Finite Group Databasebeta

← #11803887

Subgroups — #11803887

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63440C211yesmaximal, characteristic
2C4×C9×C22⋊C4C211yesmaximal, characteristic
3C4×#3676C211yesmaximal, characteristic
4C2×C9⋊#95C211yesmaximal, characteristic
5#10588630C211yesmaximal, characteristic
6#10588626C211yesmaximal, characteristic
7#10588622C211yesmaximal, characteristic
8#10588613C211yesmaximal, characteristic, complemented
9#10588613C211yesmaximal, characteristic, complemented
10#10588609C211yesmaximal, characteristic, complemented
11#10588608C211yesmaximal, characteristic, complemented
12#10588335C211yesmaximal, characteristic, complemented
13#10588334C211yesmaximal, characteristic, complemented
14#10588327C211yesmaximal, characteristic, complemented
15#10588326C211yesmaximal, characteristic, complemented
16#73447—31nomaximal
17C23×C4×C9C2211yescharacteristic
18C23×Dic9C2211yescharacteristic
19C23×Dic9C2211yescharacteristic
20C22×Dic18C2211yescharacteristic
21C2×C9×C22⋊C4C2211yescharacteristic
22C2×C9×C22⋊C4C2211yescharacteristic
23C2×C42×C9C2211yescharacteristic
24C2×C42×C9C2211yescharacteristic
25C2×#3676C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27C2×C4⋊Dic9C2211yescharacteristic
28C2×C4⋊Dic9C2211yescharacteristic
29C2×C4⋊Dic9C2211yescharacteristic
30C2×Dic9⋊C4C2211yescharacteristic
31C2×Dic9⋊C4C2211yescharacteristic
32C2×Dic9⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×Dic9⋊C4C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
38#63440C418yescomplemented
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
52C9⋊#95C2211yescharacteristic
53C2×#878—31no—
54C3×C4×C22⋊C4D311yescharacteristic
55C4×#217—31no—
56C2×C3⋊#95—31no—
57#4950—31no—
58#4946—31no—
59#4942—31no—
60#4933—31no—
61#4933—31no—
62#4929—31no—
63#4928—31no—
64#4655—31no—
65#4654—31no—
66#4647—31no—
67#4646—31no—
68C24×C9C2311yescharacteristic
69C22×C4×C9—41no—
70C22×C4×C9—41no—
71C22×C4×C9Q814yescomplemented
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×Dic9—22no—
79C22×Dic9—41no—
80C22×Dic9—41no—
81C22×Dic9—41no—
82C22×Dic9—41no—
83C22×Dic9C2×C414yes—
84C22×Dic9C2311yescharacteristic
85C22×Dic9C2311yescharacteristic
86C22×Dic9C2311yescharacteristic
87C22×Dic9C2311yescharacteristic
88C22×Dic9C2311yescharacteristic
89C22×Dic9C2311yescharacteristic
90C22×Dic9C2311yescharacteristic
91C22×Dic9C2311yescharacteristic
92C2×Dic18—41no—
93C2×Dic18—41no—
94C2×Dic18C2×C414yescomplemented
95C9×C22⋊C4—22no—
96C9×C22⋊C4C2×C414yes—
97C42×C9—41no—
98C42×C9—41no—
99#3676—22no—
100#3676C2×C414yes—
101C4⋊Dic9—41no—
102C4⋊Dic9—41no—
103C4⋊Dic9C2×C414yescomplemented
104Dic9⋊C4—41no—
105Dic9⋊C4—41no—
106Dic9⋊C4—41no—
107Dic9⋊C4—41no—
108Dic9⋊C4C2×C414yescomplemented
109Dic9⋊C4C2×C414yescomplemented
110C4×Dic9—41no—
111C4×Dic9—41no—
112#2329—91noSylow
113C23×C3×C4C2×D311yescharacteristic
114C23×Dic3—31no—
115C23×Dic3—31no—
116C22×Dic6—31no—
117C2×C3×C22⋊C4C2×D311yescharacteristic
118C2×C3×C22⋊C4C2×D311yescharacteristic
119C2×C3×C42C2×D311yescharacteristic
120C2×C3×C42C2×D311yescharacteristic
121C2×#217—31no—
122C2×#217—31no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×Dic3⋊C4—31no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—31no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134#878—38no—
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—
145C3⋊#95—31no—
146C3⋊#95—31no—
147C3⋊#95—31no—
148C3⋊#95—31no—
149C23×C9—21no—
150C23×C9—21no—
151C23×C9—21no—
152C23×C9—21no—
153C23×C9C22×C412yes—
154C23×C9C2×Q812yes—
155C23×C9#4112yes—
156C23×C9C2411yescharacteristic
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—44no—
172C2×C4×C9C22×C412yes—
173C2×C4×C9C22×C412yes—
174C2×C4×C9C2×Q812yes—
175C2×C4×C9C2×Q812yes—
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×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—44no—
197C2×Dic9—44no—
198C2×Dic9C22×C412yes—
199C2×Dic9C22×C412yes—
200C2×Dic9C22×C412yes—
201C2×Dic9C22×C412yes—
202Dic18—44no—
203C2×C22⋊Q8—91no—
204#391—91no—
205#391—91no—
206#389—91no—
207#389—91no—
208#387—91no—
209#387—91no—
210#387—91no—
211#387—91no—
212#385—91no—
213#385—91no—
214#380—91no—
215C4×C22⋊C4—91no—
216C4×C22⋊C4D911yescharacteristic
217C2×#95—91no—
218C24×C3C22×D311yescharacteristic
219C22×C3×C4—41no—
220C22×C3×C4—41no—
221C22×C3×C4Dic614yes—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—34no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—62no—
238C22×Dic3—121no—
239C22×Dic3—121no—
240C22×Dic3—121no—
241C22×Dic3—121no—
242C2×Dic6—34no—
243C2×Dic6—121no—
244C2×Dic6—121no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4C4×D314yes—
247C3×C42—41no—
248C3×C42—41no—
249#217—34no—
250#217—62no—
251C4⋊Dic3—34no—
252C4⋊Dic3—121no—
253C4⋊Dic3—121no—
254Dic3⋊C4—34no—
255Dic3⋊C4—34no—
256Dic3⋊C4—121no—
257Dic3⋊C4—121no—
258Dic3⋊C4—121no—
259Dic3⋊C4—121no—
260C4×Dic3—121no—
261C4×Dic3—121no—
262C22×C9—22no—
263C22×C9—22no—
264C22×C9—22no—
265C22×C9—22no—
266C22×C9—22no—
267C22×C9—22no—
268C22×C9C4×Q814yes—
269C22×C9C23×C411yescharacteristic
270C22×C9C22×Q811yescharacteristic
271C22×C9C2×#4111yescharacteristic
272C22×C9H(5,𝔽2)11yescharacteristic
273C22×C9H(5,𝔽2)11yescharacteristic
274C22×C9H(5,𝔽2)11yescharacteristic
275C22×C92−1+411yescharacteristic
276C4×C9—22no—
277C4×C9—22no—
278C4×C9—22no—
279C4×C9—22no—
280C4×C9—41no—
281C4×C9—41no—
282Dic9—22no—
283Dic9—22no—
284Dic9—22no—
285Dic9—22no—
286Dic9—41no—
287Dic9—41no—
288Dic9—41no—
289Dic9—41no—
290C22×Q8—91no—
291C23×C4—91no—
292C23×C4—91no—
293C23×C4C2×D911yescharacteristic
294C22⋊Q8—98no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—91no—
302C2×C4⋊C4—91no—
303C2×C4⋊C4—91no—
304C2×C22⋊C4—91no—
305C2×C22⋊C4—91no—
306C2×C22⋊C4C2×D911yescharacteristic
307C2×C22⋊C4C2×D911yescharacteristic
308C2×C42—91no—
309C2×C42—91no—
310C2×C42C2×D911yescharacteristic
311C2×C42C2×D911yescharacteristic
312#95—91no—
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#95—91no—
322#95—91no—
323#95—91no—
324#95C2×D911yescharacteristic
325#95C2×D911yescharacteristic
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3C2×Dic612yes—
331C23×C3C2×C4×D312yes—
332C23×C3#23512yes—
333C23×C3C23×D311yescharacteristic
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—44no—
349C2×C3×C4C2×Dic612yes—
350C2×C3×C4C2×Dic612yes—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4C2×C4×D312yes—
353C2×Dic3—32no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
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—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—124no—
378C2×Dic3—124no—
379Dic6—124no—
380C2×C9—24no—
381C2×C9C2×C4×Q811yescharacteristic
382C2×C9#51811yescharacteristic
383C2×C9#52011yescharacteristic
384C2×C9#53811yescharacteristic
385C2×C9#53911yescharacteristic
386C2×C9#54311yescharacteristic
387C2×C9#54411yescharacteristic
388C24C22×D911yescharacteristic
389C2×Q8—94no—
390C2×Q8—361no—
391C2×Q8—361no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—91no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—94no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—182no—
404C22×C4—361no—
405C22×C4—361no—
406C22×C4—361no—
407C22×C4—361no—
408C22×C4Dic1814yescomplemented
409C22×C4C22×D911yescharacteristic
410C22×C4C22×D911yescharacteristic
411C22×C4C22×D911yescharacteristic
412C22×C4C22×D911yescharacteristic
413C22×C4C22×D911yescharacteristic
414C22×C4C22×D911yescharacteristic
415C4⋊C4—94no—
416C4⋊C4—94no—
417C4⋊C4—94no—
418C4⋊C4—361no—
419C4⋊C4—361no—
420C4⋊C4—361no—
421C4⋊C4—361no—
422C4⋊C4—361no—
423C4⋊C4—361no—
424C22⋊C4—22no—
425C22⋊C4—94no—
426C22⋊C4—182no—
427C22⋊C4C4×D914yes—
428C42—41no—
429C42—41no—
430C42—361no—
431C42—361no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3C4×Dic614yes—
439C22×C3C22×Dic611yescharacteristic
440C22×C3C22×C4×D311yescharacteristic
441C22×C3C2×#23511yescharacteristic
442C22×C3#100411yescharacteristic
443C22×C3#100411yescharacteristic
444C22×C3#100911yescharacteristic
445C22×C3#101011yescharacteristic
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—41no—
451C3×C4—41no—
452Dic3—62no—
453Dic3—62no—
454Dic3—62no—
455Dic3—62no—
456Dic3—121no—
457Dic3—121no—
458Dic3—121no—
459Dic3—121no—
460C9#232911yescharacteristic, complemented, Sylow
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23C2×Dic1812yes—
466C23C2×C4×D912yes—
467C23#369712yes—
468C23C23×D911yescharacteristic
469Q8—364no—
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—44no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—181no—
490C2×C4—181no—
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—181no—
507C2×C4—181no—
508C2×C4—181no—
509C2×C4—364no—
510C2×C4—364no—
511C2×C4C2×Dic1812yes—
512C2×C4C2×Dic1812yes—
513C2×C4C2×C4×D912yes—
514C2×C4C2×C4×D912yes—
515C2×C3—24no—
516C2×C3C2×C4×Dic611yescharacteristic
517C2×C3#548311yescharacteristic
518C2×C3#551911yescharacteristic
519C2×C3#554511yescharacteristic
520C2×C3#554611yescharacteristic
521C2×C3#556011yescharacteristic
522C2×C3#556411yescharacteristic
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22C4×Dic1814yes—
530C22C22×Dic1811yescharacteristic
531C22C22×C4×D911yescharacteristic
532C22C2×#369711yescharacteristic
533C22#6371011yescharacteristic
534C22#6371011yescharacteristic
535C22#6371511yescharacteristic
536C22#6371611yescharacteristic
537C4—22no—
538C4—22no—
539C4—22no—
540C4—22no—
541C4—41no—
542C4—41no—
543C4—182no—
544C4—182no—
545C4—182no—
546C4—182no—
547C4—361no—
548C4—361no—
549C4—361no—
550C4—361no—
551C3#7344711yescharacteristic
552C2—24no—
553C2C2×C4×Dic1811yescharacteristic
554C2#1058958511yescharacteristic
555C2#1058962111yescharacteristic
556C2#1058964711yescharacteristic
557C2#1058964811yescharacteristic
558C2#1058966211yescharacteristic
559C2#1058966611yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC4×C9×C22⋊C4C2
prime radicalC24×C3C22×D3
cosocleC23×C9C24
hypercenterC4×C22⋊C4D9
hypocenterC9#2329
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10588613C2semidirect
9. #10588613C2semidirect
10. #10588609C2semidirect
11. #10588608C2semidirect
12. #10588335C2semidirect
13. #10588334C2semidirect
14. #10588327C2semidirect
15. #10588326C2semidirect
38. #63440C4semidirect
71. C22×C4×C9Q8semidirect
94. C2×Dic18C2×C4semidirect
103. C4⋊Dic9C2×C4semidirect
108. Dic9⋊C4C2×C4semidirect
109. Dic9⋊C4C2×C4semidirect
408. C22×C4Dic18semidirect
460. C9#2329semidirect

Maximal subgroups

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

subgroupindex
C2×#634402
C4×C9×C22⋊C42
C4×#36762
C2×C9⋊#952
#105886302
#105886262
#105886222
#105886132
#105886092
#105886082
#105883352
#105883342
#105883272
#105883262
#734473