Finite Group Databasebeta

← #24990131

Subgroups — #24990131

Order 11008.

438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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#19137213C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic
3#19132502C212yesmaximal
4#19132500C212yesmaximal
5C43×#1463C211yesmaximal, characteristic
6C2×#13063284C411yescharacteristic
7C2×#13063284C411yescharacteristic
8#14582863C2212yes—
9#14582798—21no—
10#14582798—21no—
11#14582798—21no—
12#14582798—21no—
13#14582759C411yescharacteristic
14#14582759C411yescharacteristic
15#14582759C2211yescharacteristic
16#14582759C2211yescharacteristic
17#14582625—21no—
18#14582625—21no—
19C22×C4⋊C4×C43C2211yescharacteristic
20C43×#407C2212yes—
21C43×#324—21no—
22C43×#324—21no—
23C2×#10621877—22no—
24#13063284—42no—
25#13063284—42no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C22⋊Dic43C2×C411yescharacteristic
33C2×C22⋊Dic43C2×C411yescharacteristic
34C2×C22⋊Dic43C2×C411yescharacteristic
35C2×C22⋊Dic43C2×C411yescharacteristic
36C2×C4×Dic43—21no—
37C2×C4×Dic43—21no—
38C22⋊(C43⋊C8)—22no—
39C22⋊(C43⋊C8)—22no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43C2×C411yescharacteristic
46C23×C4×C43C2311yescharacteristic
47C2×M16×C43—22no—
48C2×C4⋊C4×C43—22no—
49C2×C4⋊C4×C43—22no—
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43D411yescharacteristic
54C22⋊C8×C43—22no—
55C22⋊C8×C43—22no—
56C24×C43C22×C411yescharacteristic
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—81no—
64C22×C4×C43—81no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43#4112yes—
72C22×C4×C43#4112yes—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77M16×C43—82no—
78C2×C8×C43—42no—
79C4⋊C4×C43—22no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—22no—
83C22⋊Dic43—41no—
84C22⋊Dic43—41no—
85C22⋊Dic43—41no—
86C22⋊Dic43—41no—
87C4⋊Dic43—42no—
88C4⋊Dic43—42no—
89C4⋊Dic43—81no—
90C4⋊Dic43—81no—
91C4⋊Dic43—81no—
92C4⋊Dic43—81no—
93C4×Dic43—42no—
94C4×Dic43—42no—
95#10621877—82no—
96C2×C43⋊C8—42no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—41no—
100C23×C43—41no—
101C23×C43C2×C22⋊C411yescharacteristic
102C23×C43#11711yescharacteristic
103C23×C43#11711yescharacteristic
104C2×C4×C43—24no—
105C2×C4×C43—24no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—42no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—42no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43#10012yes—
121C2×C4×C43#10112yes—
122C2×C4×C43#12312yes—
123C2×C4×C43#12312yes—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C8×C43—82no—
137C43⋊C8—82no—
138#8757—431nomaximal, Sylow
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—42no—
148C22×C43—42no—
149C22×C43#38111yescharacteristic
150C22×C43C2×#10011yescharacteristic
151C22×C43C2×#10111yescharacteristic
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—22no—
155C4×C43—22no—
156C4×C43—41no—
157C4×C43—41no—
158Dic43—81no—
159Dic43—81no—
160Dic43—81no—
161Dic43—81no—
162#2316—431no—
163#1463—431no—
164#1463D4311yescharacteristic
165#1305—432no—
166#1305—432no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43—41no—
170C2×C43—41no—
171C2×C43#182111yescharacteristic
172C2×C43#182811yescharacteristic
173C2×C43#183011yescharacteristic
174C2×#117—431no—
175C2×#117—431no—
176C22×C4⋊C4C2×D4311yescharacteristic
177#407—432no—
178#407C2×D4312yes—
179#389—861no—
180#389—861no—
181#389—861no—
182#389—861no—
183#380—431no—
184#380—431no—
185#380—431no—
186#380—431no—
187#324—21no—
188#324—21no—
189#324—861no—
190#324—861no—
191C43#875711yescharacteristic, complemented, Sylow
192C23×C4C4×D4311yescharacteristic
193C23×C4C4×D4311yescharacteristic
194C23×C4C22×D4311yescharacteristic
195C2×M16—22no—
196C2×M16—862no—
197#117—1722no—
198#117—1722no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4D17211yescharacteristic
208C2×C4⋊C4D17211yescharacteristic
209C2×C4⋊C4C22⋊D4311yescharacteristic
210C2×C4⋊C4C22⋊D4311yescharacteristic
211C2×C22⋊C4—431no—
212C2×C22⋊C4—431no—
213C2×C22⋊C4—431no—
214C2×C22⋊C4—431no—
215C2×C42—861no—
216C2×C42—861no—
217C22⋊C8—22no—
218C22⋊C8—22no—
219C22⋊C8—862no—
220C22⋊C8—862no—
221#95—861no—
222#95—861no—
223#95—861no—
224#95—861no—
225C24C2×C4×D4311yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—81no—
233C22×C4—81no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4—861no—
238C22×C4(C2×D43)⋊C411yescharacteristic
239C22×C4(C2×D43)⋊C411yescharacteristic
240C22×C4(C2×D43)⋊C411yescharacteristic
241C22×C4(C2×D43)⋊C411yescharacteristic
242C22×C4C2×D17211yescharacteristic
243C22×C4#1062190012yes—
244C22×C4#1062190012yes—
245C22×C4C2×C22⋊D4311yescharacteristic
246M16—82no—
247M16—3442no—
248C2×C8—42no—
249C2×C8—1722no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—3441no—
255C4⋊C4—3441no—
256C4⋊C4—3441no—
257C4⋊C4—3441no—
258C4⋊C4—1722no—
259C4⋊C4—1722no—
260C22⋊C4—1721no—
261C22⋊C4—1721no—
262C22⋊C4—1721no—
263C22⋊C4—1721no—
264C42—1722no—
265C42—1722no—
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23C2×(C2×D43)⋊C411yescharacteristic
271C23#1306328111yescharacteristic
272C23#1306328111yescharacteristic
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4#1306324112yes—
302C2×C4#1306324312yes—
303C2×C4#1306330612yes—
304C2×C4#1306330912yes—
305C8—82no—
306C8—3442no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22#1458276011yescharacteristic
318C22C2×#1306324111yescharacteristic
319C22C2×#1306324311yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—41no—
325C4—41no—
326C4—3441no—
327C4—3441no—
328C4—3441no—
329C4—3441no—
330C2—21no—
331C2—21no—
332C2—41no—
333C2—41no—
334C2#1913467311yescharacteristic
335C2#1913470111yescharacteristic
336C2#1913470711yescharacteristic
subgroupG/H
centerC22#14582760
commutator, prime radicalC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1463C2
socleC22×C43#381
cosocleC23×C4×C43C23
hypercenter#1463D43
hypocenterC43#8757
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
191. C43#8757semidirect

Maximal subgroups

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

subgroupindex
#191372132
#191329252
#191325022
#191325002
C43×#14632
#875743