Finite Group Databasebeta

← #24985473

Subgroups — #24985473

Order 11008.

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

normal subgroups only

This group has 446 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#19141555C211yesmaximal, characteristic
2#19135838C211yesmaximal, characteristic, complemented
3#19135728C211yesmaximal, characteristic
4#19132418C211yesmaximal, characteristic, complemented
5#19132417C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#2057C211yesmaximal, characteristic, complemented
8C2×#13063320—21no—
9C2×#13063249—21no—
10C2×#13063249—21no—
11C2×#13063245—21no—
12#14582834—21no—
13#14582821—21no—
14#14582817—21no—
15#14582801C2211yescharacteristic
16#14582797C2211yescharacteristic
17#14582796—21no—
18#14582789—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
28C22×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30#13063320—42no—
31#13063320—42no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×C4⋊Dic43D411yescharacteristic
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×C4×Dic43—21no—
45#13063249—42no—
46#13063249—42no—
47#13063245—42no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C22×Q8×C43—21no—
51C22×C8×C43—21no—
52C4⋊Q8×C43—42no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#107×C43—42no—
60#95×C43—21no—
61C23×D43—21no—
62C2×Q8×C43—22no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—41no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—41no—
80C2×D172—41no—
81C2×C8×C43—22no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C42×C43—41no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—42no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—81no—
101(C2×D43)⋊C4—81no—
102C4⋊Dic43—21no—
103C4⋊Dic43—41no—
104C4⋊Dic43—41no—
105C4⋊Dic43D812yes—
106Dic43⋊C4—42no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109Dic43⋊C4—81no—
110C4×Dic43—42no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C23×C43#12011yescharacteristic
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125Q8×C43—42no—
126Q8×C43—42no—
127Q8×C43—81no—
128Q8×C43—81no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—41no—
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—81no—
143C2×C4×C43—81no—
144C2×C4×C43C2×D811yescharacteristic
145C2×C4×C43#13511yescharacteristic
146C2×C4×C43#13511yescharacteristic
147C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C43#13711yescharacteristic
149C2×C4×C43#13711yescharacteristic
150C2×Dic43—22no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159D172—42no—
160D172—81no—
161C8×C43—42no—
162C43⋊C8—81no—
163C43⋊C8—81no—
164#7765—431nomaximal, Sylow
165C22×C43#44711yescharacteristic
166C22×C43#45211yescharacteristic
167C22×C43#45211yescharacteristic
168C22×C43#45411yescharacteristic
169C22×C43#45511yescharacteristic
170C22×C43#45611yescharacteristic
171C22×C43B(4,𝔽2)11yescharacteristic
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C2×D43—81no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—81no—
186C4×C43—82no—
187C4×C43—81no—
188Dic43—42no—
189Dic43—81no—
190Dic43—81no—
191#2727—431no—
192#2057D4311yescharacteristic, complemented
193#2043—431no—
194#2023—431no—
195#1271—431no—
196#1271—431no—
197#1270—431no—
198C2×C43#159811yescharacteristic
199C2×C43#160311yescharacteristic
200C2×C43#160611yescharacteristic
201C2×C43#163811yescharacteristic
202C2×C43#164111yescharacteristic
203C2×C43#164711yescharacteristic
204C2×C43#166411yescharacteristic
205D43—161no—
206C2×C4⋊Q8C2×D4311yescharacteristic
207C2×#126—861no—
208C2×#107—21no—
209C2×#103—861no—
210C2×#103—861no—
211C2×#102—861no—
212#399—861no—
213#396—861no—
214#394—861no—
215#390—431no—
216#389—431no—
217#389—861no—
218#389C2×D4311yescharacteristic
219#388—861no—
220#340—21no—
221#340—861no—
222#336—431no—
223#336—431no—
224#336C2×D4311yescharacteristic
225C43#776511yescharacteristic, complemented, Sylow
226C22×Q8—21no—
227C22×D4—431no—
228C22×C8—21no—
229C22×C8—861no—
230C22×C8—861no—
231C4⋊Q8—42no—
232#126—1722no—
233#126—1722no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
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⋊C4C22⋊D4311yescharacteristic
244C2×C4⋊C4C22⋊D4311yescharacteristic
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C42—861no—
252C2×C42C22×D4311yescharacteristic
253#107—42no—
254#103—1722no—
255#103—1722no—
256#102—1722no—
257#95—21no—
258#95—861no—
259#95—861no—
260C24—861no—
261C2×Q8—22no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—1721no—
270C2×D4—1721no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4D4×D4311yescharacteristic
278C22×C4D4×D4311yescharacteristic
279C22×C4C2×C22⋊D4311yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—1721no—
284C2×C8—1721no—
285C2×C8—1721no—
286C2×C8—1721no—
287C2×C8—1721no—
288C2×C8—1721no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—432no—
299C4⋊C4—861no—
300C4⋊C4—3441no—
301C4⋊C4—1721no—
302C4⋊C4—1721no—
303C4⋊C4—1722no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C22⋊C4—3441no—
307C22⋊C4—3441no—
308C22⋊C4—1722no—
309C22⋊C4—1722no—
310C22⋊C4—1721no—
311C22⋊C4—1721no—
312C22⋊C4—1721no—
313C22⋊C4—1721no—
314C42—41no—
315C42—1722no—
316C23—1721no—
317C23—1721no—
318C23—1721no—
319C23—1721no—
320C23—1721no—
321C23—1721no—
322C23—1721no—
323C23#1306329311yescharacteristic
324Q8—42no—
325Q8—42no—
326Q8—81no—
327Q8—81no—
328D4—3441no—
329D4—1722no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—862no—
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×C4D8×D4311yescharacteristic
355C2×C4#1306334511yescharacteristic
356C2×C4#1306334811yescharacteristic
357C2×C4#1306334911yescharacteristic
358C2×C4#1306335611yescharacteristic
359C2×C4#1306335711yescharacteristic
360C8—42no—
361C8—3441no—
362C8—3441no—
363C22—3441no—
364C22—3441no—
365C22—3441no—
366C22—3441no—
367C22—3441no—
368C22—3441no—
369C22—3441no—
370C22#1458303111yescharacteristic
371C22#1458305911yescharacteristic
372C22#1458306011yescharacteristic
373C22#1458307011yescharacteristic
374C22#1458307511yescharacteristic
375C22#1458308111yescharacteristic
376C22#1458308511yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—81no—
384C4—82no—
385C4—81no—
386C4—3441no—
387C4—3441no—
388C4—1722no—
389C2—6881no—
390C2#1913352811yescharacteristic
391C2#1913355611yescharacteristic
392C2#1913357411yescharacteristic
393C2#1913376611yescharacteristic
394C2#1913378711yescharacteristic
395C2#1913382711yescharacteristic
396C2#1913392711yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2057C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#2057D43
hypocenterC43#7765
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. #19135838C2semidirect
4. #19132418C2semidirect
5. #19132417C2semidirect
7. C43×#2057C2semidirect
192. #2057D43semidirect
225. C43#7765semidirect

Maximal subgroups

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

subgroupindex
#191415552
#191358382
#191357282
#191324182
#191324172
#191324152
C43×#20572
#776543