Finite Group Databasebeta

← #25009658

Subgroups — #25009658

Order 11008.

342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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#19139833C211yesmaximal, characteristic
2#19135941C211yesmaximal, characteristic
3#19133639C211yesmaximal, characteristic
4#19133636C211yesmaximal, characteristic
5#19132621C211yesmaximal, characteristic
6#19132540C211yesmaximal, characteristic
7C43×#1353C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583235—21no—
10#14583234—21no—
11#14582941—21no—
12#14582841—21no—
13#14582838C2211yescharacteristic
14#14582796—21no—
15#14582794—21no—
16#14582768C2211yescharacteristic
17#14582763—21no—
18#14582763—21no—
19#14582750—21no—
20#14582660—21no—
21#14582637—21no—
22#14582635—21no—
23#14582625C2211yescharacteristic
24C43×#400C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27#13063324—41no—
28#13063316—41no—
29#13063304—21no—
30#13063304—21no—
31#13063284—21no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×C4⋊Dic43D411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43—21no—
41C2×C4×Dic43D411yescharacteristic
42#13063259—41no—
43#13063259—41no—
44#13063258—41no—
45#13063257—41no—
46#13063250—41no—
47#13063248—41no—
48C22⋊(C43⋊C8)—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95D411yescharacteristic
55C2×M16×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43C2311yescharacteristic
58C22⋊C8×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×Dic86—21no—
72C2×Dic86—21no—
73M16×C43—22no—
74M16×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C22⋊Dic43—41no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43—21no—
83C4⋊Dic43—21no—
84C4⋊Dic43—41no—
85C4⋊Dic43—41no—
86Dic43⋊C4—42no—
87Dic43⋊C4—42no—
88Dic43⋊C4—42no—
89Dic43⋊C4—42no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—81no—
93C4×Dic43—21no—
94C4×Dic43—42no—
95C4×Dic43—42no—
96C4×Dic43—41no—
97C4×Dic43Q1612yes—
98C2×C43⋊C8—41no—
99C23×C43#12011yescharacteristic
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43C2×Q1611yescharacteristic
113C2×C4×C43#13711yescharacteristic
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128Dic86—81no—
129Dic86—81no—
130C8×C43—42no—
131C8×C43—81no—
132C43⋊C8—81no—
133#12257—431nomaximal, Sylow
134C22×C43—21no—
135C22×C43—21no—
136C22×C43#45111yescharacteristic
137C22×C43#45611yescharacteristic
138C22×C43B(4,𝔽2)11yescharacteristic
139C4×C43—21no—
140C4×C43—21no—
141C4×C43—41no—
142C4×C43—41no—
143C4×C43—81no—
144C4×C43—81no—
145Dic43—24no—
146Dic43—81no—
147Dic43—81no—
148Dic43—81no—
149Dic43—81no—
150Dic43—81no—
151#2571—431no—
152#2060—431no—
153#1617—431no—
154#1617—431no—
155#1353—431no—
156#1353D4311yescharacteristic
157#1325—431no—
158C2×C43—21no—
159C2×C43—21no—
160C2×C43#160511yescharacteristic
161C2×C43#219811yescharacteristic
162C2×C43#220411yescharacteristic
163#544—431no—
164#484—861no—
165#484—861no—
166#428—861no—
167#400—431no—
168#400—861no—
169#400C2×D4311yescharacteristic
170#389—861no—
171#389—861no—
172#384—431no—
173#382—861no—
174#382—861no—
175C4×C4⋊C4—861no—
176#343C2×D4311yescharacteristic
177#339—861no—
178#328—861no—
179#328—861no—
180#324—431no—
181#324C2×D4311yescharacteristic
182C43#1225711yescharacteristic, complemented, Sylow
183C2×M16—21no—
184C4⋊Q8—1721no—
185#125—1721no—
186C22⋊Q8—861no—
187C22⋊Q8—861no—
188#117—861no—
189C2×C4⋊C4—431no—
190C2×C4⋊C4—431no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4—861no—
193C2×C4⋊C4—861no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4D17211yescharacteristic
197C2×C4⋊C4C22×D4311yescharacteristic
198C2×C42—431no—
199C2×C42—861no—
200C2×C42—861no—
201#107—1721no—
202#107—1721no—
203#107—1721no—
204#106—1721no—
205#103—1721no—
206#103—1721no—
207C22⋊C8—21no—
208C22⋊C8—861no—
209#95—21no—
210#95—21no—
211#95—431no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95D17211yescharacteristic
218C2×Q8—861no—
219C2×Q8—861no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4—861no—
225C22×C4—861no—
226C22×C4C2×D17211yescharacteristic
227C22×C4D4×D4311yescharacteristic
228C22×C4D4×D4311yescharacteristic
229M16—22no—
230M16—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—1721no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—861no—
237C4⋊C4—861no—
238C4⋊C4—861no—
239C4⋊C4—861no—
240C4⋊C4—3441no—
241C4⋊C4—1721no—
242C4⋊C4—1721no—
243C4⋊C4—1721no—
244C4⋊C4—1721no—
245C4⋊C4—1722no—
246C4⋊C4—1722no—
247C4⋊C4—1722no—
248C4⋊C4—1722no—
249C22⋊C4—1721no—
250C42—432no—
251C42—861no—
252C42—1721no—
253C42—1722no—
254C42—1722no—
255C23#1306329511yescharacteristic
256Q8—3441no—
257Q8—3441no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4Q16×D4311yescharacteristic
285C2×C4#1306335411yescharacteristic
286C8—42no—
287C8—81no—
288C8—3441no—
289C22—21no—
290C22—21no—
291C22#1458305611yescharacteristic
292C22#1458308311yescharacteristic
293C22#1458308711yescharacteristic
294C4—21no—
295C4—21no—
296C4—41no—
297C4—41no—
298C4—81no—
299C4—81no—
300C4—864no—
301C4—3441no—
302C4—3441no—
303C4—3441no—
304C4—3441no—
305C4—3441no—
306C2—21no—
307C2—21no—
308C2#1913357011yescharacteristic
309C2#1913659211yescharacteristic
310C2#1913662211yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1353C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1353D43
hypocenterC43#12257
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
182. C43#12257semidirect

Maximal subgroups

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

subgroupindex
#191398332
#191359412
#191336392
#191336362
#191326212
#191325402
C43×#13532
#1225743