Finite Group Databasebeta

← #11868821

Subgroups — #11868821

Order 1152.

913 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×Dic3×#41C211yesmaximal, characteristic
2C2×#63918C211yesmaximal, characteristic, complemented
3#10592931C211yesmaximal, characteristic
4C3×#5232C211yesmaximal, characteristic
5#10591546C212yesmaximal, complemented
6#10591544C212yesmaximal, complemented
7#10591410C212yesmaximal, complemented
8#10591408C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10#10591131C211yesmaximal, characteristic, complemented
11#10591115C211yesmaximal, characteristic, complemented
12#82508—31nomaximal
13#78870—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×#627—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×Q8×Dic3C2211yescharacteristic
19C3×Q8×Dic3C2211yescharacteristic
20C3×D4×Dic3—21no—
21C3×D4×Dic3—21no—
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×#926—21no—
25C3×#926C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4×Dic3—21no—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C2×Dic3⋊Dic3—21no—
31#63918—21no—
32#63918—21no—
33#63918C2212yes—
34#63918C2212yes—
35#63662C2212yes—
36#63659C2212yes—
37C3×#835C2212yes—
38C3×#832C2212yes—
39#63576C2212yes—
40#63575C2212yes—
41#63574C2212yes—
42#63573C2212yes—
43Dic3⋊(C3⋊C8)C2212yes—
44Dic3⋊(C3⋊C8)C2212yes—
45C3×C4×#41—31no—
46Dic3×#41D311yescharacteristic
47C2×#888—31no—
48C2×#869—31no—
49C3×#417—31no—
50#5232—31no—
51#5232—31no—
52#5232—61no—
53#5232D311yescharacteristic
54#5121—31no—
55#5118—31no—
56#5021—32no—
57#5020—32no—
58#5008—32no—
59#5007—32no—
60#4995—31no—
61#4995—31no—
62#4964—31no—
63#4924—31no—
64#4793—32no—
65#4791—32no—
66#4761—32no—
67#4759—32no—
68C32×#41—22no—
69C32×#41Q814yescomplemented
70C2×C32×Q8C2311yescharacteristic
71C2×C32×D4—21no—
72C2×C32×D4C2311yescharacteristic
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3D411yescharacteristic
80C22×C3×Dic3D411yescharacteristic
81C2×#627—22no—
82C2×#627—22no—
83C2×#627—44no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86#3748—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—21no—
89C3×#217—21no—
90C3×#217—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4×Dic3—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×#208—22no—
105C2×C3×C3⋊C8C2312yes—
106Dic3⋊Dic3—22no—
107Dic3⋊Dic3—22no—
108#3079—91noSylow
109C2×C3×#41—21no—
110C2×C3×#41C2×D311yescharacteristic
111C2×C3×#41C2×D311yescharacteristic
112C22×Dic6—61no—
113C22×Dic6—61no—
114C2×C3×M16—31no—
115C3×C4×Q8—31no—
116C3×C4×Q8—31no—
117C3×C4×D4—31no—
118C3×C4×D4—31no—
119C3×C4×D4—61no—
120C3×C4×D4—61no—
121C3×#117—31no—
122C3×#117—61no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C42—31no—
125C2×C3×C42—61no—
126Q8×Dic3C2×D311yescharacteristic
127Q8×Dic3C2×D311yescharacteristic
128D4×Dic3—21no—
129D4×Dic3—21no—
130D4×Dic3C2×D311yescharacteristic
131D4×Dic3C2×D311yescharacteristic
132#926—21no—
133#926C2×D311yescharacteristic
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—61no—
137C2×C4⋊Dic3—61no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139C2×Dic3⋊C4—61no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3C2×D311yescharacteristic
142C2×#208—31no—
143C2×#208—31no—
144C2×#208—61no—
145C2×#208C2×D311yescharacteristic
146#888—32no—
147#888—32no—
148#888—61no—
149#888—61no—
150#869—32no—
151#869—32no—
152#869—61no—
153#869—61no—
154C3×#103—32no—
155C3×#102—32no—
156#835—32no—
157#835—32no—
158#835—62no—
159#835C2×D312yes—
160#832—32no—
161#832—32no—
162#832—62no—
163#832C2×D312yes—
164#818—32no—
165#817—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—32no—
168#808—32no—
169#808—32no—
170#808—32no—
171#807—32no—
172#807—32no—
173#807—32no—
174C4⋊(C3⋊C8)—32no—
175C4⋊(C3⋊C8)—32no—
176C23×C32—21no—
177C23×C32C2×D411yescharacteristic
178C32×Q8—21no—
179C32×Q8C2×Q812yescomplemented
180C32×D4—24no—
181C32×D4—21no—
182C32×D4C2×Q812yescomplemented
183C2×C32×C4—21no—
184C2×C32×C4—24no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×Q812yes—
187C2×C32×C4#4112yes—
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—42no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3—42no—
198C2×C3×Dic3—42no—
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203#627—44no—
204#627—44no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207C2×C4⋊Q8—91no—
208C4×#41—31no—
209#477—92no—
210#476—92no—
211#475—92no—
212#474—92no—
213#428—91no—
214#428—91no—
215#423—91no—
216#417—31no—
217#417—91no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—24no—
221C3×#41—42no—
222C3×#41Dic614yescomplemented
223C3×#41Dic614yescomplemented
224C2×C3×Q8—21no—
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—41no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C22×D311yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—41no—
239C22×C3×C4—61no—
240C22×C3×C4—61no—
241C22×C3×C4—61no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3—121no—
250C22×Dic3#6711yescharacteristic
251C22×Dic3#6711yescharacteristic
252C2×Dic6—62no—
253C2×Dic6—62no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C2×Dic6—124no—
257C2×Dic6—124no—
258C3×M16—62no—
259C2×C3×C8—32no—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4—61no—
268C3×C22⋊C4—61no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—61no—
274C3×C42—61no—
275C3×C42—61no—
276#217—21no—
277#217—21no—
278#217—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—32no—
283C4⋊Dic3—32no—
284C4⋊Dic3—62no—
285C4⋊Dic3—62no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3—121no—
290C4⋊Dic3C22×D311yescharacteristic
291C4⋊Dic3C22×D312yes—
292C4⋊Dic3C22×D311yescharacteristic
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3#6711yescharacteristic
299C4×Dic3#6711yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302#208—22no—
303#208—62no—
304#208—62no—
305#208—122no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—62no—
309C2×C3⋊C8C22×D312yes—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—22no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32C22⋊Q812yes—
316C22×C32C22×D411yescharacteristic
317C32×C4—22no—
318C32×C4C22⋊Q812yes—
319C32×C4C22×Q811yescharacteristic
320C32×C4C2×#4111yescharacteristic
321C3⋊Dic3—42no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—42no—
325C3×Dic3—41no—
326C3×Dic3—41no—
327C3×Dic3AGL(1,ℤ/8)12yes—
328C3×Dic3#13712yes—
329C2×#41D3211yescharacteristic
330C22×Q8—181no—
331C2×M16—31no—
332C2×M16—91no—
333C4⋊Q8—92no—
334C4⋊Q8—92no—
335C4⋊Q8—181no—
336C4⋊Q8—181no—
337C4×Q8—31no—
338C4×Q8—31no—
339C4×D4—31no—
340C4×D4—31no—
341C4×D4—61no—
342C4×D4—61no—
343#117—31no—
344#117—61no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—91no—
347C2×C4⋊C4—181no—
348C2×C42—31no—
349C2×C42—61no—
350#107—92no—
351#107—92no—
352#106—92no—
353#106—92no—
354C4⋊C8—92no—
355C4⋊C8—92no—
356#103—32no—
357#103—92no—
358#102—32no—
359#102—92no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—41no—
364C23×C3D3×D411yescharacteristic
365C23×C3C2×#6711yescharacteristic
366C3×Q8—21no—
367C3×Q8—21no—
368C3×Q8—22no—
369C3×Q8—41no—
370C3×Q8C2×Dic612yescomplemented
371C3×Q8C2×Dic612yescomplemented
372C3×D4—24no—
373C3×D4—24no—
374C3×D4—21no—
375C3×D4—21no—
376C3×D4—22no—
377C3×D4—41no—
378C3×D4—44no—
379C3×D4C2×Dic612yescomplemented
380C3×D4C2×Dic612yescomplemented
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—44no—
394C2×C3×C4—41no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—62no—
400C2×C3×C4—122no—
401C2×C3×C4—122no—
402C2×C3×C4—122no—
403C2×C3×C4C2×Dic612yes—
404C2×C3×C4C2×Dic612yes—
405C2×C3×C4#23512yes—
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4#23712yes—
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—42no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—122no—
422C2×Dic3—122no—
423C2×Dic3—122no—
424C2×Dic3—242no—
425C2×Dic3C2×#6711yescharacteristic
426C2×Dic3C2×#6711yescharacteristic
427C2×Dic3C2×#6711yescharacteristic
428C2×Dic3C2×#6711yescharacteristic
429Dic6—124no—
430Dic6—124no—
431Dic6—124no—
432Dic6—124no—
433C3×C8—62no—
434C3⋊C8—22no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C3⋊C8—122no—
438C2×C32—22no—
439C2×C32—42no—
440C2×C32C2×C22⋊Q811yescharacteristic
441C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
442C2×C32C2×#13711yescharacteristic
443#41—22no—
444#41#62714yescomplemented
445C2×Q8—182no—
446C2×Q8—182no—
447C2×Q8—364no—
448C2×Q8C2×D3211yescharacteristic
449C2×D4—21no—
450C2×D4C2×D3211yescharacteristic
451C22×C4—21no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—181no—
458C22×C4C2×D3211yescharacteristic
459M16—62no—
460M16—182no—
461C2×C8—32no—
462C2×C8—92no—
463C4⋊C4—32no—
464C4⋊C4—31no—
465C4⋊C4—31no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C4⋊C4—61no—
469C4⋊C4—92no—
470C4⋊C4—182no—
471C4⋊C4—182no—
472C4⋊C4—181no—
473C22⋊C4—61no—
474C22⋊C4—61no—
475C22⋊C4—61no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—31no—
480C42—61no—
481C42—61no—
482C42—61no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—81no—
499C22×C3—81no—
500C22×C3#87812yes—
501C22×C3#92412yes—
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C22×#6711yescharacteristic
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—32no—
510C3×C4—32no—
511C3×C4—42no—
512C3×C4—61no—
513C3×C4—61no—
514C3×C4—121no—
515C3×C4—121no—
516C3×C4—122no—
517C3×C4#87812yes—
518C3×C4#92412yes—
519C3×C4C22×Dic611yescharacteristic
520C3×C4C22×Dic611yescharacteristic
521C3×C4C2×#23511yescharacteristic
522C3×C4C2×#23711yescharacteristic
523Dic3—21no—
524Dic3—21no—
525Dic3—42no—
526Dic3—41no—
527Dic3—41no—
528Dic3—122no—
529Dic3—122no—
530Dic3—242no—
531Dic3#94912yes—
532Dic3#95112yes—
533C32#307911yescharacteristic, complemented, Sylow
534C23—21no—
535C23D3×#6711yescharacteristic
536Q8—21no—
537Q8—364no—
538Q8—364no—
539Q8C2×#62712yescomplemented
540D4—24no—
541D4—21no—
542D4C2×#62712yescomplemented
543C2×C4—21no—
544C2×C4—24no—
545C2×C4—31no—
546C2×C4—31no—
547C2×C4—31no—
548C2×C4—31no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—62no—
554C2×C4—122no—
555C2×C4—122no—
556C2×C4—122no—
557C2×C4—182no—
558C2×C4—362no—
559C2×C4#380412yes—
560C2×C4C2×#62712yes—
561C2×C4D3×#6711yescharacteristic
562C2×C4C22×D3211yescharacteristic
563C8—62no—
564C8—182no—
565C2×C3—22no—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—42no—
571C2×C3—42no—
572C2×C3—42no—
573C2×C3—82no—
574C2×C3C2×#87811yescharacteristic
575C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
576C2×C3D3×#13711yescharacteristic
577C2×C3C2×#92411yescharacteristic
578C2×C3C2×#94911yescharacteristic
579C2×C3C2×#95111yescharacteristic
580C22—21no—
581C22—21no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22#6396412yes—
586C22C2×D3×#6711yescharacteristic
587C4—22no—
588C4—32no—
589C4—32no—
590C4—61no—
591C4—61no—
592C4—122no—
593C4—121no—
594C4—121no—
595C4—362no—
596C4#6396412yes—
597C4C2×#380411yescharacteristic
598C4C22×#62711yescharacteristic
599C3—21no—
600C3#7887011yescharacteristic, complemented
601C3#8250811yescharacteristic, complemented
602C2—22no—
603C2—42no—
604C2D3×#94911yescharacteristic
605C2D3×#95111yescharacteristic
606C2C2×#6396411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63918C2semidirect
5. #10591546C2semidirect
6. #10591544C2semidirect
7. #10591410C2semidirect
8. #10591408C2semidirect
9. #10591139C2semidirect
10. #10591131C2semidirect
11. #10591115C2semidirect
69. C32×#41Q8semidirect
179. C32×Q8C2×Q8semidirect
182. C32×D4C2×Q8semidirect
222. C3×#41Dic6semidirect
223. C3×#41Dic6semidirect
370. C3×Q8C2×Dic6semidirect
371. C3×Q8C2×Dic6semidirect
379. C3×D4C2×Dic6semidirect
380. C3×D4C2×Dic6semidirect
444. #41#627semidirect
533. C32#3079semidirect
539. Q8C2×#627semidirect
542. D4C2×#627semidirect
600. C3#78870semidirect
601. C3#82508semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C2×#639182
#105929312
C3×#52322
#105915462
#105915442
#105914102
#105914082
#105911392
#105911312
#105911152
#825083
#788703