Finite Group Databasebeta

← #11920100

Subgroups — #11920100

Order 1152.

514 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 48 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×D4×C22⋊C9C211yesmaximal, characteristic
2#10589534C212yesmaximal, complemented
3#72130—31nomaximal
4C23×C22⋊C9C411yescharacteristic, complemented
5C23×C22⋊C9C2211yescharacteristic
6D4×C22⋊C9—22no—
7C2×C4×C22⋊C9C411yescharacteristic, complemented
8C2×(C22⋊C9)⋊C4—22no—
9#63393—41nomaximal
10C23×C3×D4D311yescharacteristic
11#5247—32no—
12C2×#834—32no—
13C2×#834—31no—
14C2×#834—31no—
15C22×C22⋊C9—21no—
16C22×C22⋊C9—41no—
17C22×C22⋊C9—41no—
18C22×C22⋊C9C2×C411yescharacteristic
19C22×C22⋊C9D412yes—
20C2×D4×C9—41no—
21C4×C22⋊C9—21no—
22(C22⋊C9)⋊C4—42no—
23#3676—42no—
24#1781—91noSylow
25C25×C3Dic311yescharacteristic
26C25×C3C2×D311yescharacteristic
27C22×C3×D4—22no—
28C22×C3×D4—31no—
29C22×C3×D4—31no—
30C22×C3×D4—31no—
31C22×C3×D4—31no—
32C22×C3×D4—62no—
33C23×C3×C4Dic311yescharacteristic
34C2×#217—32no—
35C2×#217—32no—
36C2×#217—62no—
37C2×#217—62no—
38#834—64no—
39#834—61no—
40#834—61no—
41#834—61no—
42#834—61no—
43C23×C9—41no—
44C23×C9—41no—
45C2×C22⋊C9—22no—
46C2×C22⋊C9—21no—
47C2×C22⋊C9—41no—
48C2×C22⋊C9C22⋊C411yescharacteristic
49D4×C9—82no—
50C2×C4×C9—41no—
51C2×Dic9—82no—
52C23×D4D911yescharacteristic
53C2×#99—92no—
54C2×#99—91no—
55C2×#99—91no—
56#379—92no—
57C24×C3—21no—
58C24×C3—31no—
59C24×C3—32no—
60C24×C3—31no—
61C24×C3—31no—
62C24×C3—31no—
63C24×C3—41no—
64C24×C3—41no—
65C24×C3—61no—
66C24×C3—121no—
67C24×C3—121no—
68C24×C3C2×Dic311yescharacteristic
69C24×C3#6712yes—
70C2×C3×D4—34no—
71C2×C3×D4—31no—
72C2×C3×D4—31no—
73C2×C3×D4—31no—
74C2×C3×D4—61no—
75C2×C3×D4—62no—
76C2×C3×D4—62no—
77C2×C3×D4—62no—
78C2×C3×D4—62no—
79C2×C3×D4—62no—
80C2×C3×D4—62no—
81C2×C3×D4—62no—
82C2×C3×D4S411yescharacteristic
83C22×C3×C4—21no—
84C22×C3×C4—31no—
85C22×C3×C4—31no—
86C22×C3×C4—61no—
87C22×Dic3—62no—
88C22×Dic3—62no—
89#217—62no—
90#217—62no—
91#217—62no—
92#217—62no—
93#217—122no—
94#217—122no—
95#217—124no—
96C22×C9—41no—
97C22×C9—42no—
98C22×C9—81no—
99C22×C9—161no—
100C22×C9—161no—
101C22⋊C9#9911yescharacteristic, complemented
102C4×C9—81no—
103Dic9—162no—
104C25Dic911yescharacteristic, complemented
105C25C2×D911yescharacteristic
106C22×D4—22no—
107C22×D4—31no—
108C22×D4—31no—
109C22×D4—31no—
110C22×D4—31no—
111C22×D4—62no—
112C23×C4Dic911yescharacteristic, complemented
113C2×C22⋊C4—92no—
114C2×C22⋊C4—92no—
115C2×C22⋊C4—182no—
116C2×C22⋊C4—182no—
117#99—184no—
118#99—181no—
119#99—181no—
120#99—181no—
121#99—181no—
122C23×C3—22no—
123C23×C3—21no—
124C23×C3—31no—
125C23×C3—32no—
126C23×C3—31no—
127C23×C3—32no—
128C23×C3—31no—
129C23×C3—32no—
130C23×C3—32no—
131C23×C3—31no—
132C23×C3—41no—
133C23×C3—61no—
134C23×C3—61no—
135C23×C3—61no—
136C23×C3—61no—
137C23×C3—62no—
138C23×C3—64no—
139C23×C3—61no—
140C23×C3—121no—
141C23×C3—122no—
142C23×C3—121no—
143C23×C3—121no—
144C23×C3—121no—
145C23×C3—121no—
146C23×C3—122no—
147C23×C3—121no—
148C23×C3—121no—
149C23×C3—121no—
150C23×C3—121no—
151C23×C3—122no—
152C23×C3#21711yescharacteristic
153C23×C3SL(2,ℤ/4)11yescharacteristic
154C23×C3C2×S411yescharacteristic
155C3×D4—22no—
156C3×D4—62no—
157C3×D4—62no—
158C3×D4—64no—
159C3×D4—62no—
160C2×C3×C4—32no—
161C2×C3×C4—31no—
162C2×C3×C4—61no—
163C2×C3×C4—61no—
164C2×C3×C4—61no—
165C2×C3×C4SL(2,ℤ/4)11yescharacteristic
166C2×Dic3—122no—
167C2×Dic3—122no—
168C2×Dic3—122no—
169C2×Dic3—122no—
170C2×Dic3—122no—
171C2×Dic3—122no—
172C2×C9—41no—
173C2×C9—82no—
174C2×C9—81no—
175C2×C9—161no—
176C24—21no—
177C24—31no—
178C24—32no—
179C24—31no—
180C24—31no—
181C24—31no—
182C24—41no—
183C24—41no—
184C24—61no—
185C24—121no—
186C24—121no—
187C24C2×Dic911yescharacteristic
188C24#61112yes—
189C2×D4—34no—
190C2×D4—31no—
191C2×D4—31no—
192C2×D4—31no—
193C2×D4—61no—
194C2×D4—62no—
195C2×D4—62no—
196C2×D4—62no—
197C2×D4—62no—
198C2×D4—62no—
199C2×D4—62no—
200C2×D4—62no—
201C2×D4(C22⋊C9)⋊C211yescharacteristic
202C22×C4—21no—
203C22×C4—31no—
204C22×C4—31no—
205C22×C4—61no—
206C22×C4—182no—
207C22×C4—182no—
208C22⋊C4—182no—
209C22⋊C4—182no—
210C22⋊C4—182no—
211C22⋊C4—182no—
212C22⋊C4—362no—
213C22⋊C4—362no—
214C22⋊C4—364no—
215C22×C3—21no—
216C22×C3—31no—
217C22×C3—31no—
218C22×C3—32no—
219C22×C3—32no—
220C22×C3—31no—
221C22×C3—41no—
222C22×C3—41no—
223C22×C3—62no—
224C22×C3—62no—
225C22×C3—61no—
226C22×C3—61no—
227C22×C3—62no—
228C22×C3—61no—
229C22×C3—62no—
230C22×C3—61no—
231C22×C3—122no—
232C22×C3—121no—
233C22×C3—121no—
234C22×C3—121no—
235C22×C3—121no—
236C22×C3—121no—
237C22×C3—121no—
238C22×C3—122no—
239C22×C3—122no—
240C22×C3—122no—
241C22×C3#83411yescharacteristic
242C22×C3C2×SL(2,ℤ/4)11yescharacteristic
243C22×C3GL(2,ℤ/4)12yes—
244C3×C4—21no—
245C3×C4—61no—
246Dic3—242no—
247Dic3—242no—
248C9—41noSylow
249C23—22no—
250C23—21no—
251C23—31no—
252C23—32no—
253C23—31no—
254C23—32no—
255C23—31no—
256C23—32no—
257C23—32no—
258C23—31no—
259C23—41no—
260C23—61no—
261C23—61no—
262C23—61no—
263C23—61no—
264C23—62no—
265C23—64no—
266C23—61no—
267C23—121no—
268C23—122no—
269C23—121no—
270C23—121no—
271C23—121no—
272C23—121no—
273C23—122no—
274C23—121no—
275C23—121no—
276C23—121no—
277C23—121no—
278C23—122no—
279C23#367611yescharacteristic
280C23(C22⋊C9)⋊C411yescharacteristic, complemented
281C23C2×(C22⋊C9)⋊C211yescharacteristic
282D4—22no—
283D4—62no—
284D4—62no—
285D4—64no—
286D4—62no—
287C2×C4—32no—
288C2×C4—31no—
289C2×C4—61no—
290C2×C4—61no—
291C2×C4—61no—
292C2×C4—362no—
293C2×C4—362no—
294C2×C4—362no—
295C2×C4—362no—
296C2×C4—362no—
297C2×C4—362no—
298C2×C4(C22⋊C9)⋊C411yescharacteristic, complemented
299C2×C3—22no—
300C2×C3—21no—
301C2×C3—31no—
302C2×C3—31no—
303C2×C3—41no—
304C2×C3—62no—
305C2×C3—61no—
306C2×C3—121no—
307C2×C3#543211yescharacteristic
308C22—21no—
309C22—31no—
310C22—31no—
311C22—32no—
312C22—31no—
313C22—32no—
314C22—41no—
315C22—41no—
316C22—62no—
317C22—62no—
318C22—61no—
319C22—61no—
320C22—61no—
321C22—62no—
322C22—62no—
323C22—61no—
324C22—122no—
325C22—121no—
326C22—121no—
327C22—121no—
328C22—121no—
329C22—121no—
330C22—121no—
331C22—122no—
332C22—122no—
333C22—122no—
334C22#6339311yescharacteristic, complemented
335C22C2×(C22⋊C9)⋊C411yescharacteristic
336C22#6369412yes—
337C4—21no—
338C4—61no—
339C4—722no—
340C4—722no—
341C3#7314511yescharacteristic
342C2—22no—
343C2—21no—
344C2—31no—
345C2—31no—
346C2—41no—
347C2—62no—
348C2—61no—
349C2—121no—
350C2#1058953411yescharacteristic
subgroupG/H
centerC2#10589534
commutatorC22×C22⋊C9C2×C4
FrattiniC23×C3C2×S4
Fitting, prime radicalC23×C3×D4D3
socleC23×C3#217
cosocleC23×C22⋊C9C22
hypercenterC2×D4(C22⋊C9)⋊C2
hypocenterC22⋊C9#99
LCSG ▷ C22×C22⋊C9 ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10589534C2semidirect
4. C23×C22⋊C9C4semidirect
7. C2×C4×C22⋊C9C4semidirect
101. C22⋊C9#99semidirect
104. C25Dic9semidirect
112. C23×C4Dic9semidirect
280. C23(C22⋊C9)⋊C4semidirect
298. C2×C4(C22⋊C9)⋊C4semidirect
334. C22#63393semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊C92
#105895342
#721303
#633934