Finite Group Databasebeta

← #11807789

Subgroups — #11807789

Order 1152.

696 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63508C211yesmaximal, characteristic
2C9×#391C211yesmaximal, characteristic, complemented
3#10588909C211yesmaximal, characteristic, complemented
4#10588670C211yesmaximal, characteristic
5#10588656C211yesmaximal, characteristic, complemented
6#10588620C211yesmaximal, characteristic
7#10588613C211yesmaximal, characteristic, complemented
8#10588350C211yesmaximal, characteristic
9#10588349C211yesmaximal, characteristic
10#10588347C211yesmaximal, characteristic
11#10588344C211yesmaximal, characteristic
12#10588334C211yesmaximal, characteristic, complemented
13#10588333C211yesmaximal, characteristic, complemented
14#10588332C211yesmaximal, characteristic, complemented
15#10588327C211yesmaximal, characteristic, complemented
16#76617—31nomaximal
17C22×Q8×C9C2211yescharacteristic
18C22×C4×D9C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C42×C9C2211yescharacteristic
21#63508C418yescomplemented
22C2×(C2×D9)⋊C4C2211yescharacteristic
23C2×(C2×D9)⋊C4C2211yescharacteristic
24C2×(C2×D9)⋊C4C2211yescharacteristic
25C2×(C2×D9)⋊C4C2211yescharacteristic
26C2×(C2×D9)⋊C4C2211yescharacteristic
27C2×(C2×D9)⋊C4C2211yescharacteristic
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
38C2×C4×Dic9C2211yescharacteristic
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×#946—31no—
54C3×#391D311yescharacteristic
55#5229—31no—
56#4990—31no—
57#4976—31no—
58#4940—31no—
59#4933—31no—
60#4670—31no—
61#4669—31no—
62#4667—31no—
63#4664—31no—
64#4654—31no—
65#4653—31no—
66#4652—31no—
67#4647—31no—
68C23×D9C2311yescharacteristic
69C2×Q8×C9—41no—
70C2×Q8×C9—41no—
71C2×Q8×C9C2×C414yes—
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C22×Dic9C2311yescharacteristic
85C22×Dic9C2311yescharacteristic
86C2×C4×D9—41no—
87C2×C4×D9—41no—
88C2×C4×D9C2×C414yes—
89C9×C4⋊C4—41no—
90C42×C9—41no—
91(C2×D9)⋊C4—41no—
92(C2×D9)⋊C4—41no—
93(C2×D9)⋊C4—41no—
94(C2×D9)⋊C4—41no—
95(C2×D9)⋊C4C2×C414yes—
96(C2×D9)⋊C4C2×C414yes—
97C4⋊Dic9—41no—
98C4⋊Dic9C2×C414yes—
99Dic9⋊C4—41no—
100Dic9⋊C4—41no—
101Dic9⋊C4—41no—
102Dic9⋊C4—41no—
103Dic9⋊C4C2×C414yes—
104Dic9⋊C4C2×C414yes—
105C4×Dic9—41no—
106C4×Dic9—41no—
107C4×Dic9—41no—
108#2378—91noSylow
109C22×C3×Q8C2×D311yescharacteristic
110C22×C4×D3—31no—
111C2×C3×C4⋊C4C2×D311yescharacteristic
112C2×C3×C42C2×D311yescharacteristic
113#946—38no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—31no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—31no—
119C2×(C2×D3)⋊C4—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—31no—
127C2×Dic3⋊C4—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C3×#95C2×D311yescharacteristic
132C3×#95C2×D311yescharacteristic
133C3×#95C2×D311yescharacteristic
134C3×#95C2×D311yescharacteristic
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—31no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95—31no—
145C23×C9C2411yescharacteristic
146C22×D9—21no—
147C22×D9—21no—
148C22×D9—21no—
149C22×D9—21no—
150C22×D9—21no—
151C22×D9—21no—
152C22×D9C22×C412yes—
153Q8×C9—44no—
154C2×C4×C9—21no—
155C2×C4×C9—21no—
156C2×C4×C9—21no—
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×C9C22×C412yes—
173C2×C4×C9C22×C412yes—
174C2×C4×C9C22×C412yes—
175C2×Dic9—21no—
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×Dic9C22×C412yes—
194C2×Dic9C22×C412yes—
195C2×Dic9C22×C412yes—
196C4×D9—44no—
197C2×C22⋊Q8—91no—
198#391—91no—
199#391D911yescharacteristic, complemented
200#389—91no—
201#389—91no—
202#388—91no—
203#388—91no—
204#388—91no—
205#388—91no—
206#387—91no—
207#387—91no—
208#387—91no—
209#387—91no—
210#381—91no—
211#380—91no—
212C23×D3—31no—
213C2×C3×Q8—41no—
214C2×C3×Q8—41no—
215C2×C3×Q8C4×D314yes—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C2×C4×D3—34no—
231C2×C4×D3—121no—
232C2×C4×D3—121no—
233C3×C4⋊C4—41no—
234C3×C42—41no—
235(C2×D3)⋊C4—34no—
236(C2×D3)⋊C4—34no—
237(C2×D3)⋊C4—121no—
238(C2×D3)⋊C4—121no—
239(C2×D3)⋊C4—121no—
240(C2×D3)⋊C4—121no—
241C4⋊Dic3—34no—
242C4⋊Dic3—121no—
243Dic3⋊C4—34no—
244Dic3⋊C4—34no—
245Dic3⋊C4—121no—
246Dic3⋊C4—121no—
247Dic3⋊C4—121no—
248Dic3⋊C4—121no—
249C4×Dic3—121no—
250C4×Dic3—121no—
251C4×Dic3—121no—
252C22×C9C23×C411yescharacteristic
253C22×C9H(5,𝔽2)11yescharacteristic
254C22×C9H(5,𝔽2)11yescharacteristic
255C22×C9H(5,𝔽2)11yescharacteristic
256C22×C92−1+411yescharacteristic
257C22×C92−1+411yescharacteristic
258C22×C92−1+411yescharacteristic
259C2×D9—22no—
260C2×D9—22no—
261C2×D9—22no—
262C2×D9—41no—
263C2×D9—41no—
264C2×D9—41no—
265C2×D9—41no—
266C4×C9—22no—
267C4×C9—22no—
268C4×C9—22no—
269C4×C9—41no—
270C4×C9—41no—
271C4×C9—41no—
272C4×C9—41no—
273Dic9—22no—
274Dic9—22no—
275Dic9—22no—
276Dic9—41no—
277Dic9—41no—
278Dic9—41no—
279Dic9—41no—
280C22×Q8C2×D911yescharacteristic
281C23×C4—91no—
282C22⋊Q8—98no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—91no—
289C2×C4⋊C4—91no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4C2×D911yescharacteristic
292C2×C22⋊C4—91no—
293C2×C22⋊C4—91no—
294C2×C22⋊C4—91no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—91no—
298C2×C42—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42C2×D911yescharacteristic
302#95—91no—
303#95—91no—
304#95—91no—
305#95—91no—
306#95—91no—
307#95—91no—
308#95—91no—
309#95—91no—
310#95—91no—
311#95—91no—
312#95C2×D911yescharacteristic
313#95C2×D911yescharacteristic
314#95C2×D911yescharacteristic
315#95C2×D911yescharacteristic
316C23×C3C23×D311yescharacteristic
317C22×D3—32no—
318C22×D3—61no—
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—61no—
322C22×D3—61no—
323C22×D3—61no—
324C3×Q8—44no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
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×C4C2×C4×D312yes—
344C2×C3×C4C2×C4×D312yes—
345C2×C3×C4C2×C4×D312yes—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
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—
367C4×D3—124no—
368C2×C9#51811yescharacteristic
369C2×C9#51911yescharacteristic
370C2×C9#52011yescharacteristic
371C2×C9#56211yescharacteristic
372C2×C9#56211yescharacteristic
373C2×C9#56311yescharacteristic
374C2×C9#56311yescharacteristic
375D9—42no—
376C24—91no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8C4×D914yes—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—94no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—361no—
389C22×C4—361no—
390C22×C4C22×D911yescharacteristic
391C22×C4C22×D911yescharacteristic
392C22×C4C22×D911yescharacteristic
393C22×C4C22×D911yescharacteristic
394C22×C4C22×D911yescharacteristic
395C22×C4C22×D911yescharacteristic
396C22×C4C22×D911yescharacteristic
397C4⋊C4—41no—
398C4⋊C4—94no—
399C4⋊C4—94no—
400C4⋊C4—94no—
401C4⋊C4—361no—
402C4⋊C4—361no—
403C4⋊C4—361no—
404C4⋊C4—361no—
405C4⋊C4—361no—
406C22⋊C4—94no—
407C22⋊C4—94no—
408C22⋊C4—361no—
409C22⋊C4—361no—
410C22⋊C4—361no—
411C22⋊C4—361no—
412C42—41no—
413C42—361no—
414C42—361no—
415C42—361no—
416C22×C3C22×C4×D311yescharacteristic
417C22×C3#100411yescharacteristic
418C22×C3#100411yescharacteristic
419C22×C3#100711yescharacteristic
420C22×C3#100711yescharacteristic
421C22×C3#100911yescharacteristic
422C22×C3#101011yescharacteristic
423C2×D3—62no—
424C2×D3—62no—
425C2×D3—62no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—41no—
437Dic3—62no—
438Dic3—62no—
439Dic3—62no—
440Dic3—121no—
441Dic3—121no—
442Dic3—121no—
443Dic3—121no—
444C9#237811yescharacteristic, complemented, Sylow
445C23—92no—
446C23—181no—
447C23—181no—
448C23—181no—
449C23—181no—
450C23—181no—
451C23—181no—
452C23C23×D911yescharacteristic
453Q8—44no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—92no—
473C2×C4—92no—
474C2×C4—92no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—364no—
494C2×C4C2×C4×D912yes—
495C2×C4C2×C4×D912yes—
496C2×C4C2×C4×D912yes—
497C2×C3#548611yescharacteristic
498C2×C3#557211yescharacteristic
499C2×C3#557411yescharacteristic
500C2×C3#564611yescharacteristic
501C2×C3#564711yescharacteristic
502C2×C3#568411yescharacteristic
503C2×C3#573511yescharacteristic
504D3—122no—
505C22—182no—
506C22—182no—
507C22—182no—
508C22—361no—
509C22—361no—
510C22—361no—
511C22—361no—
512C22C22×C4×D911yescharacteristic
513C22#6371011yescharacteristic
514C22#6371011yescharacteristic
515C22#6371311yescharacteristic
516C22#6371311yescharacteristic
517C22#6371511yescharacteristic
518C22#6371611yescharacteristic
519C4—22no—
520C4—22no—
521C4—22no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—182no—
527C4—182no—
528C4—182no—
529C4—361no—
530C4—361no—
531C4—361no—
532C4—361no—
533C3#7661711yescharacteristic
534C2—362no—
535C2#1058958811yescharacteristic
536C2#1058967411yescharacteristic
537C2#1058967611yescharacteristic
538C2#1058974811yescharacteristic
539C2#1058974911yescharacteristic
540C2#1058978611yescharacteristic
541C2#1058983711yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#391C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenter#391D9
hypocenterC9#2378
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C9×#391C2semidirect
3. #10588909C2semidirect
5. #10588656C2semidirect
7. #10588613C2semidirect
12. #10588334C2semidirect
13. #10588333C2semidirect
14. #10588332C2semidirect
15. #10588327C2semidirect
21. #63508C4semidirect
199. #391D9semidirect
444. C9#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#635082
C9×#3912
#105889092
#105886702
#105886562
#105886202
#105886132
#105883502
#105883492
#105883472
#105883442
#105883342
#105883332
#105883322
#105883272
#766173