Finite Group Databasebeta

← #24984633

Subgroups — #24984633

Order 11008.

522 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137133C211yesmaximal, characteristic
2#19134662C211yesmaximal, characteristic
3#19134352C211yesmaximal, characteristic
4#19132421C211yesmaximal, characteristic, complemented
5#19132419C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1272C211yesmaximal, characteristic, complemented
8C2×#13063301C411yescharacteristic
9C2×Q8×Dic43C411yescharacteristic
10C2×C42×D43C2211yescharacteristic
11C2×(C2×D43)⋊C8—21no—
12C2×(C2×D43)⋊C8—21no—
13C2×C8×Dic43—21no—
14#14582797C2211yescharacteristic
15#14582786—21no—
16#14582773—21no—
17#14582756C411yescharacteristic
18C4⋊C4×Dic43C411yescharacteristic
19#14582750—21no—
20#14582746—21no—
21#14582654C2211yescharacteristic
22#14582654C2211yescharacteristic
23#14582653—21no—
24C43×#391C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063301—22no—
33#13063301C814yescomplemented
34Q8×Dic43—42no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C42×D43—42no—
48(C2×D43)⋊C8—24no—
49(C2×D43)⋊C8—42no—
50C8×Dic43—42no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C22×Q8×C43C2×C411yescharacteristic
55C22×C8×C43—21no—
56C22×C8×C43—21no—
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#95×C43—21no—
60#95×C43—21no—
61C23×D43C22⋊C411yescharacteristic
62C2×Q8×C43—21no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43C2×C812yes—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—22no—
81C2×C4×D43—22no—
82C2×C4×D43—41no—
83C2×C4×D43—41no—
84C2×C4×D43—41no—
85C2×C4×D43—41no—
86C2×C4×D43C2×C812yes—
87C2×C4×D43M1612yes—
88C2×C8×C43—22no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C4⋊C4×C43—41no—
95C42×C43—41no—
96(C2×D43)⋊C4—24no—
97(C2×D43)⋊C4—42no—
98C4⋊Dic43—21no—
99C4⋊Dic43—42no—
100C4⋊Dic43—41no—
101C4⋊Dic43C2×C812yes—
102Dic43⋊C4—24no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105C4×Dic43—22no—
106C4×Dic43—22no—
107C4×Dic43—41no—
108C4×Dic43—42no—
109C4×Dic43—42no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C23×C43C2×C22⋊C411yescharacteristic
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43C22⋊C812yes—
124Q8×C43—42no—
125Q8×C43—42no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43C22×C811yescharacteristic
139C2×C4×C43C2×M1611yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43#13511yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×C4×C43#13711yescharacteristic
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—22no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43C22⋊C812yes—
157C2×Dic43#9912yes—
158C2×Dic43#10412yes—
159C4×D43—42no—
160C4×D43—42no—
161C4×D43—42no—
162C4×D43—42no—
163C4×D43—42no—
164C4×D43—42no—
165C8×C43—42no—
166C8×C43—81no—
167C43⋊C8—42no—
168C43⋊C8—81no—
169#7583—431nomaximal, Sylow
170C22×C43C2×C22⋊C811yescharacteristic
171C22×C43C2×#9911yescharacteristic
172C22×C43#41311yescharacteristic
173C22×C43#41611yescharacteristic
174C22×C43#41911yescharacteristic
175C22×C43C2×#10411yescharacteristic
176C22×C43#42111yescharacteristic
177C2×D43—22no—
178C2×D43—22no—
179C2×D43—22no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—42no—
191C4×C43—81no—
192Dic43—22no—
193Dic43—22no—
194Dic43—22no—
195Dic43—42no—
196Dic43—81no—
197C4×C22⋊Q8—431no—
198#1817—431no—
199C4×C22⋊C8—431no—
200#1272—431no—
201#1272D4311yescharacteristic, complemented
202#1271—431no—
203#1271—431no—
204C2×C43#145911yescharacteristic
205C2×C43#147611yescharacteristic
206C2×C43#147911yescharacteristic
207C2×C43#150811yescharacteristic
208C2×C43#151611yescharacteristic
209C2×C43#152911yescharacteristic
210C2×C43#155411yescharacteristic
211D43—42no—
212C2×C22⋊Q8—431no—
213C2×C4×Q8—431no—
214C22×C42—431no—
215C2×C22⋊C8—861no—
216C2×C22⋊C8—861no—
217C2×C4×C8—861no—
218#391C2×D4311yescharacteristic
219#389—431no—
220#387—861no—
221#385—861no—
222#380—431no—
223C4×C4⋊C4—431no—
224C4×C4⋊C4—861no—
225C4×C22⋊C4—861no—
226#336—431no—
227#336—431no—
228#336—861no—
229#336C2×D4311yescharacteristic
230#336C2×D4311yescharacteristic
231C43#758311yescharacteristic, complemented, Sylow
232C22×Q8C4×D4311yescharacteristic
233C23×C4—431no—
234C23×C4—431no—
235C23×C4—431no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—861no—
239C22×C8—861no—
240C22⋊Q8—434no—
241C22⋊Q8—862no—
242C4×Q8—1722no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4C4×D4311yescharacteristic
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C42—431no—
252C2×C42—431no—
253C2×C42—431no—
254C2×C42—861no—
255C2×C42—861no—
256C2×C42—1722no—
257C2×C42C22×D4311yescharacteristic
258C22⋊C8—864no—
259C22⋊C8—1722no—
260C4×C8—1722no—
261#95—21no—
262#95—21no—
263#95—861no—
264#95—861no—
265#95—861no—
266C24—431no—
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8C8×D4312yes—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—432no—
277C22×C4—432no—
278C22×C4—862no—
279C22×C4—862no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—1721no—
287C22×C4—1721no—
288C22×C4—1721no—
289C22×C4—1721no—
290C22×C4C2×C4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4D4×D4311yescharacteristic
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—862no—
300C2×C8—1721no—
301C2×C8—1721no—
302C2×C8—1721no—
303C2×C8—1721no—
304C2×C8—1721no—
305C4⋊C4—41no—
306C4⋊C4—432no—
307C4⋊C4—864no—
308C4⋊C4—861no—
309C4⋊C4—1721no—
310C4⋊C4—1722no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C22⋊C4—864no—
314C22⋊C4—1722no—
315C42—41no—
316C42—862no—
317C42—862no—
318C42—1721no—
319C42—1722no—
320C42—1722no—
321C23—432no—
322C23—861no—
323C23—861no—
324C23—861no—
325C23—861no—
326C23—861no—
327C23—861no—
328C23C22⋊C4×D4311yescharacteristic
329Q8—42no—
330Q8—42no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—432no—
344C2×C4—432no—
345C2×C4—432no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—862no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4C2×C8×D4311yescharacteristic
365C2×C4M16×D4311yescharacteristic
366C2×C4#1306334611yescharacteristic
367C2×C4#1306334811yescharacteristic
368C2×C4#1306335411yescharacteristic
369C2×C4#1306335711yescharacteristic
370C8—42no—
371C8—81no—
372C8—3441no—
373C8—1722no—
374C22—862no—
375C22—862no—
376C22—862no—
377C22—1721no—
378C22—1721no—
379C22—1721no—
380C22—1721no—
381C22C22⋊C8×D4311yescharacteristic
382C22#99×D4311yescharacteristic
383C22#1458288011yescharacteristic
384C22#1458289411yescharacteristic
385C22#1458290611yescharacteristic
386C22#104×D4311yescharacteristic
387C22#1458291411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—862no—
397C4—862no—
398C4—862no—
399C4—3441no—
400C4—1722no—
401C2—1722no—
402C2#1913291011yescharacteristic
403C2#1913297611yescharacteristic
404C2#1913298811yescharacteristic
405C2#1913311311yescharacteristic
406C2#1913315011yescharacteristic
407C2#1913319911yescharacteristic
408C2#1913330411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7583
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #19132421C2semidirect
5. #19132419C2semidirect
6. #19132417C2semidirect
7. C43×#1272C2semidirect
33. #13063301C8semidirect
201. #1272D43semidirect
231. C43#7583semidirect

Maximal subgroups

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

subgroupindex
#191371332
#191346622
#191343522
#191324212
#191324192
#191324172
C43×#12722
#758343