Finite Group Databasebeta

← #11920230

Subgroups — #11920230

Order 1152.

482 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 61 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×#63689C212yesmaximal, complemented
2C2×C4×Q8⋊C9C211yesmaximal, characteristic, complemented
3#10589497C212yesmaximal, complemented
4C4⋊#3689C211yesmaximal, characteristic, complemented
5C4⋊#3688C211yesmaximal, characteristic, complemented
6#82441—31nomaximal
7C22×Q8⋊C9C2211yescharacteristic
8#63689—24no—
9C2×#3689C2212yes—
10C2×#3688C2212yes—
11#63492—41nomaximal
12C4×Q8⋊C9C2211yescharacteristic
13C4×Q8⋊C9C2211yescharacteristic
14C2×C3×C4×Q8D311yescharacteristic
15C2×#942—32no—
16#5477—31no—
17#5031—31no—
18#5031—31no—
19#5028—32no—
20#5028—32no—
21#5027—31no—
22#5027—31no—
23#4966—32no—
24#4924—31no—
25C22×C4×C9—41no—
26C2×#611—42no—
27C2×D36—41no—
28C2×Q8⋊C9D412yescomplemented
29C2×Q8⋊C9C2311yescharacteristic
30#3689—22no—
31#3688—22no—
32(C2×D9)⋊C4—42no—
33C4⋊Dic9—41no—
34#3037—91noSylow
35C22×C3×Q8C2×D311yescharacteristic
36C2×#235—32no—
37C3×C4×Q8—31no—
38C3×C4×Q8—31no—
39C3×C4×Q8C2×D311yescharacteristic
40C3×C4×Q8C2×D311yescharacteristic
41C2×C3×C4⋊C4—31no—
42C2×C3×C42—31no—
43C2×#216—32no—
44C2×#216—32no—
45#942—64no—
46#942—64no—
47C2×#215—32no—
48C2×#215—32no—
49#930—61no—
50#930—61no—
51C2×#208—32no—
52#875—32no—
53#874—31no—
54C4×D12—61no—
55C4×D12—61no—
56#869—31no—
57#810—32no—
58#810—32no—
59#809—32no—
60#809—32no—
61C4⋊(C3⋊C8)—31no—
62C4⋊(C3⋊C8)—31no—
63C4⋊(C3⋊C8)—32no—
64C23×C9—41no—
65C22×D9—42no—
66C2×C4×C9—41no—
67C2×C4×C9—41no—
68C2×C4×C9—82no—
69#611—84no—
70C2×Dic9—42no—
71D36—82no—
72Q8⋊C9C2×D411yescharacteristic
73C2×#137—92no—
74#532—91no—
75C2×C4×Q8D911yescharacteristic, complemented
76#464—92no—
77#464—92no—
78#462—91no—
79#462—91no—
80#460—91no—
81#460—91no—
82#423—91no—
83#417—92no—
84C2×C3×Q8—31no—
85C2×C3×Q8—32no—
86C2×C3×Q8D1212yes—
87C2×C3×Q8C22×D311yescharacteristic
88C22×C3×C4—31no—
89C22×C3×C4—31no—
90C22×C3×C4S411yescharacteristic
91C2×#67—62no—
92#235—64no—
93#235—64no—
94C2×D12—32no—
95C2×D12—61no—
96C2×D12—61no—
97C2×C4×D3—62no—
98C2×Dic6—32no—
99C3×C4⋊C4—31no—
100C3×C4⋊C4—31no—
101C3×C4⋊C4—61no—
102C3×C42—31no—
103C3×C42—31no—
104C3×C42—31no—
105C3×C42—31no—
106#216—64no—
107#216—62no—
108#216—62no—
109#215—64no—
110#215—62no—
111#215—62no—
112(C2×D3)⋊C4—62no—
113(C2×D3)⋊C4—62no—
114C4⋊Dic3—61no—
115C4⋊Dic3—61no—
116#208—64no—
117C2×C3⋊C8—32no—
118C2×C3⋊C8—32no—
119C22×C9—42no—
120C22×C9—41no—
121C22×C9—81no—
122C22×C9—81no—
123C2×D9—82no—
124C2×D9—82no—
125C2×D9—82no—
126C4×C9—42no—
127C4×C9—81no—
128Dic9—82no—
129C2×#41—92no—
130C22×Q8C2×D911yescharacteristic
131#137—184no—
132#137—184no—
133C2×Q16—92no—
134C2×Q16—92no—
135C2×SD16—92no—
136C2×SD16—92no—
137C2×M16—92no—
138C4⋊Q8—91no—
139#127—91no—
140#124—92no—
141#121—181no—
142#121—181no—
143C4×Q8—31no—
144C4×Q8—31no—
145C4×Q8C2×D911yescharacteristic
146C4×Q8C2×D911yescharacteristic
147C4×D4—181no—
148C4×D4—181no—
149C2×C4⋊C4—31no—
150C2×C42—31no—
151C4⋊C8—91no—
152C4⋊C8—91no—
153C4⋊C8—92no—
154#103—92no—
155#103—92no—
156#102—92no—
157#102—92no—
158C23×C3C2×S411yescharacteristic
159C22×D3—62no—
160C3×Q8—32no—
161C3×Q8—31no—
162C3×Q8—61no—
163C3×Q8C2×D1211yescharacteristic
164C2×C3×C4—22no—
165C2×C3×C4—32no—
166C2×C3×C4—32no—
167C2×C3×C4—31no—
168C2×C3×C4—31no—
169C2×C3×C4—31no—
170C2×C3×C4—31no—
171C2×C3×C4—121no—
172C2×C3×C4C2×S411yescharacteristic
173C2×C3×C4C2×S411yescharacteristic
174#67—124no—
175C2×Dic3—62no—
176D12—62no—
177D12—62no—
178D12—122no—
179D12—122no—
180C4×D3—124no—
181Dic6—62no—
182Dic6—62no—
183C3⋊C8—62no—
184C3⋊C8—62no—
185C2×C9—41no—
186C2×C9—41no—
187C2×C9—41no—
188C2×C9—82no—
189D9—162no—
190#41—184no—
191#41—184no—
192C2×Q8—31no—
193C2×Q8—32no—
194C2×Q8—92no—
195C2×Q8D3612yescomplemented
196C2×Q8C22×D911yescharacteristic
197C2×D4—92no—
198C2×D4—181no—
199C2×D4—182no—
200C2×D4—181no—
201C22×C4—31no—
202C22×C4—31no—
203C22×C4—182no—
204C22×C4(C22⋊C9)⋊C211yescharacteristic
205Q16—184no—
206Q16—182no—
207Q16—182no—
208SD16—184no—
209SD16—182no—
210SD16—182no—
211M16—184no—
212C2×C8—92no—
213C2×C8—92no—
214C4⋊C4—31no—
215C4⋊C4—31no—
216C4⋊C4—61no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C22⋊C4—182no—
220C22⋊C4—182no—
221C42—31no—
222C42—31no—
223C42—31no—
224C42—31no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3C4⋊S412yes—
228C22×C3C22×S411yescharacteristic
229C2×D3—122no—
230C2×D3—122no—
231C2×D3—122no—
232C3×C4—21no—
233C3×C4—31no—
234C3×C4—31no—
235C3×C4—32no—
236C3×C4—61no—
237C3×C4—61no—
238C3×C4#98312yes—
239Dic3—122no—
240C9—41noSylow
241C23—182no—
242C23C2×(C22⋊C9)⋊C211yescharacteristic
243Q8—32no—
244Q8—31no—
245Q8—61no—
246Q8—182no—
247Q8—182no—
248Q8C2×D3611yescharacteristic
249D4—182no—
250D4—182no—
251D4—362no—
252D4—364no—
253D4—362no—
254C2×C4—22no—
255C2×C4—31no—
256C2×C4—31no—
257C2×C4—32no—
258C2×C4—32no—
259C2×C4—31no—
260C2×C4—31no—
261C2×C4—121no—
262C2×C4—182no—
263C2×C4—364no—
264C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
265C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
266C8—182no—
267C8—182no—
268C2×C3—22no—
269C2×C3C2×C4⋊S411yescharacteristic
270C2×C3C2×#98311yescharacteristic
271C2×C3#592311yescharacteristic
272D3—242no—
273C22—21no—
274C22—21no—
275C22—362no—
276C22—362no—
277C22—362no—
278C22C4⋊((C22⋊C9)⋊C2)12yes—
279C22C22×(C22⋊C9)⋊C211yescharacteristic
280C4—21no—
281C4—31no—
282C4—32no—
283C4—31no—
284C4—61no—
285C4—61no—
286C4—362no—
287C4#6368912yescomplemented
288C3#8533111yescharacteristic
289C2—22no—
290C2—722no—
291C2C2×C4⋊((C22⋊C9)⋊C2)11yescharacteristic
292C2C2×#6368911yescharacteristic
293C2#1059309811yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
FittingC2×C3×C4×Q8D3
hypercenterC22×C4(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×D4
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#63689C2semidirect
2. C2×C4×Q8⋊C9C2semidirect
3. #10589497C2semidirect
4. C4⋊#3689C2semidirect
5. C4⋊#3688C2semidirect
28. C2×Q8⋊C9D4semidirect
75. C2×C4×Q8D9semidirect
195. C2×Q8D36semidirect
287. C4#63689semidirect

Maximal subgroups

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

subgroupindex
C2×#636892
C2×C4×Q8⋊C92
#105894972
C4⋊#36892
C4⋊#36882
#824413
#634924