Finite Group Databasebeta

← #11805212

Subgroups — #11805212

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D9C211yesmaximal, characteristic
2C9×#387C211yesmaximal, characteristic, complemented
3#10588667C211yesmaximal, characteristic
4#10588660C211yesmaximal, characteristic, complemented
5#10588656C211yesmaximal, characteristic, complemented
6C4×(C2×D9)⋊C4C211yesmaximal, characteristic
7C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
8#10588347C211yesmaximal, characteristic
9#10588347C211yesmaximal, characteristic
10#10588346C211yesmaximal, characteristic
11#10588346C211yesmaximal, characteristic
12#10588334C211yesmaximal, characteristic, complemented
13#10588333C211yesmaximal, characteristic, complemented
14#10588329C211yesmaximal, characteristic, complemented
15#10588327C211yesmaximal, characteristic, complemented
16#74962—31nomaximal
17C22×C4×D9C2211yescharacteristic
18C22×C4×D9C2211yescharacteristic
19C22×C4×D9C2211yescharacteristic
20C2×C9×C4⋊C4C2211yescharacteristic
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C42×C9C2211yescharacteristic
23C2×(C2×D9)⋊C4C2211yescharacteristic
24C2×(C2×D9)⋊C4C2211yescharacteristic
25C2×(C2×D9)⋊C4C2211yescharacteristic
26C2×(C2×D9)⋊C4C2211yescharacteristic
27C2×C4⋊Dic9C2211yescharacteristic
28C2×C4⋊Dic9C2211yescharacteristic
29C2×Dic9⋊C4C2211yescharacteristic
30C2×Dic9⋊C4C2211yescharacteristic
31C2×Dic9⋊C4C2211yescharacteristic
32C2×Dic9⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×Dic9⋊C4C2211yescharacteristic
35C2×C4×Dic9C2211yescharacteristic
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40C4⋊C4×D9C418yescomplemented
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×D3×C4⋊C4—31no—
54C3×#387D311yescharacteristic
55#4987—31no—
56#4980—31no—
57#4976—31no—
58C4×(C2×D3)⋊C4—31no—
59C4×Dic3⋊C4—31no—
60#4667—31no—
61#4667—31no—
62#4666—31no—
63#4666—31no—
64#4654—31no—
65#4653—31no—
66#4649—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—22no—
84C2×C4×D9—22no—
85C2×C4×D9—41no—
86C2×C4×D9—41no—
87C2×C4×D9—41no—
88C2×C4×D9—41no—
89C2×C4×D9C2×C414yes—
90C2×C4×D9C2×C414yes—
91C2×C4×D9C2×C414yes—
92C9×C4⋊C4—41no—
93C9×C4⋊C4C2×C414yes—
94C42×C9—41no—
95(C2×D9)⋊C4—22no—
96(C2×D9)⋊C4—22no—
97(C2×D9)⋊C4—22no—
98(C2×D9)⋊C4Q814yes—
99C4⋊Dic9—41no—
100C4⋊Dic9C2×C414yes—
101Dic9⋊C4—22no—
102Dic9⋊C4—22no—
103Dic9⋊C4—41no—
104Dic9⋊C4—41no—
105Dic9⋊C4C2×C414yes—
106Dic9⋊C4C2×C414yes—
107C4×Dic9—22no—
108C4×Dic9—22no—
109C4×Dic9—41no—
110C4×Dic9—41no—
111C4×Dic9—41no—
112#2345—91noSylow
113C22×C4×D3—31no—
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C2×C3×C4⋊C4C2×D311yescharacteristic
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C42C2×D311yescharacteristic
119C2×(C2×D3)⋊C4—31no—
120C2×(C2×D3)⋊C4—31no—
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—31no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—31no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—31no—
130C2×Dic3⋊C4—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—31no—
136D3×C4⋊C4—38no—
137C3×#95C2×D311yescharacteristic
138C3×#95C2×D311yescharacteristic
139C3×#95C2×D311yescharacteristic
140C3×#95C2×D311yescharacteristic
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95—31no—
145C3⋊#95—31no—
146C3⋊#95—31no—
147C3⋊#95—31no—
148C3⋊#95—31no—
149C23×C9C2411yescharacteristic
150C22×D9—21no—
151C22×D9—21no—
152C22×D9—21no—
153C22×D9—21no—
154C22×D9C22×C412yes—
155C22×D9C2×Q812yes—
156C22×D9#4112yes—
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×C9—21no—
172C2×C4×C9—21no—
173C2×C4×C9—21no—
174C2×C4×C9C22×C412yes—
175C2×C4×C9C22×C412yes—
176C2×C4×C9C22×C412yes—
177C2×C4×C9C2×Q812yes—
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×Dic9—21no—
193C2×Dic9C22×C412yes—
194C2×Dic9C22×C412yes—
195C2×Dic9C22×C412yes—
196C2×Dic9C2×Q812yes—
197C2×Dic9#4112yes—
198C2×Dic9#4112yes—
199C4×D9—28no—
200C4×D9—44no—
201C4×D9—44no—
202C22×C4⋊C4—91no—
203#389—91no—
204#389—91no—
205#387—91no—
206#387—91no—
207#387—91no—
208#387D911yescharacteristic, complemented
209#380—91no—
210#380—91no—
211#380—91no—
212C4×C4⋊C4—91no—
213C4×C4⋊C4—91no—
214C4×C22⋊C4—91no—
215C4×C22⋊C4—91no—
216C4×C22⋊C4—91no—
217C23×D3—31no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C2×C4×D3—34no—
233C2×C4×D3—34no—
234C2×C4×D3—34no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—121no—
238C2×C4×D3—121no—
239C2×C4×D3—121no—
240C2×C4×D3—121no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4C4×D314yes—
243C3×C42—41no—
244(C2×D3)⋊C4—34no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—34no—
249C4⋊Dic3—121no—
250Dic3⋊C4—34no—
251Dic3⋊C4—34no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—121no—
255Dic3⋊C4—121no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3—121no—
259C4×Dic3—121no—
260C4×Dic3—121no—
261C22×C9C23×C411yescharacteristic
262C22×C9C22×Q811yescharacteristic
263C22×C9C2×#4111yescharacteristic
264C22×C9C2×#4111yescharacteristic
265C22×C9C2×#4111yescharacteristic
266C22×C9H(5,𝔽2)11yescharacteristic
267C22×C9H(5,𝔽2)11yescharacteristic
268C2×D9—22no—
269C2×D9—22no—
270C2×D9—22no—
271C2×D9—22no—
272C2×D9—22no—
273C2×D9—22no—
274C2×D9C4×Q814yes—
275C4×C9—22no—
276C4×C9—22no—
277C4×C9—22no—
278C4×C9—22no—
279C4×C9—41no—
280C4×C9—41no—
281C4×C9—41no—
282Dic9—22no—
283Dic9—22no—
284Dic9—22no—
285Dic9—41no—
286Dic9—41no—
287Dic9—41no—
288Dic9#11714yes—
289C23×C4—91no—
290C23×C4—91no—
291C23×C4—91no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4—91no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—98no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4C2×D911yescharacteristic
302C2×C4⋊C4C2×D911yescharacteristic
303C2×C22⋊C4—91no—
304C2×C22⋊C4—91no—
305C2×C22⋊C4—91no—
306C2×C22⋊C4—91no—
307C2×C42—91no—
308C2×C42—91no—
309C2×C42—91no—
310C2×C42—91no—
311C2×C42—91no—
312C2×C42C2×D911yescharacteristic
313#95—91no—
314#95—91no—
315#95—91no—
316#95—91no—
317#95—91no—
318#95—91no—
319#95—91no—
320#95—91no—
321#95C2×D911yescharacteristic
322#95C2×D911yescharacteristic
323#95C2×D911yescharacteristic
324#95C2×D911yescharacteristic
325C23×C3C23×D311yescharacteristic
326C22×D3—32no—
327C22×D3—32no—
328C22×D3—32no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—61no—
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×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4D3×Q812yes—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C4×D3—68no—
376C4×D3—124no—
377C4×D3—124no—
378C2×C9C2×#11711yescharacteristic
379C2×C9C2×C4×Q811yescharacteristic
380C2×C9#51811yescharacteristic
381C2×C9#55311yescharacteristic
382C2×C9#55311yescharacteristic
383C2×C9#55411yescharacteristic
384C2×C9#55411yescharacteristic
385D9—24no—
386C24—91no—
387C22×C4—91no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—94no—
392C22×C4—94no—
393C22×C4—94no—
394C22×C4—91no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—182no—
398C22×C4—182no—
399C22×C4—361no—
400C22×C4—361no—
401C22×C4—361no—
402C22×C4—361no—
403C22×C4C22×D911yescharacteristic
404C22×C4C22×D911yescharacteristic
405C22×C4C22×D911yescharacteristic
406C22×C4C22×D911yescharacteristic
407C22×C4C22×D911yescharacteristic
408C22×C4C22×D911yescharacteristic
409C22×C4C22×D911yescharacteristic
410C4⋊C4—41no—
411C4⋊C4—94no—
412C4⋊C4—94no—
413C4⋊C4—94no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C4⋊C4—361no—
417C4⋊C4—361no—
418C4⋊C4—361no—
419C4⋊C4C4×D914yes—
420C22⋊C4—94no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C42—41no—
425C42—182no—
426C42—182no—
427C42—361no—
428C42—361no—
429C42—361no—
430C22×C3C22×C4×D311yescharacteristic
431C22×C3#100411yescharacteristic
432C22×C3C2×D3×Q811yescharacteristic
433C22×C3D3×#4111yescharacteristic
434C22×C3D3×#4111yescharacteristic
435C22×C3D3×#4111yescharacteristic
436C22×C3#100911yescharacteristic
437C2×D3—34no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—62no—
444C3×C4—22no—
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—41no—
451Dic3—34no—
452Dic3—62no—
453Dic3—62no—
454Dic3—62no—
455Dic3—121no—
456Dic3—121no—
457Dic3—121no—
458C9#234511yescharacteristic, complemented, Sylow
459C23—92no—
460C23—92no—
461C23—92no—
462C23—181no—
463C23—181no—
464C23—181no—
465C23—181no—
466C23C23×D911yescharacteristic
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—92no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—188no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—364no—
507C2×C4—364no—
508C2×C4C2×C4×D912yes—
509C2×C4C2×C4×D912yes—
510C2×C4C2×C4×D912yes—
511C2×C4Q8×D912yes—
512C2×C3D3×#11711yescharacteristic
513C2×C3#554511yescharacteristic
514C2×C3C4×D3×Q811yescharacteristic
515C2×C3#563611yescharacteristic
516C2×C3#566111yescharacteristic
517C2×C3#569011yescharacteristic
518C2×C3#570911yescharacteristic
519D3—64no—
520C22—94no—
521C22—182no—
522C22—182no—
523C22—182no—
524C22—182no—
525C22—182no—
526C22—182no—
527C22C22×C4×D911yescharacteristic
528C22#6371011yescharacteristic
529C22C2×Q8×D911yescharacteristic
530C22#41×D911yescharacteristic
531C22#41×D911yescharacteristic
532C22#41×D911yescharacteristic
533C22#6371511yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—22no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—94no—
542C4—182no—
543C4—182no—
544C4—182no—
545C4—361no—
546C4—361no—
547C4—361no—
548C3#7496211yescharacteristic
549C2—184no—
550C2D9×#11711yescharacteristic
551C2#1058964711yescharacteristic
552C2C4×Q8×D911yescharacteristic
553C2#1058973811yescharacteristic
554C2#1058976311yescharacteristic
555C2#1058979211yescharacteristic
556C2#1058981111yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#387C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenter#387D9
hypocenterC9#2345
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. #10588660C2semidirect
5. #10588656C2semidirect
7. C4×Dic9⋊C4C2semidirect
12. #10588334C2semidirect
13. #10588333C2semidirect
14. #10588329C2semidirect
15. #10588327C2semidirect
40. C4⋊C4×D9C4semidirect
208. #387D9semidirect
458. C9#2345semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D92
C9×#3872
#105886672
#105886602
#105886562
C4×(C2×D9)⋊C42
C4×Dic9⋊C42
#105883472
#105883462
#105883342
#105883332
#105883292
#105883272
#749623