Finite Group Databasebeta

← C9×#2038 #11766759

Subgroups — C9×#2038 #11766759

Order 1152.

417 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#536C211yesmaximal, characteristic
2C9×#428C211yesmaximal, characteristic, complemented
3C2×C9×#104C211yesmaximal, characteristic
4C9×#417C211yesmaximal, characteristic
5C2×C9×#101C211yesmaximal, characteristic, complemented
6C9×#391C211yesmaximal, characteristic, complemented
7C9×#339C211yesmaximal, characteristic, complemented
8C3×#2038C311yesmaximal, characteristic
9C2×C9×#41C2211yescharacteristic
10C22×Q8×C9C2211yescharacteristic
11C2×C9×M16C2211yescharacteristic
12C2×C9×M16C2211yescharacteristic
13C9×C4⋊Q8—21no—
14C9×#124—21no—
15C9×#123—22no—
16C9×C22⋊Q8—21no—
17C9×C22⋊Q8—21no—
18C9×#117C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C42×C9C2211yescharacteristic
21C9×#107—21no—
22C9×#106—21no—
23C9×#104—22no—
24C9×#103—21no—
25C9×#102—21no—
26C9×#101—22no—
27C9×#95—22no—
28C3×#536C2×C311yescharacteristic
29C3×#428C2×C311yescharacteristic
30C2×C3×#104C2×C311yescharacteristic
31C3×#417C2×C311yescharacteristic
32C2×C3×#101C2×C311yescharacteristic
33C3×#391C2×C311yescharacteristic
34C3×#339C2×C311yescharacteristic
35C9×#41—21no—
36C9×#41—21no—
37C9×#41—21no—
38C9×#41—21no—
39C2×Q8×C9—21no—
40C2×Q8×C9—21no—
41C2×Q8×C9—21no—
42C2×Q8×C9—21no—
43C2×Q8×C9—21no—
44C2×Q8×C9—21no—
45C2×Q8×C9D411yescharacteristic
46C2×D4×C9—21no—
47C2×D4×C9D411yescharacteristic
48C22×C4×C9—21no—
49C22×C4×C9—21no—
50C22×C4×C9—21no—
51C22×C4×C9D412yes—
52C22×C4×C9C2311yescharacteristic
53C9×M16—21no—
54C9×M16—21no—
55C9×M16—21no—
56C9×M16D412yes—
57C2×C8×C9—21no—
58C2×C8×C9—21no—
59C9×C4⋊C4—22no—
60C9×C4⋊C4—22no—
61C9×C4⋊C4—21no—
62C9×C4⋊C4—21no—
63C9×C4⋊C4D411yescharacteristic
64C9×C4⋊C4D411yescharacteristic
65C9×C22⋊C4—22no—
66C9×C22⋊C4—22no—
67C9×C22⋊C4—21no—
68C42×C9—21no—
69C42×C9—21no—
70C42×C9—21no—
71#2038C911yescharacteristic, direct product factor, Sylow
72C2×C3×#41C22×C311yescharacteristic
73C22×C3×Q8C22×C311yescharacteristic
74C2×C3×M16C22×C311yescharacteristic
75C2×C3×M16C22×C311yescharacteristic
76C3×C4⋊Q8—21no—
77C3×#124—21no—
78C3×#123—22no—
79C3×C22⋊Q8—21no—
80C3×C22⋊Q8—21no—
81C3×#117C22×C311yescharacteristic
82C2×C3×C4⋊C4C22×C311yescharacteristic
83C2×C3×C42C22×C311yescharacteristic
84C3×#107—21no—
85C3×#106—21no—
86C3×#104—22no—
87C3×#103—21no—
88C3×#102—21no—
89C3×#101—22no—
90C3×#95—22no—
91C23×C9—21no—
92C23×C9C2×D411yescharacteristic
93Q8×C9—21no—
94Q8×C9—21no—
95Q8×C9—41no—
96Q8×C9—41no—
97Q8×C9—41no—
98Q8×C9—41no—
99D4×C9—21no—
100D4×C9—21no—
101D4×C9—41no—
102D4×C9—41no—
103C2×C4×C9—22no—
104C2×C4×C9—21no—
105C2×C4×C9—21no—
106C2×C4×C9—22no—
107C2×C4×C9—21no—
108C2×C4×C9—22no—
109C2×C4×C9—22no—
110C2×C4×C9—41no—
111C2×C4×C9—41no—
112C2×C4×C9—41no—
113C2×C4×C9—41no—
114C2×C4×C9—42no—
115C2×C4×C9—41no—
116C2×C4×C9C2×D411yescharacteristic
117C2×C4×C9C2×D411yescharacteristic
118C2×C4×C9C2×D411yescharacteristic
119C2×C4×C9#4111yescharacteristic
120C2×C4×C9#4111yescharacteristic
121C2×C4×C9#4111yescharacteristic
122C8×C9—22no—
123C8×C9—41no—
124#536C2×C911yescharacteristic
125#428C2×C911yescharacteristic, complemented
126C2×#104C2×C911yescharacteristic
127#417C2×C911yescharacteristic
128C2×#101C2×C911yescharacteristic, complemented
129#391C2×C911yescharacteristic, complemented
130#339C2×C911yescharacteristic, complemented
131C3×#41—21no—
132C3×#41—21no—
133C3×#41—21no—
134C3×#41—21no—
135C2×C3×Q8—21no—
136C2×C3×Q8—21no—
137C2×C3×Q8—21no—
138C2×C3×Q8—21no—
139C2×C3×Q8—21no—
140C2×C3×Q8—21no—
141C2×C3×Q8C3×D411yescharacteristic
142C2×C3×D4—21no—
143C2×C3×D4C3×D411yescharacteristic
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4C3×D412yes—
148C22×C3×C4C23×C311yescharacteristic
149C3×M16—21no—
150C3×M16—21no—
151C3×M16—21no—
152C3×M16C3×D412yes—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4C3×D411yescharacteristic
160C3×C4⋊C4C3×D411yescharacteristic
161C3×C22⋊C4—22no—
162C3×C22⋊C4—22no—
163C3×C22⋊C4—21no—
164C3×C42—21no—
165C3×C42—21no—
166C3×C42—21no—
167C22×C9—21no—
168C22×C9—21no—
169C22×C9—41no—
170C22×C9—41no—
171C22×C9—41no—
172C22×C9#12011yescharacteristic
173C22×C9#12111yescharacteristic
174C22×C9#12311yescharacteristic
175C4×C9—42no—
176C4×C9—42no—
177C4×C9—41no—
178C4×C9—41no—
179C4×C9—41no—
180C4×C9—81no—
181C4×C9#12111yescharacteristic
182C4×C9#12111yescharacteristic
183C4×C9#12311yescharacteristic
184C4×C9#12411yescharacteristic
185C2×#41C22×C911yescharacteristic
186C22×Q8C22×C911yescharacteristic
187C2×M16C22×C911yescharacteristic
188C2×M16C22×C911yescharacteristic
189C4⋊Q8—21no—
190#124—21no—
191#123—22no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194#117C22×C911yescharacteristic
195C2×C4⋊C4C22×C911yescharacteristic
196C2×C42C22×C911yescharacteristic
197#107—21no—
198#106—21no—
199#104—22no—
200#103—21no—
201#102—21no—
202#101—22no—
203#95—22no—
204C23×C3—21no—
205C23×C3C2×C3×D411yescharacteristic
206C3×Q8—21no—
207C3×Q8—21no—
208C3×Q8—41no—
209C3×Q8—41no—
210C3×Q8—41no—
211C3×Q8—41no—
212C3×D4—21no—
213C3×D4—21no—
214C3×D4—41no—
215C3×D4—41no—
216C2×C3×C4—22no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—42no—
228C2×C3×C4—41no—
229C2×C3×C4C2×C3×D411yescharacteristic
230C2×C3×C4C2×C3×D411yescharacteristic
231C2×C3×C4C2×C3×D411yescharacteristic
232C2×C3×C4C3×#4111yescharacteristic
233C2×C3×C4C3×#4111yescharacteristic
234C2×C3×C4C3×#4111yescharacteristic
235C3×C8—22no—
236C3×C8—41no—
237C2×C9—21no—
238C2×C9—21no—
239C2×C9—81no—
240C2×C9#39411yescharacteristic
241C2×C9#45411yescharacteristic
242C2×C9#45611yescharacteristic
243#41—21no—
244#41—21no—
245#41—21no—
246#41—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8D4×C911yescharacteristic
254C2×D4—21no—
255C2×D4D4×C911yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4D4×C912yes—
260C22×C4C23×C911yescharacteristic
261M16—21no—
262M16—21no—
263M16—21no—
264M16D4×C912yes—
265C2×C8—21no—
266C2×C8—21no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4D4×C911yescharacteristic
272C4⋊C4D4×C911yescharacteristic
273C22⋊C4—22no—
274C22⋊C4—22no—
275C22⋊C4—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3C3×#12011yescharacteristic
285C22×C3C3×#12111yescharacteristic
286C22×C3C3×#12311yescharacteristic
287C3×C4—42no—
288C3×C4—42no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—81no—
293C3×C4C3×#12111yescharacteristic
294C3×C4C3×#12111yescharacteristic
295C3×C4C3×#12311yescharacteristic
296C3×C4C3×#12411yescharacteristic
297C9#203811yescharacteristic, direct product factor, Sylow
298C23—21no—
299C23C2×D4×C911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—41no—
303Q8—41no—
304Q8—41no—
305Q8—41no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—41no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4C2×D4×C911yescharacteristic
324C2×C4C2×D4×C911yescharacteristic
325C2×C4C2×D4×C911yescharacteristic
326C2×C4C9×#4111yescharacteristic
327C2×C4C9×#4111yescharacteristic
328C2×C4C9×#4111yescharacteristic
329C8—22no—
330C8—41no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—81no—
334C2×C3C3×#39411yescharacteristic
335C2×C3C3×#45411yescharacteristic
336C2×C3C3×#45611yescharacteristic
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22C9×#12011yescharacteristic
343C22C9×#12111yescharacteristic
344C22C9×#12311yescharacteristic
345C4—42no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—81no—
351C4C9×#12111yescharacteristic
352C4C9×#12111yescharacteristic
353C4C9×#12311yescharacteristic
354C4C9×#12411yescharacteristic
355C3C3×#203811yescharacteristic
356C2—21no—
357C2—21no—
358C2—81no—
359C2C9×#39411yescharacteristic
360C2C9×#45411yescharacteristic
361C2C9×#45611yescharacteristic
subgroupG/H
centerC22×C9#120
commutatorC22×C4C23×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC22×C3C3×#120
prime radicalC2×C3×#41C22×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C9 ◁ C22×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
2. C9×#428C2semidirect
5. C2×C9×#101C2semidirect
6. C9×#391C2semidirect
7. C9×#339C2semidirect
71. #2038C9direct (N × H)
125. #428C2×C9semidirect
128. C2×#101C2×C9semidirect
129. #391C2×C9semidirect
130. #339C2×C9semidirect
297. C9#2038direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5362
C9×#4282
C2×C9×#1042
C9×#4172
C2×C9×#1012
C9×#3912
C9×#3392
C3×#20383