Finite Group Databasebeta

← #11805170

Subgroups — #11805170

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3⋊Dic3C211yesmaximal, characteristic
2C2×#63957C211yesmaximal, characteristic
3C2×#63955C211yesmaximal, characteristic
4#10592642C211yesmaximal, characteristic
5C3×#4943C211yesmaximal, characteristic
6C3×Dic3×C22⋊C4C211yesmaximal, characteristic
7#10591716C211yesmaximal, characteristic
8#10591327C212yesmaximal, complemented
9#10591253C212yesmaximal, complemented
10#10591250C212yesmaximal, complemented
11#10591242C212yesmaximal, complemented
12#74060—31nomaximal
13#73456—31nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C2×C3×C4×Dic3C2212yes—
22C2×#3724C2212yes—
23C2×Dic3⋊Dic3C418yescomplemented
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30#63957—24no—
31#63955—24no—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×#926—31no—
41C22×C4⋊Dic3—31no—
42C22×Dic3⋊C4—31no—
43C2×#877—31no—
44C2×#877—31no—
45C2×#877—31no—
46C3×#381—31no—
47C3×C4×C22⋊C4—31no—
48#5212—31no—
49#4943—31no—
50#4943—31no—
51#4943—61no—
52#4943D311yescharacteristic
53#4942—31no—
54Dic3×C22⋊C4D311yescharacteristic
55C4×C4⋊Dic3—32no—
56#4928—32no—
57#4655—32no—
58#4653—32no—
59#4653—32no—
60#4652—32no—
61#4649—32no—
62#4647—32no—
63C24×C32C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C3⋊Dic3—22no—
66C22×C3⋊Dic3—22no—
67C22×C3⋊Dic3C2×C414yes—
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3×Dic3—22no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—24no—
74C22×C3×Dic3C2×C414yes—
75C22×C3×Dic3C2×C414yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C32×C22⋊C4—22no—
83#3757—22no—
84C3×#217—22no—
85C3×#217D414yes—
86C3×C4×Dic3—24no—
87#3724—24no—
88Dic3⋊Dic3—24no—
89Dic3⋊Dic3—24no—
90Dic3⋊Dic3C2×C414yes—
91Dic3⋊Dic3C2×C414yes—
92Dic3⋊Dic3C2×C414yes—
93Dic3⋊Dic3C2×C414yes—
94Dic32—24no—
95Dic32—24no—
96#2344—91noSylow
97C23×C3×C4—31no—
98C23×C3×C4—31no—
99C23×Dic3—31no—
100C23×Dic3—31no—
101C23×Dic3—61no—
102C23×Dic3C2×D311yescharacteristic
103C23×Dic3C2×D311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4C2×D311yescharacteristic
108C2×C3×C22⋊C4C2×D311yescharacteristic
109C2×C3×C42—32no—
110C2×#217—31no—
111C2×#217—31no—
112C2×#217—61no—
113C2×#217C2×D311yescharacteristic
114C2×#217C2×D311yescharacteristic
115#926—64no—
116C2×C4⋊Dic3—38no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—32no—
123C2×Dic3⋊C4—38no—
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—31no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3C2×D312yes—
137#877—64no—
138#877—64no—
139#877—64no—
140C3×#95—32no—
141C3×#95—32no—
142C3×#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—62no—
150C3⋊#95—62no—
151C3⋊#95C2×D312yes—
152C3⋊#95C2×D312yes—
153C3⋊#95C2×D312yes—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32C22×C412yes—
157C23×C32C2×D412yes—
158C23×C32#4112yes—
159C23×C32C2411yescharacteristic
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C3⋊Dic3—28no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C22×C412yes—
172C2×C3⋊Dic3C22×C412yes—
173C2×C3×Dic3—28no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—28no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C22×C412yes—
186C2×C3×Dic3C22×C412yes—
187C2×C3×Dic3C22×C412yes—
188C2×C3×Dic3C22×C412yes—
189C2×C3×Dic3C2×D414yes—
190C2×C3×Dic3#4114yes—
191C2×#117—91no—
192C2×#117—91no—
193C22×C4⋊C4—91no—
194#389—92no—
195#387—92no—
196#387—92no—
197#381—31no—
198#381—91no—
199#380—91no—
200C4×C4⋊C4—92no—
201C4×C22⋊C4—31no—
202C24×C3—21no—
203C24×C3C22×D311yescharacteristic
204C24×C3C22×D311yescharacteristic
205C22×C3×C4—22no—
206C22×C3×C4—31no—
207C22×C3×C4—34no—
208C22×C3×C4—34no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—64no—
215C22×C3×C4—62no—
216C22×C3×C4—62no—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D312yes—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—24no—
222C22×Dic3—34no—
223C22×Dic3—34no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—64no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3—62no—
238C22×Dic3—122no—
239C22×Dic3—122no—
240C22×Dic3C4×D314yes—
241C22×Dic3C4×D314yes—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D311yescharacteristic
244C22×Dic3C22×D311yescharacteristic
245C22×Dic3C22×D311yescharacteristic
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D311yescharacteristic
248C3×C22⋊C4—22no—
249C3×C22⋊C4—22no—
250C3×C22⋊C4—34no—
251C3×C22⋊C4—42no—
252C3×C22⋊C4—62no—
253C3×C42—64no—
254#217—22no—
255#217—62no—
256#217—62no—
257#217—122no—
258#217D1214yes—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262C4⋊Dic3—34no—
263C4⋊Dic3—64no—
264C4⋊Dic3—64no—
265Dic3⋊C4—34no—
266Dic3⋊C4—34no—
267Dic3⋊C4—34no—
268Dic3⋊C4—34no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273C4×Dic3—24no—
274C4×Dic3—64no—
275C4×Dic3—64no—
276C4×Dic3—64no—
277C4×Dic3—64no—
278C22×C32—22no—
279C22×C32—22no—
280C22×C32—24no—
281C22×C32—24no—
282C22×C32C4×D414yes—
283C22×C32C23×C411yescharacteristic
284C22×C32C22×D411yescharacteristic
285C22×C32C2×#4111yescharacteristic
286C22×C32C2×#4112yes—
287C22×C322−1+412yes—
288C32×C4—42no—
289C3⋊Dic3—22no—
290C3⋊Dic3—22no—
291C3⋊Dic3—42no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—22no—
295C3×Dic3—24no—
296C3×Dic3—42no—
297C3×Dic3#11714yescomplemented
298C23×C4—31no—
299C23×C4—31no—
300C23×C4—91no—
301#117—184no—
302#117—184no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—91no—
305C2×C4⋊C4—91no—
306C2×C4⋊C4—91no—
307C2×C4⋊C4—98no—
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—32no—
316C2×C42—92no—
317C2×C42—92no—
318#95—32no—
319#95—32no—
320#95—32no—
321#95—92no—
322#95—92no—
323#95—92no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—21no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3C2×C4×D312yes—
335C23×C3C2×C4×D312yes—
336C23×C3C2×D1212yes—
337C23×C3#23512yes—
338C23×C3D3×D412yes—
339C23×C3#23712yes—
340C23×C3C23×D311yescharacteristic
341C23×C3C23×D311yescharacteristic
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—32no—
349C2×C3×C4—34no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—34no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—68no—
358C2×C3×C4—68no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×Dic3—28no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—22no—
377C2×Dic3—28no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—32no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—68no—
388C2×Dic3—68no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—128no—
408C2×Dic3—122no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3C2×C4×D312yes—
412C2×Dic3C2×C4×D312yes—
413C2×Dic3C2×C4×D312yes—
414C2×Dic3C2×C4×D312yes—
415C2×Dic3C2×D1214yes—
416C2×Dic3#23714yes—
417C2×C32—24no—
418C2×C32C2×#11711yescharacteristic
419C2×C32C2×C4×D411yescharacteristic
420C2×C32#51911yescharacteristic
421C2×C32#54712yes—
422C2×C32#55212yes—
423C24C2×D3211yescharacteristic
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—32no—
429C22×C4—34no—
430C22×C4—34no—
431C22×C4—32no—
432C22×C4—64no—
433C22×C4—62no—
434C22×C4—62no—
435C22×C4—91no—
436C22×C4—91no—
437C22×C4—94no—
438C22×C4—92no—
439C22×C4—182no—
440C22×C4—182no—
441C22×C4C2×D3212yes—
442C4⋊C4—94no—
443C4⋊C4—94no—
444C4⋊C4—94no—
445C4⋊C4—94no—
446C4⋊C4—184no—
447C4⋊C4—184no—
448C4⋊C4—184no—
449C22⋊C4—22no—
450C22⋊C4—34no—
451C22⋊C4—62no—
452C22⋊C4—182no—
453C42—64no—
454C42—184no—
455C42—184no—
456C22×C3—24no—
457C22×C3—24no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—24no—
463C22×C3—24no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—21no—
469C22×C3—24no—
470C22×C3—44no—
471C22×C3—44no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3C4×D1214yes—
475C22×C3#67⋊C414yes—
476C22×C3C22×C4×D311yescharacteristic
477C22×C3C22×C4×D311yescharacteristic
478C22×C3C22×D1211yescharacteristic
479C22×C3C2×#23511yescharacteristic
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C2×#23712yes—
482C22×C3C2×#23711yescharacteristic
483C22×C3D3×#4112yes—
484C22×C3#101012yes—
485C22×C3#101012yes—
486C3×C4—34no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—64no—
490C3×C4—62no—
491C3×C4—62no—
492C3×C4—62no—
493C3×C4—82no—
494C3×C4—122no—
495Dic3—22no—
496Dic3—22no—
497Dic3—22no—
498Dic3—24no—
499Dic3—42no—
500Dic3—62no—
501Dic3—62no—
502Dic3—62no—
503Dic3—62no—
504Dic3—122no—
505Dic3—122no—
506Dic3—122no—
507Dic3—122no—
508Dic3—242no—
509Dic3#87714yescomplemented
510C32#234411yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23C4×D3212yes—
514C23D3×D1212yes—
515C23#380412yes—
516C23C22×D3211yescharacteristic
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—32no—
521C2×C4—34no—
522C2×C4—32no—
523C2×C4—32no—
524C2×C4—32no—
525C2×C4—34no—
526C2×C4—68no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—68no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—92no—
539C2×C4—92no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—188no—
545C2×C4—182no—
546C2×C4—182no—
547C2×C4—182no—
548C2×C3—24no—
549C2×C3—24no—
550C2×C3—22no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—44no—
556C2×C3C2×C4×D1211yescharacteristic
557C2×C3C2×#87711yescharacteristic
558C2×C3C2×#67⋊C411yescharacteristic
559C2×C3#551611yescharacteristic
560C2×C3#551611yescharacteristic
561C2×C3D3×#11711yescharacteristic
562C2×C3#554112yes—
563C2×C3#555512yes—
564C2×C3#565012yes—
565C2×C3#565512yes—
566C22—24no—
567C22—24no—
568C22—22no—
569C22—22no—
570C22#6388014yes—
571C22C2×C4×D3211yescharacteristic
572C22C2×D3×D1211yescharacteristic
573C22#6430912yes—
574C22D3×#23712yes—
575C22C2×#380411yescharacteristic
576C4—34no—
577C4—42no—
578C4—64no—
579C4—62no—
580C4—62no—
581C4—62no—
582C4—122no—
583C4—182no—
584C4—182no—
585C4—362no—
586C3—21no—
587C3#7345611yescharacteristic, complemented
588C3#7406011yescharacteristic, complemented
589C2—24no—
590C2D3×#87711yescharacteristic
591C2#1059407712yes—
592C2#1059424511yescharacteristic
593C2C2×#6388011yescharacteristic
594C2#1059511712yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2344
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591327C2semidirect
9. #10591253C2semidirect
10. #10591250C2semidirect
11. #10591242C2semidirect
23. C2×Dic3⋊Dic3C4semidirect
297. C3×Dic3#117semidirect
509. Dic3#877semidirect
510. C32#2344semidirect
587. C3#73456semidirect
588. C3#74060semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3⋊Dic32
C2×#639572
C2×#639552
#105926422
C3×#49432
C3×Dic3×C22⋊C42
#105917162
#105913272
#105912532
#105912502
#105912422
#740603
#734563