Finite Group Databasebeta

← #11868678

Subgroups — #11868678

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
1C3×#5517C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic
3#10592700C211yesmaximal, characteristic
4C3×#4995C211yesmaximal, characteristic, complemented
5#10591139C211yesmaximal, characteristic, complemented
6#10591115C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic
8#10590470C212yesmaximal, complemented
9#10590468C212yesmaximal, complemented
10#10590466C212yesmaximal, complemented
11#10590464C212yesmaximal, complemented
12#83350—31nomaximal
13#79239—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×#624—21no—
16C32×#117C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#890C2211yescharacteristic, complemented
23C3×#890C2211yescharacteristic, complemented
24C3×#888C2211yescharacteristic, complemented
25C3×#888C2211yescharacteristic, complemented
26C3×#878—21no—
27C3×#878—21no—
28C3×C4×Dic6—21no—
29C3×C4×Dic6—21no—
30C2×#3722—21no—
31#63894—21no—
32#63894—21no—
33#63894C2212yes—
34#63894C2212yes—
35#63636C2212yes—
36#63636C2212yes—
37C3×#808C2212yescomplemented
38C3×#807C2212yescomplemented
39#63576C2212yescomplemented
40#63574C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42Dic3⋊(C3⋊C8)C2212yescomplemented
43#63564C2212yes—
44#63564C2212yes—
45C3×#533—31no—
46#5517D311yescharacteristic, complemented
47C2×#893—31no—
48C2×C4×D12—31no—
49C3×#428—31no—
50#5131—31no—
51#5118—31no—
52#5087—32no—
53#5084—32no—
54#5066—32no—
55#5066—32no—
56#5001—31no—
57#5001—31no—
58#5001—31no—
59#5001—61no—
60#4995—31no—
61#4995D311yescharacteristic, complemented
62#4964—31no—
63#4924—31no—
64#4891—32no—
65#4890—32no—
66#4871—32no—
67#4870—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×C3×Dic6—21no—
78C2×C3×Dic6—21no—
79C2×#624—22no—
80C2×#624—22no—
81C2×#624—44no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85C32×C42—21no—
86#3748—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×#208—22no—
105C2×C3×C3⋊C8C2312yes—
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—31no—
115C3×C4⋊Q8—31no—
116C3×C4⋊Q8—31no—
117C3×#125—31no—
118C3×#125—31no—
119C3×C22⋊Q8—61no—
120C3×C22⋊Q8—61no—
121C3×C4×Q8—61no—
122C3×C4×Q8—61no—
123C3×#117—21no—
124C3×#117—31no—
125C3×#117C2×D311yescharacteristic
126C3×#117C2×D311yescharacteristic
127C2×C3×C4⋊C4—31no—
128C2×C3×C42—31no—
129C2×(C2×D3)⋊C4—61no—
130C2×(C2×D3)⋊C4—61no—
131#926C2×D311yescharacteristic
132C2×C4⋊Dic3C2×D311yescharacteristic
133C2×C4×Dic3C2×D311yescharacteristic
134C2×#208—31no—
135C2×#208—31no—
136C2×#208—61no—
137C2×#208C2×D311yescharacteristic
138#893—32no—
139#893—32no—
140#893—61no—
141#893—61no—
142#890C2×D311yescharacteristic, complemented
143#890C2×D311yescharacteristic, complemented
144#888C2×D311yescharacteristic, complemented
145#888C2×D311yescharacteristic, complemented
146#878—21no—
147#878—21no—
148C4×D12—32no—
149C4×D12—32no—
150C4×D12—61no—
151C4×D12—61no—
152C4×Dic6—21no—
153C4×Dic6—21no—
154C3×#107—32no—
155C3×#106—32no—
156#821—32no—
157#821—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160#809—32no—
161#809—32no—
162#809—32no—
163#809—32no—
164#809—32no—
165#809—32no—
166#809—62no—
167#809—62no—
168#808—32no—
169#808—32no—
170#808C2×D312yescomplemented
171#807—32no—
172#807—32no—
173#807C2×D312yescomplemented
174C4⋊(C3⋊C8)—32no—
175C4⋊(C3⋊C8)—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—24no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—42no—
180C22×C3⋊D3—42no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×Q812yes—
185C2×C32×C4#4112yes—
186C2×C32×C4C2411yescharacteristic
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
200C3×Dic6—42no—
201C3×Dic6—42no—
202#624—44no—
203#624—44no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#533—31no—
207C2×C4×D4—91no—
208#478—92no—
209#478—92no—
210#476—92no—
211#474—92no—
212#428—31no—
213#428—91no—
214#423—91no—
215#418—91no—
216#418—91no—
217C23×D3—61no—
218C23×D3—61no—
219C23×D3—121no—
220C2×C3×Q8—61no—
221C2×C3×Q8—61no—
222C22×C3×C4—21no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×Dic3—21no—
229C22×Dic3#6711yescharacteristic
230C22×Dic3#6711yescharacteristic
231C2×D12—34no—
232C2×D12—34no—
233C2×D12—32no—
234C2×D12—32no—
235C2×D12—62no—
236C2×D12—64no—
237C2×D12—62no—
238C2×D12—61no—
239C2×D12—62no—
240C2×D12—61no—
241C2×D12—122no—
242C2×D12—121no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—124no—
248C2×C4×D3—124no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C3×M16—62no—
252C2×C3×C8—32no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4C22×D311yescharacteristic
266C3×C4⋊C4C22×D311yescharacteristic
267C3×C4⋊C4C22×D311yescharacteristic
268C3×C4⋊C4C22×D311yescharacteristic
269C3×C22⋊C4—21no—
270C3×C22⋊C4—21no—
271C3×C22⋊C4—41no—
272C3×C22⋊C4—61no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—31no—
276C3×C42—31no—
277C3×C42—31no—
278C3×C42—31no—
279C3×C42—41no—
280C3×C42—61no—
281#217—21no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—62no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3C22×D311yescharacteristic
290C4⋊Dic3C22×D312yes—
291C4⋊Dic3C22×D311yescharacteristic
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
295Dic3⋊C4—21no—
296C4×Dic3—21no—
297C4×Dic3#6711yescharacteristic
298C4×Dic3#6711yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301#208—22no—
302#208—62no—
303#208—62no—
304#208—122no—
305C2×C3⋊C8—32no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—62no—
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×C4—41no—
318C32×C4—41no—
319C32×C4C22⋊Q812yes—
320C32×C4C22×Q811yescharacteristic
321C32×C4C2×#4111yescharacteristic
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×M16—91no—
333C4⋊Q8—31no—
334C4⋊Q8—31no—
335#125—31no—
336#125—31no—
337C22⋊Q8—61no—
338C22⋊Q8—61no—
339C4×Q8—61no—
340C4×Q8—61no—
341C4×D4—92no—
342C4×D4—92no—
343C4×D4—181no—
344C4×D4—181no—
345#117—31no—
346#117D3211yescharacteristic
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—92no—
355C4⋊C8—92no—
356#102—92no—
357#102—92no—
358#102—92no—
359#102—92no—
360C23×C3—21no—
361C23×C3D3×D411yescharacteristic
362C23×C3C2×#6711yescharacteristic
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—
375C3×Q8—122no—
376C3×Q8—122no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—62no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4—62no—
395C2×C3×C4—121no—
396C2×C3×C4—122no—
397C2×C3×C4#23512yes—
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×Q812yes—
400C2×C3×C4D3×Q812yes—
401C2×C3×C4#23912yes—
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—41no—
410C2×Dic3—42no—
411C2×Dic3C2×#6711yescharacteristic
412C2×Dic3C2×#6711yescharacteristic
413C2×Dic3C2×#6711yescharacteristic
414C2×Dic3C2×#6711yescharacteristic
415D12—34no—
416D12—34no—
417D12—64no—
418D12—64no—
419D12—64no—
420D12—62no—
421D12—62no—
422D12—122no—
423D12—124no—
424C4×D3—124no—
425C4×D3—124no—
426C4×D3—124no—
427C4×D3—124no—
428Dic6—42no—
429Dic6—42no—
430C3×C8—62no—
431C3⋊C8—22no—
432C3⋊C8—62no—
433C3⋊C8—62no—
434C3⋊C8—122no—
435C2×C32—22no—
436C2×C32C2×C22⋊Q811yescharacteristic
437C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
438C2×C32#57511yescharacteristic
439C3⋊D3—44no—
440C24—181no—
441C2×Q8—61no—
442C2×Q8—61no—
443C2×D4—92no—
444C2×D4—94no—
445C2×D4—182no—
446C2×D4—181no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—61no—
450C22×C4—182no—
451C22×C4—182no—
452C22×C4—364no—
453C22×C4C2×D3211yescharacteristic
454M16—62no—
455M16—182no—
456C2×C8—32no—
457C2×C8—92no—
458C4⋊C4—31no—
459C4⋊C4—31no—
460C4⋊C4—32no—
461C4⋊C4—61no—
462C4⋊C4—61no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C4⋊C4C2×D3211yescharacteristic
469C4⋊C4C2×D3211yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—61no—
472C22⋊C4—182no—
473C22⋊C4—182no—
474C42—21no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—61no—
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#94612yes—
490C22×C3C2×D3×D411yescharacteristic
491C22×C3C22×#6711yescharacteristic
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—41no—
509C3×C4—41no—
510C3×C4—41no—
511C3×C4—41no—
512C3×C4—61no—
513C3×C4—61no—
514C3×C4—61no—
515C3×C4—81no—
516C3×C4—81no—
517C3×C4—121no—
518C3×C4—121no—
519C3×C4—122no—
520C3×C4#89612yes—
521C3×C4#94612yes—
522C3×C4C2×#23511yescharacteristic
523C3×C4C2×D3×Q811yescharacteristic
524C3×C4C2×D3×Q811yescharacteristic
525C3×C4C2×#23911yescharacteristic
526Dic3—21no—
527Dic3—21no—
528Dic3—21no—
529Dic3—42no—
530Dic3—41no—
531Dic3—41no—
532Dic3#94912yes—
533C32#307711yescharacteristic, complemented, Sylow
534C23—182no—
535C23—184no—
536C23—362no—
537C23—362no—
538C23D3×#6711yescharacteristic
539Q8—122no—
540Q8—122no—
541D4—94no—
542D4—182no—
543D4—184no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—31no—
547C2×C4—31no—
548C2×C4—31no—
549C2×C4—31no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—62no—
554C2×C4—121no—
555C2×C4—122no—
556C2×C4—364no—
557C2×C4—364no—
558C2×C4#379712yes—
559C2×C4#379912yes—
560C2×C4D3×#6711yescharacteristic
561C2×C4C22×D3211yescharacteristic
562C8—62no—
563C8—182no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—42no—
570C2×C3C2×#89611yescharacteristic
571C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
572C2×C3#577711yescharacteristic
573C2×C3C2×#94611yescharacteristic
574C2×C3C2×#94911yescharacteristic
575C2×C3#582211yescharacteristic
576D3—124no—
577D3—124no—
578D3—244no—
579C22—21no—
580C22—21no—
581C22—184no—
582C22—368no—
583C22—362no—
584C22—362no—
585C22#6388812yes—
586C22C2×D3×#6711yescharacteristic
587C4—32no—
588C4—41no—
589C4—41no—
590C4—61no—
591C4—61no—
592C4—61no—
593C4—122no—
594C4—121no—
595C4—121no—
596C4#6388812yes—
597C4C2×#379711yescharacteristic
598C4C2×#379911yescharacteristic
599C3—21no—
600C3#7923911yescharacteristic, complemented
601C3#8335011yescharacteristic, complemented
602C2—22no—
603C2—364no—
604C2C2×#6388811yescharacteristic
605C2D3×#94911yescharacteristic
606C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#117D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5517C2semidirect
4. C3×#4995C2semidirect
5. #10591139C2semidirect
6. #10591115C2semidirect
8. #10590470C2semidirect
9. #10590468C2semidirect
10. #10590466C2semidirect
11. #10590464C2semidirect
22. C3×#890C22semidirect
23. C3×#890C22semidirect
24. C3×#888C22semidirect
25. C3×#888C22semidirect
37. C3×#808C22semidirect
38. C3×#807C22semidirect
39. #63576C22semidirect
40. #63574C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. Dic3⋊(C3⋊C8)C22semidirect
46. #5517D3semidirect
61. #4995D3semidirect
72. C2×C4⋊(C3⋊D3)Q8semidirect
142. #890C2×D3semidirect
143. #890C2×D3semidirect
144. #888C2×D3semidirect
145. #888C2×D3semidirect
170. #808C2×D3semidirect
173. #807C2×D3semidirect
533. C32#3077semidirect
600. C3#79239semidirect
601. C3#83350semidirect

Maximal subgroups

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

subgroupindex
C3×#55172
C2×#638942
#105927002
C3×#49952
#105911392
#105911152
#105910962
#105904702
#105904682
#105904662
#105904642
#833503
#792393