Finite Group Databasebeta

← #11801974

Subgroups — #11801974

Order 1152.

1836 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D9C211yesmaximal, characteristic, complemented
2C2×#63455C212yesmaximal, complemented
3C2×#63444C211yesmaximal, characteristic
4C2×#611⋊C4C211yesmaximal, characteristic, complemented
5C9×#385C211yesmaximal, characteristic, complemented
6#10588893C211yesmaximal, characteristic, complemented
7#10588669C212yesmaximal, complemented
8#10588635C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic9C211yesmaximal, characteristic, complemented
10#10588346C212yesmaximal, complemented
11#10588345C212yesmaximal, complemented
12#74379—31nomaximal
13C24×D9C2211yescharacteristic
14C23×C4×C9C2211yescharacteristic
15C22×#611C2211yescharacteristic
16C23×Dic9C2211yescharacteristic
17C22×D36C2212yes—
18C22×C4×D9—24no—
19C22×C4×D9—28no—
20C22×C4×D9C2212yes—
21C22×C4×D9C2212yes—
22C22×C4×D9C2211yescharacteristic, complemented
23C2×C9×C4⋊C4C2212yescomplemented
24C2×C9×C22⋊C4C2211yescharacteristic
25C2×C9×C22⋊C4C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27C2×(C2×D9)⋊C4C2212yes—
28C2×(C2×D9)⋊C4C2212yes—
29C2×(C2×D9)⋊C4C2212yes—
30C2×(C2×D9)⋊C4C2211yescharacteristic, complemented
31C2×(C2×D9)⋊C4C2212yescomplemented
32C2×Dic9⋊C4C2211yescharacteristic, complemented
33C2×C4×Dic9C2211yescharacteristic, complemented
34C2×C4×Dic9C2212yescomplemented
35#63455—28no—
36#63444C418yescomplemented
37#611⋊C4—24no—
38C9×#95C2212yescomplemented
39C9⋊#95C2212yescomplemented
40C9⋊#95C2212yescomplemented
41C23×C4×D3—31no—
42C2×#893—32no—
43C2×#882—31no—
44C2×#67⋊C4—31no—
45C3×#385D311yescharacteristic
46#5213—31no—
47#4989—32no—
48#4955—31no—
49Dic3×C22⋊C4—31no—
50#4666—32no—
51#4665—32no—
52C24×C9C2311yescharacteristic
53C23×D9—22no—
54C23×D9—22no—
55C23×D9—24no—
56C23×D9—24no—
57C23×D9C2×C414yescomplemented
58C23×D9C2311yescharacteristic
59C23×D9C2312yes—
60C22×C4×C9—22no—
61C22×C4×C9—24no—
62C22×C4×C9C2311yescharacteristic
63C22×C4×C9C2311yescharacteristic
64C22×C4×C9C2312yes—
65C22×C4×C9C2312yes—
66C2×#611—22no—
67C2×#611—22no—
68C2×#611C2×C414yescomplemented
69C22×Dic9—24no—
70C22×Dic9D414yescomplemented
71C22×Dic9C2312yes—
72C22×Dic9C2311yescharacteristic
73C22×Dic9C2311yescharacteristic
74C22×Dic9C2311yescharacteristic
75C2×D36—24no—
76C2×D36—24no—
77C2×D36C2×C418yescomplemented
78C2×C4×D9—232no—
79C2×C4×D9—24no—
80C2×C4×D9—24no—
81C2×C4×D9—24no—
82C2×C4×D9—24no—
83C2×C4×D9—24no—
84C2×C4×D9—22no—
85C2×C4×D9—24no—
86C2×C4×D9D418yescomplemented
87C9×C4⋊C4—24no—
88C9×C22⋊C4—22no—
89C9×C22⋊C4C2×C414yescomplemented
90#3676—22no—
91(C2×D9)⋊C4—24no—
92(C2×D9)⋊C4—24no—
93(C2×D9)⋊C4—24no—
94(C2×D9)⋊C4—22no—
95(C2×D9)⋊C4C2×C418yescomplemented
96Dic9⋊C4—22no—
97C4×Dic9—22no—
98C4×Dic9—24no—
99C4×#120—91noSylow
100C24×D3—31no—
101C23×C3×C4C2×D311yescharacteristic
102C22×#67—31no—
103C23×Dic3—31no—
104C22×D12—32no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—31no—
108C22×C4×D3—68no—
109C22×C4×D3—64no—
110C2×C3×C4⋊C4C2×D312yes—
111C2×C3×C22⋊C4C2×D311yescharacteristic
112C2×C3×C22⋊C4C2×D311yescharacteristic
113C2×#217—31no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—32no—
119C2×Dic3⋊C4—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—32no—
122#893—68no—
123#882—38no—
124#67⋊C4—64no—
125C3×#95C2×D312yes—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C23×C9—22no—
129C23×C9—22no—
130C23×C9C22×C412yes—
131C23×C9C2×D412yes—
132C23×C9#4112yes—
133C23×C9C2411yescharacteristic
134C22×D9—28no—
135C22×D9—216no—
136C22×D9—28no—
137C22×D9—28no—
138C22×D9—22no—
139C22×D9—22no—
140C22×D9—22no—
141C22×D9—22no—
142C22×D9—216no—
143C22×D9—22no—
144C22×D9—21no—
145C22×D9—22no—
146C22×D9—21no—
147C22×D9C22×C414yes—
148C22×D9C22×C412yescomplemented
149C22×D9C2×D414yes—
150C22×D9#4114yes—
151C2×C4×C9—28no—
152C2×C4×C9—22no—
153C2×C4×C9—22no—
154C2×C4×C9—22no—
155C2×C4×C9—22no—
156C2×C4×C9—21no—
157C2×C4×C9—21no—
158C2×C4×C9—22no—
159C2×C4×C9—22no—
160C2×C4×C9C22×C414yescomplemented
161C2×C4×C9C2×D414yes—
162#611—28no—
163C2×Dic9—21no—
164C2×Dic9—22no—
165C2×Dic9—21no—
166C2×Dic9—28no—
167C2×Dic9—22no—
168C2×Dic9—22no—
169C2×Dic9—22no—
170C2×Dic9C22×C412yescomplemented
171C2×Dic9C2×D412yes—
172C2×Dic9C2×D412yes—
173C2×Dic9C2×D414yes—
174D36—216no—
175C4×D9—216no—
176C4×D9—216no—
177C4×D9—44no—
178C24×C4—91no—
179C2×#120—91no—
180C2×C4×D4—92no—
181C2×C4×D4—91no—
182#386—91no—
183#386—92no—
184#385—92no—
185#385D911yescharacteristic, complemented
186#379—91no—
187C4×C22⋊C4—91no—
188C4×C22⋊C4—92no—
189C24×C3C22×D311yescharacteristic
190C23×D3—32no—
191C23×D3—34no—
192C23×D3—31no—
193C23×D3—64no—
194C23×D3—64no—
195C23×D3—62no—
196C23×D3—62no—
197C22×C3×C4—22no—
198C22×C3×C4—24no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D312yes—
203C2×#67—34no—
204C2×#67—62no—
205C2×#67—62no—
206C22×Dic3—31no—
207C22×Dic3—34no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—32no—
211C22×Dic3—64no—
212C2×D12—38no—
213C2×D12—64no—
214C2×D12—64no—
215C2×C4×D3—38no—
216C2×C4×D3—64no—
217C2×C4×D3—64no—
218C2×C4×D3—64no—
219C2×C4×D3—64no—
220C2×C4×D3—632no—
221C2×C4×D3—64no—
222C2×C4×D3—62no—
223C2×C4×D3—64no—
224C3×C4⋊C4—24no—
225C3×C22⋊C4—22no—
226C3×C22⋊C4C4×D314yes—
227#217—62no—
228(C2×D3)⋊C4—38no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—64no—
233Dic3⋊C4—62no—
234C4×Dic3—62no—
235C4×Dic3—64no—
236C22×C9—24no—
237C22×C9—22no—
238C22×C9—22no—
239C22×C9—24no—
240C22×C9C4×D414yescomplemented
241C22×C9C23×C411yescharacteristic
242C22×C9C22×D412yes—
243C22×C9C22×D411yescharacteristic
244C22×C9C2×#4111yescharacteristic
245C22×C9C2×#4112yes—
246C2×D9—232no—
247C2×D9—24no—
248C2×D9—24no—
249C2×D9—24no—
250C2×D9—24no—
251C2×D9—24no—
252C2×D9—24no—
253C2×D9—24no—
254C2×D9—22no—
255C2×D9—41no—
256C2×D9—41no—
257C2×D9—42no—
258C2×D9C4×D418yescomplemented
259C4×C9—24no—
260C4×C9—24no—
261C4×C9—41no—
262C4×C9—41no—
263Dic9—22no—
264Dic9—22no—
265Dic9—42no—
266Dic9#12014yescomplemented
267C25—91no—
268C22×D4—91no—
269C22×D4—92no—
270C23×C4—91no—
271C23×C4—92no—
272C23×C4—91no—
273C23×C4—92no—
274C23×C4—184no—
275C23×C4—188no—
276C23×C4C2×D911yescharacteristic
277#120—98no—
278C4×D4—184no—
279C4×D4—188no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4C2×D912yescomplemented
282C2×C22⋊C4—92no—
283C2×C22⋊C4—91no—
284C2×C22⋊C4—92no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4—92no—
287C2×C22⋊C4—92no—
288C2×C22⋊C4C2×D911yescharacteristic
289C2×C22⋊C4C2×D911yescharacteristic
290C2×C42—91no—
291C2×C42—92no—
292#95—92no—
293#95—92no—
294#95C2×D912yescomplemented
295C23×C3—22no—
296C23×C3—22no—
297C23×C3C2×C4×D312yes—
298C23×C3D3×D412yes—
299C23×C3#23912yes—
300C23×C3C23×D311yescharacteristic
301C22×D3—34no—
302C22×D3—34no—
303C22×D3—34no—
304C22×D3—32no—
305C22×D3—616no—
306C22×D3—68no—
307C22×D3—68no—
308C22×D3—616no—
309C22×D3—68no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—61no—
316C22×D3—61no—
317C22×D3—62no—
318C2×C3×C4—28no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4C2×C4×D314yes—
328C2×C3×C4D3×D414yes—
329#67—68no—
330C2×Dic3—34no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—68no—
335C2×Dic3—61no—
336C2×Dic3—62no—
337C2×Dic3—61no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341D12—616no—
342C4×D3—616no—
343C4×D3—616no—
344C4×D3—124no—
345C2×C9—24no—
346C2×C9C2×C4×D411yescharacteristic
347C2×C9C2×C4×D412yes—
348C2×C9C2×#12011yescharacteristic
349C2×C9#52511yescharacteristic
350C2×C9#52512yes—
351D9—28no—
352D9—42no—
353C24—92no—
354C24—94no—
355C24—91no—
356C24—184no—
357C24—184no—
358C24—182no—
359C24—182no—
360C24C22×D911yescharacteristic
361C2×D4—94no—
362C2×D4—98no—
363C2×D4—184no—
364C2×D4—184no—
365C2×D4—182no—
366C2×D4—182no—
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—91no—
370C22×C4—94no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—98no—
374C22×C4—92no—
375C22×C4—184no—
376C22×C4—184no—
377C22×C4—184no—
378C22×C4—182no—
379C22×C4—184no—
380C22×C4—184no—
381C22×C4—1832no—
382C22×C4—184no—
383C22×C4—184no—
384C22×C4C22×D911yescharacteristic
385C22×C4C22×D911yescharacteristic
386C22×C4C22×D912yes—
387C22×C4C22×D912yes—
388C4⋊C4—24no—
389C4⋊C4—182no—
390C22⋊C4—22no—
391C22⋊C4—98no—
392C22⋊C4—182no—
393C22⋊C4—184no—
394C22⋊C4—184no—
395C22⋊C4—182no—
396C22⋊C4—184no—
397C22⋊C4C4×D914yescomplemented
398C42—184no—
399C42—182no—
400C22×C3—22no—
401C22×C3—24no—
402C22×C3—22no—
403C22×C3—24no—
404C22×C3#89314yes—
405C22×C3C22×C4×D311yescharacteristic
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D412yes—
408C22×C3C2×#23911yescharacteristic
409C22×C3D3×#4112yes—
410C2×D3—38no—
411C2×D3—632no—
412C2×D3—64no—
413C2×D3—64no—
414C2×D3—64no—
415C2×D3—64no—
416C2×D3—64no—
417C2×D3—64no—
418C2×D3—62no—
419C2×D3—64no—
420C2×D3—121no—
421C2×D3—121no—
422C2×D3—122no—
423C3×C4—24no—
424C3×C4—24no—
425C3×C4—41no—
426C3×C4—41no—
427Dic3—34no—
428Dic3—62no—
429Dic3—62no—
430Dic3—122no—
431C9C4×#12011yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—94no—
435C23—94no—
436C23—94no—
437C23—92no—
438C23—1816no—
439C23—188no—
440C23—1816no—
441C23—188no—
442C23—182no—
443C23—182no—
444C23—188no—
445C23—182no—
446C23—182no—
447C23—181no—
448C23—182no—
449C23—181no—
450C23—182no—
451C23C2×C4×D912yes—
452C23D4×D912yes—
453C23#370112yes—
454C23C23×D911yescharacteristic
455D4—1816no—
456D4—188no—
457C2×C4—28no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—94no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—92no—
470C2×C4—1816no—
471C2×C4—1816no—
472C2×C4—188no—
473C2×C4—181no—
474C2×C4—182no—
475C2×C4—181no—
476C2×C4—182no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—364no—
480C2×C4C2×C4×D914yescomplemented
481C2×C4D4×D914yes—
482C2×C3—24no—
483C2×C3C2×#89311yescharacteristic
484C2×C3C4×D3×D412yes—
485C2×C3D3×#12011yescharacteristic
486C2×C3#562712yes—
487C2×C3#565611yescharacteristic
488D3—68no—
489D3—122no—
490C22—24no—
491C22—22no—
492C22—24no—
493C22—22no—
494C22—98no—
495C22—1832no—
496C22—184no—
497C22—184no—
498C22—184no—
499C22—184no—
500C22—184no—
501C22—184no—
502C22—182no—
503C22—184no—
504C22—362no—
505C22—361no—
506C22—361no—
507C22#6345514yescomplemented
508C22C22×C4×D911yescharacteristic
509C22C2×D4×D912yes—
510C22C2×D4×D911yescharacteristic
511C22C2×#370111yescharacteristic
512C22#41×D912yes—
513C4—24no—
514C4—24no—
515C4—41no—
516C4—41no—
517C4—94no—
518C4—182no—
519C4—182no—
520C4—362no—
521C3#7437911yescharacteristic
522C2—24no—
523C2—188no—
524C2—362no—
525C2C2×#6345511yescharacteristic
526C2C4×D4×D912yes—
527C2D9×#12011yescharacteristic
528C2#1058972912yes—
529C2#1058975811yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#385C2
prime radicalC2×#63444C2
cosocleC23×C9C24
hypercenter#385D9
hypocenterC9C4×#120
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C23×C4×D9C2semidirect
2. C2×#63455C2semidirect
4. C2×#611⋊C4C2semidirect
5. C9×#385C2semidirect
6. #10588893C2semidirect
7. #10588669C2semidirect
8. #10588635C2semidirect
9. C22⋊C4×Dic9C2semidirect
10. #10588346C2semidirect
11. #10588345C2semidirect
22. C22×C4×D9C22semidirect
23. C2×C9×C4⋊C4C22semidirect
30. C2×(C2×D9)⋊C4C22semidirect
31. C2×(C2×D9)⋊C4C22semidirect
32. C2×Dic9⋊C4C22semidirect
33. C2×C4×Dic9C22semidirect
34. C2×C4×Dic9C22semidirect
36. #63444C4semidirect
38. C9×#95C22semidirect
39. C9⋊#95C22semidirect
40. C9⋊#95C22semidirect
57. C23×D9C2×C4semidirect
68. C2×#611C2×C4semidirect
70. C22×Dic9D4semidirect
77. C2×D36C2×C4semidirect
86. C2×C4×D9D4semidirect
89. C9×C22⋊C4C2×C4semidirect
95. (C2×D9)⋊C4C2×C4semidirect
148. C22×D9C22×C4semidirect
160. C2×C4×C9C22×C4semidirect
170. C2×Dic9C22×C4semidirect
185. #385D9semidirect
240. C22×C9C4×D4semidirect
258. C2×D9C4×D4semidirect
266. Dic9#120semidirect
281. C2×C4⋊C4C2×D9semidirect
294. #95C2×D9semidirect
397. C22⋊C4C4×D9semidirect
431. C9C4×#120semidirect
480. C2×C4C2×C4×D9semidirect
507. C22#63455semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D92
C2×#634552
C2×#634442
C2×#611⋊C42
C9×#3852
#105888932
#105886692
#105886352
C22⋊C4×Dic92
#105883462
#105883452
#743793