Finite Group Databasebeta

← #24993890

Subgroups — #24993890

Order 11008.

424 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 89 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#19145803C211yesmaximal, characteristic
2#19137399C211yesmaximal, characteristic
3#19135538C211yesmaximal, characteristic
4#19133198C211yesmaximal, characteristic
5#19133147C211yesmaximal, characteristic
6#19132461C211yesmaximal, characteristic
7C43×#1285C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063317C2211yescharacteristic
10#14583308C412yescomplemented
11#14583268C412yescomplemented
12#14583235—21no—
13#14583230—21no—
14#14583207—22no—
15C4×#10621877C2211yescharacteristic
16#14582794—21no—
17#14582784—21no—
18#14582783—21no—
19#14582782—21no—
20#14582780—21no—
21#14582767C2211yescharacteristic
22C4×Dic43⋊C4—21no—
23#14582659—21no—
24#14582659—21no—
25#14582640—22no—
26#14582637—21no—
27#14582637—21no—
28C43×#432C2211yescharacteristic
29C43×#432C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621877—21no—
32#13063325C2×C411yescharacteristic
33#13063325C2×C411yescharacteristic
34#13063317—21no—
35#13063317—21no—
36#13063317—21no—
37#13063317C2×C412yes—
38#13063317D412yes—
39#13063304—21no—
40#13063304—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43#13063284—21no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—21no—
49C2×Dic43⋊C4—21no—
50C2×C4×Dic43—21no—
51C2×C4×Dic43—21no—
52#13063259—22no—
53#13063257—22no—
54#13063250—22no—
55#13063250—22no—
56#13063236—21no—
57C4×C43⋊C8—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95D411yescharacteristic
65C43⋊#95D411yescharacteristic
66C2×C4⋊C4×C43—21no—
67C2×C42×C43D411yescharacteristic
68C2×C42×C43D411yescharacteristic
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74#97×C43—21no—
75#97×C43C2×C412yes—
76#95×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C2×Dic86—21no—
87C2×Dic86—21no—
88C2×C8×C43—22no—
89C2×C8×C43—41no—
90C4⋊C4×C43—42no—
91C42×C43—41no—
92C42×C43—41no—
93C42×C43C22×C411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43#4111yescharacteristic
96C42×C43#4111yescharacteristic
97C22⋊Dic43—41no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43C22⋊C412yes—
105C4⋊Dic43C22⋊C412yes—
106Dic43⋊C4—22no—
107Dic43⋊C4—22no—
108Dic43⋊C4—22no—
109Dic43⋊C4—22no—
110Dic43⋊C4—42no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113Dic43⋊C4—81no—
114C4×Dic43—42no—
115C4×Dic43—41no—
116C4×Dic43—81no—
117#10621877—22no—
118#10621877—41no—
119C2×C43⋊C8—41no—
120C23×C43#12011yescharacteristic
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—22no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12311yescharacteristic
137C2×Dic43—22no—
138C2×Dic43—22no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151Dic86—42no—
152Dic86—81no—
153C8×C43—42no—
154C8×C43—81no—
155C43⋊C8—42no—
156#9380—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43#38611yescharacteristic
160C22×C43#45511yescharacteristic
161C22×C43#45611yescharacteristic
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—42no—
169C4×C43—81no—
170Dic43—42no—
171Dic43—42no—
172Dic43—81no—
173Dic43—81no—
174Dic43—81no—
175Dic43—81no—
176#3236—431no—
177#2336—431no—
178#1986—431no—
179#1528—431no—
180#1515—431no—
181#1288—431no—
182#1285D4311yescharacteristic
183C2×C43—21no—
184C2×C43—21no—
185C2×C43#188211yescharacteristic
186C2×C43#190611yescharacteristic
187C2×C43#191211yescharacteristic
188#533—431no—
189C2×#125—431no—
190#501—432no—
191#491—432no—
192#484—861no—
193#483—861no—
194#479—862no—
195#432C2×D4311yescharacteristic
196#432C2×D4311yescharacteristic
197C4×M16—431no—
198#389—861no—
199#387—861no—
200#387—861no—
201#387—861no—
202#387—861no—
203#383—431no—
204C4×C4⋊C4—861no—
205C4×C4⋊C4C2×D4311yescharacteristic
206#339—861no—
207#339—861no—
208#330—862no—
209#328—861no—
210#328—861no—
211C43#938011yescharacteristic, complemented, Sylow
212C2×M16—861no—
213C4⋊Q8—431no—
214C4⋊Q8—431no—
215#125—432no—
216#125—432no—
217#125—861no—
218#125—861no—
219#125—861no—
220C22⋊Q8—861no—
221C22⋊Q8—861no—
222C4×Q8—861no—
223C4×Q8—861no—
224#117—861no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C42—861no—
233C2×C42—861no—
234C2×C42D17211yescharacteristic
235C2×C42D17211yescharacteristic
236C2×C42C22×D4311yescharacteristic
237#107—862no—
238#106—862no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241#103—862no—
242#103—862no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245#97—21no—
246#97—861no—
247#97C4×D4312yes—
248C4×C8—861no—
249#95—21no—
250#95—431no—
251#95—431no—
252#95—861no—
253#95—861no—
254#95—861no—
255#95—861no—
256#95—861no—
257#95—861no—
258C2×Q8—861no—
259C2×Q8—861no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4C2×D17211yescharacteristic
267C22×C4D4×D4311yescharacteristic
268C22×C4D4×D4311yescharacteristic
269M16—862no—
270M16—1721no—
271C2×C8—22no—
272C2×C8—41no—
273C2×C8—1721no—
274C4⋊C4—42no—
275C4⋊C4—432no—
276C4⋊C4—432no—
277C4⋊C4—862no—
278C4⋊C4—862no—
279C4⋊C4—862no—
280C4⋊C4—862no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—3441no—
288C4⋊C4—1722no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C22⋊C4—1721no—
292C42—41no—
293C42—41no—
294C42—3441no—
295C42—1722no—
296C42—1721no—
297C42C2×C4×D4311yescharacteristic
298C42#1062189811yescharacteristic
299C42D4×D4311yescharacteristic
300C42#1062190211yescharacteristic
301C23#1306329511yescharacteristic
302Q8—3441no—
303Q8—1722no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—862no—
315C2×C4—862no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4C22⋊C4×D4311yescharacteristic
329C2×C4#1306328711yescharacteristic
330C2×C4C4×D17211yescharacteristic
331C2×C4#1306329811yescharacteristic
332C2×C4#1306330011yescharacteristic
333C2×C4#1306331011yescharacteristic
334C8—42no—
335C8—81no—
336C8—1722no—
337C22—21no—
338C22—21no—
339C22#1458277711yescharacteristic
340C22#1458307911yescharacteristic
341C22#1458308411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—81no—
350C4—3441no—
351C4—3441no—
352C4—3441no—
353C4—3441no—
354C4—1722no—
355C4—1722no—
356C2—21no—
357C2—21no—
358C2#1913496311yescharacteristic
359C2#1913509511yescharacteristic
360C2#1913513111yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1285C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1285D43
hypocenterC43#9380
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
10. #14583308C4semidirect
11. #14583268C4semidirect
211. C43#9380semidirect

Maximal subgroups

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

subgroupindex
#191458032
#191373992
#191355382
#191331982
#191331472
#191324612
C43×#12852
#938043