Finite Group Databasebeta

← #11857042

Subgroups — #11857042

Order 1152.

627 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#388C211yesmaximal, characteristic
2#10588660C211yesmaximal, characteristic, complemented
3#10588658C211yesmaximal, characteristic, complemented
4#10588631C211yesmaximal, characteristic
5#10588631C211yesmaximal, characteristic
6#10588625C211yesmaximal, characteristic
7#10588625C211yesmaximal, characteristic
8#10588624C211yesmaximal, characteristic
9#10588624C211yesmaximal, characteristic
10#10588613C211yesmaximal, characteristic, complemented
11C42×Dic9C211yesmaximal, characteristic, complemented
12#10588335C211yesmaximal, characteristic, complemented
13#10588334C211yesmaximal, characteristic, complemented
14#10588333C211yesmaximal, characteristic, complemented
15#10588332C211yesmaximal, characteristic, complemented
16#75823—31nomaximal
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×C9×C22⋊C4C2211yescharacteristic
19C2×C9×C22⋊C4C2211yescharacteristic
20C2×C9×C22⋊C4C2211yescharacteristic
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×C4×Dic9C2211yescharacteristic
33C2×C4×Dic9C2211yescharacteristic
34C2×C4×Dic9C2211yescharacteristic
35C2×C4×Dic9C2211yescharacteristic
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
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×#388D311yescharacteristic
53#4980—31no—
54#4978—31no—
55#4951—31no—
56#4951—31no—
57#4945—31no—
58#4945—31no—
59#4944—31no—
60#4944—31no—
61#4933—31no—
62C42×Dic3—31no—
63#4655—31no—
64#4654—31no—
65#4653—31no—
66#4652—31no—
67C24×C9C2311yescharacteristic
68C22×C4×C9C2311yescharacteristic
69C22×C4×C9C2311yescharacteristic
70C22×C4×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×Dic9C2311yescharacteristic
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2311yescharacteristic
77C22×Dic9C2311yescharacteristic
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C9×C4⋊C4—22no—
83C9×C22⋊C4—22no—
84C9×C22⋊C4—22no—
85C9×C22⋊C4—22no—
86C42×C9—22no—
87#3676—22no—
88#3676—22no—
89#3676—22no—
90#3676—22no—
91C4⋊Dic9—22no—
92C4⋊Dic9—22no—
93Dic9⋊C4—22no—
94Dic9⋊C4—22no—
95Dic9⋊C4—22no—
96Dic9⋊C4—22no—
97C4×Dic9—22no—
98C4×Dic9—22no—
99C4×Dic9—22no—
100C4×Dic9—22no—
101C4×Dic9—22no—
102C4×Dic9—22no—
103#2866—91noSylow
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C22⋊C4C2×D311yescharacteristic
106C2×C3×C22⋊C4C2×D311yescharacteristic
107C2×C3×C22⋊C4C2×D311yescharacteristic
108C2×C3×C42C2×D311yescharacteristic
109C2×#217—31no—
110C2×#217—31no—
111C2×#217—31no—
112C2×#217—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×Dic3⋊C4—31no—
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—31no—
125C3×#95C2×D311yescharacteristic
126C3×#95C2×D311yescharacteristic
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×C9—21no—
140C23×C9—21no—
141C23×C9—21no—
142C23×C9—21no—
143C23×C9—21no—
144C23×C9—21no—
145C23×C9—21no—
146C23×C9C2411yescharacteristic
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#4112yes—
163C2×C4×C9#4112yes—
164C2×C4×C9#4112yes—
165C2×Dic9—21no—
166C2×Dic9—21no—
167C2×Dic9—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#4112yes—
186C2×Dic9#4112yes—
187C2×Dic9#4112yes—
188C2×Dic9#4112yes—
189#388—91no—
190#388—91no—
191#388—91no—
192#388—91no—
193#388—91no—
194#388—91no—
195#388D911yescharacteristic
196#387—91no—
197#387—91no—
198#387—91no—
199#387—91no—
200#387—91no—
201#387—91no—
202#387—91no—
203C43—91no—
204C24×C3C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C3×C4⋊C4—22no—
220C3×C22⋊C4—22no—
221C3×C22⋊C4—22no—
222C3×C22⋊C4—22no—
223C3×C42—22no—
224#217—62no—
225#217—62no—
226#217—62no—
227#217—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234C4×Dic3—62no—
235C4×Dic3—62no—
236C4×Dic3—62no—
237C4×Dic3—62no—
238C4×Dic3—62no—
239C4×Dic3—62no—
240C22×C9—41no—
241C22×C9—41no—
242C22×C9—41no—
243C22×C9—41no—
244C22×C9—41no—
245C22×C9—41no—
246C22×C9—41no—
247C22×C9C2×#4111yescharacteristic
248C22×C9C2×#4111yescharacteristic
249C22×C9C2×#4111yescharacteristic
250C22×C9C2×#4111yescharacteristic
251C22×C9C2×#4111yescharacteristic
252C22×C9C2×#4111yescharacteristic
253C22×C9C2×#4111yescharacteristic
254C4×C9—22no—
255C4×C9—22no—
256C4×C9—22no—
257C4×C9—41no—
258C4×C9—41no—
259C4×C9—41no—
260Dic9—22no—
261Dic9—22no—
262Dic9—22no—
263Dic9—22no—
264Dic9—41no—
265Dic9—41no—
266Dic9—41no—
267Dic9—41no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4C2×D911yescharacteristic
275C2×C22⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—91no—
279C2×C22⋊C4C2×D911yescharacteristic
280C2×C22⋊C4C2×D911yescharacteristic
281C2×C22⋊C4C2×D911yescharacteristic
282C2×C42—91no—
283C2×C42—91no—
284C2×C42—91no—
285C2×C42—91no—
286C2×C42—91no—
287C2×C42—91no—
288C2×C42C2×D911yescharacteristic
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#95—91no—
300#95—91no—
301#95C2×D911yescharacteristic
302#95C2×D911yescharacteristic
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3C23×D311yescharacteristic
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
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#23512yes—
327C2×C3×C4#23712yes—
328C2×C3×C4#23712yes—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
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×C9—81no—
354C2×C9#52911yescharacteristic
355C2×C9#52911yescharacteristic
356C2×C9#52911yescharacteristic
357C2×C9#52911yescharacteristic
358C2×C9#52911yescharacteristic
359C2×C9#52911yescharacteristic
360C2×C9#52911yescharacteristic
361C24C22×D911yescharacteristic
362C22×C4—91no—
363C22×C4—91no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—91no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4C22×D911yescharacteristic
371C22×C4C22×D911yescharacteristic
372C22×C4C22×D911yescharacteristic
373C22×C4C22×D911yescharacteristic
374C22×C4C22×D911yescharacteristic
375C22×C4C22×D911yescharacteristic
376C4⋊C4—22no—
377C4⋊C4—182no—
378C4⋊C4—182no—
379C4⋊C4—182no—
380C4⋊C4—182no—
381C4⋊C4—182no—
382C4⋊C4—182no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—182no—
387C22⋊C4—182no—
388C22⋊C4—182no—
389C22⋊C4—182no—
390C42—22no—
391C42—182no—
392C42—182no—
393C42—182no—
394C42—182no—
395C42—182no—
396C42—182no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3C2×#23511yescharacteristic
405C22×C3C2×#23711yescharacteristic
406C22×C3C2×#23711yescharacteristic
407C22×C3D3×#4111yescharacteristic
408C22×C3D3×#4111yescharacteristic
409C22×C3D3×#4111yescharacteristic
410C22×C3D3×#4111yescharacteristic
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—41no—
417Dic3—62no—
418Dic3—62no—
419Dic3—62no—
420Dic3—62no—
421Dic3—121no—
422Dic3—121no—
423Dic3—121no—
424Dic3—121no—
425C9#286611yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23C23×D911yescharacteristic
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
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—92no—
450C2×C4—92no—
451C2×C4—92no—
452C2×C4—92no—
453C2×C4—181no—
454C2×C4—181no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—181no—
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#369712yes—
474C2×C4#369912yes—
475C2×C4#369912yes—
476C2×C3—81no—
477C2×C3#552811yescharacteristic
478C2×C3#553811yescharacteristic
479C2×C3#555711yescharacteristic
480C2×C3#560011yescharacteristic
481C2×C3#564911yescharacteristic
482C2×C3#568011yescharacteristic
483C2×C3#570611yescharacteristic
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22C2×#369711yescharacteristic
492C22C2×#369911yescharacteristic
493C22C2×#369911yescharacteristic
494C22#41×D911yescharacteristic
495C22#41×D911yescharacteristic
496C22#41×D911yescharacteristic
497C22#41×D911yescharacteristic
498C4—22no—
499C4—22no—
500C4—22no—
501C4—41no—
502C4—41no—
503C4—41no—
504C4—182no—
505C4—182no—
506C4—182no—
507C4—182no—
508C4—361no—
509C4—361no—
510C4—361no—
511C4—361no—
512C3#7582311yescharacteristic
513C2—81no—
514C2#1058963011yescharacteristic
515C2#1058964011yescharacteristic
516C2#1058965911yescharacteristic
517C2#1058970211yescharacteristic
518C2#1058975111yescharacteristic
519C2#1058978211yescharacteristic
520C2#1058980811yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#388C2
prime radicalC24×C3C22×D3
hypercenter#388D9
hypocenterC9#2866
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #10588660C2semidirect
3. #10588658C2semidirect
10. #10588613C2semidirect
11. C42×Dic9C2semidirect
12. #10588335C2semidirect
13. #10588334C2semidirect
14. #10588333C2semidirect
15. #10588332C2semidirect
425. C9#2866semidirect

Maximal subgroups

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

subgroupindex
C9×#3882
#105886602
#105886582
#105886312
#105886252
#105886242
#105886132
C42×Dic92
#105883352
#105883342
#105883332
#105883322
#758233