Finite Group Databasebeta

← #11868686

Subgroups — #11868686

Order 1152.

975 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595049C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic
3#10592830C211yesmaximal, characteristic
4C3×#5121C211yesmaximal, characteristic, complemented
5C3×#5118C211yesmaximal, characteristic, complemented
6#10591130C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic
8#10590774C212yesmaximal, complemented
9#10590769C212yesmaximal, complemented
10#10590764C212yesmaximal, complemented
11#10590759C212yesmaximal, complemented
12#79239—31nomaximal
13#79059—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×#624—21no—
16C2×C32×M16C2211yescharacteristic
17#64135C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#63964—21no—
23#63964—21no—
24C2×#3722—21no—
25#63918C2211yescharacteristic, complemented
26#63918C2211yescharacteristic, complemented
27C4×#627—21no—
28C4×#627—21no—
29#63894—21no—
30#63894—21no—
31#63894C2212yes—
32#63894C2212yes—
33#63869C2211yescharacteristic, complemented
34#63869C2211yescharacteristic, complemented
35#63648C2212yes—
36#63648C2212yes—
37C3×#818C2212yescomplemented
38C3×#817C2212yescomplemented
39C3×Dic3⋊C8C2212yescomplemented
40C3×Dic3⋊C8C2212yescomplemented
41#63575C2212yescomplemented
42#63573C2212yescomplemented
43#63564C2212yes—
44#63564C2212yes—
45#5517—31no—
46C2×#893—31no—
47C2×C4×D12—31no—
48#5470—31no—
49C3×#428—31no—
50C3×#423—31no—
51#5131—31no—
52#5131—31no—
53#5131—31no—
54#5131—61no—
55#5121—31no—
56#5121D311yescharacteristic, complemented
57#5118D311yescharacteristic, complemented
58#5001—31no—
59#4964—31no—
60#4891—32no—
61#4890—32no—
62#4871—32no—
63#4870—32no—
64#4847—32no—
65#4847—32no—
66#4846—32no—
67#4842—32no—
68C23×C3⋊D3—21no—
69C22×C32×C4C2311yescharacteristic
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)—22no—
72C2×C4⋊(C3⋊D3)Q814yescomplemented
73C2×C4⋊(C3⋊D3)C2312yes—
74C22×C3×Dic3—21no—
75C22×C3×Dic3D411yescharacteristic
76C22×C3×Dic3D411yescharacteristic
77C2×#627—21no—
78C2×#627—21no—
79C2×#624—22no—
80C2×#624—22no—
81C2×#624—44no—
82C32×M16—22no—
83C2×C32×C8C2312yes—
84#3757—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4×C3⋊Dic3—21no—
88C3×#217—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3—21no—
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×#208—22no—
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101#3724—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105Dic3⋊Dic3—21no—
106#3722—22no—
107#3722—22no—
108#3077—91noSylow
109C22×D12—31no—
110C22×D12—31no—
111C22×D12—61no—
112C22×C4×D3—61no—
113C22×C4×D3—61no—
114C2×C3×M16—21no—
115C2×C3×M16—31no—
116C2×C3×M16C2×D311yescharacteristic
117C2×C3×M16C2×D311yescharacteristic
118C3×#117—31no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C42—31no—
121C2×(C2×D3)⋊C4—61no—
122C2×(C2×D3)⋊C4—61no—
123#926—31no—
124#926—31no—
125#926—61no—
126#926C2×D311yescharacteristic
127C2×C4⋊Dic3C2×D311yescharacteristic
128#924—61no—
129#924—61no—
130C2×C4×Dic3C2×D311yescharacteristic
131C2×#208C2×D311yescharacteristic
132#893—32no—
133#893—32no—
134#893—61no—
135#893—61no—
136#890—31no—
137#890—31no—
138#888—31no—
139#888—31no—
140#878—61no—
141#878—61no—
142C4×D12—32no—
143C4×D12—32no—
144C4×D12—61no—
145C4×D12—61no—
146#870—31no—
147#870—31no—
148#869—31no—
149#869—31no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C4×Dic6—61no—
154C3×#107—32no—
155C3×#106—32no—
156C3×C4⋊C8—32no—
157C3×C4⋊C8—32no—
158#821—32no—
159#821—32no—
160#821—32no—
161#821—32no—
162#821—32no—
163#821—32no—
164#821—62no—
165#821—62no—
166#818—32no—
167#818C2×D312yescomplemented
168#817—32no—
169#817C2×D312yescomplemented
170Dic3⋊C8C2×D312yescomplemented
171Dic3⋊C8C2×D312yescomplemented
172#809—32no—
173#809—32no—
174#808—32no—
175#807—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—24no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—42no—
180C22×C3⋊D3—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×Q812yes—
183C2×C32×C4#4112yes—
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C4⋊(C3⋊D3)—24no—
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)C2×Q814yes—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—41no—
195C2×C3×Dic3—42no—
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200#627—42no—
201#627—42no—
202#624—44no—
203#624—44no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#533—91no—
207C2×C4×D4—91no—
208#478—92no—
209#478—92no—
210#476—92no—
211#474—92no—
212#428—31no—
213#428—91no—
214#423—31no—
215#418—91no—
216#418—91no—
217C23×D3—61no—
218C23×D3—61no—
219C23×D3—121no—
220C22×C3×C4—21no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×Dic3—21no—
227C22×Dic3D1211yescharacteristic
228C22×Dic3D1211yescharacteristic
229C2×D12—34no—
230C2×D12—34no—
231C2×D12—32no—
232C2×D12—32no—
233C2×D12—62no—
234C2×D12—64no—
235C2×D12—61no—
236C2×D12—62no—
237C2×D12—61no—
238C2×D12—62no—
239C2×D12—121no—
240C2×D12—122no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—124no—
246C2×C4×D3—124no—
247C2×Dic6—61no—
248C2×Dic6—61no—
249C2×Dic6—61no—
250C2×Dic6—61no—
251C3×M16—22no—
252C3×M16—22no—
253C3×M16—42no—
254C3×M16—62no—
255C2×C3×C8—22no—
256C2×C3×C8—32no—
257C2×C3×C8C22×D312yes—
258C2×C3×C8C22×D312yes—
259C3×C4⋊C4—32no—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—61no—
263C3×C22⋊C4—61no—
264C3×C42—31no—
265C3×C42—31no—
266C3×C42—31no—
267C3×C42—31no—
268C3×C42—61no—
269#217—21no—
270#217—61no—
271#217—61no—
272#217—121no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277C4⋊Dic3—21no—
278C4⋊Dic3—31no—
279C4⋊Dic3—31no—
280C4⋊Dic3—31no—
281C4⋊Dic3—31no—
282C4⋊Dic3—61no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3C22×D312yes—
289C4⋊Dic3C22×D311yescharacteristic
290C4⋊Dic3C22×D311yescharacteristic
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—61no—
295Dic3⋊C4—61no—
296Dic3⋊C4—61no—
297Dic3⋊C4—61no—
298Dic3⋊C4—61no—
299C4×Dic3—21no—
300C4×Dic3—61no—
301C4×Dic3—61no—
302C4×Dic3—121no—
303C4×Dic3D1211yescharacteristic
304C4×Dic3D1211yescharacteristic
305C4×Dic3C22×D311yescharacteristic
306C4×Dic3C22×D311yescharacteristic
307#208—22no—
308C2×C3⋊C8C22×D312yes—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32C22⋊Q812yes—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—24no—
314C2×C3⋊D3—48no—
315C2×C3⋊D3—42no—
316C2×C3⋊D3—42no—
317C32×C4C22⋊Q812yes—
318C32×C4C22×Q811yescharacteristic
319C32×C4C2×#4111yescharacteristic
320C3⋊Dic3—41no—
321C3⋊Dic3—41no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—21no—
325C3×Dic3—42no—
326C3×Dic3—41no—
327C3×Dic3—41no—
328C3×Dic3AGL(1,ℤ/8)12yes—
329C22×D4—91no—
330C23×C4—181no—
331C2×M16—31no—
332C2×M16D3211yescharacteristic
333C4⋊Q8—91no—
334C4⋊Q8—91no—
335#125—91no—
336#125—91no—
337C22⋊Q8—181no—
338C22⋊Q8—181no—
339C4×Q8—181no—
340C4×Q8—181no—
341C4×D4—92no—
342C4×D4—92no—
343C4×D4—181no—
344C4×D4—181no—
345#117—31no—
346#117—91no—
347C2×C4⋊C4—31no—
348C2×C22⋊C4—181no—
349C2×C42—31no—
350#107—32no—
351#107—92no—
352#106—32no—
353#106—92no—
354C4⋊C8—32no—
355C4⋊C8—32no—
356#102—92no—
357#102—92no—
358#102—92no—
359#102—92no—
360C23×C3—21no—
361C23×C3C2×D1211yescharacteristic
362C23×C3D3×D411yescharacteristic
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—122no—
368C22×D3—124no—
369C22×D3—122no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3—122no—
373C22×D3—242no—
374C22×D3—242no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—22no—
379C2×C3×C4—31no—
380C2×C3×C4—31no—
381C2×C3×C4—31no—
382C2×C3×C4—31no—
383C2×C3×C4—62no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—62no—
387C2×C3×C4—121no—
388C2×C3×C4—122no—
389C2×C3×C4C2×D1211yescharacteristic
390C2×C3×C4#23512yes—
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4#23712yes—
393C2×C3×C4D3×Q812yes—
394C2×C3×C4D3×Q812yes—
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×Dic3—22no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—41no—
402C2×Dic3—42no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—121no—
408C2×Dic3—121no—
409C2×Dic3C2×D1211yescharacteristic
410C2×Dic3C2×D1211yescharacteristic
411C2×Dic3C2×D1211yescharacteristic
412C2×Dic3C2×D1211yescharacteristic
413D12—34no—
414D12—34no—
415D12—64no—
416D12—64no—
417D12—64no—
418D12—62no—
419D12—62no—
420D12—122no—
421D12—124no—
422C4×D3—124no—
423C4×D3—124no—
424C4×D3—124no—
425C4×D3—124no—
426Dic6—122no—
427Dic6—122no—
428Dic6—122no—
429Dic6—122no—
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—42no—
433C3×C8—62no—
434C3⋊C8—22no—
435C2×C32—22no—
436C2×C32C2×C22⋊Q811yescharacteristic
437C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
438C2×C32#57511yescharacteristic
439C3⋊D3—44no—
440C24—181no—
441C2×Q8—181no—
442C2×Q8—181no—
443C2×D4—92no—
444C2×D4—94no—
445C2×D4—181no—
446C2×D4—182no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—61no—
450C22×C4—182no—
451C22×C4—182no—
452C22×C4—364no—
453C22×C4C2×D3211yescharacteristic
454M16—22no—
455M16—62no—
456C2×C8—32no—
457C2×C8C2×D3212yes—
458C4⋊C4—31no—
459C4⋊C4—31no—
460C4⋊C4—32no—
461C4⋊C4—61no—
462C4⋊C4—91no—
463C4⋊C4—91no—
464C4⋊C4—181no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C4⋊C4—181no—
468C4⋊C4—181no—
469C4⋊C4—181no—
470C22⋊C4—61no—
471C22⋊C4—182no—
472C22⋊C4—182no—
473C22⋊C4—181no—
474C42—31no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—61no—
479C42—181no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—22no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3#89612yes—
489C22×C3#89712yes—
490C22×C3C22×D1211yescharacteristic
491C22×C3C2×D3×D411yescharacteristic
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—124no—
495C2×D3—128no—
496C2×D3—128no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—242no—
502C2×D3—242no—
503C2×D3—248no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—32no—
508C3×C4—61no—
509C3×C4—61no—
510C3×C4—61no—
511C3×C4—121no—
512C3×C4—122no—
513C3×C4—121no—
514C3×C4#89612yes—
515C3×C4#89712yes—
516C3×C4C2×#23511yescharacteristic
517C3×C4C2×#23711yescharacteristic
518C3×C4C2×D3×Q811yescharacteristic
519C3×C4C2×D3×Q811yescharacteristic
520Dic3—21no—
521Dic3—21no—
522Dic3—21no—
523Dic3—41no—
524Dic3—42no—
525Dic3—41no—
526Dic3—121no—
527Dic3—121no—
528Dic3—121no—
529Dic3—121no—
530Dic3—241no—
531Dic3—241no—
532Dic3#90812yes—
533C32#307711yescharacteristic, complemented, Sylow
534C23—182no—
535C23—184no—
536C23—362no—
537C23—362no—
538C23D3×D1211yescharacteristic
539Q8—362no—
540Q8—362no—
541D4—94no—
542D4—182no—
543D4—184no—
544C2×C4—31no—
545C2×C4—31no—
546C2×C4—31no—
547C2×C4—31no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—121no—
553C2×C4—122no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—364no—
557C2×C4—364no—
558C2×C4#379712yes—
559C2×C4D3×D1211yescharacteristic
560C2×C4#380412yes—
561C2×C4C22×D3211yescharacteristic
562C8—22no—
563C8—62no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—42no—
570C2×C3C2×#89611yescharacteristic
571C2×C3C2×#89711yescharacteristic
572C2×C3C2×#90811yescharacteristic
573C2×C3#574811yescharacteristic
574C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
575C2×C3#577711yescharacteristic
576D3—124no—
577D3—124no—
578D3—244no—
579C22—21no—
580C22—21no—
581C22—184no—
582C22—368no—
583C22—362no—
584C22—362no—
585C22#6389512yes—
586C22C2×D3×D1211yescharacteristic
587C4—32no—
588C4—61no—
589C4—61no—
590C4—61no—
591C4—122no—
592C4—121no—
593C4—121no—
594C4—361no—
595C4—361no—
596C4#6389512yes—
597C4C2×#379711yescharacteristic
598C4C2×#380411yescharacteristic
599C3—21no—
600C3#7905911yescharacteristic, complemented
601C3#7923911yescharacteristic, complemented
602C2—22no—
603C2—364no—
604C2D3×#90811yescharacteristic
605C2#1059471111yescharacteristic
606C2C2×#6389511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×M16D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10595049C2semidirect
4. C3×#5121C2semidirect
5. C3×#5118C2semidirect
6. #10591130C2semidirect
8. #10590774C2semidirect
9. #10590769C2semidirect
10. #10590764C2semidirect
11. #10590759C2semidirect
25. #63918C22semidirect
26. #63918C22semidirect
33. #63869C22semidirect
34. #63869C22semidirect
37. C3×#818C22semidirect
38. C3×#817C22semidirect
39. C3×Dic3⋊C8C22semidirect
40. C3×Dic3⋊C8C22semidirect
41. #63575C22semidirect
42. #63573C22semidirect
56. #5121D3semidirect
57. #5118D3semidirect
72. C2×C4⋊(C3⋊D3)Q8semidirect
167. #818C2×D3semidirect
169. #817C2×D3semidirect
170. Dic3⋊C8C2×D3semidirect
171. Dic3⋊C8C2×D3semidirect
533. C32#3077semidirect
600. C3#79059semidirect
601. C3#79239semidirect

Maximal subgroups

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

subgroupindex
#105950492
C2×#638942
#105928302
C3×#51212
C3×#51182
#105911302
#105910962
#105907742
#105907692
#105907642
#105907592
#792393
#790593