Finite Group Databasebeta

← #11819123

Subgroups — #11819123

Order 1152.

660 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#401C211yesmaximal, characteristic, complemented
2#10588348C211yesmaximal, characteristic
3#10588348C211yesmaximal, characteristic
4#10588347C211yesmaximal, characteristic
5#10588346C211yesmaximal, characteristic
6#10588344C211yesmaximal, characteristic
7#10588344C211yesmaximal, characteristic
8D9×#95C211yesmaximal, characteristic
9#10588340C211yesmaximal, characteristic, complemented
10#10588338C211yesmaximal, characteristic, complemented
11#10588338C211yesmaximal, characteristic, complemented
12#10588335C211yesmaximal, characteristic, complemented
13#10588334C211yesmaximal, characteristic, complemented
14#10588333C211yesmaximal, characteristic, complemented
15#10588331C211yesmaximal, characteristic, complemented
16#78430—31nomaximal
17C22×C4×D9C2211yescharacteristic
18C22×C4×D9C2211yescharacteristic
19C22×C4×D9C2211yescharacteristic
20C2×(C2×D9)⋊C4C2211yescharacteristic
21C2×(C2×D9)⋊C4C2211yescharacteristic
22C2×(C2×D9)⋊C4C2211yescharacteristic
23C2×(C2×D9)⋊C4C2211yescharacteristic
24C2×C4⋊Dic9C2211yescharacteristic
25C2×C4⋊Dic9C2211yescharacteristic
26C2×Dic9⋊C4C2211yescharacteristic
27C2×Dic9⋊C4C2211yescharacteristic
28C2×Dic9⋊C4C2211yescharacteristic
29C2×Dic9⋊C4C2211yescharacteristic
30C2×C4×Dic9C2211yescharacteristic
31C2×C4×Dic9C2211yescharacteristic
32C9×#95C2211yescharacteristic
33C9×#95C2211yescharacteristic
34C9×#95C2211yescharacteristic
35C9×#95C2211yescharacteristic
36C9×#95C2211yescharacteristic
37C9×#95C2211yescharacteristic
38C9×#95C2211yescharacteristic
39C9⋊#95C2211yescharacteristic
40C9⋊#95C2211yescharacteristic
41C9⋊#95C2211yescharacteristic
42C9⋊#95C2211yescharacteristic
43C9⋊#95C2211yescharacteristic
44C9⋊#95C2211yescharacteristic
45C9⋊#95C2211yescharacteristic
46C9⋊#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C3×#401D311yescharacteristic
53#4668—31no—
54#4668—31no—
55#4667—31no—
56#4666—31no—
57#4664—31no—
58#4664—31no—
59D3×#95—31no—
60#4660—31no—
61#4658—31no—
62#4658—31no—
63#4655—31no—
64#4654—31no—
65#4653—31no—
66#4651—31no—
67C23×D9C2311yescharacteristic
68C22×C4×C9C2311yescharacteristic
69C22×C4×C9C2311yescharacteristic
70C22×C4×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2311yescharacteristic
77C22×Dic9C2311yescharacteristic
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C2×C4×D9—22no—
83C2×C4×D9—22no—
84C2×C4×D9—22no—
85C2×C4×D9—22no—
86C2×C4×D9—22no—
87C2×C4×D9—22no—
88C2×C4×D9—22no—
89C2×C4×D9—41no—
90C2×C4×D9—41no—
91(C2×D9)⋊C4—22no—
92(C2×D9)⋊C4—22no—
93(C2×D9)⋊C4—22no—
94(C2×D9)⋊C4—22no—
95C4⋊Dic9—22no—
96C4⋊Dic9—22no—
97Dic9⋊C4—22no—
98Dic9⋊C4—41no—
99Dic9⋊C4—41no—
100Dic9⋊C4—41no—
101C4×Dic9—22no—
102C4×Dic9—41no—
103#2493—91noSylow
104C22×C4×D3—31no—
105C22×C4×D3—31no—
106C22×C4×D3—31no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—31no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×Dic3⋊C4—31no—
114C2×Dic3⋊C4—31no—
115C2×Dic3⋊C4—31no—
116C2×Dic3⋊C4—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C3×#95C2×D311yescharacteristic
120C3×#95C2×D311yescharacteristic
121C3×#95C2×D311yescharacteristic
122C3×#95C2×D311yescharacteristic
123C3×#95C2×D311yescharacteristic
124C3×#95C2×D311yescharacteristic
125C3×#95C2×D311yescharacteristic
126C3⋊#95—31no—
127C3⋊#95—31no—
128C3⋊#95—31no—
129C3⋊#95—31no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—31no—
133C3⋊#95—31no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C23×C9C2411yescharacteristic
140C22×D9—21no—
141C22×D9—21no—
142C22×D9—21no—
143C22×D9—21no—
144C22×D9#4112yes—
145C22×D9#4112yes—
146C22×D9#4112yes—
147C2×C4×C9—21no—
148C2×C4×C9—21no—
149C2×C4×C9—21no—
150C2×C4×C9—21no—
151C2×C4×C9—21no—
152C2×C4×C9—21no—
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×Dic9—21no—
169C2×Dic9—21no—
170C2×Dic9—21no—
171C2×Dic9—21no—
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#4112yes—
188C2×Dic9#4112yes—
189C4×D9—44no—
190C4×D9—44no—
191C4×D9—44no—
192#401D911yescharacteristic, complemented
193#400—91no—
194#400—91no—
195#400—91no—
196#387—91no—
197#387—91no—
198#387—91no—
199#385—91no—
200#385—91no—
201#383—91no—
202#381—91no—
203#381—91no—
204#380—91no—
205C4×C22⋊C4—91no—
206C2×#95—91no—
207C23×D3—31no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—121no—
230C2×C4×D3—121no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235C4⋊Dic3—62no—
236C4⋊Dic3—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—121no—
239Dic3⋊C4—121no—
240Dic3⋊C4—121no—
241C4×Dic3—62no—
242C4×Dic3—121no—
243C22×C9C2×#4111yescharacteristic
244C22×C9C2×#4111yescharacteristic
245C22×C9C2×#4111yescharacteristic
246C22×C9C2×#4111yescharacteristic
247C22×C9C2×#4111yescharacteristic
248C22×C9H(5,𝔽2)11yescharacteristic
249C22×C92−1+411yescharacteristic
250C2×D9—22no—
251C2×D9—22no—
252C2×D9—22no—
253C2×D9—22no—
254C2×D9—22no—
255C2×D9—22no—
256C2×D9#12614yes—
257C4×C9—41no—
258C4×C9—41no—
259C4×C9—41no—
260C4×C9—41no—
261C4×C9—41no—
262C4×C9—41no—
263C4×C9—41no—
264Dic9—22no—
265Dic9—22no—
266Dic9—41no—
267Dic9—41no—
268Dic9—41no—
269Dic9—41no—
270Dic9—41no—
271C23×C4—91no—
272C23×C4—91no—
273C23×C4—91no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—91no—
280C2×C22⋊C4—91no—
281C2×C22⋊C4—91no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4—91no—
284C2×C42—91no—
285C2×C42—91no—
286#95—91no—
287#95—91no—
288#95—91no—
289#95—91no—
290#95—91no—
291#95—91no—
292#95—91no—
293#95—91no—
294#95—91no—
295#95—91no—
296#95—91no—
297#95—91no—
298#95—91no—
299#95C2×D911yescharacteristic
300#95C2×D911yescharacteristic
301#95C2×D911yescharacteristic
302#95C2×D911yescharacteristic
303#95C2×D911yescharacteristic
304#95C2×D911yescharacteristic
305#95C2×D911yescharacteristic
306C23×C3C23×D311yescharacteristic
307C22×D3—32no—
308C22×D3—32no—
309C22×D3—32no—
310C22×D3—61no—
311C22×D3—61no—
312C22×D3—61no—
313C22×D3—61no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
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×Dic3—32no—
336C2×Dic3—32no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
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—
356C4×D3—124no—
357C4×D3—124no—
358C4×D3—124no—
359C2×C9C2×#12611yescharacteristic
360C2×C9#52911yescharacteristic
361C2×C9#53911yescharacteristic
362C2×C9#55111yescharacteristic
363C2×C9#55111yescharacteristic
364C2×C9#55211yescharacteristic
365C2×C9#55211yescharacteristic
366D9—24no—
367C24—91no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—182no—
376C22×C4—182no—
377C22×C4—182no—
378C22×C4—182no—
379C22×C4—182no—
380C22×C4—182no—
381C22×C4—182no—
382C22×C4—361no—
383C22×C4—361no—
384C22×C4C22×D911yescharacteristic
385C22×C4C22×D911yescharacteristic
386C22×C4C22×D911yescharacteristic
387C22×C4C22×D911yescharacteristic
388C22×C4C22×D911yescharacteristic
389C22×C4C22×D911yescharacteristic
390C22×C4C22×D911yescharacteristic
391C4⋊C4—182no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—361no—
395C4⋊C4—361no—
396C4⋊C4—361no—
397C22⋊C4—182no—
398C22⋊C4—182no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C42—182no—
402C42—361no—
403C22×C3D3×#4111yescharacteristic
404C22×C3D3×#4111yescharacteristic
405C22×C3D3×#4111yescharacteristic
406C22×C3D3×#4111yescharacteristic
407C22×C3D3×#4111yescharacteristic
408C22×C3#100911yescharacteristic
409C22×C3#101011yescharacteristic
410C2×D3—34no—
411C2×D3—62no—
412C2×D3—62no—
413C2×D3—62no—
414C2×D3—62no—
415C2×D3—62no—
416C2×D3—62no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—41no—
420C3×C4—41no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—41no—
424Dic3—62no—
425Dic3—62no—
426Dic3—121no—
427Dic3—121no—
428Dic3—121no—
429Dic3—121no—
430Dic3—121no—
431C9#249311yescharacteristic, complemented, Sylow
432C23—92no—
433C23—92no—
434C23—92no—
435C23—181no—
436C23—181no—
437C23—181no—
438C23—181no—
439C23C23×D911yescharacteristic
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
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—92no—
462C2×C4—92no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—181no—
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—364no—
483C2×C4—364no—
484C2×C4—364no—
485C2×C3D3×#12611yescharacteristic
486C2×C3#570511yescharacteristic
487C2×C3#570511yescharacteristic
488C2×C3#570611yescharacteristic
489C2×C3#570711yescharacteristic
490C2×C3#570811yescharacteristic
491C2×C3#570811yescharacteristic
492D3—64no—
493C22—94no—
494C22—182no—
495C22—182no—
496C22—182no—
497C22—182no—
498C22—182no—
499C22—182no—
500C22#41×D911yescharacteristic
501C22#41×D911yescharacteristic
502C22#41×D911yescharacteristic
503C22#41×D911yescharacteristic
504C22#41×D911yescharacteristic
505C22#6371511yescharacteristic
506C22#6371611yescharacteristic
507C4—41no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—41no—
513C4—41no—
514C4—182no—
515C4—182no—
516C4—361no—
517C4—361no—
518C4—361no—
519C4—361no—
520C4—361no—
521C3#7843011yescharacteristic
522C2—184no—
523C2D9×#12611yescharacteristic
524C2#1058980711yescharacteristic
525C2#1058980711yescharacteristic
526C2#1058980811yescharacteristic
527C2#1058980911yescharacteristic
528C2#1058981011yescharacteristic
529C2#1058981011yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#401C2
prime radicalC23×D9C23
hypercenter#401D9
hypocenterC9#2493
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #401

Complements

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

NH ≅ G/Ntype
1. C9×#401C2semidirect
9. #10588340C2semidirect
10. #10588338C2semidirect
11. #10588338C2semidirect
12. #10588335C2semidirect
13. #10588334C2semidirect
14. #10588333C2semidirect
15. #10588331C2semidirect
192. #401D9semidirect
431. C9#2493semidirect

Maximal subgroups

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

subgroupindex
C9×#4012
#105883482
#105883472
#105883462
#105883442
D9×#952
#105883402
#105883382
#105883352
#105883342
#105883332
#105883312
#784303