Finite Group Databasebeta

← #11868168

Subgroups — #11868168

Order 1152.

669 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#575C211yesmaximal, characteristic
2C2×#63511C211yesmaximal, characteristic, complemented
3C2×#63511C211yesmaximal, characteristic, complemented
4#10589921C211yesmaximal, characteristic, complemented
5#10588915C211yesmaximal, characteristic, complemented
6#10588882C214yesmaximal, complemented
7#10588878C214yesmaximal, complemented
8C2×#63382C211yesmaximal, characteristic, complemented
9#10588799C211yesmaximal, characteristic, complemented
10#84003—31nomaximal
11C2×C9×#41C2211yescharacteristic
12C2×C9×#41C2211yescharacteristic
13C22×Dic18C2211yescharacteristic
14C9×#137—21no—
15C9×#137C2212yes—
16C9×AGL(1,ℤ/8)—21no—
17C9×AGL(1,ℤ/8)C2212yes—
18C9×#135—22no—
19C2×C9×M16C2211yescharacteristic
20#63511—22no—
21#63511—22no—
22#63511—22no—
23#63511C2214yes—
24#63510—22no—
25#63510C2214yes—
26C2×#3674—21no—
27C2×#3674C2212yescomplemented
28C2×#3672—21no—
29C2×#3672C2212yescomplemented
30C2×#3667—22no—
31C2×#3667C2211yescharacteristic
32C2×#3667C2211yescharacteristic
33C2×#3667C2211yescharacteristic
34#63394C2212yescomplemented
35#63391C2212yescomplemented
36#63382C2214yescomplemented
37#63381C2214yescomplemented
38C3×#575D311yescharacteristic
39C2×#951—31no—
40C2×#951—31no—
41#5819—31no—
42#5237—31no—
43#5204—34no—
44#5200—34no—
45C2×#824—31no—
46#5124—31no—
47C9×#41—21no—
48C9×#41—21no—
49C9×#41—21no—
50C9×#41—21no—
51C9×#41—21no—
52C9×#41—21no—
53C9×#41D412yes—
54C9×#41C2312yes—
55C2×Q8×C9D411yescharacteristic
56C2×Q8×C9C2311yescharacteristic
57C2×D4×C9—21no—
58C2×D4×C9—21no—
59C2×D4×C9D411yescharacteristic
60C2×D4×C9C2311yescharacteristic
61C22×C4×C9—21no—
62C22×C4×C9—21no—
63C22×C4×C9C2311yescharacteristic
64C22×Dic9—21no—
65C2×Dic18—21no—
66C2×Dic18—21no—
67C2×Dic18—21no—
68C2×Dic18—21no—
69C2×Dic18—21no—
70C2×Dic18C2312yes—
71C9×Q16—22no—
72C9×SD16—22no—
73C9×SD16—22no—
74C9×D8—22no—
75C9×M16—21no—
76C9×M16C2312yes—
77C2×C8×C9—21no—
78#3674—24no—
79#3674—24no—
80#3672—24no—
81#3672—24no—
82#3667—21no—
83#3667—21no—
84#3667—24no—
85#3667D412yes—
86#3667D412yes—
87#3667C2312yes—
88#3667C2312yes—
89C2×C9⋊C8—21no—
90C2×C9⋊C8—21no—
91C2×C9⋊C8—24no—
92C2×C9⋊C8C2312yes—
93#3069—91noSylow
94C2×C3×#41C2×D311yescharacteristic
95C2×C3×#41C2×D311yescharacteristic
96C22×Dic6—31no—
97C3×#137—21no—
98C3×#137C2×D312yes—
99C3×AGL(1,ℤ/8)—21no—
100C3×AGL(1,ℤ/8)C2×D312yes—
101C3×#135—22no—
102C2×C3×M16C2×D311yescharacteristic
103#951—34no—
104#951—62no—
105#951—62no—
106#951—62no—
107#948—34no—
108#948—62no—
109C2×#216—32no—
110C2×#216—61no—
111C2×#214—32no—
112C2×#214—61no—
113C2×#208—31no—
114C2×#208—31no—
115C2×#208—31no—
116C2×#208—62no—
117#836—32no—
118#833—32no—
119#824—34no—
120#822—34no—
121C23×C9—21no—
122C23×C9—21no—
123C23×C9#4111yescharacteristic
124Q8×C9—21no—
125Q8×C9—21no—
126Q8×C9—21no—
127Q8×C9C2×D412yes—
128D4×C9—22no—
129D4×C9—22no—
130D4×C9—21no—
131D4×C9—21no—
132D4×C9—21no—
133D4×C9—41no—
134D4×C9—41no—
135D4×C9C2×D412yes—
136C2×C4×C9—21no—
137C2×C4×C9—22no—
138C2×C4×C9—22no—
139C2×C4×C9—21no—
140C2×C4×C9—41no—
141C2×C4×C9—41no—
142C2×C4×C9C2×D411yescharacteristic
143C2×C4×C9C2×D411yescharacteristic
144C2×C4×C9C2×D411yescharacteristic
145C2×C4×C9C2×D411yescharacteristic
146C2×C4×C9#4111yescharacteristic
147C2×C4×C9C2411yescharacteristic
148C2×Dic9—22no—
149C2×Dic9—41no—
150C2×Dic9—41no—
151Dic18—22no—
152Dic18—22no—
153Dic18—41no—
154Dic18—41no—
155C8×C9—22no—
156C9⋊C8—22no—
157C9⋊C8—22no—
158C9⋊C8C2×D414yes—
159#575D911yescharacteristic
160C2×#137—91no—
161C2×#137—91no—
162#568—91no—
163#473—94no—
164#471—94no—
165#430—91no—
166#413—91no—
167C2×#101—91no—
168C3×#41—21no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41#6712yes—
175C3×#41C22×D312yes—
176C2×C3×Q8#6711yescharacteristic
177C2×C3×Q8C22×D311yescharacteristic
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4#6711yescharacteristic
181C2×C3×D4C22×D311yescharacteristic
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—61no—
186C2×Dic6—32no—
187C2×Dic6—61no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×Dic6—61no—
192C3×Q16—22no—
193C3×SD16—22no—
194C3×SD16—22no—
195C3×D8—22no—
196C3×M16—21no—
197C3×M16C22×D312yes—
198C2×C3×C8—21no—
199#216—64no—
200#216—64no—
201#214—64no—
202#214—64no—
203#208—32no—
204#208—32no—
205#208—32no—
206#208—32no—
207#208—64no—
208#208—61no—
209#208—61no—
210C2×C3⋊C8—32no—
211C2×C3⋊C8—64no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C22×C9—22no—
215C22×C9—41no—
216C22×C9—41no—
217C22×C9—81no—
218C22×C9—81no—
219C22×C9#12111yescharacteristic
220C22×C9#12111yescharacteristic
221C22×C9C2×#4111yescharacteristic
222C4×C9—22no—
223C4×C9—41no—
224C4×C9#12111yescharacteristic
225C4×C9#12111yescharacteristic
226C4×C9C22×D411yescharacteristic
227C4×C9C22×D411yescharacteristic
228Dic9—42no—
229C2×#41C2×D911yescharacteristic
230C2×#41C2×D911yescharacteristic
231C22×Q8—91no—
232#137—21no—
233#137—94no—
234#137—182no—
235#137—182no—
236#137—182no—
237#137C2×D912yes—
238AGL(1,ℤ/8)—21no—
239AGL(1,ℤ/8)C2×D912yes—
240#135—22no—
241C2×Q16—92no—
242C2×Q16—181no—
243C2×SD16—92no—
244C2×SD16—181no—
245#131—94no—
246#131—182no—
247C2×M16—91no—
248C2×M16—91no—
249C2×M16—91no—
250C2×M16—182no—
251C2×M16C2×D911yescharacteristic
252#108—94no—
253#101—92no—
254#101—94no—
255#100—92no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3#23711yescharacteristic
259C3×Q8—21no—
260C3×Q8—21no—
261C3×Q8—21no—
262C3×Q8C2×#6712yes—
263C3×D4—22no—
264C3×D4—22no—
265C3×D4—21no—
266C3×D4—21no—
267C3×D4—21no—
268C3×D4—41no—
269C3×D4—41no—
270C3×D4C2×#6712yes—
271C2×C3×C4—21no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4#23711yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×C3×C4C23×D311yescharacteristic
283C2×Dic3—62no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286Dic6—62no—
287Dic6—62no—
288Dic6—121no—
289Dic6—121no—
290C3×C8—22no—
291C3⋊C8—34no—
292C3⋊C8—62no—
293C3⋊C8—62no—
294C2×C9—21no—
295C2×C9—21no—
296C2×C9—21no—
297C2×C9—42no—
298C2×C9—81no—
299C2×C9C2×#12111yescharacteristic
300#41—21no—
301#41—21no—
302#41—21no—
303#41—21no—
304#41—21no—
305#41—21no—
306#41#61112yes—
307#41C22×D912yes—
308C2×Q8—92no—
309C2×Q8—181no—
310C2×Q8—181no—
311C2×Q8—181no—
312C2×Q8—181no—
313C2×Q8—181no—
314C2×Q8#61111yescharacteristic
315C2×Q8C22×D911yescharacteristic
316C2×D4—21no—
317C2×D4—21no—
318C2×D4#61111yescharacteristic
319C2×D4C22×D911yescharacteristic
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—181no—
323C22×C4C22×D911yescharacteristic
324Q16—22no—
325Q16—184no—
326Q16—184no—
327SD16—22no—
328SD16—22no—
329SD16—184no—
330SD16—184no—
331D8—22no—
332M16—21no—
333M16—92no—
334M16—92no—
335M16—92no—
336M16—92no—
337M16—184no—
338M16—181no—
339M16—181no—
340M16C22×D912yes—
341C2×C8—21no—
342C2×C8—92no—
343C2×C8—184no—
344C2×C8—181no—
345C2×C8—181no—
346C22×C3—22no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—81no—
350C22×C3—81no—
351C22×C3#93911yescharacteristic
352C22×C3#93911yescharacteristic
353C22×C3C2×#23711yescharacteristic
354C3×C4—22no—
355C3×C4—41no—
356C3×C4#93911yescharacteristic
357C3×C4#93911yescharacteristic
358C3×C4C2×D3×D411yescharacteristic
359C3×C4C22×#6711yescharacteristic
360Dic3—122no—
361C9#306911yescharacteristic, complemented, Sylow
362C23—21no—
363C23—21no—
364C23#369911yescharacteristic
365Q8—21no—
366Q8—21no—
367Q8—21no—
368Q8—182no—
369Q8—182no—
370Q8—361no—
371Q8—361no—
372Q8C2×#61112yes—
373D4—22no—
374D4—22no—
375D4—21no—
376D4—21no—
377D4—21no—
378D4—41no—
379D4—41no—
380D4C2×#61112yes—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—182no—
388C2×C4—361no—
389C2×C4—361no—
390C2×C4D4×D911yescharacteristic
391C2×C4D4×D911yescharacteristic
392C2×C4#369911yescharacteristic
393C2×C4C2×#61111yescharacteristic
394C2×C4C2×#61111yescharacteristic
395C2×C4C23×D911yescharacteristic
396C8—22no—
397C8—94no—
398C8—182no—
399C8—182no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—42no—
404C2×C3—81no—
405C2×C3C2×#93911yescharacteristic
406C22—22no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22#6350111yescharacteristic
412C22#6350111yescharacteristic
413C22C2×#369911yescharacteristic
414C4—22no—
415C4—41no—
416C4—362no—
417C4#6350111yescharacteristic
418C4#6350111yescharacteristic
419C4C2×D4×D911yescharacteristic
420C4C22×#61111yescharacteristic
421C3#8400311yescharacteristic
422C2—21no—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—81no—
427C2C2×#6350111yescharacteristic
subgroupG/H
centerC2C2×#63501
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#575C2
socleC2×C3C2×#939
prime radicalC3×#575D3
hypercenter#575D9
hypocenterC9#3069
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
2. C2×#63511C2semidirect
3. C2×#63511C2semidirect
4. #10589921C2semidirect
5. #10588915C2semidirect
6. #10588882C2semidirect
7. #10588878C2semidirect
8. C2×#63382C2semidirect
9. #10588799C2semidirect
27. C2×#3674C22semidirect
29. C2×#3672C22semidirect
34. #63394C22semidirect
35. #63391C22semidirect
36. #63382C22semidirect
37. #63381C22semidirect
361. C9#3069semidirect

Maximal subgroups

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

subgroupindex
C9×#5752
C2×#635112
#105899212
#105889152
#105888822
#105888782
C2×#633822
#105887992
#840033