Finite Group Databasebeta

← #11920237

Subgroups — #11920237

Order 1152.

346 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×#41⋊C9C211yesmaximal, characteristic
2#10589527C212yesmaximal
3#10589493C211yesmaximal, characteristic, complemented
4C4⋊#3688C211yesmaximal, characteristic, complemented
5#10589490C212yesmaximal, complemented
6#82535—31nomaximal
7C2×#41⋊C9C2211yescharacteristic
8C2×#3688C2212yes—
9#63432—41nomaximal
10C4×Q8⋊C9C2211yescharacteristic
11C4×Q8⋊C9C2211yescharacteristic
12#63421C2212yes—
13C3×C4×#41D311yescharacteristic
14#5470—31no—
15#5239—32no—
16#5031—31no—
17#5030—32no—
18#5021—31no—
19#5019—31no—
20#5018—32no—
21#5008—31no—
22#4996—32no—
23#4926—31no—
24#41⋊C9—21no—
25C2×Q8⋊C9C2311yescharacteristic
26#3688—22no—
27C42×C9—41no—
28C4⋊Dic9—41no—
29C4⋊Dic9—41no—
30Dic9⋊C4—42no—
31Dic9⋊C4—42no—
32#3116—91noSylow
33C2×C3×#41C2×D311yescharacteristic
34C3×C4×Q8C2×D311yescharacteristic
35C3×C4×Q8C2×D311yescharacteristic
36C3×C4×D4—31no—
37C3×C4×D4—31no—
38C3×#117—31no—
39C2×C3×C42—31no—
40C2×#216—32no—
41C2×#214—32no—
42#926—61no—
43#924—32no—
44#924—61no—
45#870—61no—
46#869—31no—
47#869—31no—
48C4×Dic6—32no—
49C4×Dic6—61no—
50#835—32no—
51#832—32no—
52#830—32no—
53#810—32no—
54#810—32no—
55#808—32no—
56#807—32no—
57C4⋊(C3⋊C8)—31no—
58C4⋊(C3⋊C8)—31no—
59#803—32no—
60C2×C4×C9—41no—
61C2×C4×C9—41no—
62C2×C4×C9—41no—
63C2×Dic9—42no—
64C2×Dic9—42no—
65Q8⋊C9#4111yescharacteristic
66#533—91no—
67C4×#41D911yescharacteristic
68#485—92no—
69#477—91no—
70#476—91no—
71#462—91no—
72#461—91no—
73#452—92no—
74#441—92no—
75#440—92no—
76#432—91no—
77C3×#41—21no—
78C3×#41—61no—
79C2×C3×Q8C22×D311yescharacteristic
80C2×C3×D4—31no—
81C22×C3×C4—31no—
82C22×C3×C4—31no—
83C22×C3×C4—31no—
84C2×Dic6—32no—
85C2×Dic6—61no—
86C3×C4⋊C4—31no—
87C3×C4⋊C4—31no—
88C3×C22⋊C4—61no—
89C3×C42—31no—
90C3×C42—31no—
91C3×C42—31no—
92C3×C42S411yescharacteristic
93#217—62no—
94#216—62no—
95#216—62no—
96#214—64no—
97C4⋊Dic3—32no—
98C4⋊Dic3—61no—
99C4⋊Dic3—61no—
100C4⋊Dic3—61no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103C4×Dic3—62no—
104C2×C3⋊C8—32no—
105C2×C3⋊C8—32no—
106C22×C9—41no—
107C4×C9—42no—
108C4×C9—81no—
109C4×C9—81no—
110Dic9—82no—
111Dic9—82no—
112C2×#41C2×D911yescharacteristic
113C2×Q16—92no—
114C2×SD16—92no—
115C4⋊Q8—91no—
116C4⋊Q8—91no—
117#125—181no—
118C22⋊Q8—92no—
119C22⋊Q8—181no—
120C4×Q8—92no—
121C4×Q8—181no—
122C4×Q8C2×D911yescharacteristic
123C4×Q8C2×D911yescharacteristic
124C4×D4—31no—
125C4×D4—31no—
126#117—31no—
127#117—181no—
128C2×C42—31no—
129#107—92no—
130#106—92no—
131C4⋊C8—91no—
132C4⋊C8—91no—
133#103—92no—
134#103—92no—
135#103—92no—
136#102—92no—
137C22⋊C8—92no—
138#97—92no—
139C23×C3—31no—
140C3×Q8—31no—
141C3×Q8#23511yescharacteristic
142C3×D4—32no—
143C3×D4—61no—
144C2×C3×C4—31no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—61no—
148C2×C3×C4—61no—
149C2×C3×C4—62no—
150C2×C3×C4—121no—
151C2×C3×C4C2×S411yescharacteristic
152C2×C3×C4C2×S411yescharacteristic
153C2×C3×C4C2×S411yescharacteristic
154C2×Dic3—62no—
155C2×Dic3—62no—
156Dic6—62no—
157Dic6—62no—
158Dic6—122no—
159C3⋊C8—62no—
160C3⋊C8—62no—
161C2×C9—41no—
162C2×C9—41no—
163C2×C9—41no—
164#41—21no—
165#41—61no—
166C2×Q8—92no—
167C2×Q8—181no—
168C2×Q8C22×D911yescharacteristic
169C2×D4—31no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—31no—
173Q16—182no—
174Q16—182no—
175SD16—184no—
176C2×C8—92no—
177C2×C8—92no—
178C4⋊C4—31no—
179C4⋊C4—31no—
180C4⋊C4—92no—
181C4⋊C4—181no—
182C4⋊C4—181no—
183C4⋊C4—181no—
184C4⋊C4—182no—
185C4⋊C4—182no—
186C22⋊C4—61no—
187C22⋊C4—182no—
188C42—31no—
189C42—31no—
190C42—31no—
191C42—182no—
192C42(C22⋊C9)⋊C211yescharacteristic
193C22×C3—61no—
194C22×C3—61no—
195C22×C3—61no—
196C22×C3C22×S411yescharacteristic
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—31no—
200C3×C4—31no—
201C3×C4—61no—
202C3×C4—61no—
203C3×C4#98412yes—
204Dic3—122no—
205Dic3—122no—
206C9—41noSylow
207C23—31no—
208Q8—31no—
209Q8—182no—
210Q8—182no—
211Q8—362no—
212Q8#369711yescharacteristic
213D4—32no—
214D4—61no—
215C2×C4—31no—
216C2×C4—31no—
217C2×C4—31no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—62no—
221C2×C4—121no—
222C2×C4—182no—
223C2×C4—182no—
224C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
225C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
226C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
227C8—182no—
228C8—182no—
229C2×C3—121no—
230C2×C3#591211yescharacteristic
231C2×C3C2×#98411yescharacteristic
232C2×C3#592311yescharacteristic
233C22—61no—
234C22—61no—
235C22—61no—
236C22C22×(C22⋊C9)⋊C211yescharacteristic
237C4—21no—
238C4—21no—
239C4—31no—
240C4—31no—
241C4—61no—
242C4—61no—
243C4—362no—
244C4—362no—
245C4#6369012yes—
246C3#8533811yescharacteristic
247C2—121no—
248C2#1059308711yescharacteristic
249C2C2×#6369011yescharacteristic
250C2#1059309811yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
FittingC3×C4×#41D3
prime radicalC2×C3×#41C2×D3
hypercenterC42(C22⋊C9)⋊C2
hypocenterQ8⋊C9#41
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #10589493C2semidirect
4. C4⋊#3688C2semidirect
5. #10589490C2semidirect

Maximal subgroups

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

subgroupindex
C4×#41⋊C92
#105895272
#105894932
C4⋊#36882
#105894902
#825353
#634324