Finite Group Databasebeta

← #24988366

Subgroups — #24988366

Order 11008.

738 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 147 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×Q8×Dic86C211yesmaximal, characteristic
2#19133281C212yesmaximal
3#19133023C212yesmaximal
4#19132919C211yesmaximal, characteristic
5C43×#1801C211yesmaximal, characteristic
6Q8×Dic86—24no—
7Q8×Dic86—24no—
8C2×#13063325C412yes—
9C2×#13063325C2211yescharacteristic
10C2×#13063324—22no—
11C2×#13063324—21no—
12C2×Q8×Dic43—21no—
13C2×C4×Dic86C412yes—
14C2×C4×Dic86C2211yescharacteristic
15#14582952C2212yes—
16#14582644—24no—
17#14582629—24no—
18#14582625—22no—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#423C2212yes—
21C2×#101×C43—21no—
22C43×#343—21no—
23C22×Dic86—22no—
24C22×Dic86—21no—
25C22×Dic86C2×C411yescharacteristic
26#13063325—22no—
27#13063325—24no—
28#13063325—24no—
29#13063325D414yes—
30#13063324—216no—
31#13063324—28no—
32Q8×Dic43—28no—
33C4×Dic86—24no—
34C4×Dic86—22no—
35C4×Dic86—24no—
36C4×Dic86D414yes—
37C2×C4⋊Dic43—22no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43C2×C412yes—
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—21no—
43C2×C4×Dic43—22no—
44C2×C4×Dic43—21no—
45C4⋊(C43⋊C8)—22no—
46C22⋊(C43⋊C8)—22no—
47C4×C43⋊C8—22no—
48C22×Q8×C43D411yescharacteristic
49C2×M16×C43—22no—
50C4×Q8×C43—22no—
51C4×Q8×C43—22no—
52C2×C4⋊C4×C43D412yes—
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C42×C43C2×C412yes—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—22no—
57C4⋊C8×C43—22no—
58#101×C43—42no—
59C2×Q8×C43—22no—
60C2×Q8×C43—22no—
61C2×Q8×C43SD1612yes—
62C2×Q8×C43Q1612yes—
63C22×C4×C43C22⋊C412yes—
64C22×C4×C43C22⋊C412yes—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—22no—
70C22×Dic43—21no—
71C2×Dic86—21no—
72C2×Dic86—24no—
73C2×Dic86—28no—
74C2×Dic86—24no—
75C2×Dic86—82no—
76C2×Dic86—84no—
77C2×Dic86C22⋊C412yes—
78M16×C43—42no—
79M16×C43—42no—
80C2×C8×C43—42no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—24no—
83C42×C43—22no—
84C42×C43—22no—
85C42×C43C2×D412yes—
86C42×C43C2×D412yes—
87C4⋊Dic43—28no—
88C4⋊Dic43—21no—
89C4⋊Dic43—22no—
90C4⋊Dic43—24no—
91C4⋊Dic43C22⋊C414yes—
92C4⋊Dic43C22⋊C412yes—
93Dic43⋊C4—28no—
94Dic43⋊C4—24no—
95C4×Dic43—28no—
96C4×Dic43—24no—
97C2×C43⋊C8—42no—
98C23×C43C2×C22⋊C411yescharacteristic
99Q8×C43—24no—
100Q8×C43—24no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—42no—
107C2×C4×C43#10314yes—
108C2×C4×C43C2×C22⋊C411yescharacteristic
109C2×C4×C43C2×C22⋊C411yescharacteristic
110C2×C4×C43#12012yes—
111C2×C4×C43#12012yes—
112C2×C4×C43C2×SD1611yescharacteristic
113C2×C4×C43C2×Q1611yescharacteristic
114C2×C4×C43#13712yes—
115C2×Dic43—24no—
116C2×Dic43—22no—
117C2×Dic43—24no—
118C2×Dic43—22no—
119C2×Dic43—44no—
120C2×Dic43—42no—
121Dic86—24no—
122Dic86—22no—
123Dic86—84no—
124Dic86—88no—
125Dic86#10114yescomplemented
126C8×C43—82no—
127C43⋊C8—82no—
128#8396—431nomaximal, Sylow
129C22×C43—21no—
130C22×C43—21no—
131C22×C43#37911yescharacteristic
132C22×C43C2×#10311yescharacteristic
133C22×C43#41911yescharacteristic
134C4×C43—22no—
135C4×C43—21no—
136C4×C43—24no—
137C4×C43—42no—
138C4×C43C2×#10112yes—
139C4×C43#44812yes—
140C4×C43#45112yes—
141Dic43—24no—
142Dic43—44no—
143Dic43—42no—
144C2×Q82—431no—
145#1801D4311yescharacteristic
146#1549—432no—
147#1487—432no—
148#1461—431no—
149C2×C43—21no—
150C2×C43—21no—
151C2×C43#178411yescharacteristic
152C2×C43#178711yescharacteristic
153C2×C43#179511yescharacteristic
154Q82—864no—
155Q82—864no—
156C2×C4⋊Q8—431no—
157C2×C4⋊Q8—432no—
158C2×C4⋊Q8—862no—
159C2×C4⋊Q8—861no—
160C2×C4×Q8—431no—
161C2×C4×Q8—432no—
162C2×C4×Q8—861no—
163C2×C4×Q8C2×D4311yescharacteristic
164#431—432no—
165#423C2×D4312yes—
166C2×#101—21no—
167#343—21no—
168#332—864no—
169Q8⋊C8—864no—
170#324—862no—
171C43#839611yescharacteristic, complemented, Sylow
172C22×Q8—431no—
173C22×Q8—862no—
174C22×Q8—861no—
175C22×Q8C22⋊D4311yescharacteristic
176C2×M16—22no—
177C4⋊Q8—434no—
178C4⋊Q8—864no—
179C4⋊Q8—864no—
180C4⋊Q8—8616no—
181C4⋊Q8—868no—
182C4⋊Q8—862no—
183C4×Q8—22no—
184C4×Q8—22no—
185C4×Q8—434no—
186C4×Q8—864no—
187C4×Q8—864no—
188C4×Q8—868no—
189C4×Q8—862no—
190C2×C4⋊C4—431no—
191C2×C4⋊C4—432no—
192C2×C4⋊C4—862no—
193C2×C4⋊C4—862no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4D17212yes—
197C2×C4⋊C4C22⋊D4311yescharacteristic
198C2×C42—862no—
199C2×C42—861no—
200C2×C42C4×D4312yes—
201C2×C42C22×D4311yescharacteristic
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—862no—
205#101—42no—
206C22⋊C8—862no—
207C4×C8—862no—
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—432no—
211C2×Q8—864no—
212C2×Q8—868no—
213C2×Q8—861no—
214C2×Q8—864no—
215C2×Q8—3442no—
216C2×Q8—3444no—
217C2×Q8#1062188312yes—
218C2×Q8#1062188512yes—
219C22×C4—861no—
220C22×C4—862no—
221C22×C4—861no—
222C22×C4(C2×D43)⋊C412yes—
223C22×C4(C2×D43)⋊C412yes—
224C22×C4C2×C4×D4311yescharacteristic
225C22×C4C2×D17211yescharacteristic
226C22×C4C2×C22⋊D4311yescharacteristic
227M16—42no—
228M16—42no—
229C2×C8—42no—
230C2×C8—1722no—
231C4⋊C4—22no—
232C4⋊C4—24no—
233C4⋊C4—432no—
234C4⋊C4—434no—
235C4⋊C4—868no—
236C4⋊C4—868no—
237C4⋊C4—861no—
238C4⋊C4—862no—
239C4⋊C4—864no—
240C4⋊C4—864no—
241C42—22no—
242C42—22no—
243C42—868no—
244C42—864no—
245C42D4×D4312yes—
246C42D4×D4312yes—
247C23C2×(C2×D43)⋊C411yescharacteristic
248Q8—24no—
249Q8—24no—
250Q8—434no—
251Q8—864no—
252Q8—862no—
253Q8—3444no—
254Q8—3448no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—864no—
262C2×C4—862no—
263C2×C4—864no—
264C2×C4—862no—
265C2×C4—1724no—
266C2×C4—1722no—
267C2×C4#1306324814yes—
268C2×C4C22⋊C4×D4311yescharacteristic
269C2×C4C22⋊C4×D4311yescharacteristic
270C2×C4#1306329312yes—
271C2×C4#1306329512yes—
272C2×C4C2×#1062188311yescharacteristic
273C2×C4C2×#1062188511yescharacteristic
274C2×C4#1306335512yes—
275C8—82no—
276C8—3442no—
277C22—21no—
278C22—21no—
279C22#1458275411yescharacteristic
280C22C2×#1306324811yescharacteristic
281C22#1458290711yescharacteristic
282C4—21no—
283C4—24no—
284C4—22no—
285C4—42no—
286C4—864no—
287C4—1724no—
288C4—1722no—
289C4#101×D4312yes—
290C4#1458303712yes—
291C4#1458305412yes—
292C2—21no—
293C2—21no—
294C2#1913451711yescharacteristic
295C2#1913452911yescharacteristic
296C2#1913456611yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1801C2
socleC22×C43#379
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1801D43
hypocenterC43#8396
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
125. Dic86#101semidirect
171. C43#8396semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic862
#191332812
#191330232
#191329192
C43×#18012
#839643