Finite Group Databasebeta

← #25014922

Subgroups — #25014922

Order 11008.

472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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
1#19139580C211yesmaximal, characteristic
2C2×#14582697C214yesmaximal
3C4×#13063244C211yesmaximal, characteristic
4C43×#1801C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6C2×#13063323C2212yes—
7C2×#13063244C2212yes—
8C4×#10621877—21no—
9#14582829—21no—
10#14582829—21no—
11#14582804C412yes—
12#14582797—21no—
13#14582797—21no—
14C4×C4⋊Dic43C411yescharacteristic
15#14582697—28no—
16#14582668—21no—
17C2×C4×Q8×C43C2211yescharacteristic
18C43×#423—21no—
19C2×#101×C43C2212yes—
20C43×#343—21no—
21C22×Dic86C2×C412yes—
22C2×#10621877—22no—
23#13063325—41no—
24#13063325—41no—
25#13063323—24no—
26#13063323—24no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—22no—
32C2×C4×Dic43C2×C412yes—
33#13063244—22no—
34#13063244D414yes—
35#13063236—41no—
36C4×C43⋊C8—41no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—21no—
40C22×Q8×C43C2311yescharacteristic
41C2×M16×C43—22no—
42C4×Q8×C43—41no—
43C4×Q8×C43—41no—
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C4⋊C8×C43—41no—
51C4⋊C8×C43—41no—
52#101×C43—24no—
53C2×Q8×C43—41no—
54C2×Q8×C43—41no—
55C2×Q8×C43C2×D412yes—
56C2×Q8×C43#4112yes—
57C22×C4×C43C22⋊C411yescharacteristic
58C22×C4×C43C22⋊C411yescharacteristic
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×Dic43—22no—
65C22×Dic43—22no—
66C2×Dic86—24no—
67C2×Dic86—42no—
68C2×Dic86—42no—
69M16×C43—42no—
70M16×C43—42no—
71C2×C8×C43—42no—
72C4⋊C4×C43—41no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C42×C43—21no—
76C42×C43—21no—
77C42×C43—21no—
78C42×C43—21no—
79C42×C43—21no—
80C42×C43—21no—
81C4⋊Dic43—24no—
82C4⋊Dic43—42no—
83C4⋊Dic43—41no—
84C4⋊Dic43—41no—
85Dic43⋊C4—44no—
86Dic43⋊C4—42no—
87Dic43⋊C4—42no—
88C4×Dic43—24no—
89#10621877—24no—
90#10621877—42no—
91C2×C43⋊C8—42no—
92C23×C43C2×C22⋊C411yescharacteristic
93Q8×C43—42no—
94Q8×C43—42no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—22no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43#9911yescharacteristic
109C2×C4×C43#9911yescharacteristic
110C2×C4×C43C4×D412yes—
111C2×C4×C43#12112yes—
112C2×C4×C43#12411yescharacteristic
113C2×C4×C43#12711yescharacteristic
114C2×Dic43—24no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117C2×Dic43—42no—
118C2×Dic43—42no—
119C2×Dic43—42no—
120Dic86—84no—
121C8×C43—82no—
122C43⋊C8—44no—
123#13227—431nomaximal, Sylow
124C22×C43—21no—
125C22×C43—21no—
126C22×C43#39011yescharacteristic
127C22×C43C2×#9911yescharacteristic
128C22×C43#41011yescharacteristic
129C4×C43—21no—
130C4×C43—22no—
131C4×C43—21no—
132C4×C43—22no—
133C4×C43—21no—
134C4×C43—41no—
135C4×C43—41no—
136C4×C43—41no—
137C4×C43#35612yescomplemented
138Dic43—44no—
139Dic43—82no—
140#2546—431no—
141C2×#356—434no—
142#1801D4311yescharacteristic
143C4×#101—431no—
144C2×C43—21no—
145C2×C43—21no—
146C2×C43#196411yescharacteristic
147C2×C43C2×#35611yescharacteristic
148C2×C43#213511yescharacteristic
149C2×C4⋊Q8—432no—
150C2×C4⋊Q8—431no—
151C2×C4×Q8C2×D4311yescharacteristic
152#423—21no—
153C2×#101—432no—
154C2×#101C2×D4312yes—
155C4×M16—861no—
156#398—861no—
157#398—861no—
158#391—432no—
159#389—861no—
160#389—861no—
161C4×C4⋊C4—431no—
162#356—868no—
163#343—21no—
164#343—861no—
165C43#1322711yescharacteristic, complemented, Sylow
166C22×Q8—432no—
167C22×Q8C22×D4311yescharacteristic
168C2×M16—22no—
169C2×M16—862no—
170C4⋊Q8—864no—
171C4⋊Q8—864no—
172C4⋊Q8—1721no—
173C4⋊Q8—1721no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—861no—
177C2×C4⋊C4—861no—
178C2×C4⋊C4—861no—
179C2×C4⋊C4—862no—
180C2×C4⋊C4—862no—
181C2×C4⋊C4C4×D4311yescharacteristic
182C2×C4⋊C4D17211yescharacteristic
183C2×C4⋊C4C22⋊D4311yescharacteristic
184C2×C42—432no—
185C2×C42C4×D4311yescharacteristic
186C2×C42D17211yescharacteristic
187C2×C42C22⋊D4311yescharacteristic
188C4⋊C8—41no—
189C4⋊C8—41no—
190#101—24no—
191#101—434no—
192#101—862no—
193#97—1721no—
194C4×C8—1721no—
195#95—861no—
196#95—862no—
197#95—862no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8—864no—
201C2×Q8—1722no—
202C2×Q8—1722no—
203C2×Q8D4×D4312yes—
204C2×Q8#1062190212yes—
205C22×C4—862no—
206C22×C4—862no—
207C22×C4(C2×D43)⋊C411yescharacteristic
208C22×C4(C2×D43)⋊C411yescharacteristic
209C22×C4(C2×D43)⋊C411yescharacteristic
210C22×C4(C2×D43)⋊C411yescharacteristic
211C22×C4C2×C4×D4311yescharacteristic
212C22×C4C2×D17211yescharacteristic
213C22×C4C2×C22⋊D4311yescharacteristic
214M16—42no—
215M16—42no—
216M16—864no—
217M16—1722no—
218C2×C8—42no—
219C2×C8—1722no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—864no—
224C4⋊C4—1722no—
225C4⋊C4—1721no—
226C4⋊C4—1721no—
227C4⋊C4—1724no—
228C4⋊C4—1722no—
229C4⋊C4—1722no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—864no—
237C23C2×(C2×D43)⋊C411yescharacteristic
238Q8—42no—
239Q8—42no—
240Q8—3444no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—864no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4—1722no—
260C2×C4#1306323911yescharacteristic
261C2×C4#1306323911yescharacteristic
262C2×C4#1306328712yes—
263C2×C4#1306330012yes—
264C2×C4#1306331411yescharacteristic
265C2×C4#1306332111yescharacteristic
266C8—82no—
267C8—1724no—
268C22—21no—
269C22—21no—
270C22#1458280011yescharacteristic
271C22C2×#1306323911yescharacteristic
272C22#1458287211yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—3442no—
282C4—1724no—
283C4#1458269712yescomplemented
284C2—21no—
285C2—21no—
286C2#1913543011yescharacteristic
287C2C2×#1458269711yescharacteristic
288C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1801C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC22×Q8×C43C23
hypercenter#1801D43
hypocenterC43#13227
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
137. C4×C43#356semidirect
165. C43#13227semidirect
283. C4#14582697semidirect

Maximal subgroups

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

subgroupindex
#191395802
C2×#145826972
C4×#130632442
C43×#18012
#1322743