Finite Group Databasebeta

← C2×#577⋊C9 #11919801

Subgroups — C2×#577⋊C9 #11919801

Order 1152.

629 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 629 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4⋊C9C211yesmaximal, characteristic, complemented
2C2×#63700C211yesmaximal, characteristic, complemented
3#577⋊C9C214yesmaximal, direct product factor
4C2×#131⋊C9C211yesmaximal, characteristic, complemented
5C2×C3×#577C311yesmaximal, characteristic
62−1+4⋊C9—21no—
72−1+4⋊C9C2212yescomplemented
8#63700—21no—
9#63700C2212yescomplemented
10C2×#41⋊C9—21no—
11C2×#41⋊C9C2211yescharacteristic
12C22×Q8⋊C9—21no—
13C2×C9×SD16—41nomaximal
14#131⋊C9C2212yescomplemented
15C2×C3×2−1+4C2×C311yescharacteristic
16C2×C3×H(5,𝔽2)C2×C311yescharacteristic
17C3×#577—34no—
18C3×#577C2×C314yes—
19C2×C3×#137—31no—
20C2×C3×AGL(1,ℤ/8)—31no—
21C2×C3×#135—31no—
22C22×C3×SD16—31no—
23C2×C3×#131C2×C311yescharacteristic
24C2×Q8×C9—41no—
25C2×D4×C9—41no—
26#41⋊C9—22no—
27#41⋊C9D411yescharacteristic
28#41⋊C9C2311yescharacteristic
29C2×Q8⋊C9—22no—
30C2×Q8⋊C9D411yescharacteristic
31C9×SD16—44no—
32C2×C8×C9—41no—
33C2×#577C911yescharacteristic, complemented, Sylow
34C3×2−1+4—21no—
35C3×2−1+4—32no—
36C3×2−1+4—61no—
37C3×2−1+4C22×C312yes—
38C3×H(5,𝔽2)—21no—
39C3×H(5,𝔽2)—32no—
40C3×H(5,𝔽2)—61no—
41C3×H(5,𝔽2)C22×C312yes—
42C2×C3×#41—21no—
43C2×C3×#41—31no—
44C2×C3×#41—31no—
45C2×C3×#41—61no—
46C2×C3×#41C22×C311yescharacteristic
47C22×C3×Q8—21no—
48C22×C3×Q8—31no—
49C22×C3×D4—31no—
50C22×C3×D4—61no—
51C3×#137—34no—
52C3×#137—34no—
53C3×AGL(1,ℤ/8)—34no—
54C3×AGL(1,ℤ/8)—34no—
55C3×#135—34no—
56C3×#135—34no—
57C2×C3×Q16—31no—
58C2×C3×SD16—32no—
59C2×C3×SD16—34no—
60C2×C3×SD16—34no—
61C2×C3×SD16—31no—
62C2×C3×SD16A411yescharacteristic
63C2×C3×D8—31no—
64C3×#131—32no—
65C3×#131C22×C312yes—
66C2×C3×M16—31no—
67C22×C3×C8—31no—
68C23×C9—81no—
69Q8×C9—42no—
70Q8×C9—81no—
71D4×C9—42no—
72D4×C9—81no—
73C2×C4×C9—41no—
74C2×C4×C9—81no—
75Q8⋊C9C2×D411yescharacteristic
76C8×C9—42no—
77C2×2−1+4C2×C911yescharacteristic
78C2×H(5,𝔽2)C2×C911yescharacteristic, complemented
79#577—34no—
80#577C2×C914yescomplemented
81C2×#137—31no—
82C2×AGL(1,ℤ/8)—31no—
83C2×#135—31no—
84C22×SD16—31no—
85C2×#131C2×C911yescharacteristic, complemented
86C24×C3—61no—
87C3×#41—22no—
88C3×#41—31no—
89C3×#41—31no—
90C3×#41—32no—
91C3×#41—32no—
92C3×#41—32no—
93C3×#41—32no—
94C3×#41—61no—
95C3×#41—61no—
96C3×#41—61no—
97C3×#41—61no—
98C3×#41—64no—
99C3×#41—62no—
100C3×#41—62no—
101C3×#41—62no—
102C3×#41C3×D411yescharacteristic
103C3×#41C23×C311yescharacteristic
104C2×C3×Q8—22no—
105C2×C3×Q8—32no—
106C2×C3×Q8—32no—
107C2×C3×Q8—31no—
108C2×C3×Q8—61no—
109C2×C3×Q8—61no—
110C2×C3×Q8—61no—
111C2×C3×Q8—62no—
112C2×C3×Q8C3×D411yescharacteristic
113C2×C3×Q8C2×A411yescharacteristic
114C2×C3×D4—31no—
115C2×C3×D4—32no—
116C2×C3×D4—32no—
117C2×C3×D4—31no—
118C2×C3×D4—61no—
119C2×C3×D4—61no—
120C2×C3×D4—61no—
121C2×C3×D4—61no—
122C2×C3×D4—64no—
123C2×C3×D4—62no—
124C2×C3×D4—62no—
125C2×C3×D4—61no—
126C2×C3×D4C2×A411yescharacteristic
127C22×C3×C4—31no—
128C22×C3×C4—61no—
129C22×C3×C4—61no—
130C22×C3×C4—61no—
131C3×Q16—34no—
132C3×SD16—38no—
133C3×SD16—34no—
134C3×SD16C2×A414yes—
135C3×D8—34no—
136C3×M16—32no—
137C3×M16—32no—
138C2×C3×C8—31no—
139C2×C3×C8—32no—
140C2×C3×C8—32no—
141C2×C3×C8C2×A411yescharacteristic
142C22×C9—41no—
143C22×C9—82no—
144C22×C9—162no—
145C4×C9—41no—
146C4×C9—41no—
147C4×C9—82no—
1482−1+4—21no—
1492−1+4—32no—
1502−1+4—61no—
1512−1+4C22×C912yes—
152H(5,𝔽2)—21no—
153H(5,𝔽2)—32no—
154H(5,𝔽2)—61no—
155H(5,𝔽2)C22×C912yescomplemented
156C2×#41—21no—
157C2×#41—31no—
158C2×#41—31no—
159C2×#41—61no—
160C2×#41C22×C911yescharacteristic
161C22×Q8—21no—
162C22×Q8—31no—
163C22×D4—31no—
164C22×D4—61no—
165#137—34no—
166#137—34no—
167AGL(1,ℤ/8)—34no—
168AGL(1,ℤ/8)—34no—
169#135—34no—
170#135—34no—
171C2×Q16—31no—
172C2×SD16—32no—
173C2×SD16—34no—
174C2×SD16—34no—
175C2×SD16—31no—
176C2×SD16C22⋊C911yescharacteristic
177C2×D8—31no—
178#131—32no—
179#131C22×C912yescomplemented
180C2×M16—31no—
181C22×C8—31no—
182C23×C3—21no—
183C23×C3—31no—
184C23×C3—62no—
185C23×C3—62no—
186C23×C3—61no—
187C23×C3—242no—
188C3×Q8—21no—
189C3×Q8—31no—
190C3×Q8—32no—
191C3×Q8—62no—
192C3×Q8—62no—
193C3×Q8—61no—
194C3×Q8C2×C3×D411yescharacteristic
195C3×Q8C22×A412yes—
196C3×D4—21no—
197C3×D4—31no—
198C3×D4—31no—
199C3×D4—32no—
200C3×D4—32no—
201C3×D4—62no—
202C3×D4—62no—
203C3×D4—62no—
204C3×D4—62no—
205C3×D4—62no—
206C3×D4—62no—
207C3×D4—61no—
208C3×D4C22×A412yes—
209C2×C3×C4—21no—
210C2×C3×C4—31no—
211C2×C3×C4—31no—
212C2×C3×C4—31no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—62no—
218C2×C3×C4—62no—
219C2×C3×C4—62no—
220C2×C3×C4—61no—
221C2×C3×C4—62no—
222C2×C3×C4C22×A411yescharacteristic
223C3×C8—32no—
224C3×C8C22×A412yes—
225C2×C9—41no—
226C2×C9—42no—
227C2×C9—162no—
228C24—61no—
229#41—22no—
230#41—31no—
231#41—31no—
232#41—32no—
233#41—32no—
234#41—32no—
235#41—32no—
236#41—61no—
237#41—61no—
238#41—61no—
239#41—61no—
240#41—64no—
241#41—62no—
242#41—62no—
243#41—62no—
244#41D4×C911yescharacteristic
245#41C23×C911yescharacteristic
246C2×Q8—22no—
247C2×Q8—32no—
248C2×Q8—32no—
249C2×Q8—31no—
250C2×Q8—61no—
251C2×Q8—61no—
252C2×Q8—61no—
253C2×Q8—62no—
254C2×Q8D4×C911yescharacteristic
255C2×Q8C2×C22⋊C911yescharacteristic
256C2×D4—31no—
257C2×D4—32no—
258C2×D4—32no—
259C2×D4—31no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4—61no—
263C2×D4—61no—
264C2×D4—64no—
265C2×D4—62no—
266C2×D4—62no—
267C2×D4—61no—
268C2×D4C2×C22⋊C911yescharacteristic
269C22×C4—31no—
270C22×C4—61no—
271C22×C4—61no—
272C22×C4—61no—
273Q16—34no—
274SD16—38no—
275SD16—34no—
276SD16C2×C22⋊C914yes—
277D8—34no—
278M16—32no—
279M16—32no—
280C2×C8—31no—
281C2×C8—32no—
282C2×C8—32no—
283C2×C8C2×C22⋊C911yescharacteristic
284C22×C3—22no—
285C22×C3—31no—
286C22×C3—31no—
287C22×C3—42no—
288C22×C3—62no—
289C22×C3—62no—
290C22×C3—122no—
291C22×C3—242no—
292C22×C3—242no—
293C22×C3D4×A411yescharacteristic
294C3×C4—22no—
295C3×C4—31no—
296C3×C4—31no—
297C3×C4—62no—
298C3×C4D4×A411yescharacteristic
299C3×C4C23×A411yescharacteristic
300C9—41noSylow
301C23—21no—
302C23—31no—
303C23—62no—
304C23—62no—
305C23—61no—
306C23—242no—
307Q8—21no—
308Q8—31no—
309Q8—32no—
310Q8—62no—
311Q8—62no—
312Q8—61no—
313Q8C2×D4×C911yescharacteristic
314Q8C22×C22⋊C912yes—
315D4—21no—
316D4—31no—
317D4—31no—
318D4—32no—
319D4—32no—
320D4—62no—
321D4—62no—
322D4—62no—
323D4—62no—
324D4—62no—
325D4—62no—
326D4—61no—
327D4C22×C22⋊C912yes—
328C2×C4—21no—
329C2×C4—31no—
330C2×C4—31no—
331C2×C4—31no—
332C2×C4—31no—
333C2×C4—31no—
334C2×C4—62no—
335C2×C4—62no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—61no—
340C2×C4—62no—
341C2×C4C22×C22⋊C911yescharacteristic
342C8—32no—
343C8C22×C22⋊C912yes—
344C2×C3—42no—
345C2×C3—61no—
346C2×C3—61no—
347C2×C3—122no—
348C2×C3#577⋊C312yes—
349C2×C3C2×D4×A411yescharacteristic
350C22—22no—
351C22—31no—
352C22—31no—
353C22—42no—
354C22—62no—
355C22—62no—
356C22—122no—
357C22—242no—
358C22—242no—
359C22D4×C22⋊C911yescharacteristic
360C4—22no—
361C4—31no—
362C4—31no—
363C4—62no—
364C4D4×C22⋊C911yescharacteristic
365C4C23×C22⋊C911yescharacteristic
366C3C2×#577⋊C311yescharacteristic
367C2—42no—
368C2—61no—
369C2—61no—
370C2—122no—
371C2#577⋊C912yesdirect product factor
372C2C2×D4×C22⋊C911yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutator#41C23×C9
FrattiniC3×C4C23×A4
Fitting, prime radicalC2×C3×#577C3
cosocleC3×#41C23×C3
hypercenterC2×C3×SD16A4
hypocenterQ8C2×D4×C9
LCSG ▷ #41 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×SD16

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4⋊C9C2semidirect
2. C2×#63700C2semidirect
3. #577⋊C9C2direct (N × H)
4. C2×#131⋊C9C2semidirect
7. 2−1+4⋊C9C22semidirect
9. #63700C22semidirect
14. #131⋊C9C22semidirect
33. C2×#577C9semidirect
78. C2×H(5,𝔽2)C2×C9semidirect
80. #577C2×C9semidirect
85. C2×#131C2×C9semidirect
155. H(5,𝔽2)C22×C9semidirect
179. #131C22×C9semidirect
371. C2#577⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×2−1+4⋊C92
C2×#637002
#577⋊C92
C2×#131⋊C92
C2×C3×#5773
C2×C9×SD164