Finite Group Databasebeta

← #25017019

Subgroups — #25017019

Order 11008.

304 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 67 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#19145678C211yesmaximal, characteristic
2#19136284C211yesmaximal, characteristic
3#19132767C212yesmaximal, complemented
4#19132763C212yesmaximal, complemented
5C43×#2135C211yesmaximal, characteristic
6#14583511C411yescharacteristic
7#14583294C411yescharacteristic
8#14583278C2211yescharacteristic
9#14583267C2211yescharacteristic
10#14583253C411yescharacteristic
11#14583118—21no—
12#14583106—21no—
13#14583061—21no—
14#14583055—21no—
15#14582960C411yescharacteristic
16C2×#13063244—21no—
17#14582698C2212yes—
18#14582696—21no—
19C43×#536C2211yescharacteristic
20C43×#413—21no—
21C43×#356—21no—
22C43×#356C2212yes—
23C2×#10621885—21no—
24C2×#10621885—21no—
25C2×#10621885—21no—
26C2×#10621883—21no—
27C2×#10621877—41no—
28#13063325C2×C411yescharacteristic
29#13063318—41no—
30#13063317C2×C411yescharacteristic
31#13063315—41no—
32#13063304—21no—
33C4×Dic86—21no—
34C4⋊(C43⋊C8)—21no—
35#13063249—21no—
36#13063249—21no—
37#13063249—21no—
38#13063246—21no—
39#13063244—22no—
40#13063244—41no—
41C22⋊(C43⋊C8)—21no—
42#13063236C2×C411yescharacteristic
43C4×C43⋊C8C2×C411yescharacteristic
44C2×#41×C43D411yescharacteristic
45C22×Q8×C43D411yescharacteristic
46C2×M16×C43—41no—
47C4⋊Q8×C43D411yescharacteristic
48C4⋊Q8×C43C2311yescharacteristic
49#124×C43C2×C411yescharacteristic
50#124×C43D411yescharacteristic
51#123×C43—41no—
52C22⋊Q8×C43—41no—
53#117×C43C2×C411yescharacteristic
54#101×C43—22no—
55#100×C43—41no—
56#41×C43—81no—
57C2×Q8×C43—21no—
58C2×Q8×C43—81no—
59C2×Q8×C43C22⋊C411yescharacteristic
60C2×Q8×C43C2×D411yescharacteristic
61C2×Q8×C43C2×D411yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C22⋊C411yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C22⋊C411yescharacteristic
67C2×Dic86—21no—
68M16×C43—42no—
69M16×C43—81no—
70C2×C8×C43—81no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43—41no—
73C4⋊C4×C43—41no—
74C22⋊C4×C43—21no—
75C22⋊C4×C43—41no—
76C22⋊C4×C43—41no—
77C42×C43C22⋊C411yescharacteristic
78C42×C43C22×C411yescharacteristic
79C22⋊Dic43—41no—
80#10621885—81no—
81#10621885—81no—
82#10621885—81no—
83#10621883—81no—
84C4⋊Dic43—21no—
85C4⋊Dic43—41no—
86Dic43⋊C4—41no—
87Dic43⋊C4—41no—
88Dic43⋊C4—41no—
89C4×Dic43—41no—
90#10621877—42no—
91#10621877—81no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—81no—
95C23×C43—21no—
96C23×C43#9911yescharacteristic
97Q8×C43—41no—
98Q8×C43—41no—
99Q8×C43—41no—
100Q8×C43—81no—
101D4×C43—41no—
102D4×C43—81no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43#9911yescharacteristic
114C2×C4×C43C2×C22⋊C411yescharacteristic
115C2×Dic43—41no—
116C2×Dic43—41no—
117Dic86—41no—
118Dic86—41no—
119C8×C43—82no—
120C43⋊C8—41no—
121C43⋊C8—41no—
122C43⋊C8—82no—
123#13612—431nomaximal, Sylow
124C22×C43—21no—
125C22×C43—41no—
126C22×C43—41no—
127C22×C43—81no—
128C22×C43C2×#9911yescharacteristic
129C4×C43—21no—
130C4×C43—21no—
131C4×C43—41no—
132C4×C43—41no—
133C4×C43—41no—
134C4×C43—41no—
135C4×C43—41no—
136Dic43—81no—
137Dic43—81no—
138#3223—431no—
139#2135D4311yescharacteristic
140#2133—431no—
141#1413—432no—
142#1411—432no—
143C2×C43—21no—
144C2×C43—41no—
145C2×C43—81no—
146C2×C43#212711yescharacteristic
147#541—431no—
148#536C2×D4311yescharacteristic
149#497—431no—
150#494—431no—
151#491—431no—
152#488—431no—
153#464—861no—
154#462—861no—
155#452—861no—
156#451—861no—
157#433—431no—
158#413—21no—
159C2×#101—861no—
160#356—21no—
161#356—432no—
162#356C2×D4312yes—
163#355—861no—
164C43#1361211yescharacteristic, complemented, Sylow
165C2×#41C22⋊D4311yescharacteristic
166C22×Q8D17211yescharacteristic
167C2×Q16—861no—
168C2×Q16—861no—
169C2×Q16—861no—
170C2×SD16—861no—
171C2×M16—41no—
172C2×M16—1721no—
173C4⋊Q8—431no—
174C4⋊Q8C22⋊D4311yescharacteristic
175C4⋊Q8C22×D4311yescharacteristic
176#126—1721no—
177#125—431no—
178#125—1721no—
179#124C4×D4311yescharacteristic
180#124D17211yescharacteristic
181#123—41no—
182C22⋊Q8—41no—
183C22⋊Q8—861no—
184C4×Q8—861no—
185#117C4×D4311yescharacteristic
186C4⋊C8—861no—
187#103—861no—
188#103—861no—
189#103—861no—
190#102—861no—
191#101—22no—
192#101—862no—
193#101—1721no—
194#100—41no—
195C22⋊C8—861no—
196#97—431no—
197C4×C8—431no—
198#41—81no—
199C2×Q8—21no—
200C2×Q8—81no—
201C2×Q8—861no—
202C2×Q8(C2×D43)⋊C411yescharacteristic
203C2×Q8C2×D17211yescharacteristic
204C2×Q8C2×C22⋊D4311yescharacteristic
205C2×D4—21no—
206C2×D4(C2×D43)⋊C411yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4(C2×D43)⋊C411yescharacteristic
210Q16—3441no—
211Q16—3441no—
212Q16—3441no—
213SD16—3441no—
214M16—42no—
215M16—81no—
216M16—3441no—
217M16—1722no—
218C2×C8—81no—
219C2×C8—861no—
220C2×C8—861no—
221C2×C8—3441no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—861no—
226C4⋊C4—1721no—
227C4⋊C4—1721no—
228C4⋊C4—1721no—
229C4⋊C4—1721no—
230C22⋊C4—21no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—1721no—
234C42—1721no—
235C42(C2×D43)⋊C411yescharacteristic
236C42C2×C4×D4311yescharacteristic
237C23—21no—
238C23#1306323911yescharacteristic
239Q8—41no—
240Q8—41no—
241Q8—41no—
242Q8—81no—
243Q8—1721no—
244Q8—1721no—
245D4—41no—
246D4—81no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—1721no—
258C2×C4—1721no—
259C2×C4#1306323911yescharacteristic
260C2×C4C2×(C2×D43)⋊C411yescharacteristic
261C8—82no—
262C8—3442no—
263C8—1721no—
264C8—1721no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22C2×#1306323911yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—3441no—
278C4—3441no—
279C2—21no—
280C2—41no—
281C2—81no—
282C2#1913626211yescharacteristic
subgroupG/H
centerC2#19136262
commutatorC42×C43C22×C4
FrattiniC4⋊Q8C22×D43
FittingC43×#2135C2
socleC2×C43#2127
prime radicalC2×#41×C43D4
cosocleC4⋊Q8×C43C23
hypercenter#2135D43
hypocenterC43#13612
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #536 ◁ #2135

Complements

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

NH ≅ G/Ntype
3. #19132767C2semidirect
4. #19132763C2semidirect
164. C43#13612semidirect

Maximal subgroups

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

subgroupindex
#191456782
#191362842
#191327672
#191327632
C43×#21352
#1361243