Finite Group Databasebeta

← #25008969

Subgroups — #25008969

Order 11008.

354 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 55 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#19142090C211yesmaximal, characteristic, complemented
2#19135821C211yesmaximal, characteristic
3#19133598C211yesmaximal, characteristic
4#19132622C211yesmaximal, characteristic, complemented
5#19132602C211yesmaximal, characteristic, complemented
6#19132538C211yesmaximal, characteristic, complemented
7C43×#1616C211yesmaximal, characteristic
8#14583210—21no—
9C2×#13063252—21no—
10#14582900—21no—
11#14582841—21no—
12#14582832—21no—
13#14582829C2211yescharacteristic
14#14582796—21no—
15#14582786—21no—
16#14582784—21no—
17#14582766—21no—
18#14582764C2211yescharacteristic
19#14582668C2211yescharacteristic
20#14582633—21no—
21#14582625C2211yescharacteristic
22C43×#537C2211yescharacteristic
23C43×#481—21no—
24C43×#400C2211yescharacteristic
25C43×#327—21no—
26C43×#324C2211yescharacteristic
27C2×#10621877—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43D411yescharacteristic
30C2×C4⋊Dic43D411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43D411yescharacteristic
36#13063258—41no—
37#13063252—42no—
38#13063249—41no—
39#13063246—41no—
40#13063246—41no—
41C22⋊(C43⋊C8)—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95D411yescharacteristic
50C2×#41×C43—21no—
51C22⋊Q8×C43—41no—
52#121×C43—21no—
53#121×C43—21no—
54#121×C43—41no—
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C4⋊C4×C43C2311yescharacteristic
57#106×C43—41no—
58#102×C43—41no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43D411yescharacteristic
63#41×C43—41no—
64#41×C43—41no—
65#41×C43—41no—
66#41×C43—41no—
67C2×Q8×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—41no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C2×C8×C43—41no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C4⋊Dic43—42no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92Dic43⋊C4—42no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—81no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—42no—
99#10621877—41no—
100#10621877—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C23×C43—41no—
104C23×C43#12011yescharacteristic
105Q8×C43—41no—
106Q8×C43—41no—
107D4×C43—41no—
108D4×C43—41no—
109D4×C43—81no—
110D4×C43—81no—
111D4×C43—81no—
112D4×C43—81no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
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×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43#13511yescharacteristic
129C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
130C2×Dic43—22no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C8×C43—81no—
143C43⋊C8—81no—
144C43⋊C8—81no—
145#12147—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—81no—
149C22×C43—81no—
150C22×C43—81no—
151C22×C43#44911yescharacteristic
152C22×C43#45411yescharacteristic
153C22×C43B(4,𝔽2)11yescharacteristic
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—81no—
159C4×C43—81no—
160C4×C43—81no—
161Dic43—42no—
162Dic43—81no—
163Dic43—81no—
164Dic43—81no—
165#2769—431no—
166#2040—431no—
167#1616D4311yescharacteristic
168#1610—431no—
169#1353—431no—
170#1346—431no—
171#1324—431no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—161no—
175C2×C43#159711yescharacteristic
176C2×C43#220111yescharacteristic
177C2×C43#220411yescharacteristic
178#537C2×D4311yescharacteristic
179#481—21no—
180#480—861no—
181C2×#104—861no—
182#417—861no—
183#400—861no—
184#400C2×D4311yescharacteristic
185#398—431no—
186#398—861no—
187#389—861no—
188#387—861no—
189#387—861no—
190#383—861no—
191#382—431no—
192#343—431no—
193#327—21no—
194#327—861no—
195#324—431no—
196#324C2×D4311yescharacteristic
197C43#1214711yescharacteristic, complemented, Sylow
198C2×#41—21no—
199C2×M16—861no—
200C22⋊Q8—41no—
201#121—21no—
202#121—21no—
203#121—41no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4C22⋊D4311yescharacteristic
211C2×C4⋊C4C22×D4311yescharacteristic
212C2×C42—431no—
213C2×C42—861no—
214#107—1721no—
215#106—41no—
216#104—1722no—
217#103—1721no—
218#102—41no—
219#102—1721no—
220#102—1721no—
221C22⋊C8—21no—
222C22⋊C8—861no—
223#95—21no—
224#95—21no—
225#95—431no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231#95—861no—
232#95—861no—
233#95C22⋊D4311yescharacteristic
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4D4×D4311yescharacteristic
251C22×C4D4×D4311yescharacteristic
252C22×C4C2×C22⋊D4311yescharacteristic
253M16—1721no—
254M16—1721no—
255C2×C8—41no—
256C2×C8—1721no—
257C2×C8—1721no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—3441no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1722no—
266C4⋊C4—1722no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C42—861no—
272C42—861no—
273C42—1722no—
274C23—41no—
275C23#1306329311yescharacteristic
276Q8—41no—
277Q8—41no—
278D4—41no—
279D4—41no—
280D4—81no—
281D4—81no—
282D4—81no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—862no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4#1306334611yescharacteristic
312C2×C4#1306335211yescharacteristic
313C8—81no—
314C8—3441no—
315C8—3441no—
316C22—21no—
317C22—21no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22#1458304311yescharacteristic
322C22#1458307011yescharacteristic
323C22#1458308511yescharacteristic
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—3441no—
332C4—3441no—
333C4—3441no—
334C4—1722no—
335C2—21no—
336C2—21no—
337C2—161no—
338C2#1913352311yescharacteristic
339C2#1913660611yescharacteristic
340C2#1913661911yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1616C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#537C22
hypercenter#1616D43
hypocenterC43#12147
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1616

Complements

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

NH ≅ G/Ntype
1. #19142090C2semidirect
4. #19132622C2semidirect
5. #19132602C2semidirect
6. #19132538C2semidirect
197. C43#12147semidirect

Maximal subgroups

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

subgroupindex
#191420902
#191358212
#191335982
#191326222
#191326022
#191325382
C43×#16162
#1214743