Finite Group Databasebeta

← #3489⋊C9 #11919743

Subgroups — #3489⋊C9 #11919743

Order 1152.

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

normal subgroups only

This group has 680 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⋊C9C211yesmaximal, characteristic, complemented
2C22×#41⋊C9C211yesmaximal, characteristic, complemented
3D4×Q8⋊C9C212yesmaximal, complemented
4#548⋊C9C212yesmaximal, complemented
5#520⋊C9C211yesmaximal, characteristic, complemented
6C3×#3489C311yesmaximal, characteristic
72−1+4⋊C9—22no—
8C2×#41⋊C9—22no—
9C2×#41⋊C9C2211yescharacteristic
10C2×#41⋊C9C2211yescharacteristic
11C22×Q8⋊C9C2211yescharacteristic
12C22×Q8⋊C9C2212yescomplemented
13C9×#121—41nomaximal
14C4×Q8⋊C9C2212yescomplemented
15C2×C3×2−1+4C2×C311yescharacteristic
16C22×C3×#41C2×C311yescharacteristic
17C3×D4×Q8C2×C312yes—
18C3×#548C2×C312yes—
19C3×#547—32no—
20C3×#546—32no—
21C3×#537—31no—
22C3×#536—31no—
23C3×#525—31no—
24C2×C3×C22⋊Q8—31no—
25C3×#520C2×C311yescharacteristic
26C2×D4×C9—41no—
27C2×D4×C9—42no—
28C22×C4×C9—41no—
29#41⋊C9—21no—
30#41⋊C9D412yescomplemented
31C2×Q8⋊C9—21no—
32C2×Q8⋊C9—22no—
33C2×Q8⋊C9C2311yescharacteristic
34C9×C4⋊C4—41no—
35C9×C22⋊C4—42no—
36#3489C911yescharacteristic, complemented, Sylow
37C3×2−1+4—22no—
38C3×2−1+4—62no—
39C2×C3×#41—22no—
40C2×C3×#41—31no—
41C2×C3×#41—32no—
42C2×C3×#41—31no—
43C2×C3×#41—31no—
44C2×C3×#41—62no—
45C2×C3×#41C22×C311yescharacteristic
46C2×C3×#41C22×C311yescharacteristic
47C22×C3×Q8—31no—
48C22×C3×Q8C22×C311yescharacteristic
49C22×C3×Q8C22×C312yes—
50C22×C3×D4—31no—
51C23×C3×C4—31no—
52C3×C4⋊Q8—32no—
53C3×#124—32no—
54C3×#123—34no—
55C3×#123—32no—
56C3×C22⋊Q8—32no—
57C3×C22⋊Q8—31no—
58C3×C22⋊Q8—31no—
59C3×C22⋊Q8—32no—
60C3×C22⋊Q8—32no—
61C3×C22⋊Q8—32no—
62C3×#121—32no—
63C3×#121—34no—
64C3×#121—31no—
65C3×#121A411yescharacteristic
66C3×#120—32no—
67C3×C4×Q8C22×C312yes—
68C3×C4×D4—32no—
69C3×C4×D4—32no—
70C3×C4×D4—32no—
71C3×#117—31no—
72C2×C3×C4⋊C4—32no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C22⋊C4—32no—
75C23×C9—41no—
76C23×C9—42no—
77D4×C9—82no—
78D4×C9—84no—
79C2×C4×C9—41no—
80C2×C4×C9—41no—
81C2×C4×C9—42no—
82C2×C4×C9—82no—
83Q8⋊C9C2×D411yescharacteristic
84C2×2−1+4C2×C911yescharacteristic, complemented
85C22×#41C2×C911yescharacteristic, complemented
86D4×Q8C2×C912yescomplemented
87#548C2×C912yescomplemented
88#547—32no—
89#546—32no—
90#537—31no—
91#536—31no—
92#525—31no—
93C2×C22⋊Q8—31no—
94#520C2×C911yescharacteristic, complemented
95C24×C3—31no—
96C3×#41—21no—
97C3×#41—32no—
98C3×#41—62no—
99C3×#41—62no—
100C3×#41—62no—
101C3×#41—62no—
102C3×#41—62no—
103C3×#41—64no—
104C3×#41—64no—
105C3×#41—62no—
106C3×#41—61no—
107C3×#41C3×D412yes—
108C2×C3×Q8—21no—
109C2×C3×Q8—22no—
110C2×C3×Q8—31no—
111C2×C3×Q8—32no—
112C2×C3×Q8—31no—
113C2×C3×Q8—62no—
114C2×C3×Q8—62no—
115C2×C3×Q8—61no—
116C2×C3×Q8—62no—
117C2×C3×Q8C23×C311yescharacteristic
118C2×C3×D4—31no—
119C2×C3×D4—31no—
120C2×C3×D4—32no—
121C2×C3×D4—32no—
122C2×C3×D4—32no—
123C2×C3×D4—62no—
124C2×C3×D4—62no—
125C2×C3×D4C2×A412yes—
126C2×C3×D4C2×A411yescharacteristic
127C22×C3×C4—31no—
128C22×C3×C4—32no—
129C22×C3×C4—32no—
130C22×C3×C4—31no—
131C22×C3×C4—32no—
132C22×C3×C4—31no—
133C22×C3×C4—31no—
134C22×C3×C4—31no—
135C22×C3×C4—62no—
136C22×C3×C4—62no—
137C22×C3×C4C2×A411yescharacteristic
138C3×C4⋊C4—32no—
139C3×C4⋊C4—34no—
140C3×C4⋊C4—32no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—32no—
143C3×C4⋊C4C2×A411yescharacteristic
144C3×C22⋊C4—34no—
145C3×C22⋊C4—32no—
146C3×C22⋊C4—32no—
147C3×C22⋊C4—32no—
148C3×C22⋊C4—32no—
149C3×C22⋊C4C2×A412yes—
150C3×C42—32no—
151C22×C9—42no—
152C22×C9—41no—
153C22×C9—81no—
154C22×C9—81no—
155C22×C9—82no—
156C22×C9—82no—
157C22×C9—82no—
158C4×C9—42no—
159C4×C9—81no—
160C4×C9—82no—
1612−1+4—22no—
1622−1+4—62no—
163C2×#41—22no—
164C2×#41—31no—
165C2×#41—32no—
166C2×#41—31no—
167C2×#41—31no—
168C2×#41—62no—
169C2×#41C22×C911yescharacteristic
170C2×#41C22×C911yescharacteristic
171C22×Q8—31no—
172C22×Q8C22×C912yes—
173C22×Q8C22×C911yescharacteristic
174C22×D4—31no—
175C23×C4—31no—
176C4⋊Q8—32no—
177#124—32no—
178#123—34no—
179#123—32no—
180C22⋊Q8—32no—
181C22⋊Q8—31no—
182C22⋊Q8—31no—
183C22⋊Q8—32no—
184C22⋊Q8—32no—
185C22⋊Q8—32no—
186#121—32no—
187#121—34no—
188#121—31no—
189#121C22⋊C911yescharacteristic
190#120—32no—
191C4×Q8C22×C912yes—
192C4×D4—32no—
193C4×D4—32no—
194C4×D4—32no—
195#117—31no—
196C2×C4⋊C4—32no—
197C2×C4⋊C4—31no—
198C2×C22⋊C4—32no—
199C23×C3—31no—
200C23×C3—31no—
201C23×C3—62no—
202C23×C3—62no—
203C23×C3—121no—
204C23×C3C22×A412yes—
205C23×C3C22×A411yescharacteristic
206C3×Q8—31no—
207C3×Q8—62no—
208C3×Q8—61no—
209C3×Q8—62no—
210C3×Q8—61no—
211C3×Q8—62no—
212C3×Q8C2×C3×D411yescharacteristic
213C3×D4—24no—
214C3×D4—22no—
215C3×D4—32no—
216C3×D4—32no—
217C3×D4—61no—
218C3×D4—61no—
219C3×D4—64no—
220C3×D4—64no—
221C3×D4—122no—
222C2×C3×C4—22no—
223C2×C3×C4—31no—
224C2×C3×C4—32no—
225C2×C3×C4—32no—
226C2×C3×C4—32no—
227C2×C3×C4—32no—
228C2×C3×C4—31no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—62no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4—62no—
235C2×C3×C4—62no—
236C2×C3×C4—64no—
237C2×C3×C4—62no—
238C2×C3×C4—122no—
239C2×C3×C4C22×A412yes—
240C2×C3×C4C22×A411yescharacteristic
241C2×C3×C4C22×A411yescharacteristic
242C2×C9—41no—
243C2×C9—41no—
244C2×C9—41no—
245C2×C9—82no—
246C2×C9—162no—
247C24—31no—
248#41—21no—
249#41—32no—
250#41—62no—
251#41—62no—
252#41—62no—
253#41—62no—
254#41—62no—
255#41—64no—
256#41—64no—
257#41—62no—
258#41—61no—
259#41D4×C912yescomplemented
260C2×Q8—21no—
261C2×Q8—22no—
262C2×Q8—31no—
263C2×Q8—32no—
264C2×Q8—31no—
265C2×Q8—62no—
266C2×Q8—62no—
267C2×Q8—61no—
268C2×Q8—62no—
269C2×Q8C23×C911yescharacteristic
270C2×D4—31no—
271C2×D4—31no—
272C2×D4—32no—
273C2×D4—32no—
274C2×D4—32no—
275C2×D4—62no—
276C2×D4—62no—
277C2×D4C2×C22⋊C912yes—
278C2×D4C2×C22⋊C911yescharacteristic
279C22×C4—31no—
280C22×C4—32no—
281C22×C4—32no—
282C22×C4—31no—
283C22×C4—32no—
284C22×C4—31no—
285C22×C4—31no—
286C22×C4—31no—
287C22×C4—62no—
288C22×C4—62no—
289C22×C4C2×C22⋊C911yescharacteristic
290C4⋊C4—32no—
291C4⋊C4—34no—
292C4⋊C4—32no—
293C4⋊C4—31no—
294C4⋊C4—32no—
295C4⋊C4C2×C22⋊C911yescharacteristic
296C22⋊C4—34no—
297C22⋊C4—32no—
298C22⋊C4—32no—
299C22⋊C4—32no—
300C22⋊C4—32no—
301C22⋊C4C2×C22⋊C912yes—
302C42—32no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—32no—
309C22×C3—61no—
310C22×C3—61no—
311C22×C3—61no—
312C22×C3—61no—
313C22×C3—61no—
314C22×C3—124no—
315C22×C32−1+4⋊C312yes—
316C22×C3C23×A411yescharacteristic
317C3×C4—21no—
318C3×C4—22no—
319C3×C4—31no—
320C3×C4—31no—
321C3×C4—61no—
322C3×C4—62no—
323C3×C4—62no—
324C3×C4D4×A412yes—
325C9—41noSylow
326C23—31no—
327C23—31no—
328C23—62no—
329C23—62no—
330C23—121no—
331C23C22×C22⋊C912yes—
332C23C22×C22⋊C911yescharacteristic
333Q8—31no—
334Q8—62no—
335Q8—61no—
336Q8—62no—
337Q8—61no—
338Q8—62no—
339Q8C2×D4×C911yescharacteristic
340D4—24no—
341D4—22no—
342D4—32no—
343D4—32no—
344D4—61no—
345D4—61no—
346D4—64no—
347D4—64no—
348D4—122no—
349C2×C4—22no—
350C2×C4—31no—
351C2×C4—32no—
352C2×C4—32no—
353C2×C4—32no—
354C2×C4—32no—
355C2×C4—31no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—62no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—64no—
364C2×C4—62no—
365C2×C4—122no—
366C2×C4C22×C22⋊C912yes—
367C2×C4C22×C22⋊C911yescharacteristic
368C2×C4C22×C22⋊C911yescharacteristic
369C2×C3—22no—
370C2×C3—42no—
371C2×C3—62no—
372C2×C3—121no—
373C2×C3C2×D4×A411yescharacteristic
374C2×C3C2×2−1+4⋊C311yescharacteristic
375C2×C3#594511yescharacteristic
376C22—21no—
377C22—21no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—32no—
382C22—61no—
383C22—61no—
384C22—61no—
385C22—61no—
386C22—61no—
387C22—124no—
388C222−1+4⋊C912yescomplemented
389C22C23×C22⋊C911yescharacteristic
390C4—21no—
391C4—22no—
392C4—31no—
393C4—31no—
394C4—61no—
395C4—62no—
396C4—62no—
397C4D4×C22⋊C912yes—
398C3#3489⋊C311yescharacteristic
399C2—22no—
400C2—42no—
401C2—62no—
402C2—121no—
403C2C2×D4×C22⋊C911yescharacteristic
404C2C2×2−1+4⋊C911yescharacteristic
405C2#1059312011yescharacteristic
subgroupG/H
center, Frattini, socleC22×C3C23×A4
commutatorC2×Q8C23×C9
Fitting, prime radicalC3×#3489C3
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. C22×#41⋊C9C2semidirect
3. D4×Q8⋊C9C2semidirect
4. #548⋊C9C2semidirect
5. #520⋊C9C2semidirect
12. C22×Q8⋊C9C22semidirect
14. C4×Q8⋊C9C22semidirect
30. #41⋊C9D4semidirect
36. #3489C9semidirect
84. C2×2−1+4C2×C9semidirect
85. C22×#41C2×C9semidirect
86. D4×Q8C2×C9semidirect
87. #548C2×C9semidirect
94. #520C2×C9semidirect
259. #41D4×C9semidirect
388. C222−1+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
C22×#41⋊C92
D4×Q8⋊C92
#548⋊C92
#520⋊C92
C3×#34893
C9×#1214