Finite Group Databasebeta

← #24993500

Subgroups — #24993500

Order 11008.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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#19144726C211yesmaximal, characteristic
2#19136958C211yesmaximal, characteristic
3#19135539C211yesmaximal, characteristic
4#19133106C211yesmaximal, characteristic
5#19133043C211yesmaximal, characteristic
6#19132452C211yesmaximal, characteristic
7C43×#1300C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×C4×Dic86—21no—
10C2×C4×Dic86C2211yescharacteristic
11#14583230—21no—
12#14583185C412yescomplemented
13#14583110C412yescomplemented
14#14583057—21no—
15#14583007—22no—
16#14582956C2211yescharacteristic
17C4×C4⋊Dic43—21no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582750—22no—
20#14582750—21no—
21#14582744—21no—
22#14582660—22no—
23#14582635—21no—
24#14582635—21no—
25#14582631—22no—
26C43×#432C2211yescharacteristic
27C4×M16×C43C2211yescharacteristic
28C43×#376C2211yescharacteristic
29C22×Dic86D411yescharacteristic
30C2×Dic172—22no—
31#13063325C2×C411yescharacteristic
32#13063325C2×C411yescharacteristic
33#13063317—21no—
34#13063304—21no—
35#13063304—21no—
36C4×Dic86—28no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×Dic86—21no—
41C4×Dic86C2×C412yes—
42C4×Dic86D412yes—
43#13063284—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—22no—
47C2×Dic43⋊C4—21no—
48C2×C4×Dic43—22no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43—22no—
51C2×C4×Dic43D412yes—
52#13063257—22no—
53C4⋊(C43⋊C8)—21no—
54#13063250—22no—
55#13063250—22no—
56C22⋊(C43⋊C8)—21no—
57#13063236—21no—
58C43⋊#95—22no—
59C43⋊#95—21no—
60C2×M16×C43—21no—
61C2×C42×C43—21no—
62C2×C42×C43C2311yescharacteristic
63C4⋊C8×C43C2×C412yes—
64C22⋊C8×C43—21no—
65#97×C43—21no—
66#97×C43—21no—
67C4×C8×C43—21no—
68#95×C43—21no—
69#95×C43D411yescharacteristic
70#95×C43D411yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—22no—
79C2×Dic86—21no—
80C2×Dic86—24no—
81C2×Dic86—21no—
82C2×Dic86—21no—
83C2×Dic86C22⋊C412yes—
84M16×C43—22no—
85M16×C43—41no—
86C2×C8×C43—22no—
87C2×C8×C43—41no—
88C42×C43—24no—
89C42×C43C22×C411yescharacteristic
90C42×C43C2×D411yescharacteristic
91C42×C43#4111yescharacteristic
92C42×C43#4111yescharacteristic
93C22⋊Dic43—41no—
94C4⋊Dic43—24no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43C22⋊C412yes—
101Dic43⋊C4—28no—
102Dic43⋊C4—22no—
103Dic43⋊C4—22no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106C4×Dic43—28no—
107C4×Dic43—22no—
108C4×Dic43—22no—
109C4×Dic43—41no—
110C4×Dic43—42no—
111C4×Dic43—82no—
112C2×C43⋊C8—41no—
113Dic172—44no—
114C23×C43#12011yescharacteristic
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43C2×C22⋊C411yescharacteristic
126C2×C4×C43C4×D411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12311yescharacteristic
131C2×Dic43—24no—
132C2×Dic43—22no—
133C2×Dic43—24no—
134C2×Dic43—22no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141Dic86—24no—
142Dic86—22no—
143Dic86—42no—
144Dic86—81no—
145Dic86#10414yes—
146C8×C43—42no—
147C8×C43—42no—
148C43⋊C8—81no—
149#9324—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43#38611yescharacteristic
153C22×C43#45511yescharacteristic
154C22×C43#45611yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—42no—
161C4×C43—42no—
162C4×C43C2×#10412yes—
163Dic43—24no—
164Dic43—44no—
165Dic43—42no—
166Dic43—81no—
167Dic43—81no—
168#3113—431no—
169#2276—431no—
170#1986—431no—
171#1506—431no—
172#1491—431no—
173#1300D4311yescharacteristic
174#1285—431no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43#188211yescharacteristic
178C2×C43#189611yescharacteristic
179C2×C43#190511yescharacteristic
180#533—431no—
181C2×C4×Q8—431no—
182C2×C4×Q8—861no—
183#483—861no—
184#475—432no—
185#462—432no—
186#451—861no—
187#441—862no—
188#432—431no—
189#432C2×D4311yescharacteristic
190C4×M16C2×D4311yescharacteristic
191C4×C4⋊C4—431no—
192C4×C4⋊C4—862no—
193C4×C4⋊C4—861no—
194C4×C4⋊C4—861no—
195#376—861no—
196#376C2×D4311yescharacteristic
197#339—862no—
198#328—861no—
199#328—861no—
200Q8⋊C8—862no—
201C43#932411yescharacteristic, complemented, Sylow
202C22×Q8—431no—
203C2×Q16—862no—
204C2×M16—21no—
205C4⋊Q8—431no—
206C4⋊Q8—431no—
207#125—861no—
208C22⋊Q8—861no—
209C22⋊Q8—861no—
210C4×Q8—432no—
211C4×Q8—432no—
212C4×Q8—868no—
213C4×Q8—861no—
214C4×Q8—861no—
215C4×Q8—861no—
216C4×Q8—861no—
217#117—861no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—862no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4—861no—
222C2×C42—21no—
223C2×C42—432no—
224C2×C42—862no—
225C2×C42—861no—
226C2×C42—862no—
227C2×C42C22×D4311yescharacteristic
228#106—862no—
229C4⋊C8—861no—
230C4⋊C8C4×D4312yes—
231#103—862no—
232#103—862no—
233C22⋊C8—21no—
234C22⋊C8—861no—
235#97—21no—
236#97—21no—
237#97—861no—
238C4×C8—21no—
239#95—21no—
240#95—862no—
241#95—861no—
242#95D17211yescharacteristic
243#95D17211yescharacteristic
244C2×Q8—432no—
245C2×Q8—864no—
246C2×Q8—861no—
247C2×Q8—861no—
248C2×Q8—861no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—861no—
252C22×C4—862no—
253C22×C4—861no—
254C22×C4C2×D17211yescharacteristic
255C22×C4D4×D4311yescharacteristic
256C22×C4D4×D4311yescharacteristic
257Q16—1724no—
258M16—22no—
259M16—41no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—1721no—
263C4⋊C4—432no—
264C4⋊C4—868no—
265C4⋊C4—864no—
266C4⋊C4—862no—
267C4⋊C4—862no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C22⋊C4—1721no—
276C42—24no—
277C42—868no—
278C42—862no—
279C42—862no—
280C42—3442no—
281C42—1722no—
282C42—1721no—
283C42C2×C4×D4311yescharacteristic
284C42#1062189811yescharacteristic
285C42D4×D4311yescharacteristic
286C42#1062190211yescharacteristic
287C23#1306329511yescharacteristic
288Q8—434no—
289Q8—864no—
290Q8—862no—
291Q8—3441no—
292Q8—1722no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—864no—
304C2×C4—862no—
305C2×C4—864no—
306C2×C4—862no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1722no—
310C2×C4—1721no—
311C2×C4—1722no—
312C2×C4—1721no—
313C2×C4C22⋊C4×D4311yescharacteristic
314C2×C4#1306328711yescharacteristic
315C2×C4C4×D17211yescharacteristic
316C2×C4#1306329811yescharacteristic
317C2×C4#1306330011yescharacteristic
318C2×C4#1306331011yescharacteristic
319C8—42no—
320C8—42no—
321C8—3441no—
322C22—21no—
323C22—21no—
324C22#1458277711yescharacteristic
325C22#1458307811yescharacteristic
326C22#1458308311yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—42no—
333C4—42no—
334C4—864no—
335C4—3441no—
336C4—3441no—
337C4—1724no—
338C4—1722no—
339C4#104×D4312yes—
340C2—21no—
341C2—21no—
342C2#1913496511yescharacteristic
343C2#1913503711yescharacteristic
344C2#1913508811yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1300C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1300D43
hypocenterC43#9324
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
12. #14583185C4semidirect
13. #14583110C4semidirect
201. C43#9324semidirect

Maximal subgroups

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

subgroupindex
#191447262
#191369582
#191355392
#191331062
#191330432
#191324522
C43×#13002
#932443