Finite Group Databasebeta

← #11805738

Subgroups — #11805738

Order 1152.

1764 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2C32×#387C211yesmaximal, characteristic, complemented
3#10592689C211yesmaximal, characteristic, complemented
4#10592686C211yesmaximal, characteristic, complemented
5#10592679C211yesmaximal, characteristic, complemented
6C4×#3752C211yesmaximal, characteristic, complemented
7C4×#3752C211yesmaximal, characteristic, complemented
8#10592369C211yesmaximal, characteristic, complemented
9#10592365C211yesmaximal, characteristic, complemented
10#10592364C211yesmaximal, characteristic
11#10592364C211yesmaximal, characteristic
12#10592363C211yesmaximal, characteristic, complemented
13C3⋊D3×#95C211yesmaximal, characteristic, complemented
14#10592350C211yesmaximal, characteristic, complemented
15#10592347C211yesmaximal, characteristic, complemented
16#75306—34nomaximal
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36C2×C4×C3⋊Dic3C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38#64102C418yescomplemented
39C32×#95C2211yescharacteristic
40C32×#95C2211yescharacteristic
41C32×#95C2211yescharacteristic
42C32×#95C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53C2×#893—34no—
54C3×#387D314yescomplemented
55#4990—34no—
56#4987—34no—
57#4980—34no—
58C4×(C2×D3)⋊C4—34no—
59C4×(C2×D3)⋊C4—34no—
60#4670—34no—
61#4666—34no—
62#4665—34no—
63#4665—34no—
64#4664—34no—
65D3×#95—34no—
66#4651—34no—
67#4648—34no—
68C23×C3⋊D3C2311yescharacteristic
69C23×C3⋊D3C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C2×C4⋊(C3⋊D3)—22no—
84C2×C4⋊(C3⋊D3)—22no—
85C2×C4⋊(C3⋊D3)C2×C414yes—
86C2×C4×C3⋊D3—22no—
87C2×C4×C3⋊D3—22no—
88C2×C4×C3⋊D3—22no—
89C2×C4×C3⋊D3—22no—
90C2×C4×C3⋊D3—41no—
91C2×C4×C3⋊D3—41no—
92C2×C4×C3⋊D3—41no—
93C2×C4×C3⋊D3—41no—
94C2×C4×C3⋊D3—41no—
95C2×C4×C3⋊D3—41no—
96C2×C4×C3⋊D3C2×C414yes—
97C2×C4×C3⋊D3C2×C414yescomplemented
98C32×C4⋊C4—41no—
99C32×C4⋊C4C2×C414yescomplemented
100C32×C42—41no—
101#3752—22no—
102#3752—22no—
103#3752—22no—
104#3752—22no—
105#3752—41no—
106#3752—41no—
107#3752C2×C414yes—
108#3752C2×C414yescomplemented
109C4⋊(C3⋊Dic3)—41no—
110C4×C3⋊Dic3—22no—
111C4×C3⋊Dic3—22no—
112C4×C3⋊Dic3—41no—
113C4×C3⋊Dic3C2×C414yescomplemented
114#2353—91noSylow
115C22×D12—34no—
116C22×C4×D3—34no—
117C22×C4×D3—34no—
118C22×C4×D3—34no—
119C22×C4×D3—34no—
120C2×C3×C4⋊C4C2×D314yes—
121C2×C3×C4⋊C4C2×D314yes—
122C2×C3×C42C2×D314yes—
123C2×(C2×D3)⋊C4—34no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—34no—
126C2×(C2×D3)⋊C4—34no—
127C2×(C2×D3)⋊C4—34no—
128C2×(C2×D3)⋊C4—34no—
129C2×(C2×D3)⋊C4—34no—
130C2×(C2×D3)⋊C4—34no—
131C2×C4⋊Dic3—34no—
132C2×C4×Dic3—34no—
133C2×C4×Dic3—34no—
134C2×C4×Dic3—34no—
135C2×C4×Dic3—34no—
136#893—332no—
137C3×#95C2×D314yes—
138C3×#95C2×D314yes—
139C3×#95C2×D314yes—
140C3×#95C2×D314yes—
141C3⋊#95—34no—
142C3⋊#95—34no—
143C3⋊#95—34no—
144C3⋊#95—34no—
145C3⋊#95—34no—
146C3⋊#95—34no—
147C3⋊#95—34no—
148C3⋊#95—34no—
149C3⋊#95—34no—
150C3⋊#95—34no—
151C23×C32C2411yescharacteristic
152C22×C3⋊D3—21no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3—21no—
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3C22×C412yes—
163C22×C3⋊D3C22×C412yes—
164C22×C3⋊D3#4112yes—
165C22×C3⋊D3#4112yes—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C22×C412yes—
186C2×C32×C4#4112yes—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3C22×C412yes—
203C2×C3⋊Dic3C22×C412yes—
204C2×C3⋊Dic3#4112yes—
205C4⋊(C3⋊D3)—28no—
206C4×C3⋊D3—44no—
207C4×C3⋊D3—44no—
208C4×C3⋊D3—44no—
209C4×C3⋊D3—44no—
210C2×C4×D4—91no—
211#388—91no—
212#388—91no—
213#387—91no—
214#387C3⋊D311yescharacteristic, complemented
215#386—91no—
216#386—91no—
217#383—91no—
218#381—91no—
219#380—91no—
220C4×C22⋊C4—91no—
221C4×C22⋊C4—91no—
222C4×C22⋊C4—91no—
223#376—91no—
224C2×#95—91no—
225C23×D3—34no—
226C23×D3—34no—
227C22×C3×C4C22×D314yes—
228C22×C3×C4C22×D314yes—
229C22×C3×C4C22×D314yes—
230C22×C3×C4C22×D314yes—
231C22×C3×C4C22×D314yes—
232C22×C3×C4C22×D314yes—
233C22×C3×C4C22×D314yes—
234C22×Dic3—34no—
235C22×Dic3—34no—
236C22×Dic3—34no—
237C22×Dic3—34no—
238C22×Dic3—34no—
239C22×Dic3—34no—
240C2×D12—316no—
241C2×D12—68no—
242C2×D12—68no—
243C2×C4×D3—316no—
244C2×C4×D3—316no—
245C2×C4×D3—68no—
246C2×C4×D3—68no—
247C2×C4×D3—68no—
248C2×C4×D3—68no—
249C2×C4×D3—124no—
250C2×C4×D3—124no—
251C2×C4×D3—124no—
252C2×C4×D3—124no—
253C2×C4×D3—124no—
254C2×C4×D3—124no—
255C3×C4⋊C4—44no—
256C3×C4⋊C4C4×D3116yescomplemented
257C3×C42—44no—
258(C2×D3)⋊C4—316no—
259(C2×D3)⋊C4—316no—
260(C2×D3)⋊C4—68no—
261(C2×D3)⋊C4—68no—
262(C2×D3)⋊C4—68no—
263(C2×D3)⋊C4—68no—
264(C2×D3)⋊C4—124no—
265(C2×D3)⋊C4—124no—
266C4⋊Dic3—124no—
267C4×Dic3—316no—
268C4×Dic3—68no—
269C4×Dic3—68no—
270C4×Dic3—124no—
271C22×C32C23×C411yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C32C2×#4111yescharacteristic
276C22×C32H(5,𝔽2)11yescharacteristic
277C22×C32H(5,𝔽2)11yescharacteristic
278C2×C3⋊D3—22no—
279C2×C3⋊D3—22no—
280C2×C3⋊D3—22no—
281C2×C3⋊D3—22no—
282C2×C3⋊D3—22no—
283C2×C3⋊D3—22no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3#11714yes—
292C32×C4—22no—
293C32×C4—22no—
294C32×C4—22no—
295C32×C4—22no—
296C32×C4—41no—
297C32×C4—41no—
298C32×C4—41no—
299C3⋊Dic3—22no—
300C3⋊Dic3—22no—
301C3⋊Dic3—22no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C22×D4—91no—
306C23×C4—91no—
307C23×C4—91no—
308C23×C4—91no—
309C23×C4—91no—
310C4×D4—98no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4C2×C3⋊D311yescharacteristic
313C2×C4⋊C4C2×C3⋊D311yescharacteristic
314C2×C22⋊C4—91no—
315C2×C22⋊C4—91no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—91no—
318C2×C22⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—91no—
322C2×C42—91no—
323C2×C42—91no—
324C2×C42—91no—
325C2×C42—91no—
326C2×C42C2×C3⋊D311yescharacteristic
327#95—91no—
328#95—91no—
329#95—91no—
330#95—91no—
331#95—91no—
332#95—91no—
333#95—91no—
334#95—91no—
335#95—91no—
336#95—91no—
337#95C2×C3⋊D311yescharacteristic
338#95C2×C3⋊D311yescharacteristic
339#95C2×C3⋊D311yescharacteristic
340#95C2×C3⋊D311yescharacteristic
341C23×C3C23×D314yes—
342C22×D3—38no—
343C22×D3—38no—
344C22×D3—38no—
345C22×D3—38no—
346C22×D3—64no—
347C22×D3—64no—
348C22×D3—64no—
349C22×D3—64no—
350C22×D3—64no—
351C22×D3—64no—
352C22×D3—64no—
353C22×D3—64no—
354C22×D3—64no—
355C22×D3—64no—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4C2×C4×D318yes—
374C2×C3×C4C2×C4×D318yes—
375C2×C3×C4C2×C4×D318yes—
376C2×C3×C4#23918yes—
377C2×Dic3—38no—
378C2×Dic3—38no—
379C2×Dic3—38no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—64no—
383C2×Dic3—64no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—64no—
387C2×Dic3—64no—
388C2×Dic3—64no—
389C2×Dic3—64no—
390C2×Dic3—64no—
391C2×Dic3—64no—
392C2×Dic3—64no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395D12—632no—
396C4×D3—1216no—
397C4×D3—1216no—
398C4×D3—1216no—
399C4×D3—1216no—
400C2×C32C2×#11711yescharacteristic
401C2×C32C4×#4111yescharacteristic
402C2×C32#51811yescharacteristic
403C2×C32#55111yescharacteristic
404C2×C32#55111yescharacteristic
405C2×C32#55311yescharacteristic
406C2×C32#55311yescharacteristic
407C3⋊D3—24no—
408C3⋊D3—42no—
409C24—91no—
410C24—91no—
411C2×D4—94no—
412C2×D4—182no—
413C2×D4—182no—
414C22×C4—91no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—94no—
418C22×C4—94no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—182no—
423C22×C4—182no—
424C22×C4—182no—
425C22×C4—182no—
426C22×C4—361no—
427C22×C4—361no—
428C22×C4—361no—
429C22×C4—361no—
430C22×C4—361no—
431C22×C4—361no—
432C22×C4C22×C3⋊D311yescharacteristic
433C22×C4C22×C3⋊D311yescharacteristic
434C22×C4C22×C3⋊D311yescharacteristic
435C22×C4C22×C3⋊D311yescharacteristic
436C22×C4C22×C3⋊D311yescharacteristic
437C22×C4C22×C3⋊D311yescharacteristic
438C22×C4C22×C3⋊D311yescharacteristic
439C4⋊C4—41no—
440C4⋊C4—361no—
441C4⋊C4C4×C3⋊D314yescomplemented
442C22⋊C4—94no—
443C22⋊C4—94no—
444C22⋊C4—182no—
445C22⋊C4—182no—
446C22⋊C4—182no—
447C22⋊C4—182no—
448C22⋊C4—361no—
449C22⋊C4—361no—
450C42—41no—
451C42—94no—
452C42—182no—
453C42—182no—
454C42—361no—
455C22×C3C22×C4×D314yes—
456C22×C3#100414yes—
457C22×C3C2×#23914yes—
458C22×C3D3×#4114yes—
459C22×C3D3×#4114yes—
460C22×C3D3×#4114yes—
461C22×C3#100914yes—
462C2×D3—316no—
463C2×D3—68no—
464C2×D3—68no—
465C2×D3—68no—
466C2×D3—68no—
467C2×D3—68no—
468C2×D3—68no—
469C2×D3—68no—
470C2×D3—68no—
471C2×D3—68no—
472C2×D3—124no—
473C2×D3—124no—
474C2×D3—124no—
475C2×D3—124no—
476C3×C4—28no—
477C3×C4—28no—
478C3×C4—28no—
479C3×C4—28no—
480C3×C4—44no—
481C3×C4—44no—
482C3×C4—44no—
483Dic3—68no—
484Dic3—68no—
485Dic3—68no—
486Dic3—124no—
487Dic3—124no—
488Dic3—124no—
489C32#235311yescharacteristic, complemented, Sylow
490C23—92no—
491C23—92no—
492C23—92no—
493C23—92no—
494C23—181no—
495C23—181no—
496C23—181no—
497C23—181no—
498C23—181no—
499C23—181no—
500C23—181no—
501C23—181no—
502C23—181no—
503C23—181no—
504C23C23×C3⋊D311yescharacteristic
505D4—188no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—92no—
524C2×C4—92no—
525C2×C4—92no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—364no—
542C2×C4—364no—
543C2×C4—364no—
544C2×C4—364no—
545C2×C4C2×C4×C3⋊D312yes—
546C2×C4C2×C4×C3⋊D312yes—
547C2×C4C2×C4×C3⋊D312yes—
548C2×C4#383212yes—
549C2×C3D3×#11714yes—
550C2×C3#554514yes—
551C2×C3C4×#23914yes—
552C2×C3#563714yes—
553C2×C3#566114yes—
554C2×C3#569514yes—
555C2×C3#570514yes—
556D3—616no—
557D3—128no—
558C22—94no—
559C22—182no—
560C22—182no—
561C22—182no—
562C22—182no—
563C22—182no—
564C22—182no—
565C22—182no—
566C22—182no—
567C22—182no—
568C22—361no—
569C22—361no—
570C22—361no—
571C22—361no—
572C22C22×C4×C3⋊D311yescharacteristic
573C22#6436111yescharacteristic
574C22C2×#383211yescharacteristic
575C22#41×C3⋊D311yescharacteristic
576C22#41×C3⋊D311yescharacteristic
577C22#41×C3⋊D311yescharacteristic
578C22#6436611yescharacteristic
579C4—22no—
580C4—22no—
581C4—22no—
582C4—22no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—182no—
587C4—182no—
588C4—182no—
589C4—361no—
590C4—361no—
591C4—361no—
592C3#7530614yescomplemented
593C2—184no—
594C2—362no—
595C2C3⋊D3×#11711yescharacteristic
596C2#1059601611yescharacteristic
597C2C4×#383211yescharacteristic
598C2#1059610811yescharacteristic
599C2#1059613211yescharacteristic
600C2#1059616611yescharacteristic
601C2#1059617611yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#387C2
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#387C3⋊D3
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C32×#387C2semidirect
3. #10592689C2semidirect
4. #10592686C2semidirect
5. #10592679C2semidirect
6. C4×#3752C2semidirect
7. C4×#3752C2semidirect
8. #10592369C2semidirect
9. #10592365C2semidirect
12. #10592363C2semidirect
13. C3⋊D3×#95C2semidirect
14. #10592350C2semidirect
15. #10592347C2semidirect
38. #64102C4semidirect
54. C3×#387D3semidirect
97. C2×C4×C3⋊D3C2×C4semidirect
99. C32×C4⋊C4C2×C4semidirect
108. #3752C2×C4semidirect
113. C4×C3⋊Dic3C2×C4semidirect
214. #387C3⋊D3semidirect
256. C3×C4⋊C4C4×D3semidirect
441. C4⋊C4C4×C3⋊D3semidirect
489. C32#2353semidirect
592. C3#75306semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C32×#3872
#105926892
#105926862
#105926792
C4×#37522
#105923692
#105923652
#105923642
#105923632
C3⋊D3×#952
#105923502
#105923472
#753063