Finite Group Databasebeta

← #11803495

Subgroups — #11803495

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63874C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4#10592686C211yesmaximal, characteristic
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6C3×#4973C211yesmaximal, characteristic, complemented
7#10591352C211yesmaximal, characteristic, complemented
8#10591327C212yesmaximal, complemented
9#10591259C212yesmaximal
10#10591250C212yesmaximal, complemented
11#10591194C212yesmaximal
12#76611—31nomaximal
13#73762—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×#3724C2211yescharacteristic
24C2×#3724C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×#3722C2211yescharacteristic
29C2×#3722C2211yescharacteristic
30C2×#3722C2212yes—
31C2×Dic32C2212yes—
32#63874—24no—
33#63871C418yescomplemented
34Dic3×Dic6—24no—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×#946—31no—
41C2×Q8×Dic3—31no—
42C2×#897—31no—
43C2×#872—31no—
44C2×#872—31no—
45C2×C4×Dic6—31no—
46C3×#391—31no—
47C3×C4×C4⋊C4—31no—
48#4987—31no—
49#4987—31no—
50#4987—61no—
51#4984—31no—
52Dic3×C4⋊C4D311yescharacteristic, complemented
53#4973D311yescharacteristic, complemented
54#4940—32no—
55#4928—31no—
56#4928—32no—
57#4670—32no—
58#4670—32no—
59#4669—32no—
60#4653—32no—
61#4652—32no—
62#4647—32no—
63C23×C3⋊D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3C2×C414yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2×C414yes—
80C32×C4⋊C4—22no—
81#3752—42no—
82C4⋊(C3⋊Dic3)—22no—
83C3×C4⋊Dic3C2×C414yes—
84C3×C4×Dic3—22no—
85C3×C4×Dic3—42no—
86C3×C4×Dic3D414yes—
87#3724—22no—
88#3724—22no—
89Dic3⋊Dic3—24no—
90Dic3⋊Dic3—42no—
91Dic3⋊Dic3C2×C418yes—
92#3722—22no—
93#3722—22no—
94#3722C2×C418yes—
95Dic32—24no—
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—21no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C4⋊C4C2×D311yescharacteristic
106C2×C3×C42—31no—
107C2×C3×C42—31no—
108C2×C3×C42—32no—
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—62no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—61no—
126C2×C4⋊Dic3C2×D311yescharacteristic
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—31no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3C2×D311yescharacteristic
137C2×C4×Dic3C2×D312yes—
138C2×C4×Dic3C2×D311yescharacteristic
139#897—38no—
140#872—64no—
141#872—64no—
142C4×Dic6—64no—
143C3×#95—32no—
144C3×#95—32no—
145C3×#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—62no—
151C3⋊#95C2×D312yes—
152C3⋊#95C2×D312yes—
153C3⋊#95C2×D312yes—
154C23×C32C2411yescharacteristic
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3—21no—
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3C22×C412yes—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C22×C412yes—
166C2×C32×C4C2×D412yes—
167C2×C32×C4#4112yes—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C22×C412yes—
174C4×C3⋊D3—28no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C22×C414yes—
190C2×C3×Dic3C22×C414yes—
191C2×C3×Dic3C2×D412yes—
192C2×C3×Dic3C2×D412yes—
193C3×Dic6—28no—
194C2×C22⋊Q8—91no—
195C2×C4×Q8—91no—
196C2×#117—91no—
197#391—31no—
198#389—92no—
199#389—91no—
200#388—92no—
201#388—92no—
202#387—92no—
203#380—91no—
204C4×C4⋊C4—31no—
205C23×D3—31no—
206C23×D3—31no—
207C23×D3—61no—
208C2×C3×Q8—34no—
209C2×C3×Q8—62no—
210C2×C3×Q8—62no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—32no—
214C22×C3×C4—31no—
215C22×C3×C4—32no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D312yes—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—61no—
228C22×Dic3—62no—
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D311yescharacteristic
235C2×C4×D3—34no—
236C2×C4×D3—34no—
237C2×C4×D3—64no—
238C2×C4×D3—62no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—122no—
243C2×C4×D3—122no—
244C2×Dic6—22no—
245C2×Dic6—22no—
246C2×Dic6C4×D314yes—
247C3×C4⋊C4—22no—
248C3×C4⋊C4—22no—
249C3×C4⋊C4—34no—
250C3×C4⋊C4—42no—
251C3×C42—34no—
252C3×C42—62no—
253C3×C42—122no—
254(C2×D3)⋊C4—38no—
255(C2×D3)⋊C4—38no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—122no—
261(C2×D3)⋊C4—122no—
262(C2×D3)⋊C4—124no—
263C4⋊Dic3—38no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3—64no—
267C4⋊Dic3—122no—
268C4⋊Dic3—122no—
269C4⋊Dic3C4×D314yes—
270Dic3⋊C4—38no—
271Dic3⋊C4—64no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—122no—
277C4×Dic3—22no—
278C4×Dic3—42no—
279C4×Dic3—64no—
280C4×Dic3—64no—
281C4×Dic3D1214yes—
282C22×C32C23×C411yescharacteristic
283C22×C32C22×D411yescharacteristic
284C22×C32C2×#4111yescharacteristic
285C22×C32H(5,𝔽2)11yescharacteristic
286C22×C322−1+411yescharacteristic
287C22×C322−1+411yescharacteristic
288C22×C322−1+411yescharacteristic
289C2×C3⋊D3—22no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—22no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C32×C4—42no—
297C32×C4C4×D414yes—
298C3⋊Dic3—22no—
299C3⋊Dic3—42no—
300C3×Dic3—24no—
301C3×Dic3—24no—
302C3×Dic3—22no—
303C3×Dic3—22no—
304C3×Dic3—41no—
305C3×Dic3—41no—
306C22×Q8—31no—
307C23×C4—91no—
308C22⋊Q8—98no—
309C4×Q8—184no—
310#117—184no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—92no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—92no—
316C2×C4⋊C4—91no—
317C2×C4⋊C4—92no—
318C2×C4⋊C4D3211yescharacteristic
319C2×C22⋊C4—92no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—91no—
322C2×C22⋊C4—92no—
323C2×C42—31no—
324C2×C42—31no—
325C2×C42—32no—
326C2×C42—92no—
327#95—32no—
328#95—32no—
329#95—32no—
330#95—92no—
331#95—92no—
332C23×C3—21no—
333C23×C3C23×D311yescharacteristic
334C23×C3C23×D311yescharacteristic
335C22×D3—32no—
336C22×D3—32no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C22×D3—121no—
356C3×Q8—68no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—34no—
367C2×C3×C4—34no—
368C2×C3×C4—32no—
369C2×C3×C4—32no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4C2×D1212yes—
390C2×C3×C4#23512yes—
391C2×C3×C4D3×D412yes—
392C2×C3×C4#23712yes—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—62no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—122no—
423C2×Dic3—122no—
424C2×Dic3—122no—
425C2×Dic3C2×C4×D314yes—
426C2×Dic3C2×C4×D314yes—
427C2×Dic3C2×D1212yes—
428C2×Dic3C2×D1212yes—
429C4×D3—68no—
430C4×D3—68no—
431C4×D3—128no—
432Dic6—28no—
433C2×C32C2×C4×D411yescharacteristic
434C2×C32#51911yescharacteristic
435C2×C32#52011yescharacteristic
436C2×C32#53611yescharacteristic
437C2×C32#53711yescharacteristic
438C2×C32#54111yescharacteristic
439C2×C32#54211yescharacteristic
440C3⋊D3—42no—
441C24—91no—
442C2×Q8—34no—
443C2×Q8—62no—
444C2×Q8—62no—
445C22×C4—31no—
446C22×C4—32no—
447C22×C4—32no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—91no—
452C22×C4—94no—
453C22×C4—92no—
454C22×C4—182no—
455C22×C4—182no—
456C22×C4C2×D3212yes—
457C22×C4C2×D3211yescharacteristic
458C4⋊C4—22no—
459C4⋊C4—34no—
460C4⋊C4—98no—
461C4⋊C4—182no—
462C4⋊C4—182no—
463C4⋊C4—184no—
464C4⋊C4—182no—
465C4⋊C4—362no—
466C22⋊C4—98no—
467C22⋊C4—182no—
468C22⋊C4—182no—
469C22⋊C4—362no—
470C42—34no—
471C42—62no—
472C42—122no—
473C42—184no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3C22×C4×D311yescharacteristic
482C22×C3C22×C4×D311yescharacteristic
483C22×C3C22×D1211yescharacteristic
484C22×C3C2×#23511yescharacteristic
485C22×C3C2×D3×D411yescharacteristic
486C22×C3C2×#23711yescharacteristic
487C22×C3#100411yescharacteristic
488C22×C3#100711yescharacteristic
489C22×C3#100711yescharacteristic
490C22×C3#100711yescharacteristic
491C22×C3#100911yescharacteristic
492C22×C3#101011yescharacteristic
493C22×C3#101011yescharacteristic
494C22×C3#101011yescharacteristic
495C2×D3—64no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—121no—
513C2×D3—121no—
514C2×D3—121no—
515C2×D3—121no—
516C3×C4—24no—
517C3×C4—42no—
518C3×C4—42no—
519C3×C4—64no—
520C3×C4—64no—
521C3×C4—62no—
522C3×C4—62no—
523C3×C4—82no—
524C3×C4—121no—
525C3×C4—121no—
526C3×C4C4×D1214yes—
527C3×C4#67⋊C414yes—
528Dic3—24no—
529Dic3—22no—
530Dic3—22no—
531Dic3—24no—
532Dic3—41no—
533Dic3—41no—
534Dic3—62no—
535Dic3—62no—
536Dic3—122no—
537Dic3—122no—
538Dic3—122no—
539Dic3—242no—
540C32#232311yescharacteristic, complemented, Sylow
541C23—92no—
542C23—181no—
543C23—181no—
544C23—181no—
545C23—181no—
546C23—181no—
547C23—181no—
548C23C22×D3211yescharacteristic
549Q8—68no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—34no—
554C2×C4—34no—
555C2×C4—32no—
556C2×C4—32no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—62no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—92no—
572C2×C4—181no—
573C2×C4—181no—
574C2×C4—188no—
575C2×C4—182no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4C4×D3212yes—
579C2×C4D3×D1212yes—
580C2×C4#380412yes—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3C2×C4×D1211yescharacteristic
589C2×C3C2×#67⋊C411yescharacteristic
590C2×C3#551011yescharacteristic
591C2×C3#552611yescharacteristic
592C2×C3#554611yescharacteristic
593C2×C3#556111yescharacteristic
594C2×C3#557211yescharacteristic
595C2×C3#557211yescharacteristic
596C2×C3#557411yescharacteristic
597C2×C3#558311yescharacteristic
598C2×C3#562811yescharacteristic
599C2×C3#562911yescharacteristic
600C2×C3#568211yescharacteristic
601C2×C3#573111yescharacteristic
602D3—124no—
603D3—122no—
604D3—122no—
605C22—182no—
606C22—182no—
607C22—182no—
608C22—361no—
609C22—361no—
610C22—361no—
611C22—361no—
612C22C2×C4×D3211yescharacteristic
613C22C2×D3×D1211yescharacteristic
614C22#6430911yescharacteristic
615C22#6431411yescharacteristic
616C22#6431511yescharacteristic
617C22#6431611yescharacteristic
618C22C2×#380411yescharacteristic
619C4—42no—
620C4—64no—
621C4—64no—
622C4—62no—
623C4—62no—
624C4—121no—
625C4—121no—
626C4—182no—
627C4—362no—
628C4#6388014yes—
629C3—21no—
630C3#7376211yescharacteristic, complemented
631C3#7661111yescharacteristic, complemented
632C2—362no—
633C2#1059434711yescharacteristic
634C2#1059436111yescharacteristic
635C2#1059438011yescharacteristic
636C2#1059452311yescharacteristic
637C2C2×#6388011yescharacteristic
638C2#1059512111yescharacteristic
639C2#1059535411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×Dic6C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
6. C3×#4973C2semidirect
7. #10591352C2semidirect
8. #10591327C2semidirect
10. #10591250C2semidirect
33. #63871C4semidirect
52. Dic3×C4⋊C4D3semidirect
53. #4973D3semidirect
540. C32#2323semidirect
630. C3#73762semidirect
631. C3#76611semidirect

Maximal subgroups

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

subgroupindex
C2×#638742
C2×#638712
C2×Dic3×Dic62
#105926862
C3×Dic3×C4⋊C42
C3×#49732
#105913522
#105913272
#105912592
#105912502
#105911942
#766113
#737623