Finite Group Databasebeta

← #24985512

Subgroups — #24985512

Order 11008.

460 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 81 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#19141524C211yesmaximal, characteristic
2#19135928C211yesmaximal, characteristic, complemented
3#19135842C211yesmaximal, characteristic, complemented
4#19135732C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C2×#13063310—21no—
10C2×#13063256—21no—
11C2×#13063250—21no—
12C2×#13063250—21no—
13C2×#13063247—21no—
14#14582832—21no—
15#14582826—21no—
16#14582825—21no—
17#14582801C2211yescharacteristic
18#14582797C2211yescharacteristic
19#14582773—21no—
20#14582770—21no—
21#14582662—21no—
22#14582661—21no—
23#14582654C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C22×C43⋊C8—21no—
31#13063325—42no—
32#13063310—42no—
33#13063310—42no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×C4⋊Dic43D411yescharacteristic
38C2×C4⋊Dic43D411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46#13063256—42no—
47#13063250—42no—
48#13063250—42no—
49#13063247—42no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60#95×C43—21no—
61C23×D43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—41no—
71C2×D172—21no—
72C2×D172—41no—
73C2×D172—41no—
74C2×D172SD1612yes—
75C2×C4×D43—42no—
76C2×C4×D43—81no—
77C2×C4×D43—81no—
78C2×Dic86—22no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C42×C43—41no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—42no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—41no—
103C4⋊Dic43—22no—
104C4⋊Dic43—22no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110C4⋊Dic43—41no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113Dic43⋊C4—81no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C23×C43#12011yescharacteristic
118C22×D43—22no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43C2×SD1611yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—42no—
152C2×Dic43—41no—
153C2×Dic43—81no—
154C2×Dic43—81no—
155D172—42no—
156D172—81no—
157C4×D43—84no—
158Dic86—42no—
159Dic86—42no—
160Dic86—81no—
161Dic86—81no—
162C8×C43—81no—
163C8×C43—81no—
164C43⋊C8—42no—
165#7770—431nomaximal, Sylow
166C22×C43#44911yescharacteristic
167C22×C43#45011yescharacteristic
168C22×C43#45211yescharacteristic
169C22×C43#45411yescharacteristic
170C22×C43#45511yescharacteristic
171C22×C43#45611yescharacteristic
172C22×C43B(4,𝔽2)11yescharacteristic
173C2×D43—42no—
174C2×D43—42no—
175C2×D43—42no—
176C2×D43—81no—
177C2×D43—81no—
178C2×D43—81no—
179C2×D43—81no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—81no—
187C4×C43—81no—
188Dic43—82no—
189Dic43—81no—
190Dic43—81no—
191Dic43—81no—
192#2724—431no—
193#2058—431no—
194#2043—431no—
195#2023—431no—
196#1271—431no—
197#1271D4311yescharacteristic, complemented
198#1270—431no—
199C2×C43#159711yescharacteristic
200C2×C43#160111yescharacteristic
201C2×C43#160311yescharacteristic
202C2×C43#163511yescharacteristic
203C2×C43#164011yescharacteristic
204C2×C43#165411yescharacteristic
205C2×C43#166411yescharacteristic
206D43—82no—
207C2×C4⋊Q8—431no—
208C2×#123—861no—
209C2×#106—861no—
210C2×#103—861no—
211C2×#103—861no—
212C2×#102—861no—
213#398—861no—
214#397—861no—
215#397—861no—
216#390—431no—
217#389—431no—
218#389C2×D4311yescharacteristic
219#385—861no—
220#385—861no—
221#340—861no—
222#340—861no—
223#336—431no—
224#336C2×D4311yescharacteristic
225#336C2×D4311yescharacteristic
226C43#777011yescharacteristic, complemented, Sylow
227C22×Q8—861no—
228C22×D4—431no—
229C23×C4—861no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—861no—
233C4⋊Q8—1722no—
234#123—1722no—
235#123—1722no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—431no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4D17211yescharacteristic
245C2×C4⋊C4D17211yescharacteristic
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C42C22×D4311yescharacteristic
252#106—1722no—
253#103—1722no—
254#103—1722no—
255#102—1722no—
256#95—21no—
257#95—861no—
258#95—861no—
259#95—861no—
260#95—861no—
261C24—861no—
262C2×Q8—862no—
263C2×Q8—1721no—
264C2×Q8—1721no—
265C2×Q8—1721no—
266C2×Q8—1721no—
267C2×Q8—1721no—
268C2×D4—432no—
269C2×D4—861no—
270C2×D4—1721no—
271C2×D4—1721no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—3441no—
278C22×C4—3441no—
279C22×C4—1722no—
280C22×C4—1721no—
281C22×C4C2×D17211yescharacteristic
282C22×C4D4×D4311yescharacteristic
283C22×C4D4×D4311yescharacteristic
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—862no—
291C2×C8—1721no—
292C2×C8—1721no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—862no—
299C4⋊C4—862no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—3441no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C4⋊C4—1721no—
307C4⋊C4—1721no—
308C4⋊C4—1721no—
309C22⋊C4—1722no—
310C22⋊C4—1722no—
311C22⋊C4—1722no—
312C22⋊C4—1721no—
313C22⋊C4—1721no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C42—41no—
317C23—862no—
318C23—1721no—
319C23—1721no—
320C23—1721no—
321C23—1721no—
322C23—1721no—
323C23—1721no—
324C23#1306329511yescharacteristic
325Q8—3441no—
326Q8—3441no—
327Q8—1722no—
328Q8—1722no—
329D4—3441no—
330D4—1722no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—3444no—
344C2×C4—3441no—
345C2×C4—3441no—
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—1722no—
355C2×C4—1721no—
356C2×C4SD16×D4311yescharacteristic
357C2×C4#1306334711yescharacteristic
358C2×C4#1306334811yescharacteristic
359C2×C4#1306334911yescharacteristic
360C2×C4#1306335211yescharacteristic
361C2×C4#1306335811yescharacteristic
362C8—81no—
363C8—81no—
364C8—1722no—
365C22—3441no—
366C22—3441no—
367C22—3441no—
368C22—3441no—
369C22—1722no—
370C22—1722no—
371C22—1722no—
372C22#1458304711yescharacteristic
373C22#1458305111yescharacteristic
374C22#1458306311yescharacteristic
375C22#1458307311yescharacteristic
376C22#1458307811yescharacteristic
377C22#1458308411yescharacteristic
378C22#1458308711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—81no—
386C4—81no—
387C4—3442no—
388C4—3441no—
389C4—3441no—
390C4—3441no—
391C2—3442no—
392C2#1913352711yescharacteristic
393C2#1913354811yescharacteristic
394C2#1913356011yescharacteristic
395C2#1913374911yescharacteristic
396C2#1913378411yescharacteristic
397C2#1913388011yescharacteristic
398C2#1913393111yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#1271D43
hypocenterC43#7770
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #19135928C2semidirect
3. #19135842C2semidirect
5. #19132419C2semidirect
7. C43×#1271C2semidirect
197. #1271D43semidirect
226. C43#7770semidirect

Maximal subgroups

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

subgroupindex
#191415242
#191359282
#191358422
#191357322
#191324192
#191324152
C43×#12712
#777043