Finite Group Databasebeta

← #24999793

Subgroups — #24999793

Order 11008.

352 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 73 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#19140253C211yesmaximal, characteristic
2#19135539C211yesmaximal, characteristic
3#19133145C211yesmaximal, characteristic
4#19133108C211yesmaximal, characteristic
5#19132489C211yesmaximal, characteristic
6#19132452C211yesmaximal, characteristic
7C43×#1288C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14582956C2211yescharacteristic
10#14582833—21no—
11#14582831—21no—
12#14582796—21no—
13#14582796—21no—
14#14582786—21no—
15#14582782—21no—
16C4×C4⋊Dic43C2211yescharacteristic
17#14582745C2211yescharacteristic
18#14582660—21no—
19#14582660—21no—
20#14582637—21no—
21#14582637—21no—
22#14582635—21no—
23#14582635—21no—
24C43×#432C2211yescharacteristic
25C4×M16×C43C2211yescharacteristic
26C43×#383C2211yescharacteristic
27#13063325Q811yescharacteristic
28#13063325Q811yescharacteristic
29#13063317—21no—
30#13063304—21no—
31#13063304—21no—
32C4×Dic86—21no—
33C4×Dic86—21no—
34#13063284—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43D411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45C4⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47#13063236—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95D411yescharacteristic
53C43⋊#95D411yescharacteristic
54C2×M16×C43—21no—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—21no—
57C22⋊C8×C43—21no—
58#97×C43—21no—
59#97×C43—21no—
60C4×C8×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43D411yescharacteristic
64#95×C43D411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C2×Dic86—21no—
75C2×Dic86—21no—
76M16×C43—22no—
77M16×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C42×C43C2×Q811yescharacteristic
81C42×C43#4111yescharacteristic
82C42×C43#4111yescharacteristic
83C42×C43#4111yescharacteristic
84C22⋊Dic43—41no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43—42no—
90C4⋊Dic43—42no—
91C4⋊Dic43—81no—
92Dic43⋊C4—42no—
93Dic43⋊C4—42no—
94Dic43⋊C4—42no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—81no—
98C4×Dic43—42no—
99C4×Dic43—41no—
100C4×Dic43—41no—
101C4×Dic43—41no—
102C2×C43⋊C8—41no—
103C23×C43#12011yescharacteristic
104C2×C4×C43—21no—
105C2×C4×C43—21no—
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×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43C22⋊Q811yescharacteristic
115C2×C4×C43C22⋊Q811yescharacteristic
116C2×C4×C43C22⋊Q811yescharacteristic
117C2×C4×C43#12411yescharacteristic
118C2×C4×C43#12411yescharacteristic
119C2×C4×C43#12411yescharacteristic
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—41no—
123C2×Dic43—41no—
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—
134Dic86—81no—
135Dic86—81no—
136C8×C43—42no—
137C8×C43—81no—
138C43⋊C8—81no—
139#10381—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43#39311yescharacteristic
143C22×C43#45511yescharacteristic
144C22×C43#45611yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—81no—
152C4×C43—81no—
153Dic43—42no—
154Dic43—42no—
155Dic43—81no—
156Dic43—81no—
157Dic43—81no—
158Dic43—81no—
159#2606—431no—
160#1986—431no—
161#1515—431no—
162#1506—431no—
163#1300—431no—
164#1288D4311yescharacteristic
165#1285—431no—
166C2×C43—21no—
167C2×C43—21no—
168C2×C43#202811yescharacteristic
169C2×C43#203111yescharacteristic
170C2×C43#203111yescharacteristic
171#533—431no—
172#432—431no—
173#432C2×D4311yescharacteristic
174C4×M16C2×D4311yescharacteristic
175#398—861no—
176#398—861no—
177#389—861no—
178#389—861no—
179#387—861no—
180#387—861no—
181#383C2×D4311yescharacteristic
182C4×C4⋊C4—431no—
183#376—431no—
184#339—861no—
185#339—861no—
186#328—861no—
187#328—861no—
188#328—861no—
189#328—861no—
190C43#1038111yescharacteristic, complemented, Sylow
191C2×M16—21no—
192C4⋊Q8—431no—
193C4⋊Q8—431no—
194#125—861no—
195C22⋊Q8—861no—
196C22⋊Q8—861no—
197C4×Q8—861no—
198C4×Q8—861no—
199#117—861no—
200C2×C4⋊C4—861no—
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×C42—431no—
208C2×C42—431no—
209C2×C42—861no—
210C2×C42C22×D4311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—861no—
213C22⋊C8—21no—
214C22⋊C8—861no—
215#97—21no—
216#97—21no—
217#97—861no—
218C4×C8—21no—
219#95—21no—
220#95—21no—
221#95—431no—
222#95—431no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95—861no—
227#95D17211yescharacteristic
228#95D17211yescharacteristic
229C2×Q8—861no—
230C2×Q8—861no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4C2×D17211yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C22×C4D4×D4311yescharacteristic
240M16—22no—
241M16—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—1721no—
245C4⋊C4—861no—
246C4⋊C4—861no—
247C4⋊C4—861no—
248C4⋊C4—861no—
249C4⋊C4—3441no—
250C4⋊C4—3441no—
251C4⋊C4—1722no—
252C4⋊C4—1722no—
253C4⋊C4—1722no—
254C4⋊C4—1722no—
255C4⋊C4—1722no—
256C4⋊C4—1721no—
257C4⋊C4—1721no—
258C22⋊C4—1721no—
259C42—1721no—
260C42—1721no—
261C42—1722no—
262C42—1721no—
263C42#1062189811yescharacteristic
264C42#1062189811yescharacteristic
265C42#1062190011yescharacteristic
266C42Q8×D4311yescharacteristic
267C23#1306329511yescharacteristic
268Q8—3441no—
269Q8—3441no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—862no—
281C2×C4—862no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4#1306330311yescharacteristic
295C2×C4#1306330311yescharacteristic
296C2×C4#1306330511yescharacteristic
297C2×C4#1306331111yescharacteristic
298C2×C4#1306331111yescharacteristic
299C2×C4#1306331311yescharacteristic
300C8—42no—
301C8—81no—
302C8—3441no—
303C22—21no—
304C22—21no—
305C22#1458281211yescharacteristic
306C22#1458307811yescharacteristic
307C22#1458308311yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—81no—
315C4—81no—
316C4—3441no—
317C4—3441no—
318C4—3441no—
319C4—3441no—
320C4—1722no—
321C4—1722no—
322C2—21no—
323C2—21no—
324C2#1913575511yescharacteristic
325C2#1913576611yescharacteristic
326C2#1913577011yescharacteristic
subgroupG/H
centerC22#14582812
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1288C2
socleC22×C43#393
prime radicalC23×C43#120
hypercenter#1288D43
hypocenterC43#10381
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
190. C43#10381semidirect

Maximal subgroups

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

subgroupindex
#191402532
#191355392
#191331452
#191331082
#191324892
#191324522
C43×#12882
#1038143