Finite Group Databasebeta

← #11807511

Subgroups — #11807511

Order 1152.

1656 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64092C211yesmaximal, characteristic
2C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
3#10592912C211yesmaximal, characteristic
4C4×#3757C211yesmaximal, characteristic, complemented
5#10592656C211yesmaximal, characteristic
6#10592650C211yesmaximal, characteristic, complemented
7#10592644C211yesmaximal, characteristic, complemented
8#10592639C211yesmaximal, characteristic, complemented
9C4×#3752C211yesmaximal, characteristic, complemented
10C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
11#10592632C211yesmaximal, characteristic, complemented
12#10592369C211yesmaximal, characteristic, complemented
13#10592365C211yesmaximal, characteristic, complemented
14#10592353C211yesmaximal, characteristic, complemented
15#10592348C211yesmaximal, characteristic, complemented
16#73479—34nomaximal
17C23×C32×C4C2211yescharacteristic
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38C2×C4×C3⋊Dic3C2211yescharacteristic
39C2×C4×C3⋊Dic3C2211yescharacteristic
40C2×C4×C3⋊Dic3C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42#64092C418yescomplemented
43C32×#95C2211yescharacteristic
44C32×#95C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53C2×#883—34no—
54C3×C4×C22⋊C4D314yescomplemented
55#5213—34no—
56C4×#217—34no—
57#4957—34no—
58#4951—34no—
59#4945—34no—
60#4940—34no—
61C4×(C2×D3)⋊C4—34no—
62C4×C4⋊Dic3—34no—
63#4933—34no—
64#4670—34no—
65#4666—34no—
66#4654—34no—
67#4649—34no—
68C24×C32C2311yescharacteristic
69C23×C3⋊D3C2311yescharacteristic
70C22×C32×C4—22no—
71C22×C32×C4—22no—
72C22×C32×C4—41no—
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C2×#638—41no—
80C2×#638—41no—
81C2×#638C2×C414yes—
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C2×C4×C3⋊D3—41no—
90C2×C4×C3⋊D3—41no—
91C2×C4×C3⋊D3C2×C414yescomplemented
92C32×C22⋊C4—22no—
93C32×C22⋊C4C2×C414yes—
94C32×C42—22no—
95C32×C42—41no—
96#3757—22no—
97#3757—41no—
98#3757C2×C414yes—
99#3752—22no—
100#3752—22no—
101#3752—22no—
102#3752—22no—
103#3752C2×C414yescomplemented
104C4⋊(C3⋊Dic3)—22no—
105C4⋊(C3⋊Dic3)C2×C414yescomplemented
106#3750—22no—
107#3750—41no—
108#3750C2×C414yescomplemented
109C4×C3⋊Dic3—22no—
110C4×C3⋊Dic3—41no—
111C4×C3⋊Dic3—41no—
112C4×C3⋊Dic3—41no—
113C4×C3⋊Dic3—41no—
114#2374—91noSylow
115C23×C3×C4C2×D314yes—
116C22×#67—34no—
117C22×C4×D3—34no—
118C2×C3×C22⋊C4C2×D314yes—
119C2×C3×C22⋊C4C2×D314yes—
120C2×C3×C42C2×D314yes—
121C2×C3×C42C2×D314yes—
122C2×#217—34no—
123C2×#217—34no—
124C2×#217—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×C4⋊Dic3—34no—
131C2×C4⋊Dic3—34no—
132C2×Dic3⋊C4—34no—
133C2×Dic3⋊C4—34no—
134C2×Dic3⋊C4—34no—
135C2×C4×Dic3—34no—
136C2×C4×Dic3—34no—
137C2×C4×Dic3—34no—
138C2×C4×Dic3—34no—
139C2×C4×Dic3—34no—
140#883—332no—
141C3×#95C2×D314yes—
142C3×#95C2×D314yes—
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×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32C22×C412yes—
158C23×C32C2411yescharacteristic
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3C22×C412yes—
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—44no—
180C2×C32×C4C22×C412yes—
181C2×C32×C4C22×C412yes—
182C2×C32×C4#4112yes—
183C2×C32×C4#4112yes—
184C2×C32×C4#4112yes—
185#638—44no—
186C2×C3⋊Dic3—21no—
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⋊Dic3—21no—
203C2×C3⋊Dic3C22×C412yes—
204C2×C3⋊Dic3C22×C412yes—
205C2×C3⋊Dic3C22×C412yes—
206C2×C3⋊Dic3#4112yes—
207C4×C3⋊D3—44no—
208C2×#123—91no—
209#390—91no—
210#388—91no—
211#388—91no—
212#388—91no—
213#388—91no—
214#387—91no—
215#387—91no—
216#386—91no—
217C4×C4⋊C4—91no—
218C4×C4⋊C4—91no—
219C4×C22⋊C4—91no—
220C4×C22⋊C4—91no—
221C4×C22⋊C4—91no—
222C4×C22⋊C4C3⋊D311yescharacteristic, complemented
223C24×C3C22×D314yes—
224C23×D3—34no—
225C22×C3×C4—28no—
226C22×C3×C4—28no—
227C22×C3×C4—44no—
228C22×C3×C4C22×D314yes—
229C22×C3×C4C22×D314yes—
230C22×C3×C4C22×D314yes—
231C22×C3×C4C22×D314yes—
232C22×C3×C4C22×D314yes—
233C22×C3×C4C22×D314yes—
234C2×#67—316no—
235C2×#67—124no—
236C2×#67—124no—
237C22×Dic3—34no—
238C22×Dic3—34no—
239C22×Dic3—34no—
240C22×Dic3—34no—
241C22×Dic3—34no—
242C22×Dic3—34no—
243C22×Dic3—34no—
244C2×C4×D3—316no—
245C2×C4×D3—124no—
246C2×C4×D3—124no—
247C3×C22⋊C4—28no—
248C3×C22⋊C4C4×D3116yes—
249C3×C42—28no—
250C3×C42—44no—
251#217—316no—
252#217—68no—
253#217—124no—
254(C2×D3)⋊C4—316no—
255(C2×D3)⋊C4—68no—
256(C2×D3)⋊C4—68no—
257(C2×D3)⋊C4—68no—
258(C2×D3)⋊C4—68no—
259C4⋊Dic3—316no—
260C4⋊Dic3—68no—
261Dic3⋊C4—316no—
262Dic3⋊C4—68no—
263Dic3⋊C4—124no—
264C4×Dic3—68no—
265C4×Dic3—124no—
266C4×Dic3—124no—
267C4×Dic3—124no—
268C4×Dic3—124no—
269C22×C32—22no—
270C22×C32—22no—
271C22×C32—22no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32C23×C411yescharacteristic
277C22×C32C2×#4111yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32H(5,𝔽2)11yescharacteristic
282C22×C32H(5,𝔽2)11yescharacteristic
283C2×C3⋊D3—22no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—41no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3—41no—
290C32×C4—22no—
291C32×C4—22no—
292C32×C4—22no—
293C32×C4—22no—
294C32×C4—22no—
295C32×C4—41no—
296C3⋊Dic3—22no—
297C3⋊Dic3—22no—
298C3⋊Dic3—22no—
299C3⋊Dic3—22no—
300C3⋊Dic3—41no—
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C22×D4—91no—
304C23×C4—91no—
305C23×C4C2×C3⋊D311yescharacteristic
306#123—98no—
307C2×C4⋊C4—91no—
308C2×C4⋊C4—91no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—91no—
312C2×C22⋊C4—91no—
313C2×C22⋊C4—91no—
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⋊C4C2×C3⋊D311yescharacteristic
321C2×C22⋊C4C2×C3⋊D311yescharacteristic
322C2×C42—91no—
323C2×C42—91no—
324C2×C42—91no—
325C2×C42—91no—
326C2×C42—91no—
327C2×C42C2×C3⋊D311yescharacteristic
328C2×C42C2×C3⋊D311yescharacteristic
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
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3C2×C4×D318yes—
346C23×C3C23×D314yes—
347C22×D3—38no—
348C22×D3—64no—
349C22×D3—64no—
350C22×D3—64no—
351C22×D3—64no—
352C22×D3—64no—
353C22×D3—64no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
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—416no—
368C2×C3×C4C2×C4×D318yes—
369C2×C3×C4C2×C4×D318yes—
370C2×C3×C4#23518yes—
371C2×C3×C4#23518yes—
372C2×C3×C4#23718yes—
373#67—1216no—
374C2×Dic3—38no—
375C2×Dic3—38no—
376C2×Dic3—38no—
377C2×Dic3—38no—
378C2×Dic3—64no—
379C2×Dic3—64no—
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—
395C4×D3—1216no—
396C2×C32—42no—
397C2×C32C4×#4111yescharacteristic
398C2×C32C4×#4111yescharacteristic
399C2×C32#51811yescharacteristic
400C2×C32#55111yescharacteristic
401C2×C32#55311yescharacteristic
402C2×C32#55311yescharacteristic
403C2×C32#55911yescharacteristic
404C3⋊D3—42no—
405C24—91no—
406C24C22×C3⋊D311yescharacteristic
407C2×D4—94no—
408C2×D4—361no—
409C2×D4—361no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—41no—
413C22×C4—91no—
414C22×C4—91no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—94no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—361no—
422C22×C4—361no—
423C22×C4C22×C3⋊D311yescharacteristic
424C22×C4C22×C3⋊D311yescharacteristic
425C22×C4C22×C3⋊D311yescharacteristic
426C22×C4C22×C3⋊D311yescharacteristic
427C22×C4C22×C3⋊D311yescharacteristic
428C22×C4C22×C3⋊D311yescharacteristic
429C4⋊C4—94no—
430C4⋊C4—94no—
431C4⋊C4—182no—
432C4⋊C4—182no—
433C4⋊C4—361no—
434C22⋊C4—22no—
435C22⋊C4—94no—
436C22⋊C4—94no—
437C22⋊C4—182no—
438C22⋊C4—182no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C22⋊C4—182no—
442C22⋊C4—361no—
443C22⋊C4C4×C3⋊D314yes—
444C42—22no—
445C42—41no—
446C42—182no—
447C42—361no—
448C42—361no—
449C42—361no—
450C42—361no—
451C22×C3—28no—
452C22×C3—28no—
453C22×C3—28no—
454C22×C3—44no—
455C22×C3—44no—
456C22×C3—44no—
457C22×C3—44no—
458C22×C3C22×C4×D314yes—
459C22×C3C2×#23514yes—
460C22×C3C2×#23514yes—
461C22×C3C2×#23714yes—
462C22×C3#100414yes—
463C22×C3D3×#4114yes—
464C22×C3#100914yes—
465C2×D3—68no—
466C2×D3—68no—
467C2×D3—68no—
468C2×D3—124no—
469C2×D3—124no—
470C2×D3—124no—
471C2×D3—124no—
472C3×C4—28no—
473C3×C4—28no—
474C3×C4—28no—
475C3×C4—28no—
476C3×C4—28no—
477C3×C4—44no—
478Dic3—68no—
479Dic3—68no—
480Dic3—68no—
481Dic3—68no—
482Dic3—124no—
483Dic3—124no—
484Dic3—124no—
485C32#237411yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—92no—
493C23—181no—
494C23—181no—
495C23—181no—
496C23—181no—
497C23—181no—
498C23—181no—
499C23C2×C4×C3⋊D312yes—
500C23C23×C3⋊D311yescharacteristic
501D4—364no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
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—44no—
516C2×C4—92no—
517C2×C4—92no—
518C2×C4—92no—
519C2×C4—92no—
520C2×C4—181no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—181no—
524C2×C4—181no—
525C2×C4—181no—
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—364no—
538C2×C4C2×C4×C3⋊D312yes—
539C2×C4C2×C4×C3⋊D312yes—
540C2×C4#382812yes—
541C2×C4#382812yes—
542C2×C4#383012yes—
543C2×C3—48no—
544C2×C3C4×#23514yes—
545C2×C3#549514yes—
546C2×C3#553014yes—
547C2×C3C4×#23714yes—
548C2×C3#554514yes—
549C2×C3#555914yes—
550C2×C3#556514yes—
551D3—128no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—182no—
560C22—182no—
561C22—182no—
562C22—361no—
563C22—361no—
564C22—361no—
565C22—361no—
566C22C22×C4×C3⋊D311yescharacteristic
567C22C2×#382811yescharacteristic
568C22C2×#382811yescharacteristic
569C22C2×#383011yescharacteristic
570C22#6436111yescharacteristic
571C22#41×C3⋊D311yescharacteristic
572C22#6436611yescharacteristic
573C4—22no—
574C4—22no—
575C4—22no—
576C4—22no—
577C4—22no—
578C4—41no—
579C4—182no—
580C4—182no—
581C4—182no—
582C4—182no—
583C4—361no—
584C4—361no—
585C4—361no—
586C3#7347914yescomplemented
587C2—42no—
588C2—362no—
589C2C4×#382811yescharacteristic
590C2#1059596611yescharacteristic
591C2#1059600111yescharacteristic
592C2C4×#383011yescharacteristic
593C2#1059601611yescharacteristic
594C2#1059603011yescharacteristic
595C2#1059603611yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×C4×C22⋊C4C2
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32#2374
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C22⋊C4C2semidirect
4. C4×#3757C2semidirect
6. #10592650C2semidirect
7. #10592644C2semidirect
8. #10592639C2semidirect
9. C4×#3752C2semidirect
10. C4×C4⋊(C3⋊Dic3)C2semidirect
11. #10592632C2semidirect
12. #10592369C2semidirect
13. #10592365C2semidirect
14. #10592353C2semidirect
15. #10592348C2semidirect
42. #64092C4semidirect
54. C3×C4×C22⋊C4D3semidirect
91. C2×C4×C3⋊D3C2×C4semidirect
103. #3752C2×C4semidirect
105. C4⋊(C3⋊Dic3)C2×C4semidirect
108. #3750C2×C4semidirect
222. C4×C22⋊C4C3⋊D3semidirect
485. C32#2374semidirect
586. C3#73479semidirect

Maximal subgroups

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

subgroupindex
C2×#640922
C32×C4×C22⋊C42
#105929122
C4×#37572
#105926562
#105926502
#105926442
#105926392
C4×#37522
C4×C4⋊(C3⋊Dic3)2
#105926322
#105923692
#105923652
#105923532
#105923482
#734793