Finite Group Databasebeta

← #11808665

Subgroups — #11808665

Order 1152.

792 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×#63454C211yesmaximal, characteristic
2C2×#63449C211yesmaximal, characteristic, complemented
3C9×#398C211yesmaximal, characteristic, complemented
4#10588674C211yesmaximal, characteristic
5#10588674C211yesmaximal, characteristic
6#10588673C211yesmaximal, characteristic
7#10588662C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic9C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic9C211yesmaximal, characteristic, complemented
10#10588353C211yesmaximal, characteristic
11#10588346C211yesmaximal, characteristic
12#10588346C211yesmaximal, characteristic
13#10588340C211yesmaximal, characteristic, complemented
14#10588336C211yesmaximal, characteristic, complemented
15#10588329C211yesmaximal, characteristic, complemented
16#77739—31nomaximal
17C22×C4×D9C2211yescharacteristic
18C22×Dic18C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C9×C4⋊C4C2211yescharacteristic
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C4⋊C4C2211yescharacteristic
23C2×(C2×D9)⋊C4C2211yescharacteristic
24C2×(C2×D9)⋊C4C2211yescharacteristic
25C2×(C2×D9)⋊C4C2211yescharacteristic
26C2×(C2×D9)⋊C4C2211yescharacteristic
27C2×(C2×D9)⋊C4C2211yescharacteristic
28C2×(C2×D9)⋊C4C2211yescharacteristic
29C2×C4⋊Dic9C2211yescharacteristic
30C2×C4⋊Dic9C2211yescharacteristic
31C2×C4⋊Dic9C2211yescharacteristic
32C2×Dic9⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×Dic9⋊C4C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42#63454—24no—
43#63449—24no—
44C9×#95C2211yescharacteristic
45C9×#95C2211yescharacteristic
46C9×#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C2×#892—31no—
55C2×#887—31no—
56C3×#398D311yescharacteristic
57#4994—31no—
58#4994—31no—
59#4993—31no—
60#4982—31no—
61Dic3×C4⋊C4—31no—
62Dic3×C4⋊C4—31no—
63#4673—31no—
64#4666—31no—
65#4666—31no—
66#4660—31no—
67#4656—31no—
68#4649—31no—
69C23×D9C2311yescharacteristic
70C22×C4×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×Dic9C2311yescharacteristic
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C2×C4×D9—22no—
85C2×C4×D9—22no—
86C2×C4×D9Q814yescomplemented
87C2×Dic18—22no—
88C2×Dic18—22no—
89C2×Dic18—22no—
90C9×C4⋊C4—22no—
91C9×C4⋊C4—22no—
92C9×C4⋊C4—22no—
93C9×C4⋊C4—22no—
94(C2×D9)⋊C4—22no—
95(C2×D9)⋊C4—22no—
96(C2×D9)⋊C4—22no—
97(C2×D9)⋊C4—22no—
98(C2×D9)⋊C4—22no—
99(C2×D9)⋊C4—22no—
100C4⋊Dic9—22no—
101C4⋊Dic9—22no—
102C4⋊Dic9—22no—
103Dic9⋊C4—22no—
104Dic9⋊C4—22no—
105Dic9⋊C4—22no—
106Dic9⋊C4—22no—
107C4×Dic9—22no—
108C4×Dic9—22no—
109C4×Dic9—22no—
110C4×Dic9—22no—
111C4×Dic9—22no—
112C4×Dic9D414yes—
113#2396—91noSylow
114C22×C4×D3—31no—
115C22×Dic6—31no—
116C2×C3×C4⋊C4C2×D311yescharacteristic
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×(C2×D3)⋊C4—31no—
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—31no—
125C2×(C2×D3)⋊C4—31no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×Dic3⋊C4—31no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—31no—
138C2×C4×Dic3—31no—
139#892—64no—
140#887—64no—
141C3×#95C2×D311yescharacteristic
142C3×#95C2×D311yescharacteristic
143C3×#95C2×D311yescharacteristic
144C3⋊#95—31no—
145C3⋊#95—31no—
146C3⋊#95—31no—
147C3⋊#95—31no—
148C3⋊#95—31no—
149C3⋊#95—31no—
150C3⋊#95—31no—
151C23×C9C2411yescharacteristic
152C22×D9—21no—
153C22×D9—21no—
154C22×D9—21no—
155C22×D9—21no—
156C22×D9—21no—
157C22×D9—21no—
158C22×D9C2×Q812yes—
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×C9—21no—
175C2×C4×C9—21no—
176C2×C4×C9C2×D412yes—
177C2×C4×C9C2×Q812yes—
178C2×C4×C9#4112yes—
179C2×C4×C9#4112yes—
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×Dic9C2×D412yes—
196C2×Dic9C2×D412yes—
197C2×Dic9C2×Q812yes—
198C2×Dic9#4112yes—
199C2×Dic9#4112yes—
200C2×Dic9#4112yes—
201C4×D9—28no—
202Dic18—28no—
203C2×C4×Q8—91no—
204C2×#117—91no—
205#400—91no—
206#399—91no—
207#398—91no—
208#398D911yescharacteristic, complemented
209#396—91no—
210#396—91no—
211#395—91no—
212#393—91no—
213C4×C4⋊C4—91no—
214C4×C4⋊C4—91no—
215C4×C4⋊C4—91no—
216C4×C22⋊C4—91no—
217C4×C22⋊C4—91no—
218C23×D3—31no—
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×C3×C4C22×D311yescharacteristic
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C2×C4×D3—34no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×Dic6—62no—
237C2×Dic6—62no—
238C2×Dic6—62no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—22no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—22no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256C4×Dic3—34no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C22×C9C22×D411yescharacteristic
263C22×C9C22×Q811yescharacteristic
264C22×C9C2×#4111yescharacteristic
265C22×C9C2×#4111yescharacteristic
266C22×C9C2×#4111yescharacteristic
267C22×C9C2×#4111yescharacteristic
268C22×C9C2×#4111yescharacteristic
269C2×D9—22no—
270C2×D9—22no—
271C2×D9—22no—
272C2×D9—41no—
273C2×D9—41no—
274C2×D9—41no—
275C2×D9—41no—
276C4×C9—22no—
277C4×C9—22no—
278C4×C9—22no—
279C4×C9—22no—
280C4×C9—41no—
281C4×C9—41no—
282C4×C9—41no—
283Dic9—22no—
284Dic9—22no—
285Dic9—22no—
286Dic9—41no—
287Dic9—41no—
288Dic9—41no—
289Dic9C22⋊Q814yes—
290C22×Q8—91no—
291C23×C4—91no—
292C4×Q8—184no—
293#117—184no—
294C2×C4⋊C4—91no—
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⋊C4C2×D911yescharacteristic
302C2×C4⋊C4C2×D911yescharacteristic
303C2×C4⋊C4C2×D911yescharacteristic
304C2×C4⋊C4C2×D911yescharacteristic
305C2×C22⋊C4—91no—
306C2×C22⋊C4—91no—
307C2×C22⋊C4—91no—
308C2×C22⋊C4—91no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4—91no—
311C2×C42—91no—
312C2×C42—91no—
313C2×C42—91no—
314C2×C42—91no—
315C2×C42—91no—
316C2×C42—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
326#95C2×D911yescharacteristic
327C23×C3C23×D311yescharacteristic
328C22×D3—32no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—61no—
333C22×D3—61no—
334C22×D3—61no—
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×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4D3×D412yes—
353C2×C3×C4#23712yes—
354C2×C3×C4D3×Q812yes—
355C2×C3×C4#23912yes—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
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—
377C4×D3—68no—
378Dic6—68no—
379C2×C9C2×C22⋊Q811yescharacteristic
380C2×C9#52511yescharacteristic
381C2×C9#52911yescharacteristic
382C2×C9#52911yescharacteristic
383C2×C9#53211yescharacteristic
384C2×C9#53311yescharacteristic
385C2×C9#53311yescharacteristic
386D9—42no—
387C24—91no—
388C2×Q8—182no—
389C2×Q8—182no—
390C2×Q8—182no—
391C22×C4—91no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—91no—
395C22×C4—94no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—182no—
400C22×C4—182no—
401C22×C4C22×D911yescharacteristic
402C22×C4C22×D911yescharacteristic
403C22×C4C22×D911yescharacteristic
404C22×C4C22×D911yescharacteristic
405C22×C4C22×D911yescharacteristic
406C22×C4C22×D911yescharacteristic
407C22×C4C22×D911yescharacteristic
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—182no—
413C4⋊C4—182no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C42—94no—
426C42—182no—
427C42—182no—
428C42—182no—
429C42—182no—
430C42—182no—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C2×#23711yescharacteristic
433C22×C3C2×D3×Q811yescharacteristic
434C22×C3C2×#23911yescharacteristic
435C22×C3D3×#4111yescharacteristic
436C22×C3D3×#4111yescharacteristic
437C22×C3D3×#4111yescharacteristic
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—41no—
450C3×C4—41no—
451C3×C4—41no—
452Dic3—34no—
453Dic3—62no—
454Dic3—62no—
455Dic3—62no—
456Dic3—121no—
457Dic3—121no—
458Dic3—121no—
459C9#239611yescharacteristic, complemented, Sylow
460C23—92no—
461C23—181no—
462C23—181no—
463C23—181no—
464C23—181no—
465C23—181no—
466C23—181no—
467C23C23×D911yescharacteristic
468Q8—188no—
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—21no—
485C2×C4—21no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—188no—
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×C4D4×D912yes—
509C2×C4#369912yes—
510C2×C4Q8×D912yes—
511C2×C4#370112yes—
512C2×C3#559611yescharacteristic
513C2×C3D3×C22⋊Q811yescharacteristic
514C2×C3#562711yescharacteristic
515C2×C3#564911yescharacteristic
516C2×C3#568811yescharacteristic
517C2×C3#569111yescharacteristic
518C2×C3#572811yescharacteristic
519D3—122no—
520C22—182no—
521C22—182no—
522C22—182no—
523C22—361no—
524C22—361no—
525C22—361no—
526C22—361no—
527C22C2×D4×D911yescharacteristic
528C22C2×#369911yescharacteristic
529C22C2×Q8×D911yescharacteristic
530C22C2×#370111yescharacteristic
531C22#41×D911yescharacteristic
532C22#41×D911yescharacteristic
533C22#41×D911yescharacteristic
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#7773911yescharacteristic
549C2—362no—
550C2#1058969811yescharacteristic
551C2D9×C22⋊Q811yescharacteristic
552C2#1058972911yescharacteristic
553C2#1058975111yescharacteristic
554C2#1058979011yescharacteristic
555C2#1058979311yescharacteristic
556C2#1058983011yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#398C2
prime radicalC23×D9C23
hypercenter#398D9
hypocenterC9#2396
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#63449C2semidirect
3. C9×#398C2semidirect
7. #10588662C2semidirect
8. C4⋊C4×Dic9C2semidirect
9. C4⋊C4×Dic9C2semidirect
13. #10588340C2semidirect
14. #10588336C2semidirect
15. #10588329C2semidirect
86. C2×C4×D9Q8semidirect
208. #398D9semidirect
459. C9#2396semidirect

Maximal subgroups

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

subgroupindex
C2×#634542
C2×#634492
C9×#3982
#105886742
#105886732
#105886622
C4⋊C4×Dic92
#105883532
#105883462
#105883402
#105883362
#105883292
#777393