Finite Group Databasebeta

← #11803491

Subgroups — #11803491

Order 1152.

1261 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic
3C2×#63855C211yesmaximal, characteristic
4C3×#5229C211yesmaximal, characteristic, complemented
5#10591352C211yesmaximal, characteristic, complemented
6#10591316C212yesmaximal
7#10591313C211yesmaximal, characteristic
8#10591286C212yesmaximal
9#10591274C211yesmaximal, characteristic, complemented
10#10591268C212yesmaximal, complemented
11#10591192C212yesmaximal, complemented
12#82744—31nomaximal
13#76611—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16Q8×C3⋊Dic3—24no—
17C2×C4⋊(C3⋊Dic3)C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C3×#946C418yescomplemented
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×Dic32C2212yes—
34#63855—24no—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C22⋊Q8—31no—
41C2×#946D311yescharacteristic
42C2×Q8×Dic3—31no—
43C2×Q8×Dic3—31no—
44C2×Q8×Dic3—61no—
45C2×#926—31no—
46C2×#872—31no—
47C3×#391—31no—
48#5229D311yescharacteristic, complemented
49#5212—31no—
50#4987—31no—
51#4984—31no—
52#4984—32no—
53#4980—32no—
54Dic3×C4⋊C4—31no—
55Dic3×C4⋊C4—31no—
56#4951—32no—
57#4951—32no—
58#4928—31no—
59#4670—32no—
60#4669—32no—
61#4652—32no—
62#4647—32no—
63C23×C3×D3C2311yescharacteristic
64C2×C32×Q8—22no—
65C2×C32×Q8—22no—
66C2×C32×Q8C2×C414yes—
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3C2×C414yes—
80C4⋊(C3⋊Dic3)—22no—
81C4⋊(C3⋊Dic3)—24no—
82C4×C3⋊Dic3—24no—
83C4×C3⋊Dic3D414yes—
84C3×(C2×D3)⋊C4C2×C418yes—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3C2×C414yes—
87C3×Dic3⋊C4C2×C418yes—
88C3×C4×Dic3—22no—
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—42no—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—42no—
95Dic32—42no—
96#2323—91noSylow
97C22×C3×Q8—21no—
98C22×C3×Q8C2×D311yescharacteristic
99C22×C3×Q8C2×D311yescharacteristic
100C23×C3×C4—31no—
101C22×C4×D3C2×D311yescharacteristic
102C3×C22⋊Q8—38no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C42—31no—
108C2×#217—31no—
109C2×#217—31no—
110C2×#217—32no—
111#946Dic318yescomplemented
112Q8×Dic3—64no—
113Q8×Dic3—64no—
114Q8×Dic3—68no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—31no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4C2×D312yes—
119#926—64no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3—62no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—32no—
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—
142C2×C4×Dic3—62no—
143C2×C4×Dic3C2×D311yescharacteristic
144#872—64no—
145C3×#95—32no—
146C3×#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95C2×D312yes—
154C3⋊#95C2×D312yes—
155C23×C32C2411yescharacteristic
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3C22×C412yes—
163C32×Q8—28no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C22×C414yes—
167C2×C32×C4C22×C412yes—
168C2×C32×C4C2×D412yes—
169C2×C32×C4#4112yes—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3C2×D412yes—
178C2×C3⋊Dic3C2×D412yes—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3C22×C412yes—
193C2×C3×Dic3C22×C414yes—
194C3×C4×D3—28no—
195C2×C22⋊Q8—31no—
196C2×C4×Q8—91no—
197C2×#117—91no—
198#391—31no—
199#389—92no—
200#389—91no—
201#388—92no—
202#388—92no—
203#387—92no—
204#380—91no—
205C4×C4⋊C4—91no—
206C24×C3—31no—
207C23×D3C22×D311yescharacteristic
208C2×C3×Q8—24no—
209C2×C3×Q8—24no—
210C2×C3×Q8—22no—
211C2×C3×Q8—22no—
212C2×C3×Q8—22no—
213C2×C3×Q8—22no—
214C2×C3×Q8—24no—
215C2×C3×Q8C4×D314yes—
216C2×C3×Q8C2×Dic314yes—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—32no—
220C22×C3×C4—31no—
221C22×C3×C4—34no—
222C22×C3×C4—32no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—62no—
226C22×C3×C4—62no—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—62no—
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D311yescharacteristic
242C22×Dic3C22×D311yescharacteristic
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D311yescharacteristic
245C2×C4×D3—22no—
246C2×C4×D3—22no—
247C2×C4×D3C2×Dic314yes—
248C3×C4⋊C4—38no—
249C3×C4⋊C4—34no—
250C3×C4⋊C4—62no—
251C3×C22⋊C4—38no—
252C3×C42—62no—
253#217—62no—
254#217—62no—
255#217—122no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—122no—
259(C2×D3)⋊C4C2×Dic318yes—
260C4⋊Dic3—22no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—64no—
264C4⋊Dic3—64no—
265C4⋊Dic3—68no—
266C4⋊Dic3—64no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3—122no—
270C4⋊Dic3C2×Dic314yes—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—122no—
274Dic3⋊C4C2×Dic318yes—
275C4×Dic3—22no—
276C4×Dic3—34no—
277C4×Dic3—34no—
278C4×Dic3—64no—
279C4×Dic3—64no—
280C4×Dic3—64no—
281C4×Dic3—68no—
282C4×Dic3—122no—
283C4×Dic3—122no—
284C22×C32C23×C411yescharacteristic
285C22×C32C22×D411yescharacteristic
286C22×C32C2×#4111yescharacteristic
287C22×C32H(5,𝔽2)11yescharacteristic
288C22×C322−1+411yescharacteristic
289C22×C322−1+411yescharacteristic
290C22×C322−1+411yescharacteristic
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C2×C3×D3—41no—
298C32×C4—24no—
299C32×C4C4×D414yes—
300C3⋊Dic3—22no—
301C3⋊Dic3—22no—
302C3⋊Dic3—42no—
303C3×Dic3—22no—
304C3×Dic3—24no—
305C3×Dic3—41no—
306C3×Dic3—41no—
307C3×Dic3—42no—
308C22×Q8D3211yescharacteristic
309C23×C4—31no—
310C22⋊Q8—38no—
311C4×Q8—184no—
312#117—184no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—32no—
315C2×C4⋊C4—31no—
316C2×C4⋊C4—91no—
317C2×C4⋊C4—91no—
318C2×C4⋊C4—91no—
319C2×C4⋊C4—92no—
320C2×C4⋊C4—92no—
321C2×C22⋊C4—32no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4—91no—
324C2×C22⋊C4—92no—
325C2×C42—31no—
326C2×C42—91no—
327C2×C42—92no—
328C2×C42—92no—
329#95—32no—
330#95—32no—
331#95—92no—
332#95—92no—
333#95—92no—
334C23×C3—21no—
335C23×C3—32no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—61no—
339C23×C3—61no—
340C23×C3—61no—
341C23×C3—61no—
342C23×C3C23×D311yescharacteristic
343C23×C3C23×D311yescharacteristic
344C22×D3—21no—
345C22×D3—21no—
346C22×D3—21no—
347C22×D3—21no—
348C22×D3—21no—
349C22×D3—21no—
350C22×D3C22×Dic312yes—
351C3×Q8—216no—
352C3×Q8—28no—
353C3×Q8—28no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—34no—
365C2×C3×C4—32no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—68no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4C2×C4×D314yes—
381C2×C3×C4C2×C4×D312yes—
382C2×C3×C4D3×D412yes—
383C2×C3×C4D3×D412yes—
384C2×C3×C4#23712yes—
385C2×C3×C4#23712yes—
386C2×C3×C4C22×Dic314yes—
387C2×C3×C4C22×Dic312yes—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—22no—
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—22no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—21no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—64no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—121no—
425C2×Dic3—121no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428C2×Dic3C22×Dic312yes—
429C2×Dic3C22×Dic314yes—
430C4×D3—28no—
431C2×C32C2×C4×D411yescharacteristic
432C2×C32#51911yescharacteristic
433C2×C32#52011yescharacteristic
434C2×C32#53611yescharacteristic
435C2×C32#53711yescharacteristic
436C2×C32#54111yescharacteristic
437C2×C32#54211yescharacteristic
438C3×D3—42no—
439C24—31no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8D3×Dic314yes—
443C22×C4—32no—
444C22×C4—31no—
445C22×C4—34no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—31no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—91no—
452C22×C4—91no—
453C22×C4—92no—
454C22×C4C2×D3212yes—
455C22×C4C2×D3211yescharacteristic
456C4⋊C4—38no—
457C4⋊C4—34no—
458C4⋊C4—62no—
459C4⋊C4—184no—
460C4⋊C4—182no—
461C4⋊C4—182no—
462C4⋊C4—182no—
463C4⋊C4—362no—
464C22⋊C4—38no—
465C22⋊C4—182no—
466C22⋊C4—182no—
467C22⋊C4—362no—
468C42—62no—
469C42—94no—
470C42—184no—
471C42—362no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—62no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—121no—
483C22×C3—121no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3C22×C4×D311yescharacteristic
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C2×D3×D411yescharacteristic
489C22×C3C2×#23711yescharacteristic
490C22×C3C2×#23711yescharacteristic
491C22×C3#100711yescharacteristic
492C22×C3#100711yescharacteristic
493C22×C3#100711yescharacteristic
494C22×C3#100711yescharacteristic
495C22×C3#100911yescharacteristic
496C22×C3#100911yescharacteristic
497C22×C3#101011yescharacteristic
498C22×C3#101011yescharacteristic
499C22×C3C23×Dic311yescharacteristic
500C2×D3—22no—
501C2×D3—22no—
502C2×D3—22no—
503C2×D3—41no—
504C2×D3—41no—
505C2×D3—41no—
506C2×D3—41no—
507C3×C4—28no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—24no—
511C3×C4—62no—
512C3×C4—64no—
513C3×C4—122no—
514C3×C4—121no—
515C3×C4—121no—
516C3×C4#67⋊C414yes—
517C3×C4D4×Dic314yes—
518Dic3—22no—
519Dic3—24no—
520Dic3—42no—
521Dic3—41no—
522Dic3—41no—
523Dic3—64no—
524Dic3—62no—
525Dic3—62no—
526Dic3—62no—
527Dic3—62no—
528Dic3—122no—
529Dic3—124no—
530Dic3—122no—
531Dic3—122no—
532C32#232311yescharacteristic, complemented, Sylow
533C23—32no—
534C23—61no—
535C23—61no—
536C23—61no—
537C23—61no—
538C23—61no—
539C23—61no—
540C23C22×D3211yescharacteristic
541Q8—28no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—34no—
545C2×C4—32no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—68no—
551C2×C4—62no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—182no—
567C2×C4—182no—
568C2×C4—182no—
569C2×C4C2×D3×Dic314yes—
570C2×C4C2×D3×Dic312yes—
571C2×C4#380512yes—
572C2×C4#381112yes—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—122no—
581C2×C3C2×#67⋊C411yescharacteristic
582C2×C3#557211yescharacteristic
583C2×C3#557411yescharacteristic
584C2×C3#562511yescharacteristic
585C2×C3#562811yescharacteristic
586C2×C3#562811yescharacteristic
587C2×C3#562911yescharacteristic
588C2×C3#562911yescharacteristic
589C2×C3#564311yescharacteristic
590C2×C3#568211yescharacteristic
591C2×C3#573111yescharacteristic
592C2×C3C2×D4×Dic311yescharacteristic
593C2×C3#581211yescharacteristic
594C2×C3#582711yescharacteristic
595D3—42no—
596C22—62no—
597C22—62no—
598C22—62no—
599C22—121no—
600C22—121no—
601C22—121no—
602C22—121no—
603C22#6431511yescharacteristic
604C22#6431511yescharacteristic
605C22#6431611yescharacteristic
606C22#6432011yescharacteristic
607C22C22×D3×Dic311yescharacteristic
608C22C2×#380511yescharacteristic
609C22C2×#381111yescharacteristic
610C4—24no—
611C4—64no—
612C4—62no—
613C4—122no—
614C4—121no—
615C4—121no—
616C4—182no—
617C4—182no—
618C4—362no—
619C4#67⋊Dic314yes—
620C3—21no—
621C3#7661111yescharacteristic, complemented
622C3#8274411yescharacteristic, complemented
623C2—122no—
624C2#1059534711yescharacteristic
625C2#1059534911yescharacteristic
626C2#1059539411yescharacteristic
627C2#1059539611yescharacteristic
628C2#1059540411yescharacteristic
629C2#1059540511yescharacteristic
630C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC22×Q8D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
4. C3×#5229C2semidirect
5. #10591352C2semidirect
9. #10591274C2semidirect
10. #10591268C2semidirect
11. #10591192C2semidirect
21. C3×#946C4semidirect
48. #5229D3semidirect
111. #946Dic3semidirect
532. C32#2323semidirect
621. C3#76611semidirect
622. C3#82744semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C3×#9462
C2×#638552
C3×#52292
#105913522
#105913162
#105913132
#105912862
#105912742
#105912682
#105911922
#827443
#766113