Finite Group Databasebeta

← #11824466

Subgroups — #11824466

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63458C212yesmaximal, complemented
2C2×#63450C211yesmaximal, characteristic, complemented
3C2×#611⋊C4C211yesmaximal, characteristic
4C2×#63440C212yesmaximal, complemented
5C9×#399C211yesmaximal, characteristic, complemented
6#10588673C211yesmaximal, characteristic, complemented
7#10588655C212yesmaximal, complemented
8#10588637C212yesmaximal
9#10588629C211yesmaximal, characteristic, complemented
10#10588357C211yesmaximal, characteristic, complemented
11#10588329C211yesmaximal, characteristic, complemented
12#78037—31nomaximal
13C22×#611C2211yescharacteristic
14C23×Dic9C2211yescharacteristic
15C22×C4×D9C2211yescharacteristic
16C22×Dic18C2212yes—
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×C9×C4⋊C4C2212yes—
19C2×C9×C22⋊C4C2212yes—
20C2×C9×C22⋊C4C2211yescharacteristic
21C2×#3676C2212yes—
22C2×(C2×D9)⋊C4C2211yescharacteristic
23C2×(C2×D9)⋊C4C2212yes—
24C2×(C2×D9)⋊C4C2212yes—
25C2×C4⋊Dic9C2212yes—
26C2×C4⋊Dic9C2211yescharacteristic
27C2×Dic9⋊C4C2212yes—
28C2×Dic9⋊C4C2211yescharacteristic
29C2×Dic9⋊C4C2212yes—
30C2×Dic9⋊C4C2212yes—
31C2×Dic9⋊C4C2212yes—
32C2×C4×Dic9C2212yes—
33C2×C4×Dic9C2211yescharacteristic
34#63458—28no—
35#63450—24no—
36#611⋊C4—24no—
37#63440—28no—
38C9×#95C2211yescharacteristic
39C9⋊#95C2211yescharacteristic
40C2×#896—32no—
41C2×#888—31no—
42C2×#67⋊C4—31no—
43C2×#878—32no—
44C3×#399D311yescharacteristic
45#4993—31no—
46#4975—32no—
47#4957—32no—
48#4949—31no—
49#4677—31no—
50#4649—31no—
51C24×C9C2311yescharacteristic
52C23×D9C2311yescharacteristic
53C22×C4×C9C2312yes—
54C22×C4×C9C2311yescharacteristic
55C22×C4×C9C2311yescharacteristic
56C22×C4×C9C2312yes—
57C2×#611—22no—
58C2×#611—22no—
59C2×#611Q814yescomplemented
60C22×Dic9—24no—
61C22×Dic9—22no—
62C22×Dic9C2312yes—
63C22×Dic9C2311yescharacteristic
64C22×Dic9C2312yes—
65C22×Dic9C2311yescharacteristic
66C22×Dic9C2311yescharacteristic
67C2×C4×D9—22no—
68C2×C4×D9—24no—
69C2×Dic18—24no—
70C2×Dic18—24no—
71C2×Dic18—24no—
72C9×C4⋊C4—22no—
73C9×C4⋊C4—24no—
74C9×C22⋊C4—24no—
75C9×C22⋊C4—22no—
76#3676—24no—
77(C2×D9)⋊C4—22no—
78(C2×D9)⋊C4—24no—
79(C2×D9)⋊C4—24no—
80C4⋊Dic9—24no—
81C4⋊Dic9—22no—
82Dic9⋊C4—24no—
83Dic9⋊C4—22no—
84Dic9⋊C4—24no—
85Dic9⋊C4—24no—
86Dic9⋊C4D418yescomplemented
87C4×Dic9—24no—
88C4×Dic9D414yes—
89#2542—91noSylow
90C22×#67—31no—
91C23×Dic3—31no—
92C22×C4×D3—31no—
93C22×Dic6—32no—
94C2×C3×C4⋊C4C2×D312yes—
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C22⋊C4C2×D311yescharacteristic
97C2×C3×C22⋊C4C2×D312yes—
98C2×#217—32no—
99C2×(C2×D3)⋊C4—32no—
100C2×(C2×D3)⋊C4—31no—
101C2×(C2×D3)⋊C4—32no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4—31no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—32no—
111#896—68no—
112#888—64no—
113#67⋊C4—64no—
114#878—68no—
115C3×#95C2×D311yescharacteristic
116C3⋊#95—31no—
117C23×C9—22no—
118C23×C9—21no—
119C23×C9—21no—
120C23×C9—22no—
121C23×C9C2×Q812yes—
122C23×C9C2411yescharacteristic
123C22×D9—22no—
124C22×D9—21no—
125C22×D9—21no—
126C22×D9—22no—
127C22×D9C2×Q812yes—
128C2×C4×C9—22no—
129C2×C4×C9—22no—
130C2×C4×C9—22no—
131C2×C4×C9—22no—
132C2×C4×C9—21no—
133C2×C4×C9—22no—
134C2×C4×C9—22no—
135C2×C4×C9—22no—
136C2×C4×C9C2×D412yes—
137C2×C4×C9C2×D414yes—
138#611—28no—
139C2×Dic9—22no—
140C2×Dic9—22no—
141C2×Dic9—22no—
142C2×Dic9—22no—
143C2×Dic9—22no—
144C2×Dic9—21no—
145C2×Dic9—22no—
146C2×Dic9—44no—
147C2×Dic9C2×D414yes—
148C2×Dic9C2×D412yes—
149C2×Dic9C2×D412yes—
150C2×Dic9C2×D414yes—
151C2×Dic9C2×Q812yes—
152C2×Dic9#4112yes—
153C4×D9—44no—
154Dic18—48no—
155C2×C4⋊Q8—91no—
156C2×C22⋊Q8—92no—
157C2×C22⋊Q8—92no—
158C2×C4×D4—91no—
159#399—91no—
160#399—91no—
161#399—91no—
162#399D911yescharacteristic, complemented
163#390—92no—
164#384—92no—
165C4×C4⋊C4—91no—
166C24×C3C22×D311yescharacteristic
167C23×D3—31no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D312yes—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D312yes—
172C2×#67—34no—
173C2×#67—62no—
174C2×#67—62no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—32no—
178C22×Dic3—31no—
179C22×Dic3—32no—
180C22×Dic3—64no—
181C22×Dic3—62no—
182C2×C4×D3—62no—
183C2×C4×D3—64no—
184C2×Dic6—64no—
185C2×Dic6—64no—
186C2×Dic6—64no—
187C3×C4⋊C4—22no—
188C3×C4⋊C4—24no—
189C3×C22⋊C4—24no—
190C3×C22⋊C4—22no—
191#217—64no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—62no—
194(C2×D3)⋊C4—64no—
195C4⋊Dic3—64no—
196C4⋊Dic3—62no—
197Dic3⋊C4—38no—
198Dic3⋊C4—64no—
199Dic3⋊C4—62no—
200Dic3⋊C4—64no—
201Dic3⋊C4—64no—
202C4×Dic3—34no—
203C4×Dic3—64no—
204C22×C9—22no—
205C22×C9—24no—
206C22×C9—41no—
207C22×C9—41no—
208C22×C9—42no—
209C22×C9C22×D411yescharacteristic
210C22×C9C22×D412yes—
211C22×C9C22×Q811yescharacteristic
212C22×C9C2×#4111yescharacteristic
213C22×C92−1+412yes—
214C2×D9—22no—
215C2×D9—24no—
216C2×D9—41no—
217C2×D9—41no—
218C2×D9—42no—
219C4×C9—22no—
220C4×C9—24no—
221C4×C9—42no—
222C4×C9—41no—
223Dic9—24no—
224Dic9—42no—
225Dic9—41no—
226Dic9C22⋊Q814yescomplemented
227Dic9#12714yes—
228C22×Q8—92no—
229C22×D4—91no—
230C23×C4—91no—
231C23×C4—91no—
232C4⋊Q8—184no—
233C22⋊Q8—188no—
234C22⋊Q8—188no—
235C4×D4—184no—
236C2×C4⋊C4—92no—
237C2×C4⋊C4—91no—
238C2×C4⋊C4—92no—
239C2×C4⋊C4—92no—
240C2×C4⋊C4—92no—
241C2×C4⋊C4—92no—
242C2×C4⋊C4—91no—
243C2×C4⋊C4C2×D912yes—
244C2×C4⋊C4C2×D911yescharacteristic
245C2×C22⋊C4—92no—
246C2×C22⋊C4—91no—
247C2×C22⋊C4—92no—
248C2×C22⋊C4—92no—
249C2×C22⋊C4C2×D911yescharacteristic
250C2×C22⋊C4C2×D912yes—
251C2×C42—91no—
252C2×C42—92no—
253#95—91no—
254#95C2×D911yescharacteristic
255C23×C3—22no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—22no—
259C23×C3D3×Q812yes—
260C23×C3C23×D311yescharacteristic
261C22×D3—32no—
262C22×D3—62no—
263C22×D3—61no—
264C22×D3—61no—
265C22×D3—62no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4D3×D412yes—
275C2×C3×C4D3×D414yes—
276#67—68no—
277C2×Dic3—32no—
278C2×Dic3—32no—
279C2×Dic3—34no—
280C2×Dic3—32no—
281C2×Dic3—32no—
282C2×Dic3—34no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—61no—
289C2×Dic3—62no—
290C2×Dic3—124no—
291C4×D3—124no—
292Dic6—128no—
293C2×C9—42no—
294C2×C9C2×C22⋊Q811yescharacteristic
295C2×C9C2×#12711yescharacteristic
296C2×C9#53611yescharacteristic
297C2×C9#54712yes—
298C2×C9D4×Q812yes—
299D9—42no—
300C24—91no—
301C24C22×D911yescharacteristic
302C2×Q8—184no—
303C2×Q8—184no—
304C2×Q8—184no—
305C2×D4—94no—
306C2×D4—182no—
307C2×D4—182no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—92no—
311C22×C4—92no—
312C22×C4—91no—
313C22×C4—182no—
314C22×C4—184no—
315C22×C4—182no—
316C22×C4—184no—
317C22×C4C22×D912yes—
318C22×C4C22×D911yescharacteristic
319C22×C4C22×D911yescharacteristic
320C22×C4C22×D912yes—
321C4⋊C4—24no—
322C4⋊C4—22no—
323C4⋊C4—98no—
324C4⋊C4—182no—
325C4⋊C4—184no—
326C4⋊C4—184no—
327C4⋊C4—184no—
328C4⋊C4—184no—
329C4⋊C4—182no—
330C22⋊C4—22no—
331C22⋊C4—24no—
332C22⋊C4—184no—
333C22⋊C4—184no—
334C22⋊C4—182no—
335C22⋊C4—184no—
336C42—94no—
337C42—184no—
338C22×C3—24no—
339C22×C3—22no—
340C22×C3—41no—
341C22×C3—42no—
342C22×C3—41no—
343C22×C3C2×D3×D412yes—
344C22×C3C2×D3×D411yescharacteristic
345C22×C3C2×D3×Q811yescharacteristic
346C22×C3D3×#4111yescharacteristic
347C22×C3#101012yes—
348C2×D3—64no—
349C2×D3—62no—
350C2×D3—121no—
351C2×D3—122no—
352C2×D3—121no—
353C3×C4—22no—
354C3×C4—24no—
355C3×C4—42no—
356C3×C4—41no—
357Dic3—34no—
358Dic3—34no—
359Dic3—64no—
360Dic3—122no—
361Dic3—121no—
362C9#254211yescharacteristic, complemented, Sylow
363C23—22no—
364C23—21no—
365C23—21no—
366C23—22no—
367C23—92no—
368C23—182no—
369C23—181no—
370C23—181no—
371C23—182no—
372C23Q8×D912yes—
373C23C23×D911yescharacteristic
374Q8—368no—
375D4—188no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—92no—
385C2×C4—92no—
386C2×C4—94no—
387C2×C4—92no—
388C2×C4—92no—
389C2×C4—94no—
390C2×C4—182no—
391C2×C4—182no—
392C2×C4—181no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4—182no—
396C2×C4—182no—
397C2×C4—364no—
398C2×C4—364no—
399C2×C4D4×D912yes—
400C2×C4D4×D914yes—
401C2×C3—42no—
402C2×C3D3×C22⋊Q811yescharacteristic
403C2×C3#563212yes—
404C2×C3#564811yescharacteristic
405C2×C3#565512yes—
406C2×C3D3×#12711yescharacteristic
407D3—122no—
408C22—22no—
409C22—24no—
410C22—41no—
411C22—42no—
412C22—41no—
413C22—182no—
414C22—184no—
415C22—361no—
416C22—362no—
417C22—361no—
418C22C2×D4×D911yescharacteristic
419C22C2×D4×D912yes—
420C22C2×Q8×D911yescharacteristic
421C22#41×D911yescharacteristic
422C22#6371612yes—
423C4—22no—
424C4—24no—
425C4—41no—
426C4—42no—
427C4—94no—
428C4—94no—
429C4—184no—
430C4—361no—
431C4—362no—
432C3#7803711yescharacteristic
433C2—42no—
434C2—362no—
435C2D9×C22⋊Q811yescharacteristic
436C2#1058973412yes—
437C2#1058975011yescharacteristic
438C2#1058975712yes—
439C2D9×#12711yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#399C2
prime radicalC22×#611C22
hypercenter#399D9
hypocenterC9#2542
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#63458C2semidirect
2. C2×#63450C2semidirect
4. C2×#63440C2semidirect
5. C9×#399C2semidirect
6. #10588673C2semidirect
7. #10588655C2semidirect
9. #10588629C2semidirect
10. #10588357C2semidirect
11. #10588329C2semidirect
59. C2×#611Q8semidirect
86. Dic9⋊C4D4semidirect
162. #399D9semidirect
226. Dic9C22⋊Q8semidirect
362. C9#2542semidirect

Maximal subgroups

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

subgroupindex
C2×#634582
C2×#634502
C2×#611⋊C42
C2×#634402
C9×#3992
#105886732
#105886552
#105886372
#105886292
#105883572
#105883292
#780373