Finite Group Databasebeta

← #24995746

Subgroups — #24995746

Order 11008.

468 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145154C211yesmaximal, characteristic
2#19135539C211yesmaximal, characteristic, complemented
3#19135514C211yesmaximal, characteristic
4C4×#13063257C211yesmaximal, characteristic, complemented
5#19133095C211yesmaximal, characteristic, complemented
6#19133091C211yesmaximal, characteristic
7C8×M16×C43C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9#14583449C2211yescharacteristic
10#14583297C411yescharacteristic, complemented
11#14583272C411yescharacteristic, complemented
12#14583250C411yescharacteristic, complemented
13#14583246C411yescharacteristic, complemented
14#14583128—21no—
15#14583128—21no—
16C4×#10621873—21no—
17C4×#10621873—21no—
18C2×#13063257—21no—
19C2×#13063251—22no—
20C4×C4⋊Dic43C2211yescharacteristic
21C4×C4⋊Dic43C2211yescharacteristic
22#14582662—21no—
23#14582660—22no—
24#14582637—22no—
25#14582634—22no—
26C43×#431C2211yescharacteristic
27C4×M16×C43C2211yescharacteristic
28C2×C4×C8×C43C2211yescharacteristic
29C43×#322—21no—
30C82×C43—21no—
31C2×#10621898—21no—
32C2×#10621873—21no—
33C2×#10621873—21no—
34#13063325C2×C411yescharacteristic
35#13063325C2×C411yescharacteristic
36#13063325C2×C411yescharacteristic
37#13063322C2×C411yescharacteristic
38#13063317—21no—
39#13063313—21no—
40#13063304—21no—
41#13063304—21no—
42#13063299—21no—
43#13063299—21no—
44C4×Dic86—21no—
45C4×Dic86—21no—
46C4×D172—21no—
47C4×D172—21no—
48#13063284—21no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43—21no—
51C2×C4×Dic43—21no—
52C2×C4×Dic43—21no—
53#13063257—24no—
54#13063257—21no—
55#13063257—21no—
56#13063251—44no—
57#13063250—21no—
58#13063250—21no—
59#13063247—21no—
60#13063247—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C2×M16×C43D412yes—
64C22×C8×C43D411yescharacteristic
65C22×C8×C43D411yescharacteristic
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C22⋊C8×C43D412yes—
69#97×C43—21no—
70C4×C8×C43—21no—
71C4×C8×C43—21no—
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43C2×C411yescharacteristic
74C4×C8×C43D411yescharacteristic
75C4×C8×C43D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C2×C22⋊D43—41no—
80C22×Dic43—41no—
81C22×Dic43—41no—
82#10621898—42no—
83#10621898—42no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—21no—
87C2×C4×D43—41no—
88C2×Dic86—21no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91M16×C43—22no—
92M16×C43SD1614yescomplemented
93C2×C8×C43—22no—
94C2×C8×C43—22no—
95C2×C8×C43—22no—
96C2×C8×C43—41no—
97C2×C8×C43C22⋊C411yescharacteristic
98C2×C8×C43C22⋊C411yescharacteristic
99C2×C8×C43C22⋊C411yescharacteristic
100C2×C8×C43C22⋊C411yescharacteristic
101C42×C43C22×C411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43#4111yescharacteristic
104C42×C43#4111yescharacteristic
105C22⋊Dic43—41no—
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—41no—
108C4⋊Dic43—22no—
109C4⋊Dic43—22no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—41no—
117C4⋊Dic43—41no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120C4×Dic43—41no—
121C4×Dic43—42no—
122C4×Dic43—42no—
123#10621873—42no—
124#10621873—42no—
125C23×C43#12711yescharacteristic
126C22×D43—41no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—41no—
130C2×C4×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12411yescharacteristic
136C2×C4×C43C2×SD1612yes—
137C2×C4×C43#13512yes—
138C22⋊D43—81no—
139C22⋊D43—81no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—81no—
146C2×Dic43—81no—
147C2×Dic43—81no—
148C2×Dic43—81no—
149D172—41no—
150D172—41no—
151D172—42no—
152D172—81no—
153C4×D43—82no—
154Dic86—41no—
155Dic86—41no—
156Dic86—42no—
157Dic86—81no—
158C8×C43—21no—
159C8×C43—21no—
160C8×C43—21no—
161C8×C43—24no—
162C8×C43—42no—
163C8×C43#10412yescomplemented
164#9717—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43#39011yescharacteristic
168C22×C43#49211yescharacteristic
169C22×C43#49511yescharacteristic
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43C2×#10411yescharacteristic
177C4×C43#42111yescharacteristic
178C4×C43C4×SD1612yes—
179C4×C43#46512yes—
180Dic43—82no—
181Dic43—82no—
182Dic43—81no—
183Dic43—81no—
184Dic43—81no—
185#3167—431no—
186#1986—431no—
187#1980—431no—
188C4×#106—431no—
189#1503—431no—
190#1502—431no—
191C8×M16D4311yescharacteristic, complemented
192C2×C43—21no—
193C2×C43—21no—
194C2×C43#196811yescharacteristic
195C2×C43#197611yescharacteristic
196C2×C43#198011yescharacteristic
197D43—161no—
198#533—431no—
199#532—431no—
200#498—431no—
201#492—431no—
202#487—431no—
203#486—431no—
204#465—861no—
205#465—861no—
206C4×SD16—861no—
207C4×SD16—861no—
208#431C2×D4311yescharacteristic
209C2×#106—861no—
210C2×#104—862no—
211C4×M16C2×D4311yescharacteristic
212C2×C4×C8C2×D4311yescharacteristic
213C4×C4⋊C4—431no—
214C4×C4⋊C4—431no—
215#340—861no—
216#339—862no—
217#328—862no—
218#327—862no—
219#322—21no—
220C82—21no—
221C43#971711yescharacteristic, complemented, Sylow
222C2×#41—861no—
223C2×SD16—861no—
224C2×SD16—861no—
225C2×M16D17212yes—
226C22×C8D17211yescharacteristic
227C22×C8D17211yescharacteristic
228C4⋊Q8—431no—
229C4⋊Q8—431no—
230C4⋊Q8—431no—
231#127—431no—
232#125—861no—
233#124—861no—
234C22⋊Q8—861no—
235C22⋊Q8—861no—
236#121—861no—
237#121—861no—
238C4×Q8—861no—
239C4×Q8—861no—
240C4×D4—861no—
241C4×D4—861no—
242#117—861no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4—861no—
245C2×C42—861no—
246C2×C42—861no—
247C2×C42C22×D4311yescharacteristic
248#106—864no—
249#106—861no—
250#106—861no—
251C4⋊C8—21no—
252#104—1724no—
253#103—861no—
254#103—861no—
255#102—861no—
256#102—861no—
257C22⋊C8D17212yes—
258#97—21no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8C4×D4311yescharacteristic
262C4×C8C4×D4311yescharacteristic
263C4×C8C22⋊D4311yescharacteristic
264C4×C8C22⋊D4311yescharacteristic
265#95—861no—
266#95—861no—
267#41—1722no—
268#41—1722no—
269C2×Q8—861no—
270C2×Q8—861no—
271C2×Q8—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—1721no—
276C22×C4—1721no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4C2×D17211yescharacteristic
280C22×C4C2×D17211yescharacteristic
281C22×C4C2×D17211yescharacteristic
282SD16—1722no—
283SD16—1722no—
284M16—22no—
285M16#1062187314yescomplemented
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8(C2×D43)⋊C411yescharacteristic
291C2×C8(C2×D43)⋊C411yescharacteristic
292C2×C8(C2×D43)⋊C411yescharacteristic
293C2×C8(C2×D43)⋊C411yescharacteristic
294C4⋊C4—862no—
295C4⋊C4—862no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C22⋊C4—1721no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C42—1722no—
310C42—1722no—
311C42—1721no—
312C42C2×C4×D4311yescharacteristic
313C42#1062189811yescharacteristic
314C42#1062189811yescharacteristic
315C42C2×C22⋊D4311yescharacteristic
316C23—1721no—
317C23#1306332211yescharacteristic
318Q8—3441no—
319Q8—1721no—
320Q8—1721no—
321Q8—1722no—
322D4—3441no—
323D4—3441no—
324D4—3441no—
325D4—1721no—
326D4—1721no—
327D4—1722no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—3441no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4—3442no—
336C2×C4—1722no—
337C2×C4—1722no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4C2×(C2×D43)⋊C411yescharacteristic
342C2×C4C4×D17211yescharacteristic
343C2×C4C4×D17211yescharacteristic
344C2×C4#1306329911yescharacteristic
345C2×C4#1306329911yescharacteristic
346C2×C4#1306331311yescharacteristic
347C2×C4C2×#1062187312yes—
348C2×C4#1306334712yes—
349C8—24no—
350C8—21no—
351C8—21no—
352C8—21no—
353C8—42no—
354C8#1306325112yescomplemented
355C22—21no—
356C22—21no—
357C22—3441no—
358C22—3441no—
359C22—3441no—
360C22#1458280111yescharacteristic
361C22#1458327211yescharacteristic
362C22#1458328311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—3442no—
367C4—3442no—
368C4—3441no—
369C4—3441no—
370C4—3441no—
371C4C2×#1306325111yescharacteristic
372C4#1458291511yescharacteristic
373C4C4×#1062187312yes—
374C4#1458312812yes—
375C2—21no—
376C2—21no—
377C2—6881no—
378C2#1913544911yescharacteristic
379C2#1913549311yescharacteristic
380C2#1913551411yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC8×M16×C43C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenterC8×M16D43
hypocenterC43#9717
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. #19135539C2semidirect
4. C4×#13063257C2semidirect
5. #19133095C2semidirect
7. C8×M16×C43C2semidirect
10. #14583297C4semidirect
11. #14583272C4semidirect
12. #14583250C4semidirect
13. #14583246C4semidirect
92. M16×C43SD16semidirect
163. C8×C43#104semidirect
191. C8×M16D43semidirect
221. C43#9717semidirect
285. M16#10621873semidirect
354. C8#13063251semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191355392
#191355142
C4×#130632572
#191330952
#191330912
C8×M16×C432
#971743