Finite Group Databasebeta

← #11790770

Subgroups — #11790770

Order 1152.

540 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589934C211yesmaximal, characteristic
2C2×C9×#104C211yesmaximal, characteristic, complemented
3C2×#63396C211yesmaximal, characteristic, complemented
4C2×#63384C211yesmaximal, characteristic, complemented
5#10588802C211yesmaximal, characteristic, complemented
6C42×Dic9C211yesmaximal, characteristic, complemented
7C2×#63364C211yesmaximal, characteristic, complemented
8#70356—31nomaximal
9C2×C9×#41C2211yescharacteristic
10C2×#3697C2211yescharacteristic
11C2×C9×M16C2211yescharacteristic
12C2×C42×C9C2211yescharacteristic
13#63509C411yescharacteristic, complemented
14#63506C411yescharacteristic, complemented
15#63502C411yescharacteristic, complemented
16#63501—22no—
17#63498C411yescharacteristic, complemented
18C4×#611—22no—
19C2×C4×Dic9—22no—
20C2×C4×Dic9C2211yescharacteristic
21C2×C4×Dic9C2211yescharacteristic
22C2×#3667C2211yescharacteristic
23C9×#104—22no—
24#63396—22no—
25#63384—22no—
26Dic9⋊C8—22no—
27#63364—22no—
28#5832—31no—
29C2×C3×#104D311yescharacteristic
30C2×#837—31no—
31C2×#825—31no—
32#5118—31no—
33C42×Dic3—31no—
34C2×#805—31no—
35C9×#41—21no—
36C9×#41—21no—
37C9×#41—21no—
38C9×#41—21no—
39C2×Q8×C9C2×C411yescharacteristic
40C2×D4×C9—21no—
41C2×D4×C9C2×C411yescharacteristic
42C22×C4×C9—21no—
43C22×C4×C9—21no—
44C22×C4×C9C2311yescharacteristic
45C2×#611—21no—
46C2×#611—22no—
47C22×Dic9—21no—
48C22×Dic9D412yes—
49#3697—21no—
50#3697—21no—
51#3697—21no—
52#3697—21no—
53C2×D36C2×C411yescharacteristic
54C2×C4×D9—21no—
55C2×Dic18C2×C411yescharacteristic
56C9×M16—21no—
57C9×M16—21no—
58C2×C8×C9—21no—
59C42×C9—21no—
60C42×C9D412yescomplemented
61#3676—22no—
62(C2×D9)⋊C4—22no—
63Dic9⋊C4—22no—
64C4×Dic9—28no—
65C4×Dic9—21no—
66C4×Dic9C2×C411yescharacteristic
67C4×Dic9C2×C411yescharacteristic
68C4×Dic9D412yes—
69C4×Dic9D412yescomplemented
70#3667—21no—
71#3667—21no—
72C2×C9⋊C8—21no—
73#1962—91noSylow
74C2×C3×#41C2×D311yescharacteristic
75C2×#235—31no—
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×C42C2×D311yescharacteristic
78#947—31no—
79#944—31no—
80#940—31no—
81#939—62no—
82#936—31no—
83C4×#67—62no—
84C2×C4×Dic3—31no—
85C2×C4×Dic3—31no—
86C2×C4×Dic3—62no—
87C2×#208—31no—
88C3×#104—22no—
89#837—62no—
90#825—62no—
91Dic3⋊C8—62no—
92#805—62no—
93C23×C9—21no—
94C23×C9C2×D411yescharacteristic
95C22×D9—21no—
96Q8×C9—21no—
97Q8×C9—21no—
98D4×C9—21no—
99D4×C9—21no—
100D4×C9—41no—
101D4×C9—41no—
102C2×C4×C9—24no—
103C2×C4×C9—22no—
104C2×C4×C9—21no—
105C2×C4×C9—41no—
106C2×C4×C9—41no—
107C2×C4×C9C22×C411yescharacteristic
108C2×C4×C9C2×D411yescharacteristic
109C2×C4×C9C2×D411yescharacteristic
110C2×C4×C9C2×D411yescharacteristic
111C2×C4×C9#4111yescharacteristic
112C2×C4×C9#4111yescharacteristic
113#611—41no—
114#611—41no—
115#611—44no—
116C2×Dic9—24no—
117C2×Dic9—22no—
118C2×Dic9—24no—
119C2×Dic9—21no—
120C2×Dic9C22⋊C412yes—
121C2×Dic9C22⋊C412yes—
122D36—21no—
123D36—21no—
124C4×D9—41no—
125C4×D9—41no—
126Dic18—21no—
127Dic18—21no—
128C8×C9—41no—
129C9⋊C8—41no—
130#532—91no—
131#423—91no—
132C2×#104—91no—
133C2×#104—91no—
134C2×#104—91no—
135C2×#104D911yescharacteristic, complemented
136C43—91no—
137C3×#41—21no—
138C3×#41—21no—
139C3×#41—21no—
140C3×#41—21no—
141C2×C3×Q8C4×D311yescharacteristic
142C2×C3×D4—21no—
143C2×C3×D4C4×D311yescharacteristic
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4C22×D311yescharacteristic
147C2×#67—62no—
148C2×#67—61no—
149C22×Dic3—32no—
150C22×Dic3—61no—
151#235—61no—
152#235—61no—
153#235—61no—
154#235—61no—
155C2×D12—31no—
156C2×C4×D3—61no—
157C2×Dic6—31no—
158C3×M16—21no—
159C3×M16—21no—
160C2×C3×C8—21no—
161C3×C42—21no—
162C3×C42#6712yes—
163#217—62no—
164(C2×D3)⋊C4—62no—
165Dic3⋊C4—62no—
166C4×Dic3—31no—
167C4×Dic3—31no—
168C4×Dic3—32no—
169C4×Dic3—32no—
170C4×Dic3—68no—
171C4×Dic3—61no—
172#208—61no—
173#208—61no—
174C2×C3⋊C8—61no—
175C22×C9—22no—
176C22×C9—41no—
177C22×C9—42no—
178C22×C9C2×C22⋊C411yescharacteristic
179C22×C9#12111yescharacteristic
180C22×C9#12111yescharacteristic
181C2×D9—41no—
182C2×D9—42no—
183C4×C9—24no—
184C4×C9—41no—
185C4×C9C4×D411yescharacteristic
186C4×C9C4×D411yescharacteristic
187C4×C9#12411yescharacteristic
188C4×C9#12711yescharacteristic
189Dic9—24no—
190Dic9—22no—
191Dic9—41no—
192Dic9#10414yescomplemented
193C2×#41—91no—
194C2×#41C2×D911yescharacteristic
195C2×M16—91no—
196C2×M16C2×D911yescharacteristic
197C4⋊Q8—91no—
198#127—91no—
199#124—91no—
200#124—91no—
201#121—182no—
202C4×D4—182no—
203C2×C42—91no—
204C2×C42—91no—
205C2×C42—182no—
206C2×C42C2×D911yescharacteristic
207C4⋊C8—182no—
208#104—22no—
209#104—182no—
210#104—182no—
211#104—182no—
212C23×C3—21no—
213C23×C3D3×D411yescharacteristic
214C22×D3—61no—
215C3×Q8—21no—
216C3×Q8—21no—
217C3×D4—21no—
218C3×D4—21no—
219C3×D4—41no—
220C3×D4—41no—
221C2×C3×C4—24no—
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4C2×C4×D311yescharacteristic
227C2×C3×C4#23511yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4#23711yescharacteristic
231C2×C3×C4C2×#6711yescharacteristic
232#67—124no—
233#67—121no—
234#67—121no—
235C2×Dic3—32no—
236C2×Dic3—32no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239C2×Dic3—62no—
240C2×Dic3—61no—
241D12—61no—
242D12—61no—
243C4×D3—121no—
244C4×D3—121no—
245Dic6—61no—
246Dic6—61no—
247C3×C8—41no—
248C3⋊C8—121no—
249C2×C9—21no—
250C2×C9—21no—
251C2×C9—81no—
252C2×C9#39011yescharacteristic
253C2×C9C2×#10412yes—
254D9—81no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41—181no—
260#41—181no—
261#41—181no—
262#41—181no—
263C2×Q8—91no—
264C2×Q8C4×D911yescharacteristic
265C2×D4—21no—
266C2×D4—91no—
267C2×D4—182no—
268C2×D4—181no—
269C2×D4C4×D911yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—92no—
273C22×C4—181no—
274C22×C4—181no—
275C22×C4C22×D911yescharacteristic
276M16—21no—
277M16—21no—
278M16—181no—
279M16—181no—
280C2×C8—21no—
281C2×C8—181no—
282C4⋊C4—182no—
283C22⋊C4—182no—
284C22⋊C4—182no—
285C42—21no—
286C42—91no—
287C42—91no—
288C42—92no—
289C42—92no—
290C42—188no—
291C42—181no—
292C42#61112yescomplemented
293C22×C3—22no—
294C22×C3—41no—
295C22×C3—42no—
296C22×C3D3×C22⋊C411yescharacteristic
297C22×C3#88411yescharacteristic
298C22×C3#93911yescharacteristic
299C2×D3—121no—
300C2×D3—122no—
301C3×C4—24no—
302C3×C4—41no—
303C3×C4#67⋊C411yescharacteristic
304C3×C4#88511yescharacteristic
305C3×C4C4×#6711yescharacteristic
306C3×C4#94011yescharacteristic
307Dic3—34no—
308Dic3—64no—
309Dic3—62no—
310Dic3—121no—
311C9#196211yescharacteristic, complemented, Sylow
312C23—21no—
313C23—181no—
314C23D4×D911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—181no—
318Q8—181no—
319D4—21no—
320D4—21no—
321D4—41no—
322D4—41no—
323D4—181no—
324D4—181no—
325D4—364no—
326D4—361no—
327D4—361no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—92no—
334C2×C4—92no—
335C2×C4—184no—
336C2×C4—184no—
337C2×C4—182no—
338C2×C4—181no—
339C2×C4—361no—
340C2×C4—361no—
341C2×C4C2×C4×D911yescharacteristic
342C2×C4#369711yescharacteristic
343C2×C4D4×D911yescharacteristic
344C2×C4D4×D911yescharacteristic
345C2×C4#369911yescharacteristic
346C2×C4C2×#61111yescharacteristic
347C8—41no—
348C8—361no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—81no—
352C2×C3D3×#10412yes—
353C2×C3#495711yescharacteristic
354D3—241no—
355C22—22no—
356C22—42no—
357C22—41no—
358C22—362no—
359C22—361no—
360C22C22⋊C4×D911yescharacteristic
361C22#6344611yescharacteristic
362C22#6350111yescharacteristic
363C4—24no—
364C4—41no—
365C4—94no—
366C4—184no—
367C4—182no—
368C4—361no—
369C4#611⋊C411yescharacteristic
370C4#6344711yescharacteristic
371C4C4×#61111yescharacteristic
372C4#6350211yescharacteristic
373C3#7035611yescharacteristic
374C2—21no—
375C2—21no—
376C2—81no—
377C2—721no—
378C2D9×#10412yes—
379C2#1058863711yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC2×C9×#104C2
socleC22×C3D3×C22⋊C4
prime radical#10589934C2
cosocleC22×C4×C9C23
hypercenterC2×#104D9
hypocenterC9#1962
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C9×#104C2semidirect
3. C2×#63396C2semidirect
4. C2×#63384C2semidirect
5. #10588802C2semidirect
6. C42×Dic9C2semidirect
7. C2×#63364C2semidirect
13. #63509C4semidirect
14. #63506C4semidirect
15. #63502C4semidirect
17. #63498C4semidirect
60. C42×C9D4semidirect
69. C4×Dic9D4semidirect
135. C2×#104D9semidirect
192. Dic9#104semidirect
292. C42#611semidirect
311. C9#1962semidirect

Maximal subgroups

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

subgroupindex
#105899342
C2×C9×#1042
C2×#633962
C2×#633842
#105888022
C42×Dic92
C2×#633642
#703563