Finite Group Databasebeta

← #24985577

Subgroups — #24985577

Order 11008.

478 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 83 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#19141556C211yesmaximal, characteristic
2#19135925C211yesmaximal, characteristic, complemented
3#19135678C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#2057C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063320—21no—
10C2×#13063256—21no—
11C2×#13063249—21no—
12#14582836—21no—
13#14582821—21no—
14#14582816—21no—
15#14582801C2211yescharacteristic
16#14582798—21no—
17#14582797C2211yescharacteristic
18#14582791—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×#107×C43—21no—
24C43×#389C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×D172D411yescharacteristic
28C2×#10621884—42no—
29C2×#10621884—42no—
30C2×#10621884—42no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33#13063320—42no—
34#13063320—42no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43D411yescharacteristic
38C2×C4⋊Dic43D411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
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—
46C2×(C2×D43)⋊C4—21no—
47C2×C4×Dic43—21no—
48#13063256—42no—
49#13063249—42no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C22×Q8×C43—21no—
53C22×C8×C43—21no—
54C4⋊Q8×C43—42no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C4⋊C4×C43D411yescharacteristic
60C2×C42×C43C2311yescharacteristic
61#107×C43—42no—
62#95×C43—21no—
63C23×D43—21no—
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—41no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×D172—21no—
80C2×D172—21no—
81C2×D172—41no—
82C2×D172—41no—
83C2×C8×C43—22no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43SD1612yescomplemented
95C42×C43—41no—
96#10621884—48no—
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—
103(C2×D43)⋊C4—81no—
104(C2×D43)⋊C4—81no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—42no—
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110C4⋊Dic43—81no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113C4×Dic43—42no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C23×C43#12011yescharacteristic
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—41no—
128Q8×C43—42no—
129Q8×C43—42no—
130Q8×C43—81no—
131Q8×C43—81no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—22no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43C2×SD1611yescharacteristic
148C2×C4×C43#13511yescharacteristic
149C2×C4×C43#13511yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C43#13711yescharacteristic
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162D172—42no—
163D172—81no—
164C8×C43—42no—
165C43⋊C8—42no—
166C43⋊C8—42no—
167#7780—431nomaximal, Sylow
168C22×C43#44911yescharacteristic
169C22×C43#45011yescharacteristic
170C22×C43#45211yescharacteristic
171C22×C43#45311yescharacteristic
172C22×C43#45611yescharacteristic
173C22×C43#45611yescharacteristic
174C22×C43B(4,𝔽2)11yescharacteristic
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C2×D43—81no—
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—42no—
189C4×C43—81no—
190C4×C43—82no—
191Dic43—81no—
192Dic43—81no—
193Dic43—81no—
194#2727—431no—
195#2058—431no—
196#2057D4311yescharacteristic, complemented
197#2013—431no—
198#1271—431no—
199#1271—431no—
200#1270—431no—
201C2×C43#160011yescharacteristic
202C2×C43#160311yescharacteristic
203C2×C43#160411yescharacteristic
204C2×C43#163111yescharacteristic
205C2×C43#165011yescharacteristic
206C2×C43#165411yescharacteristic
207C2×C43#166011yescharacteristic
208D43—161no—
209C22×SD16—861no—
210C2×C4⋊Q8C2×D4311yescharacteristic
211C2×#126—861no—
212C2×#107—21no—
213C2×#106—861no—
214C2×#103—861no—
215#399—861no—
216#396—861no—
217#394—861no—
218#390—431no—
219#389—431no—
220#389—861no—
221#389C2×D4311yescharacteristic
222#388—861no—
223#340—21no—
224#340—861no—
225#336—431no—
226#336—431no—
227#336C2×D4311yescharacteristic
228C43#778011yescharacteristic, complemented, Sylow
229C22×Q8—21no—
230C22×D4—431no—
231C2×SD16—1722no—
232C2×SD16—1722no—
233C2×SD16—1722no—
234C22×C8—21no—
235C22×C8—861no—
236C22×C8—861no—
237C4⋊Q8—42no—
238#126—1722no—
239#126—1722no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4C22⋊D4311yescharacteristic
250C2×C4⋊C4C22⋊D4311yescharacteristic
251C2×C22⋊C4—861no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C42—861no—
258C2×C42C22×D4311yescharacteristic
259#107—42no—
260#106—1722no—
261#103—1722no—
262#95—21no—
263#95—861no—
264#95—861no—
265C24—861no—
266C2×Q8—22no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—1721no—
275C2×D4—1721no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4D4×D4311yescharacteristic
283C22×C4D4×D4311yescharacteristic
284C22×C4C2×C22⋊D4311yescharacteristic
285SD16—1728no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—862no—
290C2×C8—862no—
291C2×C8—1721no—
292C2×C8—1721no—
293C2×C8—1721no—
294C2×C8—1721no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—3441no—
306C4⋊C4—1721no—
307C4⋊C4—1721no—
308C4⋊C4—1722no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C4⋊C4#1062188412yescomplemented
312C22⋊C4—3441no—
313C22⋊C4—3441no—
314C22⋊C4—1722no—
315C22⋊C4—1722no—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C22⋊C4—1721no—
319C22⋊C4—1721no—
320C42—41no—
321C42—1722no—
322C23—1721no—
323C23—1721no—
324C23—1721no—
325C23—1721no—
326C23—1721no—
327C23—1721no—
328C23—1721no—
329C23#1306329311yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—81no—
333Q8—81no—
334D4—3441no—
335D4—1722no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4C2×#1062188411yescharacteristic
361C2×C4#1306334411yescharacteristic
362C2×C4#1306334811yescharacteristic
363C2×C4#1306334911yescharacteristic
364C2×C4#1306335011yescharacteristic
365C2×C4#1306335711yescharacteristic
366C8—42no—
367C8—1722no—
368C8—1722no—
369C22—3441no—
370C22—3441no—
371C22—3441no—
372C22—3441no—
373C22—3441no—
374C22—3441no—
375C22—3441no—
376C22#1458304111yescharacteristic
377C22#1458304911yescharacteristic
378C22#1458306011yescharacteristic
379C22#1458306511yescharacteristic
380C22#1458308011yescharacteristic
381C22#1458308111yescharacteristic
382C22#1458308511yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—82no—
392C4—3441no—
393C4—3441no—
394C4—3441no—
395C2—6881no—
396C2#1913353811yescharacteristic
397C2#1913355711yescharacteristic
398C2#1913356311yescharacteristic
399C2#1913372011yescharacteristic
400C2#1913384811yescharacteristic
401C2#1913387811yescharacteristic
402C2#1913390511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2057C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#2057D43
hypocenterC43#7780
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
2. #19135925C2semidirect
4. #19132419C2semidirect
5. #19132418C2semidirect
7. C43×#2057C2semidirect
94. C4⋊C4×C43SD16semidirect
196. #2057D43semidirect
228. C43#7780semidirect
311. C4⋊C4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191415562
#191359252
#191356782
#191324192
#191324182
#191324152
C43×#20572
#778043