Finite Group Databasebeta

← #11807368

Subgroups — #11807368

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63441C211yesmaximal, characteristic
2C4×C9×C22⋊C4C211yesmaximal, characteristic
3#10588890C211yesmaximal, characteristic
4C4×#3676C211yesmaximal, characteristic
5#10588631C211yesmaximal, characteristic
6#10588624C211yesmaximal, characteristic
7#10588624C211yesmaximal, characteristic
8C4×C4⋊Dic9C211yesmaximal, characteristic, complemented
9#10588613C211yesmaximal, characteristic, complemented
10#10588613C211yesmaximal, characteristic, complemented
11C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
12#10588333C211yesmaximal, characteristic, complemented
13#10588329C211yesmaximal, characteristic, complemented
14#10588328C211yesmaximal, characteristic, complemented
15#10588327C211yesmaximal, characteristic, complemented
16#73476—31nomaximal
17C23×C4×C9C2211yescharacteristic
18C2×C9×C22⋊C4C2211yescharacteristic
19C2×C9×C22⋊C4C2211yescharacteristic
20C2×C42×C9C2211yescharacteristic
21C2×C42×C9C2211yescharacteristic
22C2×#3676C2211yescharacteristic
23C2×#3676C2211yescharacteristic
24C2×#3676C2211yescharacteristic
25C2×#3676C2211yescharacteristic
26C2×C4⋊Dic9C2211yescharacteristic
27C2×C4⋊Dic9C2211yescharacteristic
28C2×Dic9⋊C4C2211yescharacteristic
29C2×Dic9⋊C4C2211yescharacteristic
30C2×Dic9⋊C4C2211yescharacteristic
31C2×Dic9⋊C4C2211yescharacteristic
32C2×Dic9⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×C4×Dic9C2211yescharacteristic
35C2×C4×Dic9C2211yescharacteristic
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40#63441C418yescomplemented
41C9×#95C2211yescharacteristic
42C9×#95C2211yescharacteristic
43C9⋊#95C2211yescharacteristic
44C9⋊#95C2211yescharacteristic
45C9⋊#95C2211yescharacteristic
46C9⋊#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C2×#879—31no—
54C3×C4×C22⋊C4D311yescharacteristic
55#5210—31no—
56C4×#217—31no—
57#4951—31no—
58#4944—31no—
59#4944—31no—
60C4×C4⋊Dic3—31no—
61#4933—31no—
62#4933—31no—
63C4×Dic3⋊C4—31no—
64#4653—31no—
65#4649—31no—
66#4648—31no—
67#4647—31no—
68C24×C9C2311yescharacteristic
69C22×C4×C9—22no—
70C22×C4×C9—22no—
71C22×C4×C9—41no—
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C22×Dic9C2311yescharacteristic
85C22×Dic9C2311yescharacteristic
86C9×C22⋊C4—22no—
87C9×C22⋊C4C2×C414yes—
88C42×C9—22no—
89C42×C9—41no—
90#3676—22no—
91#3676—41no—
92#3676C2×C414yes—
93#3676C2×C414yes—
94C4⋊Dic9—22no—
95C4⋊Dic9C2×C414yescomplemented
96Dic9⋊C4—22no—
97Dic9⋊C4—22no—
98Dic9⋊C4—22no—
99Dic9⋊C4—41no—
100Dic9⋊C4C2×C414yescomplemented
101Dic9⋊C4C2×C414yescomplemented
102C4×Dic9—22no—
103C4×Dic9—22no—
104C4×Dic9—22no—
105C4×Dic9—41no—
106C4×Dic9—41no—
107C4×Dic9C2×C414yescomplemented
108#2373—91noSylow
109C23×C3×C4C2×D311yescharacteristic
110C2×C3×C22⋊C4C2×D311yescharacteristic
111C2×C3×C22⋊C4C2×D311yescharacteristic
112C2×C3×C42C2×D311yescharacteristic
113C2×C3×C42C2×D311yescharacteristic
114C2×#217—31no—
115C2×#217—31no—
116C2×#217—31no—
117C2×#217—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×Dic3⋊C4—31no—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132#879—38no—
133C3×#95C2×D311yescharacteristic
134C3×#95C2×D311yescharacteristic
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—31no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95—31no—
145C23×C9—21no—
146C23×C9—21no—
147C23×C9—21no—
148C23×C9—21no—
149C23×C9—21no—
150C23×C9—21no—
151C23×C9C22×C412yes—
152C23×C9C2411yescharacteristic
153C2×C4×C9—21no—
154C2×C4×C9—21no—
155C2×C4×C9—21no—
156C2×C4×C9—21no—
157C2×C4×C9—21no—
158C2×C4×C9—21no—
159C2×C4×C9—21no—
160C2×C4×C9—21no—
161C2×C4×C9—21no—
162C2×C4×C9—21no—
163C2×C4×C9—21no—
164C2×C4×C9—21no—
165C2×C4×C9—21no—
166C2×C4×C9—44no—
167C2×C4×C9C22×C412yes—
168C2×C4×C9C22×C412yes—
169C2×C4×C9#4112yes—
170C2×C4×C9#4112yes—
171C2×C4×C9#4112yes—
172C2×Dic9—21no—
173C2×Dic9—21no—
174C2×Dic9—21no—
175C2×Dic9—21no—
176C2×Dic9—21no—
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—21no—
180C2×Dic9—21no—
181C2×Dic9—21no—
182C2×Dic9—21no—
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9C22×C412yes—
192C2×Dic9C22×C412yes—
193C2×Dic9C22×C412yes—
194C2×Dic9C22×C412yes—
195C2×Dic9#4112yes—
196C2×#126—91no—
197#389—91no—
198#388—91no—
199#388—91no—
200#388—91no—
201#387—91no—
202#387—91no—
203#387—91no—
204#385—91no—
205C4×C4⋊C4—91no—
206C4×C4⋊C4—91no—
207C4×C4⋊C4—91no—
208C4×C22⋊C4—91no—
209C4×C22⋊C4D911yescharacteristic
210#376—91no—
211C24×C3C22×D311yescharacteristic
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—41no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C3×C22⋊C4—22no—
230C3×C22⋊C4C4×D314yes—
231C3×C42—22no—
232C3×C42—41no—
233#217—34no—
234#217—34no—
235#217—62no—
236#217—121no—
237C4⋊Dic3—34no—
238C4⋊Dic3—62no—
239Dic3⋊C4—34no—
240Dic3⋊C4—34no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—121no—
245C4×Dic3—34no—
246C4×Dic3—62no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249C4×Dic3—121no—
250C4×Dic3—121no—
251C22×C9—22no—
252C22×C9—22no—
253C22×C9—22no—
254C22×C9—41no—
255C22×C9—41no—
256C22×C9—41no—
257C22×C9—41no—
258C22×C9C23×C411yescharacteristic
259C22×C9C2×#4111yescharacteristic
260C22×C9C2×#4111yescharacteristic
261C22×C9C2×#4111yescharacteristic
262C22×C9C2×#4111yescharacteristic
263C22×C9H(5,𝔽2)11yescharacteristic
264C22×C92−1+411yescharacteristic
265C4×C9—22no—
266C4×C9—22no—
267C4×C9—22no—
268C4×C9—22no—
269C4×C9—22no—
270C4×C9—41no—
271Dic9—22no—
272Dic9—22no—
273Dic9—22no—
274Dic9—22no—
275Dic9—22no—
276Dic9—41no—
277Dic9—41no—
278Dic9—41no—
279C23×C4C2×D911yescharacteristic
280#126—98no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—91no—
289C2×C22⋊C4—91no—
290C2×C22⋊C4—91no—
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4C2×D911yescharacteristic
294C2×C22⋊C4C2×D911yescharacteristic
295C2×C42—91no—
296C2×C42—91no—
297C2×C42—91no—
298C2×C42—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42C2×D911yescharacteristic
302C2×C42C2×D911yescharacteristic
303#95—91no—
304#95—91no—
305#95—91no—
306#95—91no—
307#95—91no—
308#95—91no—
309#95—91no—
310#95—91no—
311#95—91no—
312#95—91no—
313#95C2×D911yescharacteristic
314#95C2×D911yescharacteristic
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3C2×C4×D312yes—
322C23×C3C23×D311yescharacteristic
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—44no—
337C2×C3×C4C2×C4×D312yes—
338C2×C3×C4C2×C4×D312yes—
339C2×C3×C4#23512yes—
340C2×C3×C4#23512yes—
341C2×C3×C4#23712yes—
342C2×Dic3—32no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×C9—42no—
367C2×C9C4×#4111yescharacteristic
368C2×C9C4×#4111yescharacteristic
369C2×C9#52011yescharacteristic
370C2×C9#55111yescharacteristic
371C2×C9#55211yescharacteristic
372C2×C9#55311yescharacteristic
373C2×C9#55611yescharacteristic
374C24C22×D911yescharacteristic
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—41no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4C22×D911yescharacteristic
387C22×C4C22×D911yescharacteristic
388C22×C4C22×D911yescharacteristic
389C22×C4C22×D911yescharacteristic
390C22×C4C22×D911yescharacteristic
391C22×C4C22×D911yescharacteristic
392C4⋊C4—94no—
393C4⋊C4—94no—
394C4⋊C4—94no—
395C4⋊C4—182no—
396C4⋊C4—182no—
397C4⋊C4—182no—
398C4⋊C4—182no—
399C4⋊C4—361no—
400C22⋊C4—22no—
401C22⋊C4—94no—
402C22⋊C4—94no—
403C22⋊C4—182no—
404C22⋊C4—361no—
405C22⋊C4C4×D914yes—
406C42—22no—
407C42—41no—
408C42—94no—
409C42—182no—
410C42—182no—
411C42—182no—
412C42—361no—
413C42—361no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3C22×C4×D311yescharacteristic
422C22×C3C2×#23511yescharacteristic
423C22×C3C2×#23511yescharacteristic
424C22×C3C2×#23711yescharacteristic
425C22×C3#100411yescharacteristic
426C22×C3D3×#4111yescharacteristic
427C22×C3#101011yescharacteristic
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—41no—
434Dic3—62no—
435Dic3—62no—
436Dic3—62no—
437Dic3—62no—
438Dic3—62no—
439Dic3—121no—
440Dic3—121no—
441Dic3—121no—
442C9#237311yescharacteristic, complemented, Sylow
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23C2×C4×D912yes—
450C23C23×D911yescharacteristic
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—44no—
465C2×C4—92no—
466C2×C4—92no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—92no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4C2×C4×D912yes—
490C2×C4C2×C4×D912yes—
491C2×C4#369712yes—
492C2×C4#369712yes—
493C2×C4#369912yes—
494C2×C3—42no—
495C2×C3C4×#23511yescharacteristic
496C2×C3#549511yescharacteristic
497C2×C3#553311yescharacteristic
498C2×C3C4×#23711yescharacteristic
499C2×C3#554111yescharacteristic
500C2×C3#554611yescharacteristic
501C2×C3#555811yescharacteristic
502C22—22no—
503C22—22no—
504C22—22no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22C22×C4×D911yescharacteristic
510C22C2×#369711yescharacteristic
511C22C2×#369711yescharacteristic
512C22C2×#369911yescharacteristic
513C22#6371011yescharacteristic
514C22#41×D911yescharacteristic
515C22#6371611yescharacteristic
516C4—22no—
517C4—22no—
518C4—22no—
519C4—22no—
520C4—22no—
521C4—41no—
522C4—182no—
523C4—182no—
524C4—182no—
525C4—182no—
526C4—182no—
527C4—361no—
528C4—361no—
529C4—361no—
530C3#7347611yescharacteristic
531C2—42no—
532C2C4×#369711yescharacteristic
533C2#1058959711yescharacteristic
534C2#1058963511yescharacteristic
535C2C4×#369911yescharacteristic
536C2#1058964311yescharacteristic
537C2#1058964811yescharacteristic
538C2#1058966011yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC4×C9×C22⋊C4C2
prime radicalC24×C3C22×D3
cosocleC23×C9C24
hypercenterC4×C22⋊C4D9
hypocenterC9#2373
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C4×C4⋊Dic9C2semidirect
9. #10588613C2semidirect
10. #10588613C2semidirect
11. C4×Dic9⋊C4C2semidirect
12. #10588333C2semidirect
13. #10588329C2semidirect
14. #10588328C2semidirect
15. #10588327C2semidirect
40. #63441C4semidirect
95. C4⋊Dic9C2×C4semidirect
100. Dic9⋊C4C2×C4semidirect
101. Dic9⋊C4C2×C4semidirect
107. C4×Dic9C2×C4semidirect
442. C9#2373semidirect

Maximal subgroups

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

subgroupindex
C2×#634412
C4×C9×C22⋊C42
#105888902
C4×#36762
#105886312
#105886242
C4×C4⋊Dic92
#105886132
C4×Dic9⋊C42
#105883332
#105883292
#105883282
#105883272
#734763