C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4928C211yesmaximal, characteristic, complemented
5#10591367C212yesmaximal
6#10591357C211yesmaximal, characteristic, complemented
7#10591333C212yesmaximal, complemented
8#10591325C211yesmaximal, characteristic
9#10591274C211yesmaximal, characteristic, complemented
10#10591255C212yesmaximal, complemented
11#10591233C212yesmaximal
12#76201—31nomaximal
13#73768—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#624C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×#3724C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×#3722C2212yes—
29C2×Dic32C2212yes—
30#63900C418yescomplemented
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×D3×C4⋊C4—31no—
39C2×D3×C4⋊C4—31no—
40C3×#389—31no—
41C3×C4×C4⋊C4—31no—
42#4987—31no—
43#4987—31no—
44#4987—32no—
45#4984—31no—
46#4978—32no—
47Dic3×C4⋊C4—31no—
48Dic3×C4⋊C4—31no—
49#4972—31no—
50C4×(C2×D3)⋊C4—31no—
51C4×(C2×D3)⋊C4—31no—
52C4×(C2×D3)⋊C4—32no—
53C4×(C2×D3)⋊C4—61no—
54C4×C4⋊Dic3D311yescharacteristic, complemented
55#4933—32no—
56#4928D311yescharacteristic, complemented
57#4667—32no—
58#4666—32no—
59#4655—32no—
60#4652—32no—
61C23×C3⋊D3C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3C2×C414yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×#624—42no—
76C2×#624—42no—
77C2×#624C2×C418yes—
78C32×C42—22no—
79#3752—22no—
80#3752Q814yes—
81C4×C3⋊Dic3—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3C2×C414yes—
85C3×C4⋊Dic3C2×C414yes—
86C3×Dic3⋊C4—42no—
87C3×C4×Dic3—42no—
88#3724C2×C418yes—
89Dic3⋊Dic3—42no—
90#3722—24no—
91Dic32—42no—
92#2345—91noSylow
93C22×C4×D3—31no—
94C22×C4×D3—31no—
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—61no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C42—21no—
104C2×C3×C42—32no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—31no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4⋊Dic3—32no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4C2×D312yes—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3C2×D312yes—
130D3×C4⋊C4—38no—
131D3×C4⋊C4—38no—
132C3×#95—32no—
133C3×#95—32no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—61no—
145C3⋊#95—61no—
146C3⋊#95C2×D312yes—
147C3⋊#95C2×D312yes—
148C23×C32C2411yescharacteristic
149C22×C3⋊D3—21no—
150C22×C3⋊D3—21no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3—21no—
153C22×C3⋊D3C22×C412yes—
154C22×C3⋊D3C2×Q812yes—
155C22×C3⋊D3#4112yes—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4C22×C412yes—
162C2×C32×C4C2×Q812yes—
163C2×C32×C4#4112yes—
164C2×C32×C4#4112yes—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3C22×C412yes—
173C2×C3⋊Dic3C2×Q812yes—
174C4×C3⋊D3—28no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C22×C414yes—
186C2×C3×Dic3C22×C414yes—
187#624—48no—
188C22×C4⋊C4—91no—
189#389—31no—
190#389—91no—
191#387—92no—
192#387—92no—
193#380—92no—
194#380—91no—
195C4×C4⋊C4—31no—
196C4×C4⋊C4—91no—
197C4×C22⋊C4—92no—
198C4×C22⋊C4—91no—
199C23×D3—31no—
200C23×D3—31no—
201C23×D3—61no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C2×C4×D3—34no—
229C2×C4×D3—34no—
230C2×C4×D3—38no—
231C2×C4×D3—38no—
232C2×C4×D3—64no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—122no—
238C2×C4×D3—122no—
239C2×C4×D3—122no—
240C2×C4×D3—122no—
241C2×C4×D3—122no—
242C2×C4×D3—122no—
243C3×C4⋊C4—34no—
244C3×C4⋊C4—34no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—122no—
248C3×C42—22no—
249C3×C42—22no—
250C3×C42—42no—
251C3×C42—122no—
252(C2×D3)⋊C4—34no—
253(C2×D3)⋊C4—34no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—64no—
260C4⋊Dic3—22no—
261C4⋊Dic3—22no—
262C4⋊Dic3—122no—
263C4⋊Dic3C4×D314yes—
264C4⋊Dic3C4×D314yes—
265Dic3⋊C4—38no—
266Dic3⋊C4—38no—
267Dic3⋊C4—42no—
268Dic3⋊C4—122no—
269C4×Dic3—42no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—122no—
273C4×Dic3—122no—
274C4×Dic3—122no—
275C22×C32C23×C411yescharacteristic
276C22×C32C22×Q811yescharacteristic
277C22×C32C2×#4111yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32H(5,𝔽2)11yescharacteristic
281C22×C32H(5,𝔽2)11yescharacteristic
282C2×C3⋊D3—22no—
283C2×C3⋊D3—22no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3C4×Q814yes—
289C32×C4—22no—
290C32×C4—41no—
291C32×C4#11714yes—
292C3⋊Dic3—22no—
293C3⋊Dic3—22no—
294C3⋊Dic3—41no—
295C3×Dic3—24no—
296C3×Dic3—24no—
297C3×Dic3—42no—
298C3×Dic3—42no—
299C23×C4—92no—
300C23×C4—91no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—32no—
306C2×C4⋊C4—98no—
307C2×C4⋊C4—92no—
308C2×C4⋊C4—92no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4—92no—
311C2×C22⋊C4—91no—
312C2×C42—32no—
313C2×C42—91no—
314C2×C42—92no—
315C2×C42D3211yescharacteristic
316#95—32no—
317#95—32no—
318#95—92no—
319#95—92no—
320#95—92no—
321#95—91no—
322#95—91no—
323C23×C3—21no—
324C23×C3C23×D311yescharacteristic
325C23×C3C23×D311yescharacteristic
326C22×D3—32no—
327C22×D3—32no—
328C22×D3—32no—
329C22×D3—32no—
330C22×D3—32no—
331C22×D3—32no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—61no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—121no—
344C22×D3—121no—
345C22×D3—121no—
346C22×D3—121no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—34no—
363C2×C3×C4—34no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4C2×C4×D312yes—
379C2×C3×C4C2×C4×D312yes—
380C2×C3×C4#23512yes—
381C2×C3×C4#23512yes—
382C2×C3×C4#23712yes—
383C2×C3×C4D3×Q812yes—
384C2×C3×C4D3×Q812yes—
385C2×C3×C4#23912yes—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—32no—
397C2×Dic3—32no—
398C2×Dic3—32no—
399C2×Dic3—32no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—62no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—121no—
423C2×Dic3C2×C4×D314yes—
424C2×Dic3C2×C4×D314yes—
425C4×D3—68no—
426C4×D3—68no—
427C4×D3—128no—
428C4×D3—128no—
429C4×D3—128no—
430C2×C32C2×#11711yescharacteristic
431C2×C32C2×C4×Q811yescharacteristic
432C2×C32#51811yescharacteristic
433C2×C32#55311yescharacteristic
434C2×C32#55311yescharacteristic
435C2×C32#55411yescharacteristic
436C2×C32#55411yescharacteristic
437C3⋊D3—24no—
438C24—91no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—32no—
442C22×C4—32no—
443C22×C4—98no—
444C22×C4—91no—
445C22×C4—91no—
446C22×C4—94no—
447C22×C4—91no—
448C22×C4—182no—
449C22×C4—182no—
450C22×C4—362no—
451C22×C4—362no—
452C22×C4C2×D3211yescharacteristic
453C22×C4C2×D3211yescharacteristic
454C22×C4C2×D3211yescharacteristic
455C4⋊C4—34no—
456C4⋊C4—34no—
457C4⋊C4—62no—
458C4⋊C4—62no—
459C4⋊C4—98no—
460C4⋊C4—122no—
461C4⋊C4—362no—
462C22⋊C4—94no—
463C22⋊C4—182no—
464C22⋊C4—184no—
465C42—22no—
466C42—122no—
467C42—182no—
468C42—362no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3C22×C4×D311yescharacteristic
477C22×C3C22×C4×D311yescharacteristic
478C22×C3C2×#23511yescharacteristic
479C22×C3C2×#23511yescharacteristic
480C22×C3C2×#23711yescharacteristic
481C22×C3#100411yescharacteristic
482C22×C3#100411yescharacteristic
483C22×C3C2×D3×Q811yescharacteristic
484C22×C3C2×D3×Q811yescharacteristic
485C22×C3C2×#23911yescharacteristic
486C22×C3D3×#4111yescharacteristic
487C22×C3D3×#4111yescharacteristic
488C22×C3#100911yescharacteristic
489C22×C3#100911yescharacteristic
490C2×D3—34no—
491C2×D3—34no—
492C2×D3—64no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—122no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—24no—
514C3×C4—42no—
515C3×C4—42no—
516C3×C4—41no—
517C3×C4—41no—
518C3×C4—64no—
519C3×C4—64no—
520C3×C4—122no—
521C3×C4—122no—
522C3×C4#87214yes—
523C3×C4#89214yes—
524Dic3—24no—
525Dic3—24no—
526Dic3—42no—
527Dic3—42no—
528Dic3—62no—
529Dic3—62no—
530Dic3—62no—
531Dic3—62no—
532Dic3—122no—
533Dic3—122no—
534Dic3—122no—
535Dic3—121no—
536Dic3—121no—
537C32#234511yescharacteristic, complemented, Sylow
538C23—92no—
539C23—92no—
540C23—92no—
541C23—181no—
542C23—181no—
543C23—181no—
544C23—181no—
545C23C22×D3211yescharacteristic
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—34no—
552C2×C4—34no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—92no—
564C2×C4—92no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—181no—
568C2×C4—181no—
569C2×C4—188no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—368no—
574C2×C4#379712yes—
575C2×C4#379912yes—
576C2×C4C4×D3212yes—
577C2×C4#380412yes—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3C2×#87211yescharacteristic
586C2×C3C2×#89211yescharacteristic
587C2×C3#551111yescharacteristic
588C2×C3#553011yescharacteristic
589C2×C3#554511yescharacteristic
590C2×C3#554511yescharacteristic
591C2×C3#555811yescharacteristic
592C2×C3C4×D3×Q811yescharacteristic
593C2×C3C4×D3×Q811yescharacteristic
594C2×C3#557911yescharacteristic
595C2×C3#561411yescharacteristic
596C2×C3#563511yescharacteristic
597C2×C3#569511yescharacteristic
598C2×C3#573011yescharacteristic
599D3—64no—
600D3—64no—
601D3—124no—
602C22—94no—
603C22—182no—
604C22—182no—
605C22—182no—
606C22—182no—
607C22—182no—
608C22—182no—
609C22C2×#379711yescharacteristic
610C22C2×#379911yescharacteristic
611C22C2×C4×D3211yescharacteristic
612C22#6430611yescharacteristic
613C22#6430711yescharacteristic
614C22#6430711yescharacteristic
615C22C2×#380411yescharacteristic
616C4—22no—
617C4—41no—
618C4—64no—
619C4—64no—
620C4—122no—
621C4—122no—
622C4—182no—
623C4—182no—
624C4—361no—
625C4#6383614yes—
626C3—21no—
627C3#7376811yescharacteristic, complemented
628C3#7620111yescharacteristic, complemented
629C2—184no—
630C2C4×#379711yescharacteristic
631C2#1059395811yescharacteristic
632C2#1059398211yescharacteristic
633C2#1059399611yescharacteristic
634C2C2×#6383611yescharacteristic
635C2#1059496711yescharacteristic
636C2#1059499111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C4×C4⋊Dic3C2semidirect
4. C3×#4928C2semidirect
6. #10591357C2semidirect
7. #10591333C2semidirect
9. #10591274C2semidirect
10. #10591255C2semidirect
30. #63900C4semidirect
54. C4×C4⋊Dic3D3semidirect
56. #4928D3semidirect
537. C32#2345semidirect
627. C3#73768semidirect
628. C3#76201semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C4×#37522
C3×C4×C4⋊Dic32
C3×#49282
#105913672
#105913572
#105913332
#105913252
#105912742
#105912552
#105912332
#762013
#737683