Finite Group Databasebeta

← #25008960

Subgroups — #25008960

Order 11008.

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

normal subgroups only

This group has 380 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#19142395C211yesmaximal, characteristic, complemented
2#19135816C211yesmaximal, characteristic
3#19133564C211yesmaximal, characteristic
4#19132626C211yesmaximal, characteristic, complemented
5#19132601C211yesmaximal, characteristic, complemented
6#19132540C211yesmaximal, characteristic, complemented
7C43×#1610C211yesmaximal, characteristic
8#14583037—21no—
9C2×#13063252—21no—
10#14582900—21no—
11#14582829—21no—
12#14582820—21no—
13#14582819C2211yescharacteristic
14#14582798—21no—
15#14582796—21no—
16#14582781—21no—
17#14582780—21no—
18#14582768C2211yescharacteristic
19#14582668C2211yescharacteristic
20#14582633—21no—
21#14582625C2211yescharacteristic
22C43×#537C2211yescharacteristic
23C43×#480—21no—
24C43×#398C2211yescharacteristic
25C43×#327—21no—
26C43×#324C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×#10621883—41no—
29C2×#10621877—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43D411yescharacteristic
39#13063252—42no—
40#13063249—41no—
41#13063248—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×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43C2311yescharacteristic
58#107×C43—41no—
59#102×C43—41no—
60C22⋊C8×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×Dic86—41no—
83C2×Dic86—81no—
84C2×C8×C43—41no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93#10621883—82no—
94C4⋊Dic43—41no—
95C4⋊Dic43—81no—
96C4⋊Dic43—81no—
97Dic43⋊C4—24no—
98Dic43⋊C4—81no—
99Dic43⋊C4—81no—
100Dic43⋊C4—81no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—81no—
104#10621877—41no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C23×C43—41no—
109C23×C43#12011yescharacteristic
110Q8×C43—41no—
111Q8×C43—41no—
112D4×C43—41no—
113D4×C43—41no—
114D4×C43—81no—
115D4×C43—81no—
116D4×C43—81no—
117D4×C43—81no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—22no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147Dic86—42no—
148Dic86—81no—
149C8×C43—81no—
150C43⋊C8—81no—
151C43⋊C8—81no—
152#12146—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43—81no—
158C22×C43#44911yescharacteristic
159C22×C43#45411yescharacteristic
160C22×C43B(4,𝔽2)11yescharacteristic
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—42no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—81no—
167C4×C43—81no—
168Dic43—42no—
169Dic43—42no—
170Dic43—81no—
171Dic43—81no—
172#2792—431no—
173#2039—431no—
174#1610D4311yescharacteristic
175#1604—431no—
176#1354—431no—
177#1346—431no—
178#1325—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—161no—
182C2×C43#159711yescharacteristic
183C2×C43#220011yescharacteristic
184C2×C43#220511yescharacteristic
185#537C2×D4311yescharacteristic
186#480—21no—
187#448—861no—
188C2×#104—861no—
189#417—861no—
190#398—861no—
191#398C2×D4311yescharacteristic
192#395—431no—
193#395—861no—
194#389—861no—
195#389—861no—
196#387—861no—
197#387—861no—
198#384—431no—
199#343—431no—
200#327—21no—
201#327—861no—
202#324—431no—
203#324C2×D4311yescharacteristic
204C43#1214611yescharacteristic, complemented, Sylow
205C2×#41—21no—
206C22×Q8—431no—
207C2×SD16—1721no—
208C2×M16—861no—
209C22⋊Q8—41no—
210#121—21no—
211#121—21no—
212#121—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C22⋊D4311yescharacteristic
222C2×C4⋊C4C22×D4311yescharacteristic
223C2×C42—431no—
224C2×C42—861no—
225#107—41no—
226#104—1722no—
227#103—1721no—
228#103—1721no—
229#102—41no—
230#102—1721no—
231C22⋊C8—21no—
232C22⋊C8—861no—
233#95—21no—
234#95—431no—
235#95—861no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95—861no—
240#95C22⋊D4311yescharacteristic
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—3441no—
247C2×Q8—1721no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4D4×D4311yescharacteristic
260C22×C4D4×D4311yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262SD16—3442no—
263M16—1721no—
264M16—1721no—
265C2×C8—41no—
266C2×C8—1721no—
267C2×C8—1721no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—864no—
275C4⋊C4—3441no—
276C4⋊C4—3441no—
277C4⋊C4—3441no—
278C4⋊C4—3441no—
279C4⋊C4—3441no—
280C4⋊C4—1721no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—861no—
284C42—861no—
285C42—3441no—
286C23—41no—
287C23#1306329311yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—3441no—
291Q8—1722no—
292D4—41no—
293D4—41no—
294D4—81no—
295D4—81no—
296D4—81no—
297D4—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—862no—
314C2×C4—862no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4#1306334411yescharacteristic
326C2×C4#1306334911yescharacteristic
327C8—81no—
328C8—3441no—
329C8—3441no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1458304111yescharacteristic
336C22#1458307011yescharacteristic
337C22#1458308511yescharacteristic
338C4—21no—
339C4—21no—
340C4—42no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—3441no—
346C4—3441no—
347C4—1722no—
348C4—1722no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2#1913352111yescharacteristic
353C2#1913659911yescharacteristic
354C2#1913662411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1610C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#537C22
hypercenter#1610D43
hypocenterC43#12146
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #19142395C2semidirect
4. #19132626C2semidirect
5. #19132601C2semidirect
6. #19132540C2semidirect
204. C43#12146semidirect

Maximal subgroups

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

subgroupindex
#191423952
#191358162
#191335642
#191326262
#191326012
#191325402
C43×#16102
#1214643