Finite Group Databasebeta

← #11817715

Subgroups — #11817715

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63488C211yesmaximal, characteristic, complemented
2C2×#63441C211yesmaximal, characteristic, complemented
3C9×#386C211yesmaximal, characteristic
4#10588902C211yesmaximal, characteristic
5#10588901C211yesmaximal, characteristic
6#10588890C211yesmaximal, characteristic, complemented
7#10588631C211yesmaximal, characteristic, complemented
8#10588629C211yesmaximal, characteristic, complemented
9#10588629C211yesmaximal, characteristic, complemented
10#10588625C211yesmaximal, characteristic, complemented
11#10588625C211yesmaximal, characteristic, complemented
12#10588341C211yesmaximal, characteristic, complemented
13#10588333C211yesmaximal, characteristic, complemented
14#10588329C211yesmaximal, characteristic, complemented
15#10588327C211yesmaximal, characteristic, complemented
16#74734—31nomaximal
17C22×D4×C9C2211yescharacteristic
18C23×C4×C9C2211yescharacteristic
19C2×C9×C22⋊C4C2211yescharacteristic
20C2×C9×C22⋊C4C2211yescharacteristic
21C2×C9×C22⋊C4C2211yescharacteristic
22C2×#3676C2211yescharacteristic
23C2×#3676C2211yescharacteristic
24C2×#3676C2211yescharacteristic
25C2×#3676C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27C2×#3676C2211yescharacteristic
28C2×#3676C2211yescharacteristic
29C2×#3676C2211yescharacteristic
30#63488—24no—
31C2×C4⋊Dic9C2211yescharacteristic
32C2×C4⋊Dic9C2211yescharacteristic
33C2×C4⋊Dic9C2211yescharacteristic
34C2×C4⋊Dic9C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×Dic9⋊C4C2211yescharacteristic
37C2×Dic9⋊C4C2211yescharacteristic
38C2×Dic9⋊C4C2211yescharacteristic
39C2×Dic9⋊C4C2211yescharacteristic
40C2×Dic9⋊C4C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42C2×C4×Dic9C2211yescharacteristic
43C2×C4×Dic9C2211yescharacteristic
44C2×C4×Dic9C2211yescharacteristic
45#63441—24no—
46C9×#95C2211yescharacteristic
47C9×#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C2×#926—31no—
55C2×#879—31no—
56C3×#386D311yescharacteristic
57#5222—31no—
58#5221—31no—
59#5210—31no—
60#4951—31no—
61#4949—31no—
62#4949—31no—
63#4945—31no—
64#4945—31no—
65#4661—31no—
66#4653—31no—
67#4649—31no—
68#4647—31no—
69C24×C9C2311yescharacteristic
70C24×C9C2311yescharacteristic
71C2×D4×C9—22no—
72C2×D4×C9—22no—
73C2×D4×C9—41no—
74C22×C4×C9—22no—
75C22×C4×C9—22no—
76C22×C4×C9—22no—
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C22×C4×C9C2311yescharacteristic
80C22×C4×C9C2311yescharacteristic
81C22×C4×C9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C22×Dic9C2311yescharacteristic
85C22×Dic9C2311yescharacteristic
86C22×Dic9C2311yescharacteristic
87C22×Dic9C2311yescharacteristic
88C22×Dic9C2311yescharacteristic
89C22×Dic9C2311yescharacteristic
90C9×C22⋊C4—22no—
91C9×C22⋊C4—22no—
92C9×C22⋊C4—41no—
93#3676—22no—
94#3676—22no—
95#3676—22no—
96#3676—22no—
97#3676—22no—
98#3676—22no—
99#3676—22no—
100#3676—41no—
101C4⋊Dic9—22no—
102C4⋊Dic9—41no—
103C4⋊Dic9—41no—
104C4⋊Dic9D414yescomplemented
105Dic9⋊C4—22no—
106Dic9⋊C4—22no—
107Dic9⋊C4—22no—
108Dic9⋊C4—22no—
109Dic9⋊C4—22no—
110Dic9⋊C4—41no—
111C4×Dic9—22no—
112C4×Dic9—22no—
113C4×Dic9—22no—
114C4×Dic9—22no—
115#2479—91noSylow
116C22×C3×D4C2×D311yescharacteristic
117C23×C3×C4C2×D311yescharacteristic
118C2×C3×C22⋊C4C2×D311yescharacteristic
119C2×C3×C22⋊C4C2×D311yescharacteristic
120C2×C3×C22⋊C4C2×D311yescharacteristic
121C2×#217—31no—
122C2×#217—31no—
123C2×#217—31no—
124C2×#217—31no—
125C2×#217—31no—
126C2×#217—31no—
127C2×#217—31no—
128C2×#217—31no—
129#926—64no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×Dic3⋊C4—31no—
135C2×Dic3⋊C4—31no—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4—31no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—31no—
140C2×C4×Dic3—31no—
141C2×C4×Dic3—31no—
142C2×C4×Dic3—31no—
143C2×C4×Dic3—31no—
144#879—64no—
145C3×#95C2×D311yescharacteristic
146C3×#95C2×D311yescharacteristic
147C3⋊#95—31no—
148C3⋊#95—31no—
149C3⋊#95—31no—
150C3⋊#95—31no—
151C3⋊#95—31no—
152C3⋊#95—31no—
153C23×C9—21no—
154C23×C9—21no—
155C23×C9—21no—
156C23×C9—21no—
157C23×C9—21no—
158C23×C9—21no—
159C23×C9—21no—
160C23×C9—21no—
161C23×C9—21no—
162C23×C9—21no—
163C23×C9—21no—
164C23×C9—21no—
165C23×C9—21no—
166C23×C9#4112yes—
167C23×C9C2411yescharacteristic
168D4×C9—44no—
169C2×C4×C9—28no—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9—21no—
173C2×C4×C9—21no—
174C2×C4×C9—21no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9C2×D412yes—
183C2×C4×C9#4112yes—
184C2×C4×C9#4112yes—
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×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—21no—
197C2×Dic9—21no—
198C2×Dic9—21no—
199C2×Dic9—21no—
200C2×Dic9—21no—
201C2×Dic9—21no—
202C2×Dic9—21no—
203C2×Dic9—21no—
204C2×Dic9—21no—
205C2×Dic9—21no—
206C2×Dic9C2×D412yes—
207C2×Dic9C2×D412yes—
208C2×Dic9#4112yes—
209C2×#126—91no—
210C2×#117—91no—
211#399—91no—
212#399—91no—
213#398—91no—
214#394—91no—
215#390—91no—
216#389—91no—
217#388—91no—
218#388—91no—
219#388—91no—
220#387—91no—
221#386D911yescharacteristic
222#385—91no—
223C4×C4⋊C4—91no—
224C24×C3C22×D311yescharacteristic
225C24×C3C22×D311yescharacteristic
226C2×C3×D4—22no—
227C2×C3×D4—22no—
228C2×C3×D4—41no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4—22no—
247C3×C22⋊C4—41no—
248#217—62no—
249#217—62no—
250#217—62no—
251#217—62no—
252#217—62no—
253#217—62no—
254#217—62no—
255#217—121no—
256C4⋊Dic3—34no—
257C4⋊Dic3—62no—
258C4⋊Dic3—121no—
259C4⋊Dic3—121no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—121no—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C22×C9—22no—
271C22×C9—22no—
272C22×C9—22no—
273C22×C9—41no—
274C22×C9—41no—
275C22×C9—41no—
276C22×C9—41no—
277C22×C9—41no—
278C22×C9—41no—
279C22×C9—41no—
280C22×C9—41no—
281C22×C9—41no—
282C22×C9—41no—
283C22×C9—41no—
284C22×C9C22×D411yescharacteristic
285C22×C9C2×#4111yescharacteristic
286C22×C9C2×#4111yescharacteristic
287C22×C9C2×#4111yescharacteristic
288C22×C9C2×#4111yescharacteristic
289C22×C9H(5,𝔽2)11yescharacteristic
290C22×C92−1+411yescharacteristic
291C4×C9—22no—
292C4×C9—22no—
293C4×C9—22no—
294C4×C9—41no—
295C4×C9—41no—
296Dic9—22no—
297Dic9—22no—
298Dic9—22no—
299Dic9—41no—
300Dic9—41no—
301Dic9—41no—
302Dic9—41no—
303Dic9—41no—
304C22×D4C2×D911yescharacteristic
305C23×C4C2×D911yescharacteristic
306#126—184no—
307#117—184no—
308C2×C4⋊C4—91no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4—91no—
317C2×C4⋊C4—91no—
318C2×C22⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—91no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4—91no—
324C2×C22⋊C4—91no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4C2×D911yescharacteristic
327C2×C22⋊C4C2×D911yescharacteristic
328C2×C22⋊C4C2×D911yescharacteristic
329C2×C42—91no—
330C2×C42—91no—
331C2×C42—91no—
332C2×C42—91no—
333#95—91no—
334#95—91no—
335#95—91no—
336#95—91no—
337#95—91no—
338#95—91no—
339#95C2×D911yescharacteristic
340#95C2×D911yescharacteristic
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3#23712yes—
355C23×C3C23×D311yescharacteristic
356C3×D4—44no—
357C2×C3×C4—28no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4#23512yes—
371C2×C3×C4D3×D412yes—
372C2×C3×C4#23712yes—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—32no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×C9—42no—
398C2×C9—81no—
399C2×C9#52511yescharacteristic
400C2×C9#52911yescharacteristic
401C2×C9#54211yescharacteristic
402C2×C9#54711yescharacteristic
403C2×C9#55011yescharacteristic
404C2×C9#55111yescharacteristic
405C2×C9#55211yescharacteristic
406C24C22×D911yescharacteristic
407C24C22×D911yescharacteristic
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—41no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—91no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4C22×D911yescharacteristic
423C22×C4C22×D911yescharacteristic
424C22×C4C22×D911yescharacteristic
425C22×C4C22×D911yescharacteristic
426C22×C4C22×D911yescharacteristic
427C4⋊C4—94no—
428C4⋊C4—182no—
429C4⋊C4—182no—
430C4⋊C4—182no—
431C4⋊C4—182no—
432C4⋊C4—182no—
433C4⋊C4—182no—
434C4⋊C4—361no—
435C4⋊C4—361no—
436C4⋊C4—361no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—41no—
440C22⋊C4—182no—
441C22⋊C4—182no—
442C22⋊C4—182no—
443C22⋊C4—182no—
444C22⋊C4—182no—
445C22⋊C4—182no—
446C22⋊C4—182no—
447C22⋊C4—361no—
448C42—182no—
449C42—182no—
450C42—182no—
451C42—182no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3C2×#23511yescharacteristic
467C22×C3C2×D3×D411yescharacteristic
468C22×C3C2×#23711yescharacteristic
469C22×C3C2×#23711yescharacteristic
470C22×C3#100411yescharacteristic
471C22×C3D3×#4111yescharacteristic
472C22×C3#101011yescharacteristic
473C3×C4—22no—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—41no—
477C3×C4—41no—
478Dic3—62no—
479Dic3—62no—
480Dic3—62no—
481Dic3—121no—
482Dic3—121no—
483Dic3—121no—
484Dic3—121no—
485Dic3—121no—
486C9#247911yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23#369912yes—
501C23C23×D911yescharacteristic
502D4—44no—
503C2×C4—28no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—92no—
517C2×C4—92no—
518C2×C4—92no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—181no—
524C2×C4—181no—
525C2×C4—181no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4#369712yes—
541C2×C4D4×D912yes—
542C2×C4#369912yes—
543C2×C3—42no—
544C2×C3—81no—
545C2×C3#549511yescharacteristic
546C2×C3#555111yescharacteristic
547C2×C3#555711yescharacteristic
548C2×C3#558611yescharacteristic
549C2×C3#559911yescharacteristic
550C2×C3#560311yescharacteristic
551C2×C3#565011yescharacteristic
552C22—22no—
553C22—22no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×#369711yescharacteristic
567C22C2×D4×D911yescharacteristic
568C22C2×#369911yescharacteristic
569C22C2×#369911yescharacteristic
570C22#6371011yescharacteristic
571C22#41×D911yescharacteristic
572C22#6371611yescharacteristic
573C4—22no—
574C4—22no—
575C4—22no—
576C4—41no—
577C4—41no—
578C4—182no—
579C4—182no—
580C4—182no—
581C4—361no—
582C4—361no—
583C4—361no—
584C4—361no—
585C4—361no—
586C3#7473411yescharacteristic
587C2—42no—
588C2—81no—
589C2#1058959711yescharacteristic
590C2#1058965311yescharacteristic
591C2#1058965911yescharacteristic
592C2#1058968811yescharacteristic
593C2#1058970111yescharacteristic
594C2#1058970511yescharacteristic
595C2#1058975211yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#386C2
prime radicalC22×C3×D4C2×D3
hypercenter#386D9
hypocenterC9#2479
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#63488C2semidirect
2. C2×#63441C2semidirect
6. #10588890C2semidirect
7. #10588631C2semidirect
8. #10588629C2semidirect
9. #10588629C2semidirect
10. #10588625C2semidirect
11. #10588625C2semidirect
12. #10588341C2semidirect
13. #10588333C2semidirect
14. #10588329C2semidirect
15. #10588327C2semidirect
104. C4⋊Dic9D4semidirect
486. C9#2479semidirect

Maximal subgroups

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

subgroupindex
C2×#634882
C2×#634412
C9×#3862
#105889022
#105889012
#105888902
#105886312
#105886292
#105886252
#105883412
#105883332
#105883292
#105883272
#747343