Finite Group Databasebeta

← #11803562

Subgroups — #11803562

Order 1152.

1002 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63500C211yesmaximal, characteristic
2C2×D4×Dic9C211yesmaximal, characteristic, complemented
3C2×#63434C211yesmaximal, characteristic, complemented
4C9×#390C211yesmaximal, characteristic, complemented
5#10588667C211yesmaximal, characteristic, complemented
6C4⋊C4×Dic9C211yesmaximal, characteristic, complemented
7#10588638C212yesmaximal, complemented
8#10588637C212yesmaximal, complemented
9#10588626C212yesmaximal, complemented
10#10588624C212yesmaximal, complemented
11#10588608C211yesmaximal, characteristic, complemented
12#76430—31nomaximal
13C22×D4×C9C2211yescharacteristic
14C22×#611C2212yes—
15C23×Dic9C2212yes—
16C22×C4×D9C2211yescharacteristic
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×C9×C22⋊C4C2212yes—
19C2×C9×C22⋊C4C2212yes—
20C2×C42×C9C2211yescharacteristic
21C2×#3676C2212yes—
22C2×#3676C2212yes—
23#63500C418yescomplemented
24D4×Dic9—24no—
25C2×(C2×D9)⋊C4C2211yescharacteristic
26C2×(C2×D9)⋊C4C2211yescharacteristic
27C2×(C2×D9)⋊C4C2212yes—
28C2×C4⋊Dic9C2211yescharacteristic
29C2×C4⋊Dic9C2211yescharacteristic
30C2×Dic9⋊C4C2211yescharacteristic
31C2×Dic9⋊C4C2211yescharacteristic
32C2×Dic9⋊C4C2212yes—
33C2×C4×Dic9C2212yes—
34C2×C4×Dic9C2211yescharacteristic
35#63434—24no—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C9⋊#95C2212yes—
39C2×#938—31no—
40C2×D4×Dic3—31no—
41C2×#872—31no—
42C3×#390D311yescharacteristic
43#4987—31no—
44Dic3×C4⋊C4—31no—
45#4958—32no—
46#4957—32no—
47#4946—32no—
48#4944—32no—
49#4928—31no—
50C24×C9C2312yes—
51C23×D9C2311yescharacteristic
52C2×D4×C9—22no—
53C2×D4×C9—22no—
54C2×D4×C9C2×C414yes—
55C22×C4×C9C2311yescharacteristic
56C22×C4×C9C2311yescharacteristic
57C22×C4×C9C2312yes—
58C22×C4×C9C2311yescharacteristic
59C2×#611—42no—
60C2×#611—42no—
61C2×#611C2×C418yescomplemented
62C22×Dic9—24no—
63C22×Dic9—42no—
64C22×Dic9—42no—
65C22×Dic9C2312yes—
66C22×Dic9C2311yescharacteristic
67C22×Dic9C2312yes—
68C22×Dic9C2311yescharacteristic
69C22×Dic9C2311yescharacteristic
70C2×C4×D9—22no—
71C2×C4×D9—22no—
72C2×C4×D9C2×C414yescomplemented
73C9×C4⋊C4—22no—
74C9×C22⋊C4—42no—
75C9×C22⋊C4—42no—
76C42×C9—22no—
77#3676—24no—
78#3676C2×C418yescomplemented
79(C2×D9)⋊C4—22no—
80(C2×D9)⋊C4—22no—
81(C2×D9)⋊C4—42no—
82C4⋊Dic9—22no—
83C4⋊Dic9C2×C414yescomplemented
84Dic9⋊C4—22no—
85Dic9⋊C4—22no—
86Dic9⋊C4—42no—
87C4×Dic9—42no—
88C4×Dic9D414yescomplemented
89#2324—91noSylow
90C22×C3×D4C2×D311yescharacteristic
91C22×#67—32no—
92C23×Dic3—32no—
93C22×C4×D3—31no—
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C22⋊C4C2×D312yes—
96C2×C3×C22⋊C4C2×D312yes—
97C2×C3×C42C2×D311yescharacteristic
98C2×#217—32no—
99C2×#217—32no—
100#938—38no—
101D4×Dic3—64no—
102C2×(C2×D3)⋊C4—31no—
103C2×(C2×D3)⋊C4—31no—
104C2×(C2×D3)⋊C4—32no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—32no—
110C2×C4×Dic3—31no—
111C2×C4×Dic3—32no—
112#872—64no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C23×C9—22no—
117C23×C9—22no—
118C23×C9—22no—
119C23×C9—22no—
120C23×C9—22no—
121C23×C9—22no—
122C23×C9C22×C414yes—
123C23×C9C2411yescharacteristic
124C22×D9—21no—
125C22×D9—21no—
126C22×D9—21no—
127C22×D9—21no—
128C22×D9—21no—
129C22×D9—21no—
130C22×D9C22×C412yes—
131D4×C9—28no—
132C2×C4×C9—21no—
133C2×C4×C9—21no—
134C2×C4×C9—22no—
135C2×C4×C9—22no—
136C2×C4×C9—21no—
137C2×C4×C9—22no—
138C2×C4×C9—21no—
139C2×C4×C9—21no—
140C2×C4×C9—21no—
141C2×C4×C9C22×C412yes—
142C2×C4×C9C2×D412yes—
143C2×C4×C9#4112yes—
144#611—48no—
145C2×Dic9—21no—
146C2×Dic9—21no—
147C2×Dic9—21no—
148C2×Dic9—22no—
149C2×Dic9—22no—
150C2×Dic9—21no—
151C2×Dic9—21no—
152C2×Dic9—21no—
153C2×Dic9—22no—
154C2×Dic9—22no—
155C2×Dic9—22no—
156C2×Dic9—48no—
157C2×Dic9C22×C414yes—
158C2×Dic9C22×C412yes—
159C2×Dic9C2×D412yes—
160C2×Dic9C2×D412yes—
161C4×D9—28no—
162C2×#121—91no—
163C2×C4×D4—91no—
164C2×#117—91no—
165#390—92no—
166#390D911yescharacteristic, complemented
167#389—91no—
168#388—92no—
169#386—92no—
170#385—92no—
171#380—91no—
172C4×C4⋊C4—91no—
173C24×C3C22×D312yes—
174C23×D3—31no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4C4×D314yes—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×#67—38no—
183C2×#67—122no—
184C2×#67—122no—
185C22×Dic3—32no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—32no—
190C22×Dic3—64no—
191C22×Dic3—122no—
192C22×Dic3—122no—
193C2×C4×D3—34no—
194C2×C4×D3—62no—
195C2×C4×D3—62no—
196C3×C4⋊C4—22no—
197C3×C22⋊C4—42no—
198C3×C22⋊C4—42no—
199C3×C42—22no—
200#217—38no—
201#217—64no—
202(C2×D3)⋊C4—62no—
203(C2×D3)⋊C4—62no—
204(C2×D3)⋊C4—122no—
205C4⋊Dic3—34no—
206C4⋊Dic3—62no—
207Dic3⋊C4—62no—
208Dic3⋊C4—62no—
209Dic3⋊C4—122no—
210C4×Dic3—34no—
211C4×Dic3—122no—
212C22×C9—24no—
213C22×C9—24no—
214C22×C9—24no—
215C22×C9—42no—
216C22×C9—42no—
217C22×C9—42no—
218C22×C9—42no—
219C22×C9C23×C411yescharacteristic
220C22×C9C22×D411yescharacteristic
221C22×C9C2×#4111yescharacteristic
222C22×C9H(5,𝔽2)11yescharacteristic
223C22×C9H(5,𝔽2)11yescharacteristic
224C22×C9H(5,𝔽2)11yescharacteristic
225C22×C92−1+411yescharacteristic
226C2×D9—22no—
227C2×D9—22no—
228C2×D9—22no—
229C2×D9—41no—
230C2×D9—41no—
231C2×D9—41no—
232C2×D9—41no—
233C4×C9—41no—
234C4×C9—41no—
235C4×C9—42no—
236C4×C9C4×D414yes—
237Dic9—22no—
238Dic9—24no—
239Dic9—22no—
240Dic9—22no—
241Dic9—42no—
242C22×D4—92no—
243C22×D4C2×D911yescharacteristic
244C23×C4—91no—
245C23×C4—92no—
246#121—98no—
247C4×D4—184no—
248#117—184no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4C2×D911yescharacteristic
255C2×C22⋊C4—92no—
256C2×C22⋊C4—92no—
257C2×C22⋊C4—91no—
258C2×C22⋊C4—91no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4C2×D912yes—
261C2×C22⋊C4C2×D912yes—
262C2×C42—91no—
263C2×C42—92no—
264C2×C42C2×D911yescharacteristic
265#95—92no—
266#95—92no—
267#95—92no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3C2×C4×D314yes—
275C23×C3C23×D311yescharacteristic
276C22×D3—32no—
277C22×D3—61no—
278C22×D3—61no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—61no—
283C3×D4—28no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4C2×C4×D312yes—
294C2×C3×C4D3×D412yes—
295C2×C3×C4#23712yes—
296#67—128no—
297C2×Dic3—34no—
298C2×Dic3—32no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—62no—
305C2×Dic3—61no—
306C2×Dic3—62no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—128no—
313C4×D3—68no—
314C2×C9—44no—
315C2×C9C2×C4×D411yescharacteristic
316C2×C9#51811yescharacteristic
317C2×C9#52011yescharacteristic
318C2×C9#53511yescharacteristic
319C2×C9#53711yescharacteristic
320C2×C9#54011yescharacteristic
321C2×C9#54211yescharacteristic
322D9—42no—
323C24—91no—
324C24C22×D912yes—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—98no—
328C2×D4—362no—
329C2×D4—362no—
330C2×D4C4×D914yes—
331C22×C4—92no—
332C22×C4—91no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—94no—
336C22×C4—92no—
337C22×C4—184no—
338C22×C4—182no—
339C22×C4—182no—
340C22×C4—362no—
341C22×C4—362no—
342C22×C4C22×D912yes—
343C22×C4C22×D911yescharacteristic
344C22×C4C22×D911yescharacteristic
345C22×C4C22×D911yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—94no—
348C4⋊C4—182no—
349C4⋊C4—182no—
350C4⋊C4—182no—
351C4⋊C4—362no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C22⋊C4—98no—
355C22⋊C4—182no—
356C22⋊C4—182no—
357C22⋊C4—184no—
358C22⋊C4—362no—
359C42—22no—
360C42—94no—
361C42—362no—
362C22×C3—24no—
363C22×C3—24no—
364C22×C3—24no—
365C22×C3—42no—
366C22×C3—42no—
367C22×C3—42no—
368C22×C3—42no—
369C22×C3C22×C4×D311yescharacteristic
370C22×C3C2×D3×D411yescharacteristic
371C22×C3C2×#23711yescharacteristic
372C22×C3#100411yescharacteristic
373C22×C3#100411yescharacteristic
374C22×C3#100911yescharacteristic
375C22×C3#101011yescharacteristic
376C2×D3—62no—
377C2×D3—62no—
378C2×D3—62no—
379C2×D3—121no—
380C2×D3—121no—
381C2×D3—121no—
382C2×D3—121no—
383C3×C4—42no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4#67⋊C414yes—
387Dic3—62no—
388Dic3—64no—
389Dic3—62no—
390Dic3—62no—
391Dic3—122no—
392C9#232411yescharacteristic, complemented, Sylow
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—92no—
400C23—181no—
401C23—181no—
402C23—181no—
403C23—181no—
404C23—181no—
405C23—181no—
406C23C2×C4×D914yes—
407C23C23×D911yescharacteristic
408D4—28no—
409D4—368no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—92no—
420C2×C4—94no—
421C2×C4—92no—
422C2×C4—92no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—181no—
426C2×C4—182no—
427C2×C4—181no—
428C2×C4—182no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4—188no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4—368no—
436C2×C4C2×C4×D912yes—
437C2×C4D4×D912yes—
438C2×C4#369912yes—
439C2×C3—44no—
440C2×C3C2×#67⋊C411yescharacteristic
441C2×C3#554511yescharacteristic
442C2×C3#554611yescharacteristic
443C2×C3#560711yescharacteristic
444C2×C3#560811yescharacteristic
445C2×C3#568211yescharacteristic
446C2×C3#571911yescharacteristic
447D3—122no—
448C22—24no—
449C22—24no—
450C22—24no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—182no—
456C22—182no—
457C22—182no—
458C22—361no—
459C22—361no—
460C22—361no—
461C22—361no—
462C22C22×C4×D911yescharacteristic
463C22C2×D4×D911yescharacteristic
464C22C2×#369911yescharacteristic
465C22#6371011yescharacteristic
466C22#6371011yescharacteristic
467C22#6371511yescharacteristic
468C22#6371611yescharacteristic
469C4—41no—
470C4—41no—
471C4—42no—
472C4—182no—
473C4—182no—
474C4—182no—
475C4—184no—
476C4—362no—
477C4#611⋊C414yes—
478C3#7643011yescharacteristic
479C2—44no—
480C2—362no—
481C2C2×#611⋊C411yescharacteristic
482C2#1058964711yescharacteristic
483C2#1058964811yescharacteristic
484C2#1058970911yescharacteristic
485C2#1058971011yescharacteristic
486C2#1058978411yescharacteristic
487C2#1058982111yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#390C2
prime radicalC2×#63500C2
cosocleC23×C9C24
hypercenter#390D9
hypocenterC9#2324
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic9C2semidirect
3. C2×#63434C2semidirect
4. C9×#390C2semidirect
5. #10588667C2semidirect
6. C4⋊C4×Dic9C2semidirect
7. #10588638C2semidirect
8. #10588637C2semidirect
9. #10588626C2semidirect
10. #10588624C2semidirect
11. #10588608C2semidirect
23. #63500C4semidirect
61. C2×#611C2×C4semidirect
72. C2×C4×D9C2×C4semidirect
78. #3676C2×C4semidirect
83. C4⋊Dic9C2×C4semidirect
88. C4×Dic9D4semidirect
166. #390D9semidirect
392. C9#2324semidirect

Maximal subgroups

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

subgroupindex
C2×#635002
C2×D4×Dic92
C2×#634342
C9×#3902
#105886672
C4⋊C4×Dic92
#105886382
#105886372
#105886262
#105886242
#105886082
#764303