Finite Group Databasebeta

← #11868162

Subgroups — #11868162

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×#568C211yesmaximal, characteristic, complemented
2#10589925C211yesmaximal, characteristic
3C2×#63511C211yesmaximal, characteristic, complemented
4C2×#63471C211yesmaximal, characteristic, complemented
5#10588822C214yesmaximal, complemented
6#10588821C214yesmaximal, complemented
7#10588814C211yesmaximal, characteristic, complemented
8C2×#63382C211yesmaximal, characteristic, complemented
9#10588800C211yesmaximal, characteristic, complemented
10#83816—31nomaximal
11C2×C9×#41C2211yescharacteristic
12C2×#3697C2211yescharacteristic
13C22×Dic18C2211yescharacteristic
14C9×#131—22no—
15C9×#131C2214yes—
16C2×C9×M16—22no—
17C2×C9×M16C2211yescharacteristic
18C2×C9×M16C2211yescharacteristic
19#63513—22no—
20#63512C2212yes—
21#63511—22no—
22#63511C2212yes—
23#63511C2214yes—
24#63505—21no—
25C2×#3674—21no—
26#63495—21no—
27C2×#3672—21no—
28C2×#3667C2211yescharacteristic
29C2×#3667C2211yescharacteristic
30#63471—22no—
31#63471—22no—
32C2×#3664C2212yescomplemented
33C2×Dic36C2212yescomplemented
34#63383C2212yescomplemented
35#63382C2214yescomplemented
36#63382C2212yescomplemented
37#63372C2214yescomplemented
38C3×#568D311yescharacteristic
39C2×#951—31no—
40#5822—31no—
41C2×#909—31no—
42#5143—34no—
43#5141—34no—
44C2×#824—31no—
45#5132—31no—
46#5125—31no—
47C9×#41—21no—
48C9×#41—21no—
49C9×#41D412yes—
50C9×#41C2312yes—
51C2×Q8×C9D411yescharacteristic
52C2×D4×C9—21no—
53C2×D4×C9D411yescharacteristic
54C22×C4×C9—21no—
55C22×C4×C9C2311yescharacteristic
56C2×#611—21no—
57C22×Dic9—21no—
58#3697—21no—
59#3697—21no—
60#3697—21no—
61#3697—21no—
62C2×D36C2311yescharacteristic
63C2×C4×D9—21no—
64C2×Dic18—21no—
65C2×Dic18—21no—
66C2×Dic18—21no—
67C2×Dic18—21no—
68C2×Dic18—21no—
69C2×Dic18C2312yes—
70C2×Dic18C2311yescharacteristic
71C9×M16—21no—
72C9×M16—24no—
73C9×M16D412yes—
74C9×M16D412yes—
75C9×M16C2312yes—
76C2×C8×C9—21no—
77C2×C8×C9—24no—
78C2×C8×C9C2312yes—
79#3675—22no—
80#3674—24no—
81#3674—22no—
82#3673—22no—
83#3672—24no—
84#3672—22no—
85#3667—21no—
86#3667—21no—
87#3667C2312yes—
88#3667C2312yes—
89C2×C9⋊C8—21no—
90C2×C9⋊C8—21no—
91#3664—24no—
92Dic36—24no—
93#3069—91noSylow
94C2×C3×#41C2×D311yescharacteristic
95C2×#235—31no—
96C22×Dic6—31no—
97C3×#131—22no—
98C3×#131C2×D314yes—
99C2×C3×M16—22no—
100C2×C3×M16C2×D311yescharacteristic
101C2×C3×M16C2×D311yescharacteristic
102#951—34no—
103#951—32no—
104#951—62no—
105#950—62no—
106#949—32no—
107C2×#216—61no—
108#942—61no—
109C2×#214—61no—
110#932—61no—
111C2×#208—31no—
112C2×#208—31no—
113#909—62no—
114#909—62no—
115C2×Dic12—32no—
116C2×#204—32no—
117#824—32no—
118#824—34no—
119#823—32no—
120#819—34no—
121C23×C9—21no—
122C23×C9#4111yescharacteristic
123C22×D9—21no—
124Q8×C9—21no—
125Q8×C9C2×D412yes—
126D4×C9—22no—
127D4×C9—22no—
128D4×C9—21no—
129D4×C9C2×D412yes—
130C2×C4×C9—21no—
131C2×C4×C9—22no—
132C2×C4×C9—22no—
133C2×C4×C9C2×D411yescharacteristic
134C2×C4×C9C2×D411yescharacteristic
135C2×C4×C9C2×D411yescharacteristic
136C2×C4×C9C2×D411yescharacteristic
137C2×C4×C9#4111yescharacteristic
138C2×C4×C9C2411yescharacteristic
139#611—41no—
140#611—41no—
141C2×Dic9—22no—
142C2×Dic9—21no—
143C2×Dic9—41no—
144C2×Dic9—41no—
145D36—21no—
146D36—21no—
147C4×D9—41no—
148C4×D9—41no—
149Dic18—21no—
150Dic18—22no—
151Dic18—22no—
152Dic18—21no—
153Dic18—41no—
154Dic18—41no—
155C8×C9—22no—
156C8×C9C2×D414yes—
157C9⋊C8—22no—
158C9⋊C8—22no—
159#575—91no—
160C2×#137—91no—
161C2×#137—91no—
162#568D911yescharacteristic, complemented
163#473—94no—
164#471—94no—
165#430—91no—
166#413—91no—
167C2×#101—91no—
168C3×#41—21no—
169C3×#41—21no—
170C3×#41D1212yes—
171C3×#41C22×D312yes—
172C2×C3×Q8D1211yescharacteristic
173C2×C3×D4—21no—
174C2×C3×D4D1211yescharacteristic
175C22×C3×C4—21no—
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—61no—
178C22×Dic3—61no—
179#235—61no—
180#235—61no—
181#235—61no—
182#235—61no—
183C2×D12—31no—
184C2×C4×D3—61no—
185C2×Dic6—32no—
186C2×Dic6—31no—
187C2×Dic6—61no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×Dic6—61no—
192C3×M16—21no—
193C3×M16—24no—
194C3×M16#6712yes—
195C3×M16#6712yes—
196C3×M16C22×D312yes—
197C2×C3×C8—21no—
198C2×C3×C8—24no—
199C2×C3×C8C22×D312yes—
200#216—62no—
201#216—64no—
202#215—62no—
203#214—62no—
204#214—64no—
205#213—62no—
206#208—32no—
207#208—32no—
208#208—61no—
209#208—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212Dic12—64no—
213#204—64no—
214C22×C9—22no—
215C22×C9—41no—
216C22×C9—81no—
217C22×C9#12111yescharacteristic
218C22×C9#12111yescharacteristic
219C22×C9C2×#4111yescharacteristic
220C2×D9—41no—
221C2×D9—81no—
222C4×C9—22no—
223C4×C9#12111yescharacteristic
224C4×C9#12111yescharacteristic
225C4×C9C22×D411yescharacteristic
226C4×C9C22×D411yescharacteristic
227Dic9—42no—
228Dic9—41no—
229C2×#41—91no—
230C2×#41C2×D911yescharacteristic
231C22×Q8—91no—
232#137—94no—
233#137—92no—
234#137—182no—
235#137—181no—
236#137—182no—
237#137—182no—
238AGL(1,ℤ/8)—92no—
239AGL(1,ℤ/8)—181no—
240#135—182no—
241C2×Q16—92no—
242C2×Q16—181no—
243C2×SD16—92no—
244C2×SD16—181no—
245#131—22no—
246#131C2×D914yes—
247C2×M16—22no—
248C2×M16—91no—
249C2×M16—91no—
250C2×M16C2×D911yescharacteristic
251C2×M16C2×D911yescharacteristic
252#108—94no—
253#101—94no—
254#101—92no—
255#100—92no—
256C23×C3—21no—
257C23×C3#23511yescharacteristic
258C22×D3—61no—
259C3×Q8—21no—
260C3×Q8C2×D1212yes—
261C3×D4—22no—
262C3×D4—22no—
263C3×D4—21no—
264C3×D4C2×D1212yes—
265C2×C3×C4—21no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4C2×D1211yescharacteristic
269C2×C3×C4C2×D1211yescharacteristic
270C2×C3×C4#23511yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×C3×C4C23×D311yescharacteristic
274#67—121no—
275#67—121no—
276C2×Dic3—62no—
277C2×Dic3—61no—
278C2×Dic3—121no—
279C2×Dic3—121no—
280D12—61no—
281D12—61no—
282C4×D3—121no—
283C4×D3—121no—
284Dic6—62no—
285Dic6—61no—
286Dic6—62no—
287Dic6—61no—
288Dic6—121no—
289Dic6—121no—
290C3×C8—22no—
291C3×C8C2×#6714yes—
292C3⋊C8—62no—
293C3⋊C8—62no—
294C2×C9—21no—
295C2×C9—21no—
296C2×C9—21no—
297C2×C9—42no—
298C2×C9C2×#12111yescharacteristic
299D9—81no—
300#41—21no—
301#41—21no—
302#41—181no—
303#41—181no—
304#41—181no—
305#41—181no—
306#41D3612yes—
307#41C22×D912yes—
308C2×Q8—92no—
309C2×Q8—91no—
310C2×Q8—181no—
311C2×Q8—181no—
312C2×Q8—181no—
313C2×Q8—181no—
314C2×Q8—181no—
315C2×Q8D3611yescharacteristic
316C2×D4—21no—
317C2×D4—91no—
318C2×D4—181no—
319C2×D4D3611yescharacteristic
320C22×C4—21no—
321C22×C4—181no—
322C22×C4—181no—
323C22×C4C22×D911yescharacteristic
324Q16—184no—
325Q16—182no—
326Q16—184no—
327SD16—182no—
328SD16—184no—
329SD16—182no—
330SD16—184no—
331D8—182no—
332M16—21no—
333M16—24no—
334M16—92no—
335M16—92no—
336M16—181no—
337M16—181no—
338M16#61112yes—
339M16#61112yes—
340M16C22×D912yes—
341C2×C8—21no—
342C2×C8—24no—
343C2×C8—181no—
344C2×C8—181no—
345C2×C8C22×D912yes—
346C22×C3—22no—
347C22×C3—41no—
348C22×C3—81no—
349C22×C3#93011yescharacteristic
350C22×C3#93011yescharacteristic
351C22×C3C2×#23511yescharacteristic
352C2×D3—121no—
353C2×D3—241no—
354C3×C4—22no—
355C3×C4#93011yescharacteristic
356C3×C4#93011yescharacteristic
357C3×C4C22×D1211yescharacteristic
358C3×C4C22×#6711yescharacteristic
359Dic3—122no—
360Dic3—121no—
361C9#306911yescharacteristic, complemented, Sylow
362C23—21no—
363C23—181no—
364C23#369711yescharacteristic
365Q8—21no—
366Q8—182no—
367Q8—181no—
368Q8—182no—
369Q8—181no—
370Q8—361no—
371Q8—361no—
372Q8C2×D3612yes—
373D4—22no—
374D4—22no—
375D4—21no—
376D4—181no—
377D4—181no—
378D4—361no—
379D4—361no—
380D4C2×D3612yes—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—181no—
385C2×C4—182no—
386C2×C4—361no—
387C2×C4—361no—
388C2×C4—361no—
389C2×C4—361no—
390C2×C4C2×D3611yescharacteristic
391C2×C4C2×D3611yescharacteristic
392C2×C4#369711yescharacteristic
393C2×C4C2×#61111yescharacteristic
394C2×C4C2×#61111yescharacteristic
395C2×C4C23×D911yescharacteristic
396C8—22no—
397C8—182no—
398C8—182no—
399C8C2×#61114yes—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—42no—
404C2×C3C2×#93011yescharacteristic
405D3—241no—
406C22—22no—
407C22—41no—
408C22—81no—
409C22—361no—
410C22—721no—
411C22#6349211yescharacteristic
412C22#6349211yescharacteristic
413C22C2×#369711yescharacteristic
414C4—22no—
415C4—361no—
416C4—362no—
417C4#6349211yescharacteristic
418C4#6349211yescharacteristic
419C4C22×D3611yescharacteristic
420C4C22×#61111yescharacteristic
421C3#8381611yescharacteristic
422C2—21no—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—721no—
427C2C2×#6349211yescharacteristic
subgroupG/H
centerC2C2×#63492
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#568C2
socleC2×C3C2×#930
prime radical#10589925C2
hypercenter#568D9
hypocenterC9#3069
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
1. C9×#568C2semidirect
3. C2×#63511C2semidirect
4. C2×#63471C2semidirect
5. #10588822C2semidirect
6. #10588821C2semidirect
7. #10588814C2semidirect
8. C2×#63382C2semidirect
9. #10588800C2semidirect
32. C2×#3664C22semidirect
33. C2×Dic36C22semidirect
34. #63383C22semidirect
35. #63382C22semidirect
36. #63382C22semidirect
37. #63372C22semidirect
162. #568D9semidirect
361. C9#3069semidirect

Maximal subgroups

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

subgroupindex
C9×#5682
#105899252
C2×#635112
C2×#634712
#105888222
#105888212
#105888142
C2×#633822
#105888002
#838163