Finite Group Databasebeta

← #11803498

Subgroups — #11803498

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C2×#63843C211yesmaximal, characteristic, complemented
4C3×#4929C211yesmaximal, characteristic, complemented
5C3×#4928C211yesmaximal, characteristic, complemented
6#10591325C211yesmaximal, characteristic
7#10591274C211yesmaximal, characteristic, complemented
8#10591259C212yesmaximal
9#10591258C212yesmaximal
10#10591251C212yesmaximal, complemented
11#10591234C212yesmaximal, complemented
12#76611—31nomaximal
13#76197—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64081—24no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×#3722C2212yes—
30C2×#3722C2212yes—
31C2×Dic32C2212yes—
32C2×Dic32C2212yes—
33#63871C418yescomplemented
34#63843—24no—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×#946—31no—
41C2×Q8×Dic3—31no—
42C2×#897—31no—
43C2×#887—31no—
44C2×#872—31no—
45C2×#872—31no—
46C2×#872—61no—
47C3×#391—31no—
48C3×#389—31no—
49#4990—32no—
50#4987—31no—
51#4987—31no—
52Dic3×C4⋊C4—31no—
53Dic3×C4⋊C4—31no—
54#4972—32no—
55#4929D311yescharacteristic, complemented
56#4928D311yescharacteristic, complemented
57#4670—32no—
58#4669—32no—
59#4669—32no—
60#4654—32no—
61#4652—32no—
62#4647—32no—
63C23×C3⋊D3C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3C2×C414yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2×C414yes—
80C32×C42—22no—
81#3752—22no—
82#3752—22no—
83#3750—22no—
84#3750—22no—
85C4×C3⋊Dic3D414yes—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3C2×C414yes—
89C3×Dic3⋊C4—42no—
90Dic3⋊Dic3—24no—
91Dic3⋊Dic3C2×C418yes—
92#3722—42no—
93#3722C2×C418yes—
94Dic32—24no—
95Dic32—42no—
96#2323—91noSylow
97C22×C3×Q8—31no—
98C22×C4×D3—31no—
99C22×C4×D3—31no—
100C22×C4×D3—61no—
101C22×Dic6C2×D311yescharacteristic
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C42—21no—
107C2×C3×C42C2×D311yescharacteristic
108C2×C3×C42C2×D311yescharacteristic
109#946—38no—
110Q8×Dic3—64no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—31no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—61no—
120C2×(C2×D3)⋊C4—61no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3C2×D311yescharacteristic
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×C4⋊Dic3C2×D311yescharacteristic
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—31no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—61no—
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—61no—
142#897—38no—
143#887—64no—
144#872—64no—
145#872—64no—
146#872—68no—
147C3×#95—32no—
148C3×#95—32no—
149C3×#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95C2×D312yes—
155C3⋊#95C2×D312yes—
156C3⋊#95C2×D312yes—
157C23×C32C2411yescharacteristic
158C22×C3⋊D3—21no—
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3C22×C412yes—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4C22×C412yes—
172C2×C32×C4C2×D412yes—
173C2×C32×C4#4112yes—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3C22×C412yes—
181C2×C3⋊Dic3C2×D412yes—
182C2×C3⋊Dic3C2×D412yes—
183C4×C3⋊D3—28no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
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×Dic3C22×C414yes—
195C2×C3×Dic3C22×C414yes—
196C3×Dic6—28no—
197C2×C22⋊Q8—91no—
198C2×C4×Q8—91no—
199C2×#117—91no—
200#391—31no—
201#389—31no—
202#389—92no—
203#388—92no—
204#388—92no—
205#387—92no—
206#380—91no—
207C4×C4⋊C4—91no—
208C23×D3—31no—
209C23×D3—31no—
210C23×D3—61no—
211C2×C3×Q8—34no—
212C2×C3×Q8—62no—
213C2×C3×Q8—62no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C2×C4×D3—34no—
241C2×C4×D3—34no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×Dic6—22no—
250C2×Dic6—22no—
251C2×Dic6C4×D314yes—
252C3×C4⋊C4—34no—
253C3×C4⋊C4—62no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—122no—
256C3×C42—24no—
257C3×C42—22no—
258C3×C42—22no—
259(C2×D3)⋊C4—38no—
260(C2×D3)⋊C4—38no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—122no—
268(C2×D3)⋊C4—122no—
269C4⋊Dic3—22no—
270C4⋊Dic3—22no—
271C4⋊Dic3—38no—
272C4⋊Dic3—64no—
273C4⋊Dic3C4×D314yes—
274Dic3⋊C4—38no—
275Dic3⋊C4—42no—
276Dic3⋊C4—64no—
277Dic3⋊C4—62no—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281Dic3⋊C4—64no—
282Dic3⋊C4—64no—
283C4×Dic3—34no—
284C4×Dic3—34no—
285C4×Dic3—64no—
286C4×Dic3—64no—
287C4×Dic3—64no—
288C4×Dic3—122no—
289C4×Dic3—122no—
290C22×C32C23×C411yescharacteristic
291C22×C32C22×D411yescharacteristic
292C22×C32C2×#4111yescharacteristic
293C22×C32H(5,𝔽2)11yescharacteristic
294C22×C322−1+411yescharacteristic
295C22×C322−1+411yescharacteristic
296C22×C322−1+411yescharacteristic
297C2×C3⋊D3—22no—
298C2×C3⋊D3—22no—
299C2×C3⋊D3—22no—
300C2×C3⋊D3—41no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3⋊D3—41no—
304C32×C4—41no—
305C32×C4—41no—
306C32×C4C4×D414yes—
307C3⋊Dic3—22no—
308C3⋊Dic3—22no—
309C3⋊Dic3—22no—
310C3×Dic3—24no—
311C3×Dic3—24no—
312C3×Dic3—42no—
313C3×Dic3—42no—
314C22×Q8—31no—
315C23×C4—91no—
316C22⋊Q8—98no—
317C4×Q8—184no—
318#117—184no—
319C2×C4⋊C4—31no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—92no—
324C2×C4⋊C4—92no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—91no—
327C2×C22⋊C4—92no—
328C2×C22⋊C4—91no—
329C2×C22⋊C4—91no—
330C2×C22⋊C4—92no—
331C2×C42—91no—
332C2×C42—92no—
333C2×C42—92no—
334C2×C42D3211yescharacteristic
335#95—32no—
336#95—32no—
337#95—32no—
338#95—92no—
339#95—92no—
340C23×C3—21no—
341C23×C3C23×D311yescharacteristic
342C23×C3C23×D311yescharacteristic
343C22×D3—32no—
344C22×D3—32no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—61no—
353C22×D3—61no—
354C22×D3—61no—
355C22×D3—61no—
356C22×D3—61no—
357C22×D3—61no—
358C22×D3—61no—
359C22×D3—61no—
360C22×D3—121no—
361C22×D3—121no—
362C22×D3—121no—
363C22×D3—121no—
364C3×Q8—68no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—34no—
383C2×C3×C4—34no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4C2×C4×D312yes—
399C2×C3×C4C2×C4×D312yes—
400C2×C3×C4D3×D412yes—
401C2×C3×C4D3×D412yes—
402C2×C3×C4#23712yes—
403C2×C3×C4#23912yes—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—32no—
415C2×Dic3—32no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—32no—
419C2×Dic3—32no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—121no—
438C2×Dic3—121no—
439C2×Dic3—121no—
440C2×Dic3—121no—
441C2×Dic3C2×C4×D314yes—
442C2×Dic3C2×C4×D314yes—
443C4×D3—616no—
444C4×D3—68no—
445C4×D3—68no—
446Dic6—28no—
447C2×C32C2×C4×D411yescharacteristic
448C2×C32#51911yescharacteristic
449C2×C32#52011yescharacteristic
450C2×C32#53611yescharacteristic
451C2×C32#53711yescharacteristic
452C2×C32#54111yescharacteristic
453C2×C32#54211yescharacteristic
454C3⋊D3—42no—
455C24—91no—
456C2×Q8—34no—
457C2×Q8—62no—
458C2×Q8—62no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—32no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—94no—
467C22×C4—182no—
468C22×C4—182no—
469C22×C4C2×D3211yescharacteristic
470C22×C4C2×D3211yescharacteristic
471C22×C4C2×D3211yescharacteristic
472C4⋊C4—34no—
473C4⋊C4—62no—
474C4⋊C4—62no—
475C4⋊C4—98no—
476C4⋊C4—122no—
477C4⋊C4—182no—
478C4⋊C4—182no—
479C4⋊C4—184no—
480C22⋊C4—98no—
481C22⋊C4—182no—
482C22⋊C4—182no—
483C22⋊C4—362no—
484C42—22no—
485C42—94no—
486C42—184no—
487C42—362no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3C22×C4×D311yescharacteristic
496C22×C3C22×C4×D311yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C22×C3C2×D3×D411yescharacteristic
499C22×C3C2×#23711yescharacteristic
500C22×C3#100411yescharacteristic
501C22×C3C2×#23911yescharacteristic
502C22×C3#100711yescharacteristic
503C22×C3#100711yescharacteristic
504C22×C3#100711yescharacteristic
505C22×C3#100911yescharacteristic
506C22×C3#101011yescharacteristic
507C22×C3#101011yescharacteristic
508C22×C3#101011yescharacteristic
509C2×D3—64no—
510C2×D3—62no—
511C2×D3—62no—
512C2×D3—62no—
513C2×D3—62no—
514C2×D3—62no—
515C2×D3—62no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—121no—
530C3×C4—24no—
531C3×C4—42no—
532C3×C4—42no—
533C3×C4—41no—
534C3×C4—41no—
535C3×C4—41no—
536C3×C4—41no—
537C3×C4—64no—
538C3×C4—64no—
539C3×C4—122no—
540C3×C4—122no—
541C3×C4#67⋊C414yes—
542C3×C4#89314yes—
543Dic3—24no—
544Dic3—24no—
545Dic3—42no—
546Dic3—42no—
547Dic3—64no—
548Dic3—62no—
549Dic3—62no—
550Dic3—62no—
551Dic3—62no—
552Dic3—62no—
553Dic3—62no—
554Dic3—122no—
555Dic3—122no—
556C32#232311yescharacteristic, complemented, Sylow
557C23—92no—
558C23—181no—
559C23—181no—
560C23—181no—
561C23—181no—
562C23—181no—
563C23—181no—
564C23C22×D3211yescharacteristic
565Q8—68no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—34no—
573C2×C4—34no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—92no—
585C2×C4—92no—
586C2×C4—92no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—188no—
594C2×C4#379612yes—
595C2×C4C4×D3212yes—
596C2×C4#381112yes—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3C2×#67⋊C411yescharacteristic
605C2×C3C2×#89311yescharacteristic
606C2×C3#554611yescharacteristic
607C2×C3#557211yescharacteristic
608C2×C3#557211yescharacteristic
609C2×C3#557411yescharacteristic
610C2×C3#560811yescharacteristic
611C2×C3#562811yescharacteristic
612C2×C3#562811yescharacteristic
613C2×C3#562911yescharacteristic
614C2×C3#568211yescharacteristic
615C2×C3#569811yescharacteristic
616C2×C3#573111yescharacteristic
617C2×C3#573311yescharacteristic
618D3—124no—
619D3—122no—
620D3—122no—
621C22—182no—
622C22—182no—
623C22—182no—
624C22—361no—
625C22—361no—
626C22—361no—
627C22—361no—
628C22C2×#379611yescharacteristic
629C22#6429711yescharacteristic
630C22#6429711yescharacteristic
631C22#6429711yescharacteristic
632C22C2×C4×D3211yescharacteristic
633C22#6430711yescharacteristic
634C22C2×#381111yescharacteristic
635C4—41no—
636C4—41no—
637C4—64no—
638C4—64no—
639C4—122no—
640C4—122no—
641C4—182no—
642C4—182no—
643C4—182no—
644C4#6388114yes—
645C3—21no—
646C3#7619711yescharacteristic, complemented
647C3#7661111yescharacteristic, complemented
648C2—362no—
649C2#1059384811yescharacteristic
650C2#1059386711yescharacteristic
651C2#1059388911yescharacteristic
652C2#1059395511yescharacteristic
653C2#1059480511yescharacteristic
654C2C2×#6388111yescharacteristic
655C2#1059492311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#63843C2semidirect
4. C3×#4929C2semidirect
5. C3×#4928C2semidirect
7. #10591274C2semidirect
10. #10591251C2semidirect
11. #10591234C2semidirect
33. #63871C4semidirect
55. #4929D3semidirect
56. #4928D3semidirect
556. C32#2323semidirect
646. C3#76197semidirect
647. C3#76611semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×#638712
C2×#638432
C3×#49292
C3×#49282
#105913252
#105912742
#105912592
#105912582
#105912512
#105912342
#766113
#761973