Finite Group Databasebeta

← #25009325

Subgroups — #25009325

Order 11008.

474 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135762C211yesmaximal, characteristic, complemented
2#19133585C211yesmaximal, characteristic, complemented
3#19133517C211yesmaximal, characteristic
4#19132595C211yesmaximal, characteristic, complemented
5#19132592C211yesmaximal, characteristic
6#19132525C211yesmaximal, characteristic, complemented
7C43×#2600C211yesmaximal, characteristic
8#14583525C2211yescharacteristic
9#14583229—21no—
10#14583050—21no—
11#14582762—21no—
12#14582666C2211yescharacteristic
13#14582665—21no—
14#14582635—21no—
15#14582635—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C2×C4×D4×C43—21no—
19C43×#397C2211yescharacteristic
20C43×#394—21no—
21C43×#392C2211yescharacteristic
22C43×#388—21no—
23C43×#387—21no—
24C43×#386—21no—
25C43×#385—21no—
26C43×#381C2211yescharacteristic
27C2×#10621883—41no—
28#13063304—21no—
29#13063304—21no—
30#13063302—41no—
31#13063302—41no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34#13063256—41no—
35#13063248—41no—
36#13063246—41no—
37C22⋊(C43⋊C8)—21no—
38C22⋊(C43⋊C8)—21no—
39C43⋊#95—41no—
40C43⋊#95—41no—
41C22×D4×C43—21no—
42C22×D4×C43D411yescharacteristic
43C23×C4×C43—21no—
44C23×C4×C43D411yescharacteristic
45C4×D4×C43—42no—
46C4×D4×C43—42no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43C2311yescharacteristic
57C2×C42×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43D411yescharacteristic
63#95×C43D411yescharacteristic
64C24×C43—21no—
65C24×C43C2×D411yescharacteristic
66C2×D4×C43—42no—
67C2×D4×C43—42no—
68C2×D4×C43—42no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43—42no—
81C22×C4×C43—81no—
82C22×C4×C43—81no—
83C22×C4×C43SD1612yescomplemented
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—41no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—42no—
93C4⋊C4×C43—42no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—42no—
97C22⋊C4×C43—42no—
98C22⋊C4×C43—42no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—81no—
102C42×C43—42no—
103C22⋊Dic43—41no—
104C22⋊Dic43—41no—
105C22⋊Dic43—41no—
106C22⋊Dic43—41no—
107#10621883—82no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—22no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43#12011yescharacteristic
126C23×C43C2×SD1611yescharacteristic
127C23×C43AGL(1,ℤ/8)11yescharacteristic
128D4×C43—42no—
129D4×C43—44no—
130D4×C43—44no—
131D4×C43—81no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—81no—
153C2×C4×C43—84no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—81no—
157C2×Dic43—81no—
158C2×Dic43—81no—
159C2×Dic43—81no—
160C2×Dic43—81no—
161Dic86—81no—
162Dic86—81no—
163C43⋊C8—81no—
164C43⋊C8—81no—
165#12204—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—42no—
173C22×C43—42no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—42no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43#45011yescharacteristic
183C22×C43#45511yescharacteristic
184C22×C43B(4,𝔽2)11yescharacteristic
185C4×C43—42no—
186C4×C43—42no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—81no—
190C4×C43—81no—
191C4×C43—81no—
192Dic43—81no—
193Dic43—81no—
194Dic43—161no—
195#2600D4311yescharacteristic
196#2030—431no—
197#1608—431no—
198#1596—431no—
199#1344—431no—
200#1343—431no—
201#1317—431no—
202C2×C43—21no—
203C2×C43—21no—
204C2×C43—41no—
205C2×C43—41no—
206C2×C43—82no—
207C2×C43#160111yescharacteristic
208C2×C43#219711yescharacteristic
209C2×C43#219811yescharacteristic
210#543—431no—
211C2×C4×D4—21no—
212#483—861no—
213#450—861no—
214#397C2×D4311yescharacteristic
215#394—21no—
216#392C2×D4311yescharacteristic
217#388—21no—
218#387—21no—
219#386—21no—
220#385—21no—
221#381—861no—
222#381C2×D4311yescharacteristic
223#342—431no—
224#342—861no—
225#328—861no—
226#328—861no—
227#323—431no—
228#323—431no—
229C43#1220411yescharacteristic, complemented, Sylow
230C22×D4—21no—
231C22×D4C22⋊D4311yescharacteristic
232C23×C4—21no—
233C23×C4C22⋊D4311yescharacteristic
234C2×SD16—1721no—
235C22⋊Q8—861no—
236C22⋊Q8—861no—
237C22⋊Q8—1721no—
238C22⋊Q8—1721no—
239C4×D4—42no—
240C4×D4—42no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C22⋊D4311yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4C22⋊D4311yescharacteristic
252C2×C22⋊C4C22×D4311yescharacteristic
253C2×C42—21no—
254#106—1721no—
255#103—1721no—
256#102—1721no—
257C22⋊C8—861no—
258C22⋊C8—861no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—1721no—
264#95—1721no—
265#95C22⋊D4311yescharacteristic
266#95C22⋊D4311yescharacteristic
267C24—21no—
268C24C2×C22⋊D4311yescharacteristic
269C2×Q8—861no—
270C2×Q8—861no—
271C2×D4—42no—
272C2×D4—41no—
273C2×D4—42no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—42no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—1721no—
291C22×C4#1062188312yescomplemented
292C22×C4C2×C22⋊D4311yescharacteristic
293C22×C4C2×C22⋊D4311yescharacteristic
294SD16—3442no—
295C2×C8—1721no—
296C2×C8—1721no—
297C4⋊C4—41no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C22⋊C4—41no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—81no—
312C22⋊C4—1721no—
313C22⋊C4—1721no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C42—42no—
317C23—21no—
318C23—21no—
319C23—22no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23#1306329411yescharacteristic
329C23C2×#1062188311yescharacteristic
330C23#1306335111yescharacteristic
331Q8—3441no—
332Q8—3441no—
333D4—42no—
334D4—44no—
335D4—44no—
336D4—81no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—84no—
359C2×C4—3441no—
360C2×C4—3441no—
361C2×C4—3441no—
362C2×C4—3441no—
363C2×C4—3441no—
364C2×C4—1721no—
365C2×C4—1721no—
366C8—3441no—
367C8—3441no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—42no—
376C22—41no—
377C22—41no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22#1458305011yescharacteristic
385C22#1458307711yescharacteristic
386C22#1458308611yescharacteristic
387C4—42no—
388C4—41no—
389C4—41no—
390C4—42no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—3441no—
395C4—3441no—
396C4—6881no—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—82no—
402C2#1913354711yescharacteristic
403C2#1913658511yescharacteristic
404C2#1913659111yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2600C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#392C22
hypercenter#2600D43
hypocenterC43#12204
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2600

Complements

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

NH ≅ G/Ntype
1. #19135762C2semidirect
2. #19133585C2semidirect
4. #19132595C2semidirect
6. #19132525C2semidirect
83. C22×C4×C43SD16semidirect
229. C43#12204semidirect
291. C22×C4#10621883semidirect

Maximal subgroups

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

subgroupindex
#191357622
#191335852
#191335172
#191325952
#191325922
#191325252
C43×#26002
#1220443