Finite Group Databasebeta

← #11868670

Subgroups — #11868670

Order 1152.

1093 conjugacy classes of subgroups.

The subgroup lattice has 673 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic, complemented
3C3×#5008C211yesmaximal, characteristic, complemented
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591479C212yesmaximal, complemented
6#10591426C212yesmaximal
7#10590583C212yesmaximal, complemented
8#10590435C212yesmaximal, complemented
9#10590340C211yesmaximal, characteristic, complemented
10#10590313C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#81060—31nomaximal
13#80965—31nomaximal
14C2×D4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C32×C4×D4C2211yescharacteristic
17D4×C3⋊Dic3C2211yescharacteristic
18C4×#638—21no—
19#64102C2211yescharacteristic
20C4⋊C4×C3⋊D3C2211yescharacteristic
21#64090—21no—
22C22⋊C4×C3⋊D3—21no—
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C42×C3⋊D3C2211yescharacteristic
25C3×#869C2211yescharacteristic, complemented
26C3×#869C2211yescharacteristic, complemented
27#63872C2212yescomplemented
28#63871—21no—
29#63871—21no—
30#63849C2212yes—
31#63843—21no—
32#63843—21no—
33C2×#3712C2212yes—
34C3×#832C2212yes—
35C3×#832C2212yes—
36C3×#808C2212yescomplemented
37C3×#807C2212yescomplemented
38C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63575C2212yescomplemented
41#63573C2212yescomplemented
42#63572C2212yescomplemented
43#63564C2212yes—
44#63564C2212yes—
45#5728—31no—
46#5728—31no—
47C4×D3×D4—31no—
48C4×D3×D4—31no—
49C4×D3×D4—61no—
50C3×#476—31no—
51C3×#474—31no—
52#5087—31no—
53#5084—31no—
54#5008D311yescharacteristic, complemented
55#5007D311yescharacteristic, complemented
56#4891—32no—
57#4881—32no—
58#4871—32no—
59#4861—32no—
60#4846—31no—
61#4842—31no—
62#4837—31no—
63#4837—31no—
64#4770—32no—
65#4770—32no—
66#4766—32no—
67#4763—32no—
68C23×C3⋊D3—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×#638—21no—
72C22×C3⋊Dic3—21no—
73D4×C3⋊D3—22no—
74D4×C3⋊D3Q814yescomplemented
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C4×C3⋊D3—21no—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×C4×C3⋊D3—44no—
80C2×C4×C3⋊D3D411yescharacteristic
81C2×C4×C3⋊D3D411yescharacteristic
82C2×C4×C3⋊D3C2311yescharacteristic
83C2×C3×Dic6—21no—
84C2×C3×Dic6—21no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3757—21no—
89#3752—21no—
90#3752—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3750—21no—
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2312yes—
99C3×C4⋊Dic3C2312yes—
100C2×C3×C3⋊C8C2312yes—
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104#3722—22no—
105Dic32—22no—
106#3712—24no—
107#3077—91noSylow
108C2×D3×D4—31no—
109C2×D3×D4—31no—
110C2×D3×D4—61no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C22×C4×D3—62no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8—31no—
116C3×C4×D4—21no—
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C2×D311yescharacteristic
119#946—61no—
120#946—61no—
121Q8×Dic3—61no—
122Q8×Dic3—61no—
123D4×Dic3—31no—
124D4×Dic3—31no—
125D4×Dic3—61no—
126C4×#67—61no—
127C4×#67—61no—
128C4×#67—62no—
129C2×ΓL(1,𝔽25)—32no—
130C2×ΓL(1,𝔽25)—32no—
131#897—61no—
132#897—61no—
133#893—31no—
134#893—31no—
135#893—61no—
136#892—32no—
137#892—32no—
138D3×C4⋊C4—31no—
139D3×C4⋊C4—31no—
140D3×C4⋊C4—61no—
141#890—32no—
142#890—32no—
143#887—61no—
144#887—61no—
145#67⋊C4—61no—
146#67⋊C4—61no—
147#67⋊C4—62no—
148D3×C22⋊C4—61no—
149D3×C22⋊C4—61no—
150D3×C22⋊C4—62no—
151C4×D12—31no—
152C4×D12—31no—
153C4×D12—61no—
154C42×D3—31no—
155C42×D3—31no—
156C42×D3—61no—
157#869C2×D311yescharacteristic, complemented
158#869C2×D311yescharacteristic, complemented
159C3×#107—32no—
160C3×#106—32no—
161C3×C4⋊C8—31no—
162C3×C4⋊C8—31no—
163C3×#102—32no—
164C3×#102—32no—
165#832C2×D312yes—
166#832C2×D312yes—
167#821—32no—
168#821—32no—
169#818—32no—
170#817—32no—
171Dic3⋊C8—32no—
172Dic3⋊C8—32no—
173#809—32no—
174#809—32no—
175#808—32no—
176#808C2×D312yescomplemented
177#807—32no—
178#807C2×D312yescomplemented
179C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
180C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
181C23×C32—21no—
182C22×C3⋊D3—21no—
183C22×C3⋊D3—24no—
184C22×C3⋊D3—42no—
185C22×C3⋊D3—42no—
186C22×C3⋊D3C2×D411yescharacteristic
187C32×D4—21no—
188C32×D4C2×Q812yes—
189C2×C32×C4—21no—
190C2×C32×C4—42no—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194#638—24no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—42no—
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C4⋊(C3⋊D3)—21no—
201C4⋊(C3⋊D3)C2×Q812yes—
202C4×C3⋊D3—22no—
203C4×C3⋊D3—41no—
204C4×C3⋊D3—42no—
205C4×C3⋊D3—42no—
206C4×C3⋊D3—42no—
207C4×C3⋊D3C2×Q812yes—
208C4×C3⋊D3#4112yes—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C3×Dic6—42no—
212C3×Dic6—42no—
213C3×C3⋊C8—22no—
214C3×C3⋊C8—22no—
215#533—91no—
216C2×C4×D4—91no—
217#478—92no—
218#478—92no—
219#476—31no—
220#476—91no—
221#474—31no—
222#474—91no—
223#428—92no—
224#423—91no—
225#418—92no—
226C23×D3—61no—
227C23×D3—61no—
228C23×D3—62no—
229C2×C3×Q8—61no—
230C2×C3×Q8—61no—
231C2×C3×D4—21no—
232C2×C3×D4C22×D311yescharacteristic
233C2×C3×D4C22×D311yescharacteristic
234C22×C3×C4—22no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C2×#67—61no—
238C2×#67—61no—
239C2×#67—62no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3—62no—
243D3×D4—34no—
244D3×D4—34no—
245D3×D4—64no—
246D3×D4—62no—
247D3×D4—62no—
248D3×D4—64no—
249C2×D12—31no—
250C2×D12—31no—
251C2×D12—61no—
252C2×C4×D3—31no—
253C2×C4×D3—31no—
254C2×C4×D3—31no—
255C2×C4×D3—31no—
256C2×C4×D3—31no—
257C2×C4×D3—31no—
258C2×C4×D3—61no—
259C2×C4×D3—61no—
260C2×C4×D3—61no—
261C2×C4×D3—61no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—61no—
269C2×C4×D3—61no—
270C2×C4×D3—128no—
271C2×C4×D3—124no—
272C2×C4×D3—124no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×C3×C8—32no—
276C2×C3×C8—32no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—32no—
279C3×C4⋊C4—32no—
280C3×C4⋊C4—61no—
281C3×C4⋊C4—61no—
282C3×C4⋊C4C22×D311yescharacteristic
283C3×C4⋊C4C22×D311yescharacteristic
284C3×C22⋊C4—22no—
285C3×C22⋊C4—21no—
286C3×C22⋊C4—21no—
287C3×C42—21no—
288C3×C42C22×D311yescharacteristic
289C3×C42C22×D311yescharacteristic
290#217—61no—
291#217—61no—
292#217—62no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—61no—
300(C2×D3)⋊C4—61no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—31no—
304C4⋊Dic3—31no—
305C4⋊Dic3—61no—
306C4⋊Dic3—62no—
307C4⋊Dic3—62no—
308C4⋊Dic3C22×D312yes—
309C4⋊Dic3C22×D312yes—
310Dic3⋊C4—62no—
311Dic3⋊C4—62no—
312Dic3⋊C4—61no—
313Dic3⋊C4—61no—
314Dic3⋊C4—62no—
315C4×Dic3—31no—
316C4×Dic3—31no—
317C4×Dic3—31no—
318C4×Dic3—31no—
319C4×Dic3—31no—
320C4×Dic3—31no—
321C4×Dic3—61no—
322C4×Dic3—61no—
323C4×Dic3—61no—
324C4×Dic3—62no—
325C4×Dic3—62no—
326C2×C3⋊C8C22×D312yes—
327C2×C3⋊C8C22×D312yes—
328ΓL(1,𝔽25)—64no—
329ΓL(1,𝔽25)—64no—
330C22×C32—22no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32C22×D411yescharacteristic
334C2×C3⋊D3—21no—
335C2×C3⋊D3—21no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—48no—
338C2×C3⋊D3—41no—
339C2×C3⋊D3—41no—
340C2×C3⋊D3C22⋊Q812yes—
341C32×C4—21no—
342C32×C4—41no—
343C32×C4AGL(1,ℤ/8)12yes—
344C32×C4C22×Q811yescharacteristic
345C32×C4C2×#4111yescharacteristic
346C3⋊Dic3—21no—
347C3⋊Dic3—21no—
348C3⋊Dic3—41no—
349C3⋊Dic3C22⋊Q812yes—
350C3×Dic3—42no—
351C3×Dic3—42no—
352C22×D4—91no—
353C23×C4—181no—
354C2×M16—92no—
355C4⋊Q8—31no—
356C4⋊Q8—31no—
357#125—92no—
358C22⋊Q8—181no—
359C22⋊Q8—181no—
360C4×Q8—181no—
361C4×Q8—181no—
362C4×D4—91no—
363C4×D4—91no—
364C4×D4—91no—
365C4×D4—181no—
366C4×D4—181no—
367C4×D4D3211yescharacteristic
368#117—92no—
369C2×C4⋊C4—91no—
370C2×C22⋊C4—181no—
371C2×C42—91no—
372#107—32no—
373#107—92no—
374#106—32no—
375#106—92no—
376C4⋊C8—31no—
377C4⋊C8—31no—
378C4⋊C8—92no—
379#102—32no—
380#102—32no—
381#102—92no—
382#102—92no—
383C23×C3—22no—
384C23×C3—21no—
385C23×C3—21no—
386C22×D3—31no—
387C22×D3—31no—
388C22×D3—61no—
389C22×D3—64no—
390C22×D3—64no—
391C22×D3—62no—
392C22×D3—68no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—124no—
396C22×D3—122no—
397C22×D3—122no—
398C22×D3—124no—
399C22×D3—122no—
400C22×D3—122no—
401C3×Q8—122no—
402C3×Q8—122no—
403C3×D4—22no—
404C3×D4—21no—
405C3×D4—21no—
406C3×D4—22no—
407C3×D4D3×Q812yes—
408C3×D4D3×Q812yes—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—44no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4D3×D411yescharacteristic
423C2×C3×C4D3×D411yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—64no—
427#67—64no—
428#67—68no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—31no—
432C2×Dic3—31no—
433C2×Dic3—31no—
434C2×Dic3—31no—
435C2×Dic3—31no—
436C2×Dic3—31no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—62no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—124no—
444C2×Dic3—122no—
445C2×Dic3—122no—
446D12—32no—
447D12—32no—
448D12—62no—
449D12—62no—
450D12—61no—
451D12—61no—
452C4×D3—32no—
453C4×D3—32no—
454C4×D3—32no—
455C4×D3—32no—
456C4×D3—62no—
457C4×D3—62no—
458C4×D3—64no—
459C4×D3—62no—
460C4×D3—62no—
461C4×D3—121no—
462C4×D3—121no—
463C4×D3—124no—
464C4×D3—122no—
465C4×D3—122no—
466C4×D3—124no—
467C4×D3—122no—
468C4×D3—124no—
469C4×D3—122no—
470C4×D3—122no—
471C4×D3—122no—
472C4×D3—122no—
473Dic6—42no—
474Dic6—42no—
475C3×C8—62no—
476C3×C8—62no—
477C3⋊C8—22no—
478C3⋊C8—22no—
479C2×C32—42no—
480C2×C32C2×C22⋊Q811yescharacteristic
481C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
482C2×C32#57511yescharacteristic
483C3⋊D3—22no—
484C3⋊D3—42no—
485C24—181no—
486C2×Q8—61no—
487C2×Q8—61no—
488C2×D4—94no—
489C2×D4—91no—
490C2×D4—182no—
491C2×D4—181no—
492C2×D4C2×D3211yescharacteristic
493C22×C4—21no—
494C22×C4—91no—
495C22×C4—91no—
496C22×C4—91no—
497C22×C4—181no—
498C22×C4—181no—
499C22×C4—181no—
500C22×C4—181no—
501C22×C4—364no—
502M16—184no—
503C2×C8—32no—
504C2×C8—32no—
505C4⋊C4—32no—
506C4⋊C4—32no—
507C4⋊C4—61no—
508C4⋊C4—61no—
509C4⋊C4—91no—
510C4⋊C4—181no—
511C4⋊C4—182no—
512C4⋊C4—182no—
513C4⋊C4C2×D3211yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—181no—
516C22⋊C4—182no—
517C22⋊C4—181no—
518C22⋊C4—181no—
519C42—91no—
520C42—91no—
521C42—91no—
522C42—182no—
523C42C2×D3211yescharacteristic
524C22×C3—24no—
525C22×C3—22no—
526C22×C3—22no—
527C22×C3—21no—
528C22×C3—42no—
529C22×C3—42no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3C2×D3×D411yescharacteristic
535C22×C3C2×D3×D411yescharacteristic
536C2×D3—32no—
537C2×D3—32no—
538C2×D3—62no—
539C2×D3—62no—
540C2×D3—62no—
541C2×D3—61no—
542C2×D3—61no—
543C2×D3—61no—
544C2×D3—61no—
545C2×D3—64no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—1216no—
549C2×D3—128no—
550C2×D3—128no—
551C2×D3—122no—
552C2×D3—122no—
553C2×D3—121no—
554C2×D3—121no—
555C2×D3—121no—
556C2×D3—121no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—22no—
562C3×C4—41no—
563C3×C4—42no—
564C3×C4—41no—
565C3×C4—41no—
566C3×C4—122no—
567C3×C4—122no—
568C3×C4#91112yes—
569C3×C4#91412yes—
570C3×C4C2×D3×Q811yescharacteristic
571C3×C4C2×D3×Q811yescharacteristic
572C3×C4D3×#4111yescharacteristic
573C3×C4D3×#4111yescharacteristic
574Dic3—32no—
575Dic3—32no—
576Dic3—42no—
577Dic3—42no—
578Dic3—62no—
579Dic3—62no—
580Dic3—61no—
581Dic3—61no—
582Dic3—61no—
583Dic3—61no—
584Dic3—121no—
585Dic3—122no—
586Dic3—121no—
587Dic3—121no—
588C32#307711yescharacteristic, complemented, Sylow
589C23—21no—
590C23—91no—
591C23—184no—
592C23—181no—
593C23—362no—
594C23—362no—
595Q8—122no—
596Q8—122no—
597D4—21no—
598D4—92no—
599D4—184no—
600D4—181no—
601D4#379712yes—
602C2×C4—21no—
603C2×C4—42no—
604C2×C4—62no—
605C2×C4—62no—
606C2×C4—91no—
607C2×C4—92no—
608C2×C4—92no—
609C2×C4—91no—
610C2×C4—91no—
611C2×C4—182no—
612C2×C4—181no—
613C2×C4—361no—
614C2×C4—362no—
615C2×C4—362no—
616C2×C4—362no—
617C2×C4—362no—
618C2×C4#381111yescharacteristic
619C2×C4#381111yescharacteristic
620C2×C4C22×D3211yescharacteristic
621C8—62no—
622C8—62no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—44no—
627C2×C3—42no—
628C2×C3—42no—
629C2×C3D3×C22⋊Q811yescharacteristic
630C2×C3D3×C22⋊Q811yescharacteristic
631C2×C3C2×#91111yescharacteristic
632C2×C3C2×#91411yescharacteristic
633C2×C3#577311yescharacteristic
634C2×C3#577711yescharacteristic
635D3—64no—
636D3—62no—
637D3—62no—
638D3—124no—
639D3—122no—
640D3—122no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—92no—
645C22—181no—
646C22—181no—
647C22—182no—
648C22—368no—
649C22—361no—
650C22—361no—
651C22C2×#381111yescharacteristic
652C4—21no—
653C4—41no—
654C4—92no—
655C4—122no—
656C4—122no—
657C4—181no—
658C4—181no—
659C4—361no—
660C4#6393712yes—
661C4C2×#379711yescharacteristic
662C4#6430611yescharacteristic
663C3—21no—
664C3#8096511yescharacteristic, complemented
665C3#8106011yescharacteristic, complemented
666C2—42no—
667C2—182no—
668C2—362no—
669C2#1059492511yescharacteristic
670C2C2×#6393711yescharacteristic
671C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenterC4×D4D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593866C2semidirect
3. C3×#5008C2semidirect
4. C3×#5007C2semidirect
5. #10591479C2semidirect
7. #10590583C2semidirect
8. #10590435C2semidirect
9. #10590340C2semidirect
10. #10590313C2semidirect
11. #10590300C2semidirect
25. C3×#869C22semidirect
26. C3×#869C22semidirect
27. #63872C22semidirect
36. C3×#808C22semidirect
37. C3×#807C22semidirect
38. C3×C4⋊(C3⋊C8)C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63575C22semidirect
41. #63573C22semidirect
42. #63572C22semidirect
54. #5008D3semidirect
55. #5007D3semidirect
74. D4×C3⋊D3Q8semidirect
157. #869C2×D3semidirect
158. #869C2×D3semidirect
176. #808C2×D3semidirect
178. #807C2×D3semidirect
179. C4⋊(C3⋊C8)C2×D3semidirect
180. C4⋊(C3⋊C8)C2×D3semidirect
588. C32#3077semidirect
664. C3#80965semidirect
665. C3#81060semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105938662
C3×#50082
C3×#50072
#105914792
#105914262
#105905832
#105904352
#105903402
#105903132
#105903002
#810603
#809653