Finite Group Databasebeta

← #11801833

Subgroups — #11801833

Order 1152.

1429 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#877C211yesmaximal, characteristic
2C2×#63955C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4#10592645C211yesmaximal, characteristic
5C3×#4946C211yesmaximal, characteristic
6#10591719C211yesmaximal, characteristic
7#10591693C211yesmaximal, characteristic
8#10591246C212yesmaximal, complemented
9#10591243C212yesmaximal, complemented
10Dic3×Dic3⋊C4C212yesmaximal, complemented
11#10591234C212yesmaximal, complemented
12#82226—31nomaximal
13#74378—31nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×#3750C2212yes—
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#877—24no—
28C2×#3724C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31#63955C418yescomplemented
32C2×Dic32—24no—
33C2×Dic32C2212yes—
34C2×Dic32C2212yes—
35C2×Dic32C2212yes—
36#63658C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×#926—31no—
42C22×C4×Dic3—31no—
43C22×C4×Dic3—31no—
44C2×#877—31no—
45C2×#877D311yescharacteristic
46C3×#385—31no—
47#5210—31no—
48#4976—32no—
49Dic3×C4⋊C4—32no—
50#4972—32no—
51#4972—32no—
52#4950—31no—
53#4946—31no—
54#4946—31no—
55#4946—31no—
56#4946—31no—
57#4946—61no—
58#4946D311yescharacteristic
59C4×Dic3⋊C4—32no—
60C4×Dic3⋊C4—32no—
61#4649—32no—
62#4647—32no—
63C24×C32C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3—22no—
67C22×C3⋊Dic3—24no—
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—24no—
72C22×C3×Dic3C2×C414yes—
73C22×C3×Dic3D414yes—
74C22×C3×Dic3Q814yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C32×C22⋊C4—22no—
82#3757C2×C414yes—
83#3750—24no—
84C3×#217—22no—
85C3×#217C2×C414yes—
86C3×Dic3⋊C4—22no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4—24no—
89C3×C4×Dic3—22no—
90C3×C4×Dic3—22no—
91#3724—24no—
92Dic3⋊Dic3—24no—
93Dic3⋊Dic3C2×C418yescomplemented
94Dic32—24no—
95Dic32—24no—
96Dic32C2×C418yescomplemented
97#2296—91noSylow
98C23×C3×C4—31no—
99C23×C3×C4—31no—
100C23×Dic3—31no—
101C23×Dic3—31no—
102C23×Dic3—61no—
103C23×Dic3C2×D311yescharacteristic
104C23×Dic3C2×D311yescharacteristic
105C3×#117—64no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊C4—32no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—31no—
111C2×C3×C22⋊C4—31no—
112C2×C3×C22⋊C4C2×D311yescharacteristic
113C2×C3×C22⋊C4C2×D311yescharacteristic
114C2×C3×C42—31no—
115C2×C3×C42—31no—
116C2×#217—31no—
117C2×#217—31no—
118C2×#217—61no—
119C2×#217C2×D311yescharacteristic
120C2×#217C2×D311yescharacteristic
121#926—38no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—62no—
131C2×Dic3⋊C4C2×D311yescharacteristic
132C2×Dic3⋊C4C2×D312yes—
133C2×Dic3⋊C4C2×D311yescharacteristic
134C2×C4×Dic3—32no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—64no—
141C2×C4×Dic3—64no—
142C2×C4×Dic3C2×D311yescharacteristic
143C2×C4×Dic3C2×D311yescharacteristic
144#877—24no—
145#877—38no—
146C3×#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—62no—
154C3⋊#95C2×D312yes—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32C22×C412yes—
158C23×C32C2×D412yes—
159C23×C32C2×Q812yes—
160C23×C32C2411yescharacteristic
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C3⋊Dic3—28no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3C22×C414yes—
171C2×C3⋊Dic3#4114yes—
172C2×C3×Dic3—28no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C4⋊C4116yescomplemented
182C2×C3×Dic3C22×C414yes—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D412yes—
187C2×C3×Dic3C2×Q812yes—
188C2×C3×Dic3C2×Q812yes—
189C2×C3×Dic3#4114yes—
190C2×#117—31no—
191C2×#117—91no—
192C22×C42—91no—
193#389—92no—
194#389—92no—
195#385—31no—
196#385—91no—
197#385—91no—
198#385—91no—
199C4×C4⋊C4—92no—
200C4×C4⋊C4—92no—
201C24×C3—21no—
202C24×C3C22×D311yescharacteristic
203C24×C3C22×D311yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—34no—
207C22×C3×C4—34no—
208C22×C3×C4—34no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C22×C3×C4—64no—
216C22×C3×C4—62no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×Dic3—22no—
222C22×Dic3—24no—
223C22×Dic3—32no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—62no—
228C22×Dic3—62no—
229C22×Dic3—64no—
230C22×Dic3—64no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3—124no—
234C22×Dic3—122no—
235C22×Dic3Dic614yes—
236C22×Dic3C4×D314yes—
237C22×Dic3#6714yes—
238C22×Dic3C22×D311yescharacteristic
239C22×Dic3C22×D311yescharacteristic
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D311yescharacteristic
243C22×Dic3C22×D311yescharacteristic
244C3×C4⋊C4—64no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C22⋊C4—22no—
248C3×C22⋊C4—22no—
249C3×C22⋊C4—34no—
250C3×C22⋊C4—42no—
251C3×C22⋊C4—62no—
252C3×C42—62no—
253C3×C42—62no—
254#217—22no—
255#217—34no—
256#217—34no—
257#217—64no—
258#217C4×D314yes—
259C4⋊Dic3—38no—
260C4⋊Dic3—64no—
261Dic3⋊C4—24no—
262Dic3⋊C4—22no—
263Dic3⋊C4—22no—
264Dic3⋊C4—38no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—124no—
271C4×Dic3—22no—
272C4×Dic3—22no—
273C4×Dic3—38no—
274C4×Dic3—38no—
275C4×Dic3—64no—
276C4×Dic3—64no—
277C4×Dic3—64no—
278C4×Dic3—64no—
279C22×C32—24no—
280C22×C32—22no—
281C22×C32—22no—
282C22×C32—24no—
283C22×C32C2×C4⋊C414yes—
284C22×C32C23×C411yescharacteristic
285C22×C32C22×D411yescharacteristic
286C22×C32C22×Q811yescharacteristic
287C22×C32C2×#4112yes—
288C22×C32C2×#4112yes—
289C32×C4—41no—
290C32×C4—41no—
291C3⋊Dic3—24no—
292C3⋊Dic3—24no—
293C3×Dic3—24no—
294C3×Dic3—24no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C3×Dic3C2×C4⋊C414yes—
298C3×Dic3C2×C4⋊C414yes—
299C23×C4—31no—
300C23×C4—31no—
301C23×C4—91no—
302#117—64no—
303#117—98no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—32no—
307C2×C4⋊C4—92no—
308C2×C4⋊C4—92no—
309C2×C4⋊C4—92no—
310C2×C4⋊C4—92no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4D3211yescharacteristic
315C2×C42—31no—
316C2×C42—31no—
317C2×C42—92no—
318C2×C42—92no—
319C2×C42—92no—
320C2×C42—184no—
321#95—32no—
322#95—92no—
323#95—92no—
324#95—92no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—21no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3C2×Dic612yes—
336C23×C3C2×C4×D312yes—
337C23×C3C2×C4×D312yes—
338C23×C3D3×D412yes—
339C23×C3D3×Q812yes—
340C23×C3C2×#6712yes—
341C23×C3C23×D311yescharacteristic
342C23×C3C23×D311yescharacteristic
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—316no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—32no—
355C2×C3×C4—32no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—34no—
359C2×C3×C4—34no—
360C2×C3×C4—42no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—42no—
364C2×C3×C4—68no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×Dic3—28no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—34no—
383C2×Dic3—34no—
384C2×Dic3—34no—
385C2×Dic3—34no—
386C2×Dic3—64no—
387C2×Dic3—64no—
388C2×Dic3—68no—
389C2×Dic3—68no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—122no—
399C2×Dic3—122no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3—128no—
403C2×Dic3Dic3⋊C4116yescomplemented
404C2×Dic3C2×Dic612yes—
405C2×Dic3C2×Dic612yes—
406C2×Dic3C2×C4×D314yes—
407C2×Dic3C2×C4×D312yes—
408C2×Dic3C2×C4×D312yes—
409C2×Dic3#23714yes—
410C2×Dic3C2×#6712yes—
411C2×Dic3C2×#6712yes—
412C2×C32—24no—
413C2×C32C22×C4⋊C411yescharacteristic
414C2×C32C4×#4112yes—
415C2×C32#52511yescharacteristic
416C2×C32#52511yescharacteristic
417C2×C32#53312yes—
418C24C2×D3211yescharacteristic
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—34no—
422C22×C4—34no—
423C22×C4—34no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—64no—
429C22×C4—62no—
430C22×C4—92no—
431C22×C4—92no—
432C22×C4—184no—
433C22×C4—182no—
434C22×C4C2×D3211yescharacteristic
435C22×C4C2×D3211yescharacteristic
436C4⋊C4—62no—
437C4⋊C4—62no—
438C4⋊C4—64no—
439C4⋊C4—98no—
440C4⋊C4—184no—
441C4⋊C4—184no—
442C4⋊C4—184no—
443C22⋊C4—22no—
444C22⋊C4—34no—
445C22⋊C4—62no—
446C22⋊C4—94no—
447C42—62no—
448C42—62no—
449C42—98no—
450C42—184no—
451C42—184no—
452C22×C3—22no—
453C22×C3—24no—
454C22×C3—24no—
455C22×C3—24no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—24no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—24no—
466C22×C3—42no—
467C22×C3—44no—
468C22×C3—42no—
469C22×C3—44no—
470C22×C3D3×C4⋊C414yes—
471C22×C3C2×Dic3⋊C414yes—
472C22×C3C22×Dic611yescharacteristic
473C22×C3C22×C4×D311yescharacteristic
474C22×C3C22×C4×D311yescharacteristic
475C22×C3C2×D3×D411yescharacteristic
476C22×C3C2×#23712yes—
477C22×C3C2×D3×Q811yescharacteristic
478C22×C3D3×#4112yes—
479C22×C3D3×#4112yes—
480C22×C3D3×#4112yes—
481C22×C3C22×#6711yescharacteristic
482C3×C4—34no—
483C3×C4—34no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4—41no—
487C3×C4—41no—
488C3×C4—64no—
489C3×C4—64no—
490C3×C4—81no—
491C3×C4—81no—
492C3×C4—121no—
493C3×C4—121no—
494Dic3—24no—
495Dic3—24no—
496Dic3—41no—
497Dic3—41no—
498Dic3—64no—
499Dic3—64no—
500Dic3—64no—
501Dic3—64no—
502Dic3—124no—
503Dic3—124no—
504Dic3C2×Dic3⋊C414yes—
505Dic3C2×Dic3⋊C414yes—
506C32#229611yescharacteristic, complemented, Sylow
507C23—22no—
508C23—22no—
509C23D3×Dic612yes—
510C23C4×D3212yes—
511C23D3×#6712yes—
512C23C22×D3211yescharacteristic
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—32no—
523C2×C4—316no—
524C2×C4—34no—
525C2×C4—34no—
526C2×C4—68no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—94no—
536C2×C4—94no—
537C2×C4—188no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C3—24no—
543C2×C3—24no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—22no—
549C2×C3—44no—
550C2×C3C2×D3×C4⋊C411yescharacteristic
551C2×C3#551712yes—
552C2×C3#552212yes—
553C2×C3C4×#23712yes—
554C2×C3#558611yescharacteristic
555C2×C3#562212yes—
556C2×C3#565611yescharacteristic
557C2×C3C22×Dic3⋊C411yescharacteristic
558C2×C3#582811yescharacteristic
559C2×C3#582811yescharacteristic
560C22—24no—
561C22—22no—
562C22—22no—
563C22—24no—
564C22D3×Dic3⋊C414yes—
565C22C2×D3×Dic611yescharacteristic
566C22C2×C4×D3211yescharacteristic
567C22D3×#23712yes—
568C22#6431212yes—
569C22C2×D3×#6711yescharacteristic
570C4—34no—
571C4—34no—
572C4—41no—
573C4—41no—
574C4—64no—
575C4—64no—
576C4—121no—
577C4—121no—
578C4—184no—
579C4—184no—
580C3—21no—
581C3#7437811yescharacteristic, complemented
582C3#8222611yescharacteristic, complemented
583C2—24no—
584C2#1059402912yes—
585C2#1059404812yes—
586C2C2×D3×Dic3⋊C411yescharacteristic
587C2#1059515411yescharacteristic
588C2#1059515911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591246C2semidirect
9. #10591243C2semidirect
10. Dic3×Dic3⋊C4C2semidirect
11. #10591234C2semidirect
31. #63955C4semidirect
93. Dic3⋊Dic3C2×C4semidirect
96. Dic32C2×C4semidirect
181. C2×C3×Dic3C4⋊C4semidirect
403. C2×Dic3Dic3⋊C4semidirect
506. C32#2296semidirect
581. C3#74378semidirect
582. C3#82226semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
C2×#639552
C22×Dic322
#105926452
C3×#49462
#105917192
#105916932
#105912462
#105912432
Dic3×Dic3⋊C42
#105912342
#822263
#743783