Finite Group Databasebeta

← #11803444

Subgroups — #11803444

Order 1152.

834 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
2C2×#63439C211yesmaximal, characteristic
3C2×C4×Dic18C211yesmaximal, characteristic, complemented
4C9×#388C211yesmaximal, characteristic
5#10588656C211yesmaximal, characteristic, complemented
6#10588652C211yesmaximal, characteristic, complemented
7#10588631C211yesmaximal, characteristic
8#10588624C211yesmaximal, characteristic
9#10588624C211yesmaximal, characteristic
10#10588622C211yesmaximal, characteristic
11#10588613C211yesmaximal, characteristic, complemented
12#10588333C211yesmaximal, characteristic, complemented
13#10588329C211yesmaximal, characteristic, complemented
14#10588327C211yesmaximal, characteristic, complemented
15#10588326C211yesmaximal, characteristic, complemented
16#75460—31nomaximal
17C23×Dic9C2211yescharacteristic
18C22×Dic18C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C9×C22⋊C4C2211yescharacteristic
21C2×C9×C22⋊C4C2211yescharacteristic
22C2×C9×C22⋊C4C2211yescharacteristic
23C2×C42×C9C2211yescharacteristic
24C2×#3676C2211yescharacteristic
25C2×#3676C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27C2×C4⋊Dic9C2211yescharacteristic
28C2×C4⋊Dic9C2211yescharacteristic
29C2×Dic9⋊C4C2211yescharacteristic
30C2×Dic9⋊C4C2211yescharacteristic
31C2×Dic9⋊C4C2211yescharacteristic
32C2×Dic9⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×Dic9⋊C4C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×Dic9⋊C4C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42#63440C418yescomplemented
43#63439—24no—
44C4×Dic18—24no—
45C9×#95C2211yescharacteristic
46C9×#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C9⋊#95C2211yescharacteristic
55C2×#878—31no—
56C2×#877—31no—
57C2×C4×Dic6—31no—
58C3×#388D311yescharacteristic
59#4976—31no—
60#4972—31no—
61#4951—31no—
62#4944—31no—
63#4944—31no—
64#4942—31no—
65#4933—31no—
66#4653—31no—
67#4649—31no—
68#4647—31no—
69#4646—31no—
70C24×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×Dic9—22no—
78C22×Dic9—22no—
79C22×Dic9C2×C414yes—
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C22×Dic9C2311yescharacteristic
85C22×Dic9C2311yescharacteristic
86C22×Dic9C2311yescharacteristic
87C22×Dic9C2311yescharacteristic
88C2×Dic18—22no—
89C2×Dic18—22no—
90C2×Dic18C2×C414yes—
91C9×C4⋊C4—41no—
92C9×C22⋊C4—22no—
93C9×C22⋊C4—41no—
94C9×C22⋊C4C2×C414yes—
95C42×C9—22no—
96#3676—22no—
97#3676—41no—
98#3676C2×C414yes—
99C4⋊Dic9—22no—
100C4⋊Dic9C2×C414yes—
101Dic9⋊C4—22no—
102Dic9⋊C4—22no—
103Dic9⋊C4—22no—
104Dic9⋊C4—22no—
105Dic9⋊C4—22no—
106Dic9⋊C4—41no—
107Dic9⋊C4C2×C414yes—
108Dic9⋊C4C2×C414yes—
109C4×Dic9—22no—
110C4×Dic9—22no—
111C4×Dic9—41no—
112C4×Dic9—41no—
113C4×Dic9D414yes—
114#2323—91noSylow
115C23×Dic3—31no—
116C22×Dic6—31no—
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C22⋊C4C2×D311yescharacteristic
119C2×C3×C22⋊C4C2×D311yescharacteristic
120C2×C3×C22⋊C4C2×D311yescharacteristic
121C2×C3×C42C2×D311yescharacteristic
122C2×#217—31no—
123C2×#217—31no—
124C2×#217—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—31no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—31no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—31no—
134C2×Dic3⋊C4—31no—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—31no—
138C2×C4×Dic3—31no—
139C2×C4×Dic3—31no—
140#878—38no—
141#877—64no—
142C4×Dic6—64no—
143C3×#95C2×D311yescharacteristic
144C3×#95C2×D311yescharacteristic
145C3⋊#95—31no—
146C3⋊#95—31no—
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×C9C22×C412yes—
160C23×C9C2411yescharacteristic
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×C9C22×C412yes—
177C2×C4×C9C22×C412yes—
178C2×C4×C9C2×D412yes—
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—28no—
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×Dic9C22×C412yes—
198C2×Dic9C22×C412yes—
199C2×Dic9C22×C412yes—
200C2×Dic9C22×C412yes—
201C2×Dic9C2×D412yes—
202C2×Dic9C2×D412yes—
203C2×Dic9#4112yes—
204Dic18—28no—
205C2×C22⋊Q8—91no—
206C2×C4×Q8—91no—
207C2×#117—91no—
208#391—91no—
209#389—91no—
210#389—91no—
211#389—91no—
212#388—91no—
213#388—91no—
214#388—91no—
215#388D911yescharacteristic
216#387—91no—
217#387—91no—
218#380—91no—
219C4×C4⋊C4—91no—
220C24×C3C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—31no—
228C22×Dic3—34no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—62no—
237C22×Dic3—62no—
238C2×Dic6—34no—
239C2×Dic6—62no—
240C2×Dic6—62no—
241C3×C4⋊C4—41no—
242C3×C22⋊C4—22no—
243C3×C22⋊C4—41no—
244C3×C22⋊C4C4×D314yes—
245C3×C42—22no—
246#217—34no—
247#217—62no—
248#217—121no—
249C4⋊Dic3—34no—
250C4⋊Dic3—62no—
251Dic3⋊C4—34no—
252Dic3⋊C4—34no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—121no—
259C4×Dic3—34no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—121no—
263C4×Dic3—121no—
264C22×C9—22no—
265C22×C9—22no—
266C22×C9—22no—
267C22×C9—41no—
268C22×C9—41no—
269C22×C9—41no—
270C22×C9—41no—
271C22×C9C23×C411yescharacteristic
272C22×C9C22×D411yescharacteristic
273C22×C9C2×#4111yescharacteristic
274C22×C9H(5,𝔽2)11yescharacteristic
275C22×C92−1+411yescharacteristic
276C22×C92−1+411yescharacteristic
277C22×C92−1+411yescharacteristic
278C4×C9—22no—
279C4×C9—22no—
280C4×C9—22no—
281C4×C9—41no—
282C4×C9—41no—
283C4×C9—41no—
284Dic9—22no—
285Dic9—22no—
286Dic9—22no—
287Dic9—22no—
288Dic9—41no—
289Dic9—41no—
290Dic9—41no—
291Dic9C4×D414yes—
292C22×Q8—91no—
293C23×C4—91no—
294C22⋊Q8—98no—
295C4×Q8—184no—
296#117—184no—
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×C4⋊C4—91no—
305C2×C4⋊C4—91no—
306C2×C4⋊C4—91no—
307C2×C4⋊C4C2×D911yescharacteristic
308C2×C22⋊C4—91no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4—91no—
311C2×C22⋊C4C2×D911yescharacteristic
312C2×C22⋊C4C2×D911yescharacteristic
313C2×C22⋊C4C2×D911yescharacteristic
314C2×C42—91no—
315C2×C42—91no—
316C2×C42—91no—
317C2×C42—91no—
318C2×C42—91no—
319C2×C42C2×D911yescharacteristic
320#95—91no—
321#95—91no—
322#95—91no—
323#95—91no—
324#95—91no—
325#95—91no—
326#95—91no—
327#95—91no—
328#95C2×D911yescharacteristic
329#95C2×D911yescharacteristic
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3C2×C4×D312yes—
337C23×C3C23×D311yescharacteristic
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×C4—21no—
353C2×C3×C4C2×C4×D312yes—
354C2×C3×C4C2×C4×D312yes—
355C2×C3×C4D3×D412yes—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—68no—
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—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381Dic6—68no—
382C2×C9—42no—
383C2×C9C2×C4×D411yescharacteristic
384C2×C9#51911yescharacteristic
385C2×C9#52011yescharacteristic
386C2×C9#53611yescharacteristic
387C2×C9#53711yescharacteristic
388C2×C9#54111yescharacteristic
389C2×C9#54211yescharacteristic
390C24C22×D911yescharacteristic
391C2×Q8—94no—
392C2×Q8—182no—
393C2×Q8—182no—
394C22×C4—91no—
395C22×C4—94no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—182no—
404C22×C4—182no—
405C22×C4C22×D911yescharacteristic
406C22×C4C22×D911yescharacteristic
407C22×C4C22×D911yescharacteristic
408C22×C4C22×D911yescharacteristic
409C22×C4C22×D911yescharacteristic
410C22×C4C22×D911yescharacteristic
411C4⋊C4—41no—
412C4⋊C4—94no—
413C4⋊C4—94no—
414C4⋊C4—94no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C4⋊C4—361no—
422C22⋊C4—22no—
423C22⋊C4—41no—
424C22⋊C4—94no—
425C22⋊C4—182no—
426C22⋊C4—361no—
427C22⋊C4C4×D914yes—
428C42—22no—
429C42—94no—
430C42—182no—
431C42—182no—
432C42—361no—
433C42—361no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3C22×C4×D311yescharacteristic
442C22×C3C2×D3×D411yescharacteristic
443C22×C3#100411yescharacteristic
444C22×C3D3×#4111yescharacteristic
445C22×C3#101011yescharacteristic
446C22×C3#101011yescharacteristic
447C22×C3#101011yescharacteristic
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—41no—
454Dic3—34no—
455Dic3—62no—
456Dic3—62no—
457Dic3—62no—
458Dic3—62no—
459Dic3—121no—
460Dic3—121no—
461Dic3—121no—
462C9#232311yescharacteristic, complemented, Sylow
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23C2×C4×D912yes—
470C23C23×D911yescharacteristic
471Q8—188no—
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—21no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—92no—
494C2×C4—188no—
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—181no—
510C2×C4—181no—
511C2×C4—181no—
512C2×C4C2×C4×D912yes—
513C2×C4C2×C4×D912yes—
514C2×C4D4×D912yes—
515C2×C3—42no—
516C2×C3#551611yescharacteristic
517C2×C3C4×D3×D411yescharacteristic
518C2×C3#554611yescharacteristic
519C2×C3#560811yescharacteristic
520C2×C3#564811yescharacteristic
521C2×C3#566911yescharacteristic
522C2×C3#570111yescharacteristic
523C22—22no—
524C22—22no—
525C22—22no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22C22×C4×D911yescharacteristic
531C22C2×D4×D911yescharacteristic
532C22#6371011yescharacteristic
533C22#41×D911yescharacteristic
534C22#6371611yescharacteristic
535C22#6371611yescharacteristic
536C22#6371611yescharacteristic
537C4—22no—
538C4—22no—
539C4—22no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—94no—
544C4—182no—
545C4—182no—
546C4—182no—
547C4—182no—
548C4—361no—
549C4—361no—
550C4—361no—
551C3#7546011yescharacteristic
552C2—42no—
553C2#1058961811yescharacteristic
554C2C4×D4×D911yescharacteristic
555C2#1058964811yescharacteristic
556C2#1058971011yescharacteristic
557C2#1058975011yescharacteristic
558C2#1058977111yescharacteristic
559C2#1058980311yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#388C2
prime radicalC24×C3C22×D3
cosocleC23×C9C24
hypercenter#388D9
hypocenterC9#2323
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic18C2semidirect
5. #10588656C2semidirect
6. #10588652C2semidirect
11. #10588613C2semidirect
12. #10588333C2semidirect
13. #10588329C2semidirect
14. #10588327C2semidirect
15. #10588326C2semidirect
42. #63440C4semidirect
462. C9#2323semidirect

Maximal subgroups

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

subgroupindex
C2×#634402
C2×#634392
C2×C4×Dic182
C9×#3882
#105886562
#105886522
#105886312
#105886242
#105886222
#105886132
#105883332
#105883292
#105883272
#105883262
#754603