Finite Group Databasebeta

← #25009171

Subgroups — #25009171

Order 11008.

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

normal subgroups only

This group has 372 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, complemented
2#19135816C211yesmaximal, characteristic
3#19133632C211yesmaximal, characteristic
4#19132623C211yesmaximal, characteristic, complemented
5#19132622C211yesmaximal, characteristic, complemented
6#19132540C211yesmaximal, characteristic, complemented
7C43×#1616C211yesmaximal, characteristic
8#14583215—21no—
9C2×#13063252—21no—
10#14582900—21no—
11#14582841—21no—
12#14582838C2211yescharacteristic
13#14582796—21no—
14#14582794—21no—
15#14582768C2211yescharacteristic
16#14582763—21no—
17#14582763—21no—
18#14582750—21no—
19#14582668C2211yescharacteristic
20#14582633—21no—
21#14582625C2211yescharacteristic
22C43×#537C2211yescharacteristic
23C43×#481—21no—
24C43×#400C2211yescharacteristic
25C43×#327—21no—
26C43×#324C2211yescharacteristic
27C2×#10621877—21no—
28C2×C4⋊Dic43D411yescharacteristic
29C2×C4⋊Dic43D411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43D411yescharacteristic
38#13063256—41no—
39#13063252—42no—
40#13063249—41no—
41#13063246—41no—
42#13063246—41no—
43C22⋊(C43⋊C8)—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—41no—
90C4⋊Dic43—41no—
91Dic43⋊C4—42no—
92Dic43⋊C4—42no—
93Dic43⋊C4—42no—
94Dic43⋊C4—42no—
95Dic43⋊C4—81no—
96C4×Dic43—21no—
97C4×Dic43—42no—
98C4×Dic43—42no—
99C4×Dic43SD1612yes—
100#10621877—41no—
101#10621877—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C23×C43—41no—
105C23×C43#12011yescharacteristic
106Q8×C43—41no—
107Q8×C43—41no—
108D4×C43—41no—
109D4×C43—41no—
110D4×C43—81no—
111D4×C43—81no—
112D4×C43—81no—
113D4×C43—81no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
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—41no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43C2×SD1611yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C2×Dic43—22no—
132C2×Dic43—22no—
133C2×Dic43—22no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C8×C43—81no—
144C43⋊C8—81no—
145C43⋊C8—81no—
146#12181—431nomaximal, Sylow
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—81no—
150C22×C43—81no—
151C22×C43—81no—
152C22×C43#44811yescharacteristic
153C22×C43#45411yescharacteristic
154C22×C43B(4,𝔽2)11yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—81no—
160C4×C43—81no—
161C4×C43—81no—
162Dic43—24no—
163Dic43—81no—
164Dic43—81no—
165Dic43—81no—
166#2571—431no—
167#2039—431no—
168#1616—431no—
169#1616D4311yescharacteristic
170#1353—431no—
171#1353—431no—
172#1325—431no—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43—161no—
176C2×C43#159911yescharacteristic
177C2×C43#219811yescharacteristic
178C2×C43#220411yescharacteristic
179#537C2×D4311yescharacteristic
180#481—21no—
181#481—861no—
182C2×#104—861no—
183#417—861no—
184#400—431no—
185#400—861no—
186#400C2×D4311yescharacteristic
187#389—861no—
188#389—861no—
189#384—431no—
190#382—861no—
191#382—861no—
192C4×C4⋊C4—861no—
193#343—431no—
194#327—21no—
195#327—861no—
196#324—431no—
197#324C2×D4311yescharacteristic
198C43#1218111yescharacteristic, complemented, Sylow
199C2×#41—21no—
200C2×M16—861no—
201C22⋊Q8—41no—
202#121—21no—
203#121—21no—
204#121—41no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4C22⋊D4311yescharacteristic
213C2×C4⋊C4C22×D4311yescharacteristic
214C2×C42—431no—
215C2×C42—861no—
216C2×C42—861no—
217#106—41no—
218#106—1721no—
219#104—1722no—
220#103—1721no—
221#102—41no—
222#102—1721no—
223#102—1721no—
224C22⋊C8—21no—
225C22⋊C8—861no—
226#95—21no—
227#95—21no—
228#95—431no—
229#95—861no—
230#95—861no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95C22⋊D4311yescharacteristic
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239C2×Q8—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4D4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253C22×C4C2×C22⋊D4311yescharacteristic
254M16—1721no—
255M16—1721no—
256C2×C8—41no—
257C2×C8—1721no—
258C2×C8—1721no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—3441no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1722no—
267C4⋊C4—1722no—
268C4⋊C4—1722no—
269C4⋊C4—1722no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C42—432no—
273C42—861no—
274C42—1722no—
275C42—1722no—
276C23—41no—
277C23#1306329311yescharacteristic
278Q8—41no—
279Q8—41no—
280D4—41no—
281D4—41no—
282D4—81no—
283D4—81no—
284D4—81no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—862no—
302C2×C4—862no—
303C2×C4—862no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4SD16×D4311yescharacteristic
314C2×C4#1306335411yescharacteristic
315C8—81no—
316C8—3441no—
317C8—3441no—
318C22—21no—
319C22—21no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22#1458303611yescharacteristic
324C22#1458307011yescharacteristic
325C22#1458308511yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—864no—
334C4—3441no—
335C4—3441no—
336C4—3441no—
337C2—21no—
338C2—21no—
339C2—161no—
340C2#1913353311yescharacteristic
341C2#1913658911yescharacteristic
342C2#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#12181
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. #19139833C2semidirect
4. #19132623C2semidirect
5. #19132622C2semidirect
6. #19132540C2semidirect
198. C43#12181semidirect

Maximal subgroups

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

subgroupindex
#191398332
#191358162
#191336322
#191326232
#191326222
#191325402
C43×#16162
#1218143