Finite Group Databasebeta

← #25009222

Subgroups — #25009222

Order 11008.

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

normal subgroups only

This group has 432 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#19142110C211yesmaximal, characteristic, complemented
2#19133615C211yesmaximal, characteristic
3#19133581C211yesmaximal, characteristic
4#19132618C211yesmaximal, characteristic, complemented
5#19132594C211yesmaximal, characteristic, complemented
6#19132525C211yesmaximal, characteristic, complemented
7C43×#2022C211yesmaximal, characteristic
8#14583215—21no—
9#14583210—21no—
10#14582841—21no—
11#14582840—21no—
12#14582835C2211yescharacteristic
13#14582824C2211yescharacteristic
14#14582796—21no—
15#14582787—21no—
16#14582781—21no—
17#14582772—21no—
18#14582633—21no—
19#14582633—21no—
20#14582623C2211yescharacteristic
21#14582623C2211yescharacteristic
22C43×#534C2211yescharacteristic
23C2×#123×C43—21no—
24C2×#99×C43—21no—
25C43×#381C2211yescharacteristic
26C43×#342C2211yescharacteristic
27C2×C4⋊Dic43D411yescharacteristic
28C2×C4⋊Dic43D411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C4×Dic43—21no—
36#13063258—41no—
37#13063256—41no—
38#13063246—41no—
39#13063246—41no—
40C22⋊(C43⋊C8)—21no—
41C22⋊(C43⋊C8)—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C22×D4×C43—21no—
50C23×C4×C43D411yescharacteristic
51#123×C43—42no—
52#123×C43—41no—
53#123×C43—42no—
54#121×C43—21no—
55#121×C43—21no—
56#120×C43—41no—
57C2×C4⋊C4×C43—41no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—41no—
60C2×C22⋊C4×C43D411yescharacteristic
61C2×C22⋊C4×C43C2311yescharacteristic
62#99×C43—42no—
63#95×C43—21no—
64#95×C43—21no—
65C24×C43—21no—
66C24×C43C2×D411yescharacteristic
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—44no—
92C22⋊C4×C43—22no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—44no—
98C22⋊C4×C43—41no—
99C22⋊Dic43—42no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104Dic43⋊C4—42no—
105Dic43⋊C4—42no—
106Dic43⋊C4—81no—
107Dic43⋊C4—81no—
108C4×Dic43—81no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—81no—
119C23×C43—81no—
120C23×C43#12011yescharacteristic
121C23×C43#13511yescharacteristic
122C23×C43AGL(1,ℤ/8)11yescharacteristic
123D4×C43—81no—
124D4×C43—81no—
125D4×C43—81no—
126D4×C43—81no—
127D4×C43—81no—
128D4×C43—81no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×Dic43—22no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C43⋊C8—81no—
160C43⋊C8—81no—
161#12189—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—81no—
171C22×C43—82no—
172C22×C43—81no—
173C22×C43—81no—
174C22×C43—81no—
175C22×C43—161no—
176C22×C43#44911yescharacteristic
177C22×C43#45311yescharacteristic
178C22×C43B(4,𝔽2)11yescharacteristic
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—81no—
182C4×C43—82no—
183C4×C43—81no—
184C4×C43—81no—
185Dic43—42no—
186Dic43—81no—
187Dic43—81no—
188Dic43—81no—
189#2771—431no—
190#2022D4311yescharacteristic
191#1613—431no—
192#1607—431no—
193#1352—431no—
194#1344—431no—
195#1317—431no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43—41no—
199C2×C43—41no—
200C2×C43—161no—
201C2×C43#160011yescharacteristic
202C2×C43#219811yescharacteristic
203C2×C43#220111yescharacteristic
204#534C2×D4311yescharacteristic
205C2×#123—21no—
206#481—861no—
207#480—861no—
208C2×#99—21no—
209#400—861no—
210#400—861no—
211#399—431no—
212#397—431no—
213#389—861no—
214#388—861no—
215#387—861no—
216#385—861no—
217#381C2×D4311yescharacteristic
218#342C2×D4311yescharacteristic
219#327—861no—
220#327—861no—
221#323—431no—
222#323—431no—
223C43#1218911yescharacteristic, complemented, Sylow
224C22×D4—21no—
225C23×C4C22⋊D4311yescharacteristic
226#123—42no—
227#123—41no—
228#123—42no—
229#121—21no—
230#121—21no—
231#120—41no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4C22⋊D4311yescharacteristic
244C2×C22⋊C4C22×D4311yescharacteristic
245C2×C42—861no—
246#107—1721no—
247#106—1721no—
248#102—1721no—
249#102—1721no—
250#99—42no—
251C22⋊C8—861no—
252C22⋊C8—861no—
253#95—21no—
254#95—21no—
255#95—431no—
256#95—431no—
257#95—861no—
258#95—861no—
259#95—861no—
260#95—861no—
261#95—861no—
262C24—21no—
263C24C2×C22⋊D4311yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4D4×D4311yescharacteristic
285C22×C4D4×D4311yescharacteristic
286C2×C8—1721no—
287C2×C8—1721no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—44no—
291C4⋊C4—3441no—
292C4⋊C4—3441no—
293C4⋊C4—1721no—
294C4⋊C4—1721no—
295C4⋊C4—1722no—
296C4⋊C4—1722no—
297C22⋊C4—22no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—44no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—1722no—
305C22⋊C4—1721no—
306C22⋊C4—1721no—
307C42—3441no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—81no—
316C23—81no—
317C23#1306329311yescharacteristic
318C23#1306334511yescharacteristic
319C23#1306335111yescharacteristic
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—862no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C8—3441no—
357C8—3441no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22—82no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—161no—
372C22#1458304211yescharacteristic
373C22#1458306611yescharacteristic
374C22#1458308511yescharacteristic
375C4—41no—
376C4—41no—
377C4—81no—
378C4—82no—
379C4—81no—
380C4—81no—
381C4—3441no—
382C4—3441no—
383C4—3441no—
384C4—1722no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—161no—
390C2#1913353911yescharacteristic
391C2#1913658911yescharacteristic
392C2#1913660611yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2022C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#534C22
hypercenter#2022D43
hypocenterC43#12189
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #19142110C2semidirect
4. #19132618C2semidirect
5. #19132594C2semidirect
6. #19132525C2semidirect
223. C43#12189semidirect

Maximal subgroups

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

subgroupindex
#191421102
#191336152
#191335812
#191326182
#191325942
#191325252
C43×#20222
#1218943