Finite Group Databasebeta

← #24999791

Subgroups — #24999791

Order 11008.

352 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 77 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#19135538C211yesmaximal, characteristic
2#19133145C211yesmaximal, characteristic
3#19133106C211yesmaximal, characteristic
4#19132488C211yesmaximal, characteristic
5#19132459C211yesmaximal, characteristic
6#19132451C211yesmaximal, characteristic
7C43×#2606C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14582956C2211yescharacteristic
10#14582956C2211yescharacteristic
11C4×#10621877C2211yescharacteristic
12#14582659—21no—
13#14582659—21no—
14#14582635—21no—
15#14582635—21no—
16#14582635—21no—
17#14582635—21no—
18C43×#398—21no—
19C43×#398—21no—
20C43×#389—21no—
21C43×#389—21no—
22C43×#387—21no—
23C43×#387—21no—
24C43×#383C2211yescharacteristic
25C4×C4⋊C4×C43C2211yescharacteristic
26C43×#376C2211yescharacteristic
27C2×#10621877—21no—
28#13063325Q811yescharacteristic
29#13063325Q811yescharacteristic
30#13063317—21no—
31#13063304—21no—
32#13063304—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35#13063284—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C22⋊(C43⋊C8)—21no—
39C22⋊(C43⋊C8)—21no—
40#13063236—21no—
41#13063236—21no—
42#13063236—21no—
43C4×C43⋊C8—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C42×C43—21no—
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43C2311yescharacteristic
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62#95×C43D411yescharacteristic
63#95×C43D411yescharacteristic
64#95×C43D411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×Dic86—21no—
75C2×Dic86—21no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43—42no—
80C4⋊C4×C43—42no—
81C4⋊C4×C43—81no—
82C4⋊C4×C43—81no—
83C42×C43—41no—
84C42×C43—41no—
85C42×C43—42no—
86C42×C43C2×Q811yescharacteristic
87C42×C43#4111yescharacteristic
88C42×C43#4111yescharacteristic
89C42×C43#4111yescharacteristic
90C22⋊Dic43—41no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97C4×Dic43—41no—
98#10621877—22no—
99#10621877—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C23×C43#12011yescharacteristic
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
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×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43C22⋊Q811yescharacteristic
127C2×C4×C43C22⋊Q811yescharacteristic
128C2×C4×C43C22⋊Q811yescharacteristic
129C2×C4×C43#12411yescharacteristic
130C2×C4×C43#12411yescharacteristic
131C2×C4×C43#12411yescharacteristic
132C2×Dic43—41no—
133C2×Dic43—41no—
134Dic86—81no—
135Dic86—81no—
136C43⋊C8—42no—
137C43⋊C8—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—42no—
152C4×C43—42no—
153C4×C43—81no—
154C4×C43—81no—
155C4×C43—81no—
156C4×C43—81no—
157Dic43—81no—
158Dic43—81no—
159#2606D4311yescharacteristic
160#1986—431no—
161#1515—431no—
162#1506—431no—
163#1300—431no—
164#1288—431no—
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#432—431no—
174C4×M16—431no—
175#398—21no—
176#398—21no—
177#389—21no—
178#389—21no—
179#387—21no—
180#387—21no—
181#383C2×D4311yescharacteristic
182C4×C4⋊C4C2×D4311yescharacteristic
183#376C2×D4311yescharacteristic
184#339—861no—
185#339—861no—
186#328—861no—
187#328—861no—
188#328—861no—
189#328—861no—
190C43#1038111yescharacteristic, complemented, Sylow
191C2×M16—861no—
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—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C42—21no—
208C2×C42C22⋊D4311yescharacteristic
209C2×C42C22⋊D4311yescharacteristic
210C2×C42C22×D4311yescharacteristic
211C4⋊C8—861no—
212C4⋊C8—861no—
213C22⋊C8—861no—
214C22⋊C8—861no—
215#97—861no—
216#97—861no—
217#97—861no—
218C4×C8—861no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C22⋊D4311yescharacteristic
226#95C22⋊D4311yescharacteristic
227#95C22⋊D4311yescharacteristic
228#95C22⋊D4311yescharacteristic
229C2×Q8—861no—
230C2×Q8—861no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4C2×C22⋊D4311yescharacteristic
238C22×C4C2×C22⋊D4311yescharacteristic
239C22×C4C2×C22⋊D4311yescharacteristic
240M16—862no—
241M16—1721no—
242C2×C8—1721no—
243C2×C8—1721no—
244C2×C8—1721no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—81no—
251C4⋊C4—81no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—1721no—
257C4⋊C4—1721no—
258C22⋊C4—1721no—
259C42—41no—
260C42—41no—
261C42—42no—
262C42—1721no—
263C42Q8×D4311yescharacteristic
264C42#1062190211yescharacteristic
265C42#1062190211yescharacteristic
266C42#1062190211yescharacteristic
267C23#1306329411yescharacteristic
268Q8—3441no—
269Q8—3441no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4#1306330111yescharacteristic
295C2×C4#1306330111yescharacteristic
296C2×C4#1306330111yescharacteristic
297C2×C4#1306331411yescharacteristic
298C2×C4#1306331411yescharacteristic
299C2×C4#1306331411yescharacteristic
300C8—3441no—
301C8—3441no—
302C8—1722no—
303C22—21no—
304C22—21no—
305C22#1458281011yescharacteristic
306C22#1458307711yescharacteristic
307C22#1458308211yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—3441no—
321C4—3441no—
322C2—21no—
323C2—21no—
324C2#1913575311yescharacteristic
325C2#1913576411yescharacteristic
326C2#1913576411yescharacteristic
subgroupG/H
centerC22#14582810
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2606C2
socleC22×C43#393
prime radicalC23×C43#120
hypercenter#2606D43
hypocenterC43#10381
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2606

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
#191355382
#191331452
#191331062
#191324882
#191324592
#191324512
C43×#26062
#1038143