Finite Group Databasebeta

← #24993891

Subgroups — #24993891

Order 11008.

424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 99 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#19145801C211yesmaximal, characteristic
2#19135538C211yesmaximal, characteristic
3#19133197C211yesmaximal, characteristic
4#19133145C211yesmaximal, characteristic
5#19132459C211yesmaximal, characteristic
6#19132451C211yesmaximal, characteristic
7C43×#2336C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583309C412yescomplemented
10#14583269C412yescomplemented
11#14583234—21no—
12#14583229—21no—
13#14583203—22no—
14#14582956C2211yescharacteristic
15#14582956C2211yescharacteristic
16C4×#10621877C2211yescharacteristic
17#14582659—21no—
18#14582659—21no—
19#14582641—22no—
20#14582635—21no—
21#14582635—21no—
22C2×#125×C43C2211yescharacteristic
23C43×#389—21no—
24C43×#387—21no—
25C43×#387—21no—
26C43×#387—21no—
27C43×#387—21no—
28C43×#383C2211yescharacteristic
29C4×C4⋊C4×C43—21no—
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621877—21no—
32#13063325C2×C411yescharacteristic
33#13063325C2×C411yescharacteristic
34#13063317—21no—
35#13063304—21no—
36#13063304—21no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39#13063284—21no—
40#13063258—22no—
41#13063256—22no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44#13063248—22no—
45#13063248—22no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48#13063236—21no—
49#13063236—21no—
50#13063236C2×C412yes—
51C4×C43⋊C8—21no—
52#125×C43—21no—
53#125×C43—21no—
54#125×C43C2×C412yes—
55#125×C43D412yes—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43D411yescharacteristic
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C42×C43—21no—
64C2×C42×C43—21no—
65C2×C42×C43D411yescharacteristic
66C2×C42×C43D411yescharacteristic
67C2×C42×C43C2311yescharacteristic
68#95×C43—21no—
69#95×C43—21no—
70#95×C43—21no—
71#95×C43—21no—
72#95×C43—21no—
73#95×C43—21no—
74#95×C43—21no—
75#95×C43D411yescharacteristic
76#95×C43D411yescharacteristic
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C2×Dic86—21no—
87C2×Dic86—21no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—42no—
95C4⋊C4×C43—42no—
96C4⋊C4×C43—81no—
97C4⋊C4×C43C22⋊C412yes—
98C4⋊C4×C43C22⋊C412yes—
99C42×C43—41no—
100C42×C43—41no—
101C42×C43—42no—
102C42×C43—81no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106C42×C43#4111yescharacteristic
107C22⋊Dic43—41no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114C4×Dic43—41no—
115#10621877—22no—
116#10621877—41no—
117C2×C43⋊C8—22no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C23×C43#12011yescharacteristic
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
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—41no—
142C2×C4×C43—41no—
143C2×C4×C43C2×C22⋊C411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12311yescharacteristic
149C2×Dic43—41no—
150C2×Dic43—41no—
151Dic86—42no—
152Dic86—81no—
153C43⋊C8—42no—
154C43⋊C8—42no—
155C43⋊C8—81no—
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—42no—
170C4×C43—42no—
171C4×C43—81no—
172C4×C43—81no—
173C4×C43—81no—
174Dic43—81no—
175Dic43—81no—
176#3236—431no—
177#2336D4311yescharacteristic
178#1986—431no—
179#1528—431no—
180#1515—431no—
181#1288—431no—
182#1285—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43#188211yescharacteristic
186C2×C43#190611yescharacteristic
187C2×C43#191211yescharacteristic
188#533—431no—
189C2×#125C2×D4311yescharacteristic
190#501—432no—
191#491—432no—
192#484—861no—
193#483—861no—
194#479—862no—
195#432—431no—
196#432—431no—
197C4×M16—431no—
198#389—21no—
199#387—21no—
200#387—21no—
201#387—21no—
202#387—21no—
203#383C2×D4311yescharacteristic
204C4×C4⋊C4—21no—
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—21no—
216#125—21no—
217#125—861no—
218#125C4×D4312yes—
219#125D17212yes—
220C22⋊Q8—861no—
221C22⋊Q8—861no—
222C4×Q8—861no—
223C4×Q8—861no—
224#117—861no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C22⋊D4311yescharacteristic
231C2×C4⋊C4C22⋊D4311yescharacteristic
232C2×C42—21no—
233C2×C42—21no—
234C2×C42C22⋊D4311yescharacteristic
235C2×C42C22⋊D4311yescharacteristic
236C2×C42C22×D4311yescharacteristic
237#107—862no—
238#106—862no—
239C4⋊C8—861no—
240C4⋊C8—861no—
241#103—862no—
242#103—862no—
243C22⋊C8—861no—
244C22⋊C8—861no—
245#97—432no—
246#97—861no—
247#97—861no—
248C4×C8—861no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95C22⋊D4311yescharacteristic
257#95C22⋊D4311yescharacteristic
258C2×Q8—861no—
259C2×Q8—861no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4C2×C22⋊D4311yescharacteristic
267C22×C4C2×C22⋊D4311yescharacteristic
268C22×C4C2×C22⋊D4311yescharacteristic
269M16—862no—
270M16—1721no—
271C2×C8—862no—
272C2×C8—1721no—
273C2×C8—1721no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—81no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4(C2×D43)⋊C412yes—
290C4⋊C4(C2×D43)⋊C412yes—
291C22⋊C4—1721no—
292C42—41no—
293C42—41no—
294C42—42no—
295C42—81no—
296C42—1721no—
297C42C2×C4×D4311yescharacteristic
298C42C2×D17211yescharacteristic
299C42#1062189811yescharacteristic
300C42#1062189811yescharacteristic
301C23#1306329411yescharacteristic
302Q8—3441no—
303Q8—1722no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4C2×(C2×D43)⋊C411yescharacteristic
329C2×C4C4×C22⋊D4311yescharacteristic
330C2×C4C4×C22⋊D4311yescharacteristic
331C2×C4#1306329911yescharacteristic
332C2×C4#1306329911yescharacteristic
333C2×C4#1306330811yescharacteristic
334C8—3441no—
335C8—1722no—
336C8—1722no—
337C22—21no—
338C22—21no—
339C22#1458277811yescharacteristic
340C22#1458307711yescharacteristic
341C22#1458308211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—42no—
350C4—42no—
351C4—81no—
352C4—81no—
353C4—81no—
354C4—3441no—
355C4—3441no—
356C2—21no—
357C2—21no—
358C2#1913496411yescharacteristic
359C2#1913509611yescharacteristic
360C2#1913513211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2336C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#2336D43
hypocenterC43#9380
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2336

Complements

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

NH ≅ G/Ntype
9. #14583309C4semidirect
10. #14583269C4semidirect
211. C43#9380semidirect

Maximal subgroups

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

subgroupindex
#191458012
#191355382
#191331972
#191331452
#191324592
#191324512
C43×#23362
#938043