Finite Group Databasebeta

← #11865746

Subgroups — #11865746

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C9×#41C211yesmaximal, characteristic, complemented
2C2×#63513C212yesmaximal, complemented
3#10589579C211yesmaximal, characteristic, complemented
4#10588711C212yesmaximal, complemented
5#10588710C211yesmaximal, characteristic, complemented
6#10588707C211yesmaximal, characteristic, complemented
7#10588699C212yesmaximal, complemented
8#10588698C211yesmaximal, characteristic, complemented
9#10588695C211yesmaximal, characteristic, complemented
10#10588683C212yesmaximal, complemented
11C2×C4⋊(C9⋊C8)C211yesmaximal, characteristic, complemented
12#82525—31nomaximal
13C2×C9×#41C2211yescharacteristic
14C2×#3697C2212yes—
15C4×Q8×C9C2211yescharacteristic
16C4×Q8×C9C2211yescharacteristic
17C4×D4×C9—21no—
18C4×D4×C9—21no—
19C4×D4×C9C2211yescharacteristic
20C4×D4×C9C2211yescharacteristic
21C9×#117—21no—
22C9×#117C2211yescharacteristic
23C2×C42×C9—21no—
24C2×C42×C9C2211yescharacteristic
25#63513—28no—
26C2×#3675C2212yes—
27C2×#3674C2212yes—
28C2×#3673C2212yes—
29C2×#3672C2212yes—
30#63492—21no—
31#63492—21no—
32C22×C9⋊C8C2212yes—
33#63437C2212yes—
34#63436C2211yescharacteristic
35C4×D36—21no—
36C4×D36—21no—
37#63431C2211yescharacteristic
38#63369C2212yes—
39#63369C2212yes—
40#63368C2212yes—
41#63368C2212yes—
42C4⋊(C9⋊C8)C2211yescharacteristic
43C4⋊(C9⋊C8)C2211yescharacteristic
44C4⋊(C9⋊C8)C2212yes—
45C3×C4×#41D311yescharacteristic
46C2×#950—32no—
47#5477—31no—
48#5031—31no—
49#5028—32no—
50#5027—31no—
51#5019—31no—
52#5016—32no—
53#5015—31no—
54#5002—32no—
55C2×C4⋊(C3⋊C8)—31no—
56C9×#41—22no—
57C9×#41D414yescomplemented
58C2×Q8×C9C2311yescharacteristic
59C2×D4×C9—21no—
60C2×D4×C9C2311yescharacteristic
61C22×C4×C9—21no—
62C22×C4×C9—21no—
63C22×C4×C9—21no—
64C22×C4×C9D411yescharacteristic
65C22×C4×C9D411yescharacteristic
66C22×C4×C9C2311yescharacteristic
67C2×#611—22no—
68#3697—24no—
69#3697—24no—
70C2×D36—21no—
71C2×D36—21no—
72C2×D36C2312yes—
73C2×C4×D9—22no—
74C2×Dic18C2312yes—
75C9×C4⋊C4—21no—
76C9×C4⋊C4—21no—
77C9×C4⋊C4C2311yescharacteristic
78C9×C4⋊C4C2311yescharacteristic
79C9×C22⋊C4—21no—
80C9×C22⋊C4—21no—
81C9×C22⋊C4—21no—
82C42×C9—21no—
83C42×C9—21no—
84C42×C9—21no—
85C42×C9D411yescharacteristic
86C42×C9D411yescharacteristic
87C42×C9C2311yescharacteristic
88C42×C9C2311yescharacteristic
89#3675—24no—
90#3674—24no—
91#3673—24no—
92#3672—24no—
93(C2×D9)⋊C4—22no—
94(C2×D9)⋊C4—22no—
95C4⋊Dic9—21no—
96C4⋊Dic9—21no—
97C2×C9⋊C8—24no—
98C2×C9⋊C8C2312yes—
99C2×C9⋊C8C2312yes—
100#3035—91noSylow
101C2×C3×#41C2×D311yescharacteristic
102C2×#235—32no—
103C3×C4×Q8C2×D311yescharacteristic
104C3×C4×Q8C2×D311yescharacteristic
105C3×C4×D4—21no—
106C3×C4×D4—21no—
107C3×C4×D4C2×D311yescharacteristic
108C3×C4×D4C2×D311yescharacteristic
109C3×#117—21no—
110C3×#117C2×D311yescharacteristic
111C2×C3×C42—21no—
112C2×C3×C42C2×D311yescharacteristic
113#950—68no—
114C2×#216—32no—
115C2×#215—32no—
116C2×#214—32no—
117C2×#213—32no—
118#930—61no—
119#930—61no—
120C22×C3⋊C8—32no—
121#875—32no—
122#874—31no—
123C4×D12—61no—
124C4×D12—61no—
125#869—31no—
126#810—32no—
127#810—32no—
128#809—32no—
129#809—32no—
130C4⋊(C3⋊C8)—31no—
131C4⋊(C3⋊C8)—32no—
132C4⋊(C3⋊C8)—31no—
133C23×C9—21no—
134C23×C9C2×D411yescharacteristic
135C22×D9—22no—
136Q8×C9—21no—
137Q8×C9C2×D412yes—
138D4×C9—24no—
139D4×C9—21no—
140D4×C9C2×D412yes—
141C2×C4×C9—21no—
142C2×C4×C9—24no—
143C2×C4×C9—22no—
144C2×C4×C9—21no—
145C2×C4×C9—21no—
146C2×C4×C9—41no—
147C2×C4×C9—42no—
148C2×C4×C9—42no—
149C2×C4×C9C2×D412yes—
150C2×C4×C9C2×D411yescharacteristic
151C2×C4×C9C2×D411yescharacteristic
152C2×C4×C9C2×D411yescharacteristic
153C2×C4×C9C2×D411yescharacteristic
154C2×C4×C9C2×D411yescharacteristic
155C2×C4×C9#4112yes—
156C2×C4×C9C2411yescharacteristic
157#611—44no—
158C2×Dic9—22no—
159D36—22no—
160D36—22no—
161D36—42no—
162D36—42no—
163C4×D9—44no—
164Dic18—22no—
165Dic18—22no—
166C9⋊C8—22no—
167C9⋊C8—22no—
168C2×#135—92no—
169#532—91no—
170C4×#41D911yescharacteristic, complemented
171#464—92no—
172#463—92no—
173#462—91no—
174#461—91no—
175#460—91no—
176#459—91no—
177C2×C4⋊C8—91no—
178#416—92no—
179C3×#41—22no—
180C3×#41D1214yes—
181C2×C3×Q8C22×D311yescharacteristic
182C2×C3×D4—21no—
183C2×C3×D4C22×D311yescharacteristic
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—62no—
191#235—64no—
192#235—64no—
193C2×D12—32no—
194C2×D12—61no—
195C2×D12—61no—
196C2×C4×D3—62no—
197C2×Dic6—32no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4C22×D311yescharacteristic
201C3×C4⋊C4C22×D311yescharacteristic
202C3×C22⋊C4—21no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C42—21no—
206C3×C42—21no—
207C3×C42—21no—
208C3×C42#6711yescharacteristic
209C3×C42#6711yescharacteristic
210C3×C42C22×D311yescharacteristic
211C3×C42C22×D311yescharacteristic
212#216—64no—
213#215—64no—
214#214—64no—
215#213—64no—
216(C2×D3)⋊C4—62no—
217(C2×D3)⋊C4—62no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—64no—
223C22×C9—21no—
224C22×C9—21no—
225C22×C9—22no—
226C22×C9—41no—
227C22×C9—41no—
228C22×C9#12112yes—
229C22×C9C22×D411yescharacteristic
230C2×D9—42no—
231C2×D9—42no—
232C2×D9—42no—
233C4×C9—22no—
234C4×C9—21no—
235C4×C9—21no—
236C4×C9—21no—
237C4×C9—41no—
238C4×C9—41no—
239C4×C9#12112yes—
240C4×C9#13512yescomplemented
241C4×C9C22×D411yescharacteristic
242C4×C9C2×#4111yescharacteristic
243Dic9—42no—
244C2×#41—92no—
245C2×#41C2×D911yescharacteristic
246#135—188no—
247C2×Q16—92no—
248C2×SD16—92no—
249C2×SD16—92no—
250C2×D8—92no—
251C22×C8—92no—
252C4⋊Q8—91no—
253#127—91no—
254#124—92no—
255#121—181no—
256#121—181no—
257C4×Q8C2×D911yescharacteristic
258C4×Q8C2×D911yescharacteristic
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—181no—
262C4×D4—181no—
263C4×D4C2×D911yescharacteristic
264C4×D4C2×D911yescharacteristic
265#117—21no—
266#117C2×D911yescharacteristic
267C2×C42—21no—
268C2×C42C2×D911yescharacteristic
269C4⋊C8—91no—
270C4⋊C8—91no—
271C4⋊C8—92no—
272#103—92no—
273#103—92no—
274#102—92no—
275#102—92no—
276C23×C3—21no—
277C23×C3C2×#6711yescharacteristic
278C22×D3—62no—
279C3×Q8—21no—
280C3×Q8C2×D1212yes—
281C3×D4—24no—
282C3×D4—21no—
283C3×D4C2×D1212yes—
284C2×C3×C4—21no—
285C2×C3×C4—24no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—41no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4C2×D1212yes—
293C2×C3×C4#23512yes—
294C2×C3×C4C2×#6711yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C23×D311yescharacteristic
300#67—124no—
301C2×Dic3—62no—
302D12—62no—
303D12—62no—
304D12—122no—
305D12—122no—
306C4×D3—124no—
307Dic6—62no—
308Dic6—62no—
309C3⋊C8—62no—
310C3⋊C8—62no—
311C2×C9—22no—
312C2×C9—42no—
313C2×C9C2×#12111yescharacteristic
314C2×C9C2×#13511yescharacteristic
315C2×C9#57511yescharacteristic
316D9—82no—
317#41—22no—
318#41—184no—
319#41—184no—
320#41D3614yescomplemented
321C2×Q8—92no—
322C2×Q8C22×D911yescharacteristic
323C2×D4—21no—
324C2×D4—92no—
325C2×D4—182no—
326C2×D4—181no—
327C2×D4—181no—
328C2×D4C22×D911yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—182no—
333C22×C4#61111yescharacteristic
334C22×C4#61111yescharacteristic
335C22×C4C22×D911yescharacteristic
336Q16—184no—
337SD16—184no—
338SD16—184no—
339D8—184no—
340C2×C8—92no—
341C2×C8—92no—
342C2×C8—184no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4C22×D911yescharacteristic
348C4⋊C4C22×D911yescharacteristic
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—182no—
353C22⋊C4—182no—
354C42—21no—
355C42—21no—
356C42—21no—
357C42#61111yescharacteristic
358C42#61111yescharacteristic
359C42C22×D911yescharacteristic
360C42C22×D911yescharacteristic
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—22no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3#93012yes—
367C22×C3C22×#6711yescharacteristic
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—122no—
371C3×C4—22no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4#93012yes—
378C3×C4#95012yes—
379C3×C4C22×D1211yescharacteristic
380C3×C4C2×#23511yescharacteristic
381Dic3—122no—
382C9#303511yescharacteristic, complemented, Sylow
383C23—21no—
384C23—182no—
385C23C2×#61111yescharacteristic
386Q8—21no—
387Q8—182no—
388Q8—182no—
389Q8C2×D3612yes—
390D4—24no—
391D4—21no—
392D4—182no—
393D4—182no—
394D4—362no—
395D4—364no—
396D4—362no—
397D4C2×D3612yes—
398C2×C4—21no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—182no—
407C2×C4—364no—
408C2×C4C2×D3612yes—
409C2×C4#369712yes—
410C2×C4C2×#61111yescharacteristic
411C2×C4C2×#61111yescharacteristic
412C2×C4C2×#61111yescharacteristic
413C2×C4C2×#61111yescharacteristic
414C2×C4C2×#61111yescharacteristic
415C2×C4C23×D911yescharacteristic
416C8—182no—
417C8—182no—
418C2×C3—22no—
419C2×C3—42no—
420C2×C3C2×#93011yescharacteristic
421C2×C3C2×#95011yescharacteristic
422C2×C3#582211yescharacteristic
423D3—242no—
424C22—21no—
425C22—21no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—362no—
430C22—362no—
431C22—362no—
432C22#6349212yes—
433C22C22×#61111yescharacteristic
434C4—22no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—362no—
441C4#6349212yes—
442C4#6351312yescomplemented
443C4C22×D3611yescharacteristic
444C4C2×#369711yescharacteristic
445C3#8252511yescharacteristic
446C2—22no—
447C2—42no—
448C2—722no—
449C2C2×#6349211yescharacteristic
450C2C2×#6351311yescharacteristic
451C2#1058992511yescharacteristic
subgroupG/H
centerC2×C4C2×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×#41C2
socleC22×C3C22×#67
hypercenterC4×#41D9
hypocenterC9#3035
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C4×C9×#41C2semidirect
2. C2×#63513C2semidirect
3. #10589579C2semidirect
4. #10588711C2semidirect
5. #10588710C2semidirect
6. #10588707C2semidirect
7. #10588699C2semidirect
8. #10588698C2semidirect
9. #10588695C2semidirect
10. #10588683C2semidirect
11. C2×C4⋊(C9⋊C8)C2semidirect
57. C9×#41D4semidirect
170. C4×#41D9semidirect
240. C4×C9#135semidirect
320. #41D36semidirect
382. C9#3035semidirect
442. C4#63513semidirect

Maximal subgroups

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

subgroupindex
C4×C9×#412
C2×#635132
#105895792
#105887112
#105887102
#105887072
#105886992
#105886982
#105886952
#105886832
C2×C4⋊(C9⋊C8)2
#825253