Finite Group Databasebeta

← #24988074

Subgroups — #24988074

Order 11008.

1094 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1094 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#14583449C211yesmaximal, characteristic
2#19134357C211yesmaximal, characteristic, complemented
3C2×#14582638C214yesmaximal, complemented
4C43×#1749C211yesmaximal, characteristic, complemented
5C22×#10621898C412yes—
6#14583449—28no—
7C2×#13063325C411yescharacteristic
8C2×#13063322C411yescharacteristic
9C2×#13063313C2212yes—
10C2×#13063299—21no—
11C2×#13063299—21no—
12C2×C4×D172—21no—
13C2×C4×D172—21no—
14C2×C22⋊(C43⋊C8)—21no—
15C2×#13063236C2212yes—
16#14582654—21no—
17#14582638—28no—
18C22×C42×C43C2211yescharacteristic
19C2×C22⋊C8×C43—21no—
20C2×#97×C43C2212yes—
21C43×#336—21no—
22C2×#10621898—24no—
23C2×#10621898—24no—
24C2×#10621898—44no—
25C2×#10621898—44no—
26C22×Dic86C2×C412yes—
27C22×D172—21no—
28C22×D172—21no—
29C22×D172C2×C412yes—
30C22×C22⋊D43—22no—
31C22×C4×D43—22no—
32C22×C43⋊C8—22no—
33#13063325—24no—
34#13063322—24no—
35#13063313—24no—
36#13063313D418yes—
37#13063299—28no—
38#13063299—28no—
39C4×D172—28no—
40C4×D172—28no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4—22no—
45C22⋊(C43⋊C8)—24no—
46#13063236—24no—
47C23×C4×C43C2×C411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C23×C4×C43D411yescharacteristic
50C22×C8×C43—22no—
51C2×C42×C43—24no—
52C2×C42×C43C2×C411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C42×C43C2311yescharacteristic
56C22⋊C8×C43—24no—
57#97×C43—24no—
58C24×C43C22⋊C411yescharacteristic
59C23×D43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43—22no—
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—41no—
68C22×C4×C43—41no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C2×C22⋊D43—28no—
76C2×C22⋊D43—44no—
77C2×C22⋊D43—44no—
78C22×Dic43—22no—
79#10621898—416no—
80#10621898—416no—
81C2×D172—24no—
82C2×D172—24no—
83C2×D172—22no—
84C2×D172—42no—
85C2×D172—42no—
86C2×D172—42no—
87C2×D172—42no—
88C2×D172—42no—
89C2×D172—42no—
90C2×D172C22⋊C414yes—
91C2×C4×D43—28no—
92C2×C4×D43—44no—
93C2×C4×D43—44no—
94C2×Dic86—22no—
95C2×Dic86—42no—
96C2×Dic86—42no—
97C2×Dic86C22⋊C414yes—
98C2×C8×C43—24no—
99C2×C8×C43—42no—
100C2×C8×C43—42no—
101C42×C43—22no—
102C42×C43—22no—
103C42×C43—22no—
104C42×C43C2×D414yes—
105(C2×D43)⋊C4—28no—
106(C2×D43)⋊C4—28no—
107C4⋊Dic43—24no—
108C4⋊Dic43—24no—
109C2×C43⋊C8—24no—
110C2×C43⋊C8—42no—
111C2×C43⋊C8—42no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43#10012yes—
119C23×C43C2×C22⋊C411yescharacteristic
120C22×D43—24no—
121C22×D43—42no—
122C22×D43—42no—
123C22×D43—42no—
124C22×D43—42no—
125C22×D43—42no—
126C22×D43—42no—
127C2×C4×C43—28no—
128C2×C4×C43—21no—
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—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—44no—
141C2×C4×C43—44no—
142C2×C4×C43#10012yes—
143C2×C4×C43#10412yes—
144C2×C4×C43#10412yes—
145C2×C4×C43C2×C22⋊C412yes—
146C2×C4×C43#12012yes—
147C2×C4×C43#12012yes—
148C22⋊D43—416no—
149C2×Dic43—24no—
150C2×Dic43—42no—
151C2×Dic43—42no—
152D172—44no—
153D172—48no—
154D172—48no—
155D172—44no—
156C4×D43—416no—
157Dic86—44no—
158Dic86—44no—
159C8×C43—44no—
160C43⋊C8—44no—
161#8337—431nomaximal, Sylow
162C22×C43—22no—
163C22×C43—22no—
164C22×C43—22no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43#37911yescharacteristic
170C22×C43C2×#10011yescharacteristic
171C22×C43C2×#10011yescharacteristic
172C22×C43C2×#10411yescharacteristic
173C22×C43C2×#10411yescharacteristic
174C22×C43#42111yescharacteristic
175C22×C43#42111yescharacteristic
176C2×D43—44no—
177C2×D43—44no—
178C2×D43—44no—
179C2×D43—82no—
180C2×D43—82no—
181C2×D43—82no—
182C2×D43—82no—
183C4×C43—22no—
184C4×C43—22no—
185C4×C43—22no—
186C4×C43—22no—
187C4×C43—22no—
188C4×C43—22no—
189Dic43—44no—
190C2×#532—431no—
191#1749—431no—
192#1749D4311yescharacteristic, complemented
193C2×#329—434no—
194C2×C43—42no—
195C2×C43#152511yescharacteristic
196C2×C43#153011yescharacteristic
197C2×C43#153011yescharacteristic
198C2×C43#153611yescharacteristic
199C2×C43#178311yescharacteristic
200C2×C43#178911yescharacteristic
201C2×C43#178911yescharacteristic
202D43—84no—
203C22×#41—432no—
204#532—868no—
205C2×C4⋊Q8—431no—
206C2×#127—431no—
207C2×#124—432no—
208C2×#121—861no—
209C2×#121—861no—
210C2×C4×D4—861no—
211C2×C4×D4—861no—
212C22×C42C2×D4311yescharacteristic
213C2×C22⋊C8—21no—
214C2×C22⋊C8—861no—
215C2×#97—432no—
216C2×#97C2×D4312yes—
217#336—21no—
218#336—861no—
219#329—868no—
220C43#833711yescharacteristic, complemented, Sylow
221C2×#41—864no—
222C2×#41—864no—
223C2×#41—1724no—
224C2×#41—1724no—
225C22×Q8—432no—
226C22×D4—432no—
227C22×D4—862no—
228C22×D4—861no—
229C22×D4—861no—
230C23×C4—862no—
231C23×C4C4×D4311yescharacteristic
232C23×C4D17211yescharacteristic
233C23×C4C22⋊D4311yescharacteristic
234C22×C8—22no—
235C22×C8—862no—
236C4⋊Q8—864no—
237#127—864no—
238#124—438no—
239#124—864no—
240#121—868no—
241#121—868no—
242C4×D4—868no—
243C4×D4—868no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4—861no—
246C2×C22⋊C4—862no—
247C2×C22⋊C4—862no—
248C2×C42—24no—
249C2×C42C4×D4311yescharacteristic
250C2×C42D17211yescharacteristic
251C2×C42C22⋊D4311yescharacteristic
252C2×C42C22×D4311yescharacteristic
253C22⋊C8—24no—
254C22⋊C8—864no—
255#97—24no—
256#97—864no—
257C24—862no—
258C24(C2×D43)⋊C411yescharacteristic
259#41—17216no—
260#41—17216no—
261C2×Q8—434no—
262C2×Q8—862no—
263C2×Q8—1722no—
264C2×Q8—1722no—
265C2×D4—434no—
266C2×D4—864no—
267C2×D4—864no—
268C2×D4—868no—
269C2×D4—862no—
270C2×D4—1722no—
271C2×D4—1722no—
272C2×D4—1722no—
273C2×D4—1722no—
274C2×D4—1724no—
275C2×D4—1724no—
276C2×D4—1722no—
277C2×D4—1722no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—868no—
288C22×C4—862no—
289C22×C4—1724no—
290C22×C4—1724no—
291C22×C4(C2×D43)⋊C411yescharacteristic
292C22×C4(C2×D43)⋊C411yescharacteristic
293C22×C4(C2×D43)⋊C411yescharacteristic
294C22×C4C2×C4×D4311yescharacteristic
295C22×C4C2×D17211yescharacteristic
296C22×C4C2×C22⋊D4311yescharacteristic
297C2×C8—24no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—864no—
301C2×C8—1722no—
302C2×C8—1722no—
303C4⋊C4—864no—
304C4⋊C4—864no—
305C22⋊C4—868no—
306C22⋊C4—868no—
307C42—22no—
308C42—22no—
309C42—22no—
310C42D4×D4314yes—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—864no—
318C23—1722no—
319C23—1722no—
320C23—1722no—
321C23—1722no—
322C23—1722no—
323C23—1722no—
324C23#1306324112yes—
325C23C2×(C2×D43)⋊C411yescharacteristic
326Q8—1724no—
327Q8—1724no—
328D4—1724no—
329D4—1724no—
330D4—1728no—
331D4—1728no—
332D4—17216no—
333C2×C4—28no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—864no—
349C2×C4—17216no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4#1306324112yes—
353C2×C4#1306325112yes—
354C2×C4#1306325312yes—
355C2×C4C22⋊C4×D4312yes—
356C2×C4#1306329312yes—
357C2×C4#1306329512yes—
358C8—44no—
359C8—1724no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—3442no—
368C22—3442no—
369C22—3442no—
370C22—3442no—
371C22—1724no—
372C22—1724no—
373C22—1724no—
374C22#1458275411yescharacteristic
375C22C2×#1306324111yescharacteristic
376C22C2×#1306324111yescharacteristic
377C22C2×#1306325111yescharacteristic
378C22C2×#1306325311yescharacteristic
379C22#1458291511yescharacteristic
380C22#1458291711yescharacteristic
381C4—22no—
382C4—22no—
383C4—22no—
384C4—22no—
385C4—22no—
386C4—22no—
387C4—1724no—
388C2—42no—
389C2—3444no—
390C2#1913318611yescharacteristic
391C2#1913320511yescharacteristic
392C2#1913320711yescharacteristic
393C2#1913322911yescharacteristic
394C2#1913451511yescharacteristic
395C2#1913453811yescharacteristic
396C2#1913454011yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1749C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583449C2
cosocleC2×C42×C43C23
hypercenter#1749D43
hypocenterC43#8337
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. #19134357C2semidirect
3. C2×#14582638C2semidirect
4. C43×#1749C2semidirect
192. #1749D43semidirect
220. C43#8337semidirect

Maximal subgroups

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

subgroupindex
C2×#145834492
#191343572
C2×#145826382
C43×#17492
#833743