Finite Group Databasebeta

← #11808028

Subgroups — #11808028

Order 1152.

684 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×#63460C211yesmaximal, characteristic
2C9×#387C211yesmaximal, characteristic, complemented
3#10588669C211yesmaximal, characteristic
4#10588664C211yesmaximal, characteristic, complemented
5#10588655C211yesmaximal, characteristic, complemented
6#10588620C211yesmaximal, characteristic
7#10588608C211yesmaximal, characteristic, complemented
8#10588350C211yesmaximal, characteristic
9#10588349C211yesmaximal, characteristic
10#10588348C211yesmaximal, characteristic
11#10588348C211yesmaximal, characteristic
12#10588334C211yesmaximal, characteristic, complemented
13#10588332C211yesmaximal, characteristic, complemented
14#10588331C211yesmaximal, characteristic, complemented
15#10588327C211yesmaximal, characteristic, complemented
16#74980—31nomaximal
17C22×C4×D9C2211yescharacteristic
18C2×C9×C4⋊C4C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C42×C9C2211yescharacteristic
21C2×(C2×D9)⋊C4C2211yescharacteristic
22C2×(C2×D9)⋊C4C2211yescharacteristic
23C2×(C2×D9)⋊C4C2211yescharacteristic
24C2×(C2×D9)⋊C4C2211yescharacteristic
25C2×(C2×D9)⋊C4C2211yescharacteristic
26C2×(C2×D9)⋊C4C2211yescharacteristic
27C2×C4⋊Dic9C2211yescharacteristic
28C2×C4⋊Dic9C2211yescharacteristic
29C2×C4⋊Dic9C2211yescharacteristic
30C2×C4⋊Dic9C2211yescharacteristic
31C2×Dic9⋊C4C2211yescharacteristic
32C2×Dic9⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×Dic9⋊C4C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×Dic9⋊C4C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40#63460C418yescomplemented
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×#898—31no—
54C3×#387D311yescharacteristic
55#4989—31no—
56#4984—31no—
57#4975—31no—
58#4940—31no—
59#4928—31no—
60#4670—31no—
61#4669—31no—
62#4668—31no—
63#4668—31no—
64#4654—31no—
65#4652—31no—
66#4651—31no—
67#4647—31no—
68C23×D9C2311yescharacteristic
69C22×C4×C9C2311yescharacteristic
70C22×C4×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×Dic9C2311yescharacteristic
77C22×Dic9C2311yescharacteristic
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C2×C4×D9—41no—
84C2×C4×D9—41no—
85C2×C4×D9—41no—
86C9×C4⋊C4—41no—
87C9×C4⋊C4C2×C414yescomplemented
88C42×C9—41no—
89(C2×D9)⋊C4—41no—
90(C2×D9)⋊C4—41no—
91(C2×D9)⋊C4—41no—
92(C2×D9)⋊C4C2×C414yes—
93(C2×D9)⋊C4C2×C414yes—
94(C2×D9)⋊C4C2×C414yes—
95C4⋊Dic9—41no—
96C4⋊Dic9—41no—
97C4⋊Dic9—41no—
98C4⋊Dic9C2×C414yescomplemented
99Dic9⋊C4—41no—
100Dic9⋊C4—41no—
101Dic9⋊C4—41no—
102Dic9⋊C4—41no—
103Dic9⋊C4—41no—
104Dic9⋊C4C2×C414yescomplemented
105C4×Dic9—41no—
106C4×Dic9—41no—
107C4×Dic9C2×C414yescomplemented
108#2383—91noSylow
109C22×C4×D3—31no—
110C2×C3×C4⋊C4C2×D311yescharacteristic
111C2×C3×C4⋊C4C2×D311yescharacteristic
112C2×C3×C42C2×D311yescharacteristic
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—31no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—31no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132#898—38no—
133C3×#95C2×D311yescharacteristic
134C3×#95C2×D311yescharacteristic
135C3×#95C2×D311yescharacteristic
136C3×#95C2×D311yescharacteristic
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×C9C2411yescharacteristic
146C22×D9—21no—
147C22×D9—21no—
148C22×D9—21no—
149C22×D9—21no—
150C22×D9—21no—
151C22×D9—21no—
152C22×D9C22×C412yes—
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—21no—
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9C22×C412yes—
172C2×C4×C9C22×C412yes—
173C2×C4×C9C22×C412yes—
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×Dic9—21no—
192C2×Dic9C22×C412yes—
193C2×Dic9C22×C412yes—
194C2×Dic9C22×C412yes—
195C4×D9—44no—
196C2×#126—91no—
197#389—91no—
198#389—91no—
199#389—91no—
200#388—91no—
201#388—91no—
202#388—91no—
203#387—91no—
204#387—91no—
205#387D911yescharacteristic, complemented
206#385—91no—
207#385—91no—
208#385—91no—
209#384—91no—
210#383—91no—
211C23×D3—31no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C2×C4×D3—121no—
227C2×C4×D3—121no—
228C2×C4×D3—121no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4C4×D314yes—
231C3×C42—41no—
232(C2×D3)⋊C4—34no—
233(C2×D3)⋊C4—34no—
234(C2×D3)⋊C4—34no—
235(C2×D3)⋊C4—121no—
236(C2×D3)⋊C4—121no—
237(C2×D3)⋊C4—121no—
238C4⋊Dic3—34no—
239C4⋊Dic3—121no—
240C4⋊Dic3—121no—
241C4⋊Dic3—121no—
242Dic3⋊C4—34no—
243Dic3⋊C4—121no—
244Dic3⋊C4—121no—
245Dic3⋊C4—121no—
246Dic3⋊C4—121no—
247Dic3⋊C4—121no—
248C4×Dic3—34no—
249C4×Dic3—121no—
250C4×Dic3—121no—
251C22×C9C23×C411yescharacteristic
252C22×C9H(5,𝔽2)11yescharacteristic
253C22×C9H(5,𝔽2)11yescharacteristic
254C22×C9H(5,𝔽2)11yescharacteristic
255C22×C92−1+411yescharacteristic
256C22×C92−1+411yescharacteristic
257C22×C92−1+411yescharacteristic
258C2×D9—22no—
259C2×D9—22no—
260C2×D9—22no—
261C2×D9—41no—
262C2×D9—41no—
263C2×D9—41no—
264C2×D9—41no—
265C4×C9—22no—
266C4×C9—22no—
267C4×C9—22no—
268C4×C9—41no—
269C4×C9—41no—
270C4×C9—41no—
271C4×C9—41no—
272Dic9—22no—
273Dic9—22no—
274Dic9—22no—
275Dic9—41no—
276Dic9—41no—
277Dic9—41no—
278Dic9—41no—
279C23×C4—91no—
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×C4⋊C4—91no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4C2×D911yescharacteristic
292C2×C4⋊C4C2×D911yescharacteristic
293C2×C22⋊C4—91no—
294C2×C22⋊C4—91no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—91no—
298C2×C22⋊C4—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—91no—
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#95C2×D911yescharacteristic
312#95C2×D911yescharacteristic
313#95C2×D911yescharacteristic
314#95C2×D911yescharacteristic
315C23×C3C23×D311yescharacteristic
316C22×D3—32no—
317C22×D3—61no—
318C22×D3—61no—
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—61no—
322C22×D3—61no—
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—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4C2×C4×D312yes—
342C2×C3×C4C2×C4×D312yes—
343C2×C3×C4C2×C4×D312yes—
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—
365C4×D3—124no—
366C2×C9#52011yescharacteristic
367C2×C9#52011yescharacteristic
368C2×C9#52011yescharacteristic
369C2×C9#56011yescharacteristic
370C2×C9#56311yescharacteristic
371C2×C9#56311yescharacteristic
372C2×C9#56311yescharacteristic
373D9—42no—
374C24—91no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—361no—
383C22×C4—361no—
384C22×C4—361no—
385C22×C4C22×D911yescharacteristic
386C22×C4C22×D911yescharacteristic
387C22×C4C22×D911yescharacteristic
388C22×C4C22×D911yescharacteristic
389C22×C4C22×D911yescharacteristic
390C22×C4C22×D911yescharacteristic
391C22×C4C22×D911yescharacteristic
392C4⋊C4—41no—
393C4⋊C4—94no—
394C4⋊C4—94no—
395C4⋊C4—361no—
396C4⋊C4—361no—
397C4⋊C4—361no—
398C4⋊C4—361no—
399C4⋊C4—361no—
400C4⋊C4—361no—
401C4⋊C4—361no—
402C4⋊C4—361no—
403C4⋊C4C4×D914yescomplemented
404C22⋊C4—94no—
405C22⋊C4—94no—
406C22⋊C4—94no—
407C22⋊C4—361no—
408C22⋊C4—361no—
409C22⋊C4—361no—
410C42—41no—
411C42—94no—
412C42—361no—
413C42—361no—
414C22×C3C22×C4×D311yescharacteristic
415C22×C3#100411yescharacteristic
416C22×C3#100711yescharacteristic
417C22×C3#100911yescharacteristic
418C22×C3#100911yescharacteristic
419C22×C3#101011yescharacteristic
420C22×C3#101011yescharacteristic
421C2×D3—62no—
422C2×D3—62no—
423C2×D3—62no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—41no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4—41no—
435Dic3—62no—
436Dic3—62no—
437Dic3—62no—
438Dic3—121no—
439Dic3—121no—
440Dic3—121no—
441Dic3—121no—
442C9#238311yescharacteristic, complemented, Sylow
443C23—92no—
444C23—181no—
445C23—181no—
446C23—181no—
447C23—181no—
448C23—181no—
449C23—181no—
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—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—92no—
470C2×C4—92no—
471C2×C4—92no—
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×C4—181no—
490C2×C4—364no—
491C2×C4C2×C4×D912yes—
492C2×C4C2×C4×D912yes—
493C2×C4C2×C4×D912yes—
494C2×C3#552311yescharacteristic
495C2×C3#554611yescharacteristic
496C2×C3#557411yescharacteristic
497C2×C3#564611yescharacteristic
498C2×C3#566611yescharacteristic
499C2×C3#569911yescharacteristic
500C2×C3#571211yescharacteristic
501D3—122no—
502C22—182no—
503C22—182no—
504C22—182no—
505C22—361no—
506C22—361no—
507C22—361no—
508C22—361no—
509C22C22×C4×D911yescharacteristic
510C22#6371011yescharacteristic
511C22#6371311yescharacteristic
512C22#6371511yescharacteristic
513C22#6371511yescharacteristic
514C22#6371611yescharacteristic
515C22#6371611yescharacteristic
516C4—22no—
517C4—22no—
518C4—22no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—182no—
524C4—182no—
525C4—182no—
526C4—361no—
527C4—361no—
528C4—361no—
529C4—361no—
530C3#7498011yescharacteristic
531C2—362no—
532C2#1058962511yescharacteristic
533C2#1058964811yescharacteristic
534C2#1058967611yescharacteristic
535C2#1058974811yescharacteristic
536C2#1058976811yescharacteristic
537C2#1058980111yescharacteristic
538C2#1058981411yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#387C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenter#387D9
hypocenterC9#2383
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C9×#387C2semidirect
4. #10588664C2semidirect
5. #10588655C2semidirect
7. #10588608C2semidirect
12. #10588334C2semidirect
13. #10588332C2semidirect
14. #10588331C2semidirect
15. #10588327C2semidirect
40. #63460C4semidirect
87. C9×C4⋊C4C2×C4semidirect
98. C4⋊Dic9C2×C4semidirect
104. Dic9⋊C4C2×C4semidirect
107. C4×Dic9C2×C4semidirect
205. #387D9semidirect
403. C4⋊C4C4×D9semidirect
442. C9#2383semidirect

Maximal subgroups

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

subgroupindex
C2×#634602
C9×#3872
#105886692
#105886642
#105886552
#105886202
#105886082
#105883502
#105883492
#105883482
#105883342
#105883322
#105883312
#105883272
#749803