Finite Group Databasebeta

← #3497⋊C9 #11919745

Subgroups — #3497⋊C9 #11919745

Order 1152.

670 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 105 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⋊C9C212yesmaximal, complemented
2C4⋊(#41⋊C9)C211yesmaximal, characteristic, complemented
3D4×Q8⋊C9C211yesmaximal, characteristic, complemented
4#548⋊C9C212yesmaximal, complemented
5C2×C4×Q8⋊C9C211yesmaximal, characteristic, complemented
6C3×#3497C311yesmaximal, characteristic
72−1+4⋊C9—24no—
8C2×#41⋊C9C2212yes—
9C22×Q8⋊C9C2212yes—
10C22×Q8⋊C9C2211yescharacteristic
11C9×#121—41nomaximal
12C4×Q8⋊C9C2211yescharacteristic
13C4×Q8⋊C9C2211yescharacteristic
14C2×C3×2−1+4C2×C312yes—
15C3×#550—31no—
16C3×#550C2×C311yescharacteristic
17C3×D4×Q8—31no—
18C3×D4×Q8C2×C311yescharacteristic
19C3×#548—32no—
20C3×#548C2×C312yes—
21C3×#537—32no—
22C3×#532—31no—
23C3×#532—31no—
24C2×C3×C4×Q8C2×C311yescharacteristic
25C2×D4×C9—42no—
26C2×D4×C9—41no—
27C22×C4×C9—41no—
28#41⋊C9—22no—
29C2×Q8⋊C9—22no—
30C2×Q8⋊C9D412yescomplemented
31C2×Q8⋊C9C2311yescharacteristic
32C9×C4⋊C4—41no—
33C9×C22⋊C4—42no—
34#3497C911yescharacteristic, complemented, Sylow
35C3×2−1+4—24no—
36C3×2−1+4—64no—
37C2×C3×#41—32no—
38C2×C3×#41—32no—
39C2×C3×#41—32no—
40C2×C3×#41C22×C312yes—
41C22×C3×Q8—32no—
42C22×C3×Q8C22×C312yes—
43C22×C3×Q8C22×C311yescharacteristic
44C3×C4⋊Q8—31no—
45C3×C4⋊Q8—31no—
46C3×#127—31no—
47C3×#127—31no—
48C3×#124—32no—
49C3×#124—32no—
50C3×C22⋊Q8—34no—
51C3×C22⋊Q8—32no—
52C3×C22⋊Q8—32no—
53C3×#121—32no—
54C3×#121—32no—
55C3×#121—34no—
56C3×#121—32no—
57C3×#121—31no—
58C3×#121—32no—
59C3×#121A411yescharacteristic
60C3×C4×Q8—31no—
61C3×C4×Q8—31no—
62C3×C4×Q8C22×C311yescharacteristic
63C3×C4×Q8C22×C311yescharacteristic
64C3×C4×D4—32no—
65C3×C4×D4—32no—
66C3×C4×D4—31no—
67C3×C4×D4—31no—
68C3×C4×D4—32no—
69C2×C3×C4⋊C4—31no—
70C2×C3×C42—31no—
71C23×C9—41no—
72C23×C9—42no—
73D4×C9—82no—
74D4×C9—84no—
75C2×C4×C9—41no—
76C2×C4×C9—41no—
77C2×C4×C9—42no—
78C2×C4×C9—82no—
79Q8⋊C9C2×D411yescharacteristic
80C2×2−1+4C2×C912yescomplemented
81#550—31no—
82#550C2×C911yescharacteristic, complemented
83D4×Q8—31no—
84D4×Q8C2×C911yescharacteristic, complemented
85#548—32no—
86#548C2×C912yescomplemented
87#537—32no—
88#532—31no—
89#532—31no—
90C2×C4×Q8C2×C911yescharacteristic, complemented
91C3×#41—22no—
92C3×#41—64no—
93C3×#41—64no—
94C3×#41—64no—
95C3×#41—64no—
96C3×#41—64no—
97C3×#41—64no—
98C3×#41—62no—
99C2×C3×Q8—22no—
100C2×C3×Q8—32no—
101C2×C3×Q8—31no—
102C2×C3×Q8—32no—
103C2×C3×Q8—32no—
104C2×C3×Q8—64no—
105C2×C3×Q8—64no—
106C2×C3×Q8—62no—
107C2×C3×Q8C3×D412yes—
108C2×C3×Q8C23×C311yescharacteristic
109C2×C3×D4—32no—
110C2×C3×D4—32no—
111C2×C3×D4—32no—
112C2×C3×D4—32no—
113C2×C3×D4—32no—
114C2×C3×D4—31no—
115C2×C3×D4C2×A411yescharacteristic
116C2×C3×D4C2×A412yes—
117C22×C3×C4—31no—
118C22×C3×C4—34no—
119C22×C3×C4—32no—
120C22×C3×C4—31no—
121C22×C3×C4—32no—
122C22×C3×C4C2×A411yescharacteristic
123C3×C4⋊C4—31no—
124C3×C4⋊C4—31no—
125C3×C4⋊C4—32no—
126C3×C4⋊C4—32no—
127C3×C4⋊C4—31no—
128C3×C4⋊C4—32no—
129C3×C4⋊C4C2×A411yescharacteristic
130C3×C22⋊C4—34no—
131C3×C22⋊C4—32no—
132C3×C22⋊C4—32no—
133C3×C22⋊C4—32no—
134C3×C22⋊C4C2×A412yes—
135C3×C42—31no—
136C3×C42—31no—
137C3×C42—31no—
138C3×C42—31no—
139C22×C9—42no—
140C22×C9—41no—
141C22×C9—81no—
142C22×C9—81no—
143C22×C9—82no—
144C22×C9—82no—
145C22×C9—82no—
146C4×C9—42no—
147C4×C9—81no—
148C4×C9—82no—
1492−1+4—24no—
1502−1+4—64no—
151C2×#41—32no—
152C2×#41—32no—
153C2×#41—32no—
154C2×#41C22×C912yes—
155C22×Q8—32no—
156C22×Q8C22×C912yes—
157C22×Q8C22×C911yescharacteristic
158C4⋊Q8—31no—
159C4⋊Q8—31no—
160#127—31no—
161#127—31no—
162#124—32no—
163#124—32no—
164C22⋊Q8—34no—
165C22⋊Q8—32no—
166C22⋊Q8—32no—
167#121—32no—
168#121—32no—
169#121—34no—
170#121—32no—
171#121—31no—
172#121—32no—
173#121C22⋊C911yescharacteristic
174C4×Q8—31no—
175C4×Q8—31no—
176C4×Q8C22×C911yescharacteristic
177C4×Q8C22×C911yescharacteristic
178C4×D4—32no—
179C4×D4—32no—
180C4×D4—31no—
181C4×D4—31no—
182C4×D4—32no—
183C2×C4⋊C4—31no—
184C2×C42—31no—
185C23×C3—32no—
186C23×C3C22×A412yes—
187C23×C3C22×A411yescharacteristic
188C3×Q8—32no—
189C3×Q8—31no—
190C3×Q8—32no—
191C3×Q8—64no—
192C3×Q8—62no—
193C3×Q8—62no—
194C3×Q8C2×C3×D411yescharacteristic
195C3×D4—24no—
196C3×D4—22no—
197C3×D4—64no—
198C3×D4—62no—
199C3×D4—62no—
200C3×D4—64no—
201C3×D4—62no—
202C3×D4—122no—
203C3×D4—122no—
204C2×C3×C4—22no—
205C2×C3×C4—32no—
206C2×C3×C4—32no—
207C2×C3×C4—31no—
208C2×C3×C4—31no—
209C2×C3×C4—31no—
210C2×C3×C4—31no—
211C2×C3×C4—32no—
212C2×C3×C4—62no—
213C2×C3×C4—62no—
214C2×C3×C4—62no—
215C2×C3×C4—62no—
216C2×C3×C4—68no—
217C2×C3×C4—121no—
218C2×C3×C4C22×A411yescharacteristic
219C2×C3×C4C22×A412yes—
220C2×C3×C4C22×A411yescharacteristic
221C2×C9—41no—
222C2×C9—41no—
223C2×C9—41no—
224C2×C9—82no—
225C2×C9—162no—
226#41—22no—
227#41—64no—
228#41—64no—
229#41—64no—
230#41—64no—
231#41—64no—
232#41—64no—
233#41—62no—
234C2×Q8—22no—
235C2×Q8—32no—
236C2×Q8—31no—
237C2×Q8—32no—
238C2×Q8—32no—
239C2×Q8—64no—
240C2×Q8—64no—
241C2×Q8—62no—
242C2×Q8D4×C912yescomplemented
243C2×Q8C23×C911yescharacteristic
244C2×D4—32no—
245C2×D4—32no—
246C2×D4—32no—
247C2×D4—32no—
248C2×D4—32no—
249C2×D4—31no—
250C2×D4C2×C22⋊C911yescharacteristic
251C2×D4C2×C22⋊C912yes—
252C22×C4—31no—
253C22×C4—34no—
254C22×C4—32no—
255C22×C4—31no—
256C22×C4—32no—
257C22×C4C2×C22⋊C911yescharacteristic
258C4⋊C4—31no—
259C4⋊C4—31no—
260C4⋊C4—32no—
261C4⋊C4—32no—
262C4⋊C4—31no—
263C4⋊C4—32no—
264C4⋊C4C2×C22⋊C911yescharacteristic
265C22⋊C4—34no—
266C22⋊C4—32no—
267C22⋊C4—32no—
268C22⋊C4—32no—
269C22⋊C4C2×C22⋊C912yes—
270C42—31no—
271C42—31no—
272C42—31no—
273C42—31no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—62no—
280C22×C3—62no—
281C22×C3—62no—
282C22×C3D4×A412yes—
283C22×C3C23×A411yescharacteristic
284C3×C4—22no—
285C3×C4—21no—
286C3×C4—32no—
287C3×C4—31no—
288C3×C4—31no—
289C3×C4—62no—
290C3×C4—61no—
291C3×C4—61no—
292C3×C42−1+4⋊C312yes—
293C9—41noSylow
294C23—32no—
295C23C22×C22⋊C912yes—
296C23C22×C22⋊C911yescharacteristic
297Q8—32no—
298Q8—31no—
299Q8—32no—
300Q8—64no—
301Q8—62no—
302Q8—62no—
303Q8C2×D4×C911yescharacteristic
304D4—24no—
305D4—22no—
306D4—64no—
307D4—62no—
308D4—62no—
309D4—64no—
310D4—62no—
311D4—122no—
312D4—122no—
313C2×C4—22no—
314C2×C4—31no—
315C2×C4—31no—
316C2×C4—32no—
317C2×C4—32no—
318C2×C4—31no—
319C2×C4—31no—
320C2×C4—32no—
321C2×C4—62no—
322C2×C4—62no—
323C2×C4—62no—
324C2×C4—62no—
325C2×C4—68no—
326C2×C4—121no—
327C2×C4C22×C22⋊C911yescharacteristic
328C2×C4C22×C22⋊C912yes—
329C2×C4C22×C22⋊C911yescharacteristic
330C2×C3—22no—
331C2×C3—42no—
332C2×C3—122no—
333C2×C3C2×D4×A411yescharacteristic
334C2×C3C2×2−1+4⋊C311yescharacteristic
335C2×C3#594511yescharacteristic
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—62no—
342C22—62no—
343C22—62no—
344C22D4×C22⋊C912yes—
345C22C23×C22⋊C911yescharacteristic
346C4—22no—
347C4—21no—
348C4—31no—
349C4—31no—
350C4—32no—
351C4—62no—
352C4—61no—
353C4—61no—
354C42−1+4⋊C912yescomplemented
355C3#3497⋊C311yescharacteristic
356C2—22no—
357C2—42no—
358C2—122no—
359C2C2×D4×C22⋊C911yescharacteristic
360C2C2×2−1+4⋊C911yescharacteristic
361C2#1059312011yescharacteristic
subgroupG/H
center, Frattini, socleC22×C3C23×A4
commutatorC2×Q8C23×C9
Fitting, prime radicalC3×#3497C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×#121A4
hypocenterQ8C2×D4×C9
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C3×#121

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4⋊C9C2semidirect
2. C4⋊(#41⋊C9)C2semidirect
3. D4×Q8⋊C9C2semidirect
4. #548⋊C9C2semidirect
5. C2×C4×Q8⋊C9C2semidirect
30. C2×Q8⋊C9D4semidirect
34. #3497C9semidirect
80. C2×2−1+4C2×C9semidirect
82. #550C2×C9semidirect
84. D4×Q8C2×C9semidirect
86. #548C2×C9semidirect
90. C2×C4×Q8C2×C9semidirect
242. C2×Q8D4×C9semidirect
354. C42−1+4⋊C9semidirect

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
C4⋊(#41⋊C9)2
D4×Q8⋊C92
#548⋊C92
C2×C4×Q8⋊C92
C3×#34973
C9×#1214