Finite Group Databasebeta

← C2×#10593272 #11773722

Subgroups — C2×#10593272 #11773722

Order 1152.

830 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C22×C22⋊#157C211yesmaximal, characteristic
2C2×C22⋊AGL(1,𝔽9)C212yesmaximal, complemented
3#10593272C214yesmaximal, direct product factor
4C24×C3⋊D3C411yescharacteristic
5C23×#157C411yescharacteristic
6C23×#157C2211yescharacteristic
7C22×AGL(1,𝔽9)—22no—
8C2×C22⋊#157—22no—
9C2×C22⋊#157—22no—
10C2×C22⋊#157C412yes—
11C2×C22⋊#157C2212yes—
12C22⋊AGL(1,𝔽9)—22no—
13C22⋊AGL(1,𝔽9)C2214yescomplemented
14C24×C32C811yescharacteristic, complemented
15C23×C3⋊D3—21no—
16C23×C3⋊D3—21no—
17C23×C3⋊D3—21no—
18C23×C3⋊D3—21no—
19C23×C3⋊D3—42no—
20C23×C3⋊D3—42no—
21C23×C3⋊D3C812yescomplemented
22C23×C3⋊D3C811yescharacteristic, complemented
23C23×C3⋊D3C2×C411yescharacteristic
24C23×C3⋊D3C2×C412yes—
25C22×#157—21no—
26C22×#157—21no—
27C22×#157—42no—
28C22×#157—42no—
29C22×#157C2×C412yes—
30C22×#157C2×C411yescharacteristic
31C22×#157D412yes—
32C22×#157D412yes—
33C22×#157C2311yescharacteristic
34C2×AGL(1,𝔽9)—24no—
35C2×AGL(1,𝔽9)—44no—
36C22⋊#157—24no—
37C22⋊#157—24no—
38C2×#323—91nomaximal, Sylow
39C24×D3—121no—
40C23×C32—21no—
41C23×C32—21no—
42C23×C32—42no—
43C23×C32C2×C811yescharacteristic
44C23×C32C2×C812yescomplemented
45C22×C3⋊D3—22no—
46C22×C3⋊D3—22no—
47C22×C3⋊D3—21no—
48C22×C3⋊D3—21no—
49C22×C3⋊D3—22no—
50C22×C3⋊D3—22no—
51C22×C3⋊D3—22no—
52C22×C3⋊D3—22no—
53C22×C3⋊D3—44no—
54C22×C3⋊D3—44no—
55C22×C3⋊D3—42no—
56C22×C3⋊D3—42no—
57C22×C3⋊D3—44no—
58C22×C3⋊D3—42no—
59C22×C3⋊D3—42no—
60C22×C3⋊D3—42no—
61C22×C3⋊D3—42no—
62C22×C3⋊D3—42no—
63C22×C3⋊D3C22⋊C411yescharacteristic
64C22×C3⋊D3C22⋊C411yescharacteristic
65C22×C3⋊D3C2×C811yescharacteristic
66C22×C3⋊D3C2×C812yescomplemented
67C22×C3⋊D3M1611yescharacteristic
68C22×C3⋊D3M1611yescharacteristic
69C22×C3⋊D3C22×C411yescharacteristic
70C2×#157—24no—
71C2×#157—22no—
72C2×#157—41no—
73C2×#157—42no—
74C2×#157—41no—
75C2×#157—42no—
76C2×#157—42no—
77C2×#157—42no—
78C2×#157C22⋊C412yes—
79C2×#157C2×D412yes—
80AGL(1,𝔽9)—44no—
81C22×C22⋊C4—91no—
82C2×C22⋊C8—92no—
83#323—94no—
84C24×C3—41no—
85C23×D3—121no—
86C23×D3—122no—
87C23×D3—121no—
88C23×D3—122no—
89C23×D3—122no—
90C23×D3—122no—
91C23×D3—122no—
92C23×D3—122no—
93C23×D3—128no—
94C23×D3—128no—
95C22×C32—22no—
96C22×C32—22no—
97C22×C32—42no—
98C22×C32—42no—
99C22×C32—42no—
100C22×C32C22⋊C811yescharacteristic
101C22×C32C22⋊C811yescharacteristic
102C22×C32C22×C811yescharacteristic
103C2×C3⋊D3—22no—
104C2×C3⋊D3—22no—
105C2×C3⋊D3—22no—
106C2×C3⋊D3—21no—
107C2×C3⋊D3—21no—
108C2×C3⋊D3—21no—
109C2×C3⋊D3—21no—
110C2×C3⋊D3—22no—
111C2×C3⋊D3—44no—
112C2×C3⋊D3—44no—
113C2×C3⋊D3—42no—
114C2×C3⋊D3—42no—
115C2×C3⋊D3—44no—
116C2×C3⋊D3—42no—
117C2×C3⋊D3—42no—
118C2×C3⋊D3—42no—
119C2×C3⋊D3C22⋊C811yescharacteristic
120C2×C3⋊D3C22⋊C811yescharacteristic
121C2×C3⋊D3#9912yes—
122C2×C3⋊D3#10012yes—
123C2×C3⋊D3C2×C22⋊C411yescharacteristic
124C2×C3⋊D3C2×M1611yescharacteristic
125#157—22no—
126#157—22no—
127#157—42no—
128C25—91no—
129C23×C4—91no—
130C23×C4—91no—
131C22×C8—182no—
132C2×C22⋊C4—92no—
133C2×C22⋊C4—92no—
134C2×C22⋊C4—182no—
135C2×C22⋊C4—182no—
136C22⋊C8—94no—
137C22⋊C8—182no—
138C23×C3—42no—
139C23×C3—42no—
140C23×C3—48no—
141C23×C3—41no—
142C23×C3—42no—
143C22×D3—121no—
144C22×D3—121no—
145C22×D3—121no—
146C22×D3—122no—
147C22×D3—121no—
148C22×D3—121no—
149C22×D3—121no—
150C22×D3—124no—
151C22×D3—124no—
152C22×D3—124no—
153C22×D3—124no—
154C22×D3—124no—
155C22×D3—124no—
156C22×D3—122no—
157C22×D3—122no—
158C22×D3—128no—
159C22×D3—128no—
160C22×D3—128no—
161C22×D3—1216no—
162C22×D3—128no—
163C22×D3—128no—
164C22×D3—128no—
165C22×D3—128no—
166C22×D3—1216no—
167C22×D3—1216no—
168C2×C32—21no—
169C2×C32—21no—
170C2×C32—42no—
171C2×C32#32312yescomplemented
172C2×C32C2×C22⋊C811yescharacteristic
173C3⋊D3—21no—
174C3⋊D3—21no—
175C3⋊D3—42no—
176C3⋊D3#32312yescomplemented
177C3⋊D3C2×#9911yescharacteristic
178C3⋊D3C2×#10011yescharacteristic
179C24—91no—
180C24—91no—
181C24—92no—
182C24—92no—
183C24—181no—
184C24—181no—
185C24—181no—
186C24—181no—
187C24—362no—
188C24—362no—
189C24AGL(1,𝔽9)11yescharacteristic, complemented
190C22×C4—92no—
191C22×C4—91no—
192C22×C4—92no—
193C22×C4—91no—
194C22×C4—92no—
195C22×C4—181no—
196C22×C4—181no—
197C22×C4—362no—
198C22×C4—362no—
199C2×C8—184no—
200C2×C8—364no—
201C22⋊C4—184no—
202C22⋊C4—184no—
203C22×C3—44no—
204C22×C3—44no—
205C22×C3—48no—
206C22×C3—48no—
207C22×C3—48no—
208C22×C3—41no—
209C22×C3—41no—
210C22×C3—41no—
211C2×D3—121no—
212C2×D3—121no—
213C2×D3—122no—
214C2×D3—122no—
215C2×D3—121no—
216C2×D3—121no—
217C2×D3—122no—
218C2×D3—122no—
219C2×D3—122no—
220C2×D3—122no—
221C2×D3—124no—
222C2×D3—124no—
223C2×D3—124no—
224C2×D3—124no—
225C2×D3—128no—
226C2×D3—128no—
227C2×D3—1216no—
228C2×D3—128no—
229C2×D3—128no—
230C2×D3—1216no—
231C2×D3—1216no—
232C2×D3—128no—
233C32C2×#32311yescharacteristic, complemented, Sylow
234C23—21no—
235C23—21no—
236C23—42no—
237C23—91no—
238C23—91no—
239C23—91no—
240C23—91no—
241C23—91no—
242C23—91no—
243C23—92no—
244C23—182no—
245C23—182no—
246C23—182no—
247C23—182no—
248C23—182no—
249C23—182no—
250C23—181no—
251C23—181no—
252C23—362no—
253C23—362no—
254C23—362no—
255C23—362no—
256C23—362no—
257C23—364no—
258C23—362no—
259C23—362no—
260C23—364no—
261C23—364no—
262C23C2×AGL(1,𝔽9)11yescharacteristic
263C23C2×AGL(1,𝔽9)12yescomplemented
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—184no—
267C2×C4—182no—
268C2×C4—361no—
269C2×C4—362no—
270C2×C4—361no—
271C2×C4—362no—
272C2×C4—362no—
273C2×C4—362no—
274C8—364no—
275C2×C3—42no—
276C2×C3—42no—
277C2×C3—48no—
278C2×C3—41no—
279C2×C3—42no—
280D3—122no—
281D3—121no—
282D3—121no—
283D3—122no—
284D3—122no—
285D3—128no—
286C22—22no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—91no—
292C22—91no—
293C22—92no—
294C22—92no—
295C22—91no—
296C22—91no—
297C22—181no—
298C22—181no—
299C22—181no—
300C22—181no—
301C22—182no—
302C22—182no—
303C22—182no—
304C22—182no—
305C22—362no—
306C22—362no—
307C22—362no—
308C22—362no—
309C22—364no—
310C22—364no—
311C22—364no—
312C22—362no—
313C22C22⋊AGL(1,𝔽9)11yescharacteristic
314C22C22⋊AGL(1,𝔽9)11yescharacteristic
315C22C22×AGL(1,𝔽9)11yescharacteristic
316C4—182no—
317C4—182no—
318C4—362no—
319C3—41no—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—91no—
324C2—91no—
325C2—92no—
326C2—181no—
327C2—181no—
328C2—362no—
329C2#1059327212yesdirect product factor
330C2C2×C22⋊AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC22C22⋊AGL(1,𝔽9)
commutatorC22×C32C22×C8
FrattiniC22C22×AGL(1,𝔽9)
FittingC24×C32C8
socleC22×C32C22⋊C8
prime radicalC24×C3⋊D3C4
cosocleC22×#157C23
hypercenterC24AGL(1,𝔽9)
hypocenterC32C2×#323
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊AGL(1,𝔽9)C2semidirect
3. #10593272C2direct (N × H)
13. C22⋊AGL(1,𝔽9)C22semidirect
14. C24×C32C8semidirect
21. C23×C3⋊D3C8semidirect
22. C23×C3⋊D3C8semidirect
44. C23×C32C2×C8semidirect
66. C22×C3⋊D3C2×C8semidirect
171. C2×C32#323semidirect
176. C3⋊D3#323semidirect
189. C24AGL(1,𝔽9)semidirect
233. C32C2×#323semidirect
263. C23C2×AGL(1,𝔽9)semidirect
329. C2#10593272direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊#1572
C2×C22⋊AGL(1,𝔽9)2
#105932722
C2×#3239