Finite Group Databasebeta

← C9×#2033 #11766754

Subgroups — C9×#2033 #11766754

Order 1152.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#121C211yesmaximal, characteristic
2C2×C9×#107C211yesmaximal, characteristic, complemented
3C2×C9×#102C211yesmaximal, characteristic, complemented
4C2×C9×#102C211yesmaximal, characteristic, complemented
5C2×C9×C22⋊C8C211yesmaximal, characteristic, complemented
6C9×#380C211yesmaximal, characteristic, complemented
7C9×#340C211yesmaximal, characteristic, complemented
8C3×#2033C311yesmaximal, characteristic
9C22×D4×C9—21no—
10C22×D4×C9C2211yescharacteristic
11C23×C4×C9C2211yescharacteristic
12C22×C8×C9C2211yescharacteristic
13C22×C8×C9C2211yescharacteristic
14C9×#121—22no—
15C9×#121—22no—
16C2×C9×C4⋊C4C2211yescharacteristic
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×C9×C4⋊C4C2211yescharacteristic
19C2×C9×C22⋊C4—21no—
20C2×C9×C22⋊C4—21no—
21C9×#107—22no—
22C9×#102—22no—
23C9×#102—22no—
24C9×C22⋊C8—22no—
25C9×#95—21no—
26C2×C3×#121C2×C311yescharacteristic
27C2×C3×#107C2×C311yescharacteristic
28C2×C3×#102C2×C311yescharacteristic
29C2×C3×#102C2×C311yescharacteristic
30C2×C3×C22⋊C8C2×C311yescharacteristic
31C3×#380C2×C311yescharacteristic
32C3×#340C2×C311yescharacteristic
33C24×C9—21no—
34C24×C9D411yescharacteristic
35C2×D4×C9—24no—
36C2×D4×C9—21no—
37C2×D4×C9—21no—
38C2×D4×C9—21no—
39C2×D4×C9—21no—
40C2×D4×C9—21no—
41C2×D4×C9—42no—
42C2×D4×C9—42no—
43C2×D4×C9D412yes—
44C22×C4×C9—21no—
45C22×C4×C9—21no—
46C22×C4×C9—21no—
47C22×C4×C9—21no—
48C22×C4×C9—21no—
49C22×C4×C9—21no—
50C22×C4×C9—21no—
51C22×C4×C9—21no—
52C22×C4×C9—21no—
53C22×C4×C9D411yescharacteristic
54C22×C4×C9C2311yescharacteristic
55C2×C8×C9—21no—
56C2×C8×C9—21no—
57C2×C8×C9—21no—
58C2×C8×C9—21no—
59C2×C8×C9—21no—
60C2×C8×C9D412yescomplemented
61C9×C4⋊C4—21no—
62C9×C4⋊C4—21no—
63C9×C4⋊C4—21no—
64C9×C4⋊C4—21no—
65C9×C4⋊C4—21no—
66C9×C4⋊C4D412yes—
67C9×C22⋊C4—24no—
68C9×C22⋊C4—42no—
69#2033C911yescharacteristic, direct product factor, Sylow
70C22×C3×D4—21no—
71C22×C3×D4C22×C311yescharacteristic
72C23×C3×C4C22×C311yescharacteristic
73C22×C3×C8C22×C311yescharacteristic
74C22×C3×C8C22×C311yescharacteristic
75C3×#121—22no—
76C3×#121—22no—
77C2×C3×C4⋊C4C22×C311yescharacteristic
78C2×C3×C4⋊C4C22×C311yescharacteristic
79C2×C3×C4⋊C4C22×C311yescharacteristic
80C2×C3×C22⋊C4—21no—
81C2×C3×C22⋊C4—21no—
82C3×#107—22no—
83C3×#102—22no—
84C3×#102—22no—
85C3×C22⋊C8—22no—
86C3×#95—21no—
87C23×C9—21no—
88C23×C9—21no—
89C23×C9—21no—
90C23×C9—21no—
91C23×C9—21no—
92C23×C9—21no—
93C23×C9—22no—
94C23×C9—41no—
95C23×C9—41no—
96C23×C9—41no—
97C23×C9—41no—
98C23×C9—41no—
99C23×C9—41no—
100C23×C9D812yes—
101C23×C9C2×D411yescharacteristic
102D4×C9—22no—
103D4×C9—22no—
104D4×C9—48no—
105D4×C9—41no—
106D4×C9—41no—
107C2×C4×C9—21no—
108C2×C4×C9—22no—
109C2×C4×C9—21no—
110C2×C4×C9—21no—
111C2×C4×C9—41no—
112C2×C4×C9—41no—
113C2×C4×C9—41no—
114C2×C4×C9—41no—
115C2×C4×C9—41no—
116C2×C4×C9—41no—
117C2×C4×C9—41no—
118C2×C4×C9—41no—
119C2×C4×C9—41no—
120C2×C4×C9—41no—
121C2×C4×C9—41no—
122C2×C4×C9—41no—
123C2×C4×C9C2×D411yescharacteristic
124C2×C4×C9C2×D411yescharacteristic
125C2×C4×C9C2×D411yescharacteristic
126C2×C4×C9#4111yescharacteristic
127C2×C4×C9#4111yescharacteristic
128C2×C4×C9#4111yescharacteristic
129C8×C9—22no—
130C8×C9—41no—
131C2×#121C2×C911yescharacteristic
132C2×#107C2×C911yescharacteristic, complemented
133C2×#102C2×C911yescharacteristic, complemented
134C2×#102C2×C911yescharacteristic, complemented
135C2×C22⋊C8C2×C911yescharacteristic, complemented
136#380C2×C911yescharacteristic, complemented
137#340C2×C911yescharacteristic, complemented
138C24×C3—21no—
139C24×C3C3×D411yescharacteristic
140C2×C3×D4—24no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—42no—
147C2×C3×D4—42no—
148C2×C3×D4C3×D412yes—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4C3×D411yescharacteristic
159C22×C3×C4C23×C311yescharacteristic
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8C3×D412yes—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4C3×D412yes—
172C3×C22⋊C4—24no—
173C3×C22⋊C4—42no—
174C22×C9—22no—
175C22×C9—22no—
176C22×C9—22no—
177C22×C9—41no—
178C22×C9—41no—
179C22×C9—41no—
180C22×C9—41no—
181C22×C9—42no—
182C22×C9—42no—
183C22×C9—42no—
184C22×C9—81no—
185C22×C9—81no—
186C22×C9—81no—
187C22×C9—81no—
188C22×C9#12011yescharacteristic
189C22×C9#12111yescharacteristic
190C22×C9#12311yescharacteristic
191C22×C9C2×D811yescharacteristic
192C22×C9#13511yescharacteristic
193C22×C9AGL(1,ℤ/8)11yescharacteristic
194C22×C9#13711yescharacteristic
195C4×C9—41no—
196C4×C9—42no—
197C4×C9—81no—
198C4×C9—81no—
199C4×C9#12111yescharacteristic
200C4×C9#12111yescharacteristic
201C4×C9#12311yescharacteristic
202C4×C9#12411yescharacteristic
203C22×D4—21no—
204C22×D4C22×C911yescharacteristic
205C23×C4C22×C911yescharacteristic
206C22×C8C22×C911yescharacteristic
207C22×C8C22×C911yescharacteristic
208#121—22no—
209#121—22no—
210C2×C4⋊C4C22×C911yescharacteristic
211C2×C4⋊C4C22×C911yescharacteristic
212C2×C4⋊C4C22×C911yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215#107—22no—
216#102—22no—
217#102—22no—
218C22⋊C8—22no—
219#95—21no—
220C23×C3—21no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—22no—
227C23×C3—41no—
228C23×C3—41no—
229C23×C3—41no—
230C23×C3—41no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3C3×D812yes—
234C23×C3C2×C3×D411yescharacteristic
235C3×D4—22no—
236C3×D4—22no—
237C3×D4—48no—
238C3×D4—41no—
239C3×D4—41no—
240C2×C3×C4—21no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4C2×C3×D411yescharacteristic
257C2×C3×C4C2×C3×D411yescharacteristic
258C2×C3×C4C2×C3×D411yescharacteristic
259C2×C3×C4C3×#4111yescharacteristic
260C2×C3×C4C3×#4111yescharacteristic
261C2×C3×C4C3×#4111yescharacteristic
262C3×C8—22no—
263C3×C8—41no—
264C2×C9—42no—
265C2×C9—82no—
266C2×C9#39411yescharacteristic
267C2×C9#44711yescharacteristic
268C2×C9#45211yescharacteristic
269C2×C9#46611yescharacteristic
270C2×C9#46811yescharacteristic
271C2×C9#48011yescharacteristic
272C2×C9#48211yescharacteristic
273C24—21no—
274C24D4×C911yescharacteristic
275C2×D4—24no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4D4×C912yes—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4D4×C911yescharacteristic
294C22×C4C23×C911yescharacteristic
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8D4×C912yescomplemented
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4D4×C912yes—
307C22⋊C4—24no—
308C22⋊C4—42no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3—42no—
319C22×C3—81no—
320C22×C3—81no—
321C22×C3—81no—
322C22×C3—81no—
323C22×C3C3×#12011yescharacteristic
324C22×C3C3×#12111yescharacteristic
325C22×C3C3×#12311yescharacteristic
326C22×C3C2×C3×D811yescharacteristic
327C22×C3C3×#13511yescharacteristic
328C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
329C22×C3C3×#13711yescharacteristic
330C3×C4—41no—
331C3×C4—42no—
332C3×C4—81no—
333C3×C4—81no—
334C3×C4C3×#12111yescharacteristic
335C3×C4C3×#12111yescharacteristic
336C3×C4C3×#12311yescharacteristic
337C3×C4C3×#12411yescharacteristic
338C9#203311yescharacteristic, direct product factor, Sylow
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—22no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23C9×D812yes—
353C23C2×D4×C911yescharacteristic
354D4—22no—
355D4—22no—
356D4—48no—
357D4—41no—
358D4—41no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4C2×D4×C911yescharacteristic
376C2×C4C2×D4×C911yescharacteristic
377C2×C4C2×D4×C911yescharacteristic
378C2×C4C9×#4111yescharacteristic
379C2×C4C9×#4111yescharacteristic
380C2×C4C9×#4111yescharacteristic
381C8—22no—
382C8—41no—
383C2×C3—42no—
384C2×C3—82no—
385C2×C3C3×#39411yescharacteristic
386C2×C3C3×#44711yescharacteristic
387C2×C3C3×#45211yescharacteristic
388C2×C3C3×#46611yescharacteristic
389C2×C3C3×#46811yescharacteristic
390C2×C3C3×#48011yescharacteristic
391C2×C3C3×#48211yescharacteristic
392C22—22no—
393C22—22no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22C9×#12011yescharacteristic
407C22C9×#12111yescharacteristic
408C22C9×#12311yescharacteristic
409C22C2×C9×D811yescharacteristic
410C22C9×#13511yescharacteristic
411C22C9×AGL(1,ℤ/8)11yescharacteristic
412C22C9×#13711yescharacteristic
413C4—41no—
414C4—42no—
415C4—81no—
416C4—81no—
417C4C9×#12111yescharacteristic
418C4C9×#12111yescharacteristic
419C4C9×#12311yescharacteristic
420C4C9×#12411yescharacteristic
421C3C3×#203311yescharacteristic
422C2—42no—
423C2—82no—
424C2C9×#39411yescharacteristic
425C2C9×#44711yescharacteristic
426C2C9×#45211yescharacteristic
427C2C9×#46611yescharacteristic
428C2C9×#46811yescharacteristic
429C2C9×#48011yescharacteristic
430C2C9×#48211yescharacteristic
subgroupG/H
centerC23×C9C2×D4
commutatorC22×C4C23×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC23×C3C2×C3×D4
prime radicalC2×C3×#121C2×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C9 ◁ C23×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C9×#107C2semidirect
3. C2×C9×#102C2semidirect
4. C2×C9×#102C2semidirect
5. C2×C9×C22⋊C8C2semidirect
6. C9×#380C2semidirect
7. C9×#340C2semidirect
60. C2×C8×C9D4semidirect
69. #2033C9direct (N × H)
132. C2×#107C2×C9semidirect
133. C2×#102C2×C9semidirect
134. C2×#102C2×C9semidirect
135. C2×C22⋊C8C2×C9semidirect
136. #380C2×C9semidirect
137. #340C2×C9semidirect
300. C2×C8D4×C9semidirect
338. C9#2033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1212
C2×C9×#1072
C2×C9×#1022
C2×C9×C22⋊C82
C9×#3802
C9×#3402
C3×#20333