Finite Group Databasebeta

← #24992856

Subgroups — #24992856

Order 11008.

566 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 115 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#19144635C211yesmaximal, characteristic
2C4×#13063290C211yesmaximal, characteristic
3#19135571C211yesmaximal, characteristic
4#19133093C211yesmaximal, characteristic
5#19133023C211yesmaximal, characteristic
6#19132427C211yesmaximal, characteristic
7C43×#1303C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10C2×#13063290—21no—
11#14583235—21no—
12#14583195C412yescomplemented
13#14583110C412yescomplemented
14#14583057—21no—
15C4×Dic172—22no—
16#14582952C2211yescharacteristic
17C4⋊C4×Dic43—21no—
18C4×Dic43⋊C4—21no—
19#14582750—22no—
20C42×Dic43—21no—
21C42×Dic43C2211yescharacteristic
22#14582660—21no—
23#14582660—21no—
24#14582635—22no—
25#14582629—22no—
26C43×#431C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C22×Dic86D411yescharacteristic
30C2×Dic172—22no—
31#13063325C2×C411yescharacteristic
32#13063325C2×C411yescharacteristic
33#13063317—21no—
34#13063304—21no—
35#13063304—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×Dic86C2×C412yes—
41C4×Dic86D412yes—
42#13063290—28no—
43#13063284—21no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×Dic43⋊C4—22no—
46C2×Dic43⋊C4—21no—
47C2×C4×Dic43—22no—
48C2×C4×Dic43—21no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43—22no—
51C2×C4×Dic43—21no—
52C2×C4×Dic43D411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54#13063259—22no—
55C4⋊(C43⋊C8)—21no—
56#13063250—22no—
57#13063250—22no—
58C22⋊(C43⋊C8)—21no—
59C4×C43⋊C8—21no—
60C43⋊#95—22no—
61C2×M16×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C42×C43—21no—
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43C2×C412yes—
68C22⋊C8×C43—21no—
69C4×C8×C43—21no—
70#95×C43D412yes—
71C22×C4×C43—22no—
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×Dic86—21no—
80C2×Dic86—24no—
81C2×Dic86—21no—
82C2×Dic86—21no—
83C2×Dic86C22⋊C412yes—
84M16×C43—41no—
85M16×C43—41no—
86C2×C8×C43—22no—
87C2×C8×C43—41no—
88C4⋊C4×C43—24no—
89C42×C43—41no—
90C42×C43—41no—
91C42×C43C22×C411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43#4111yescharacteristic
94C42×C43#4111yescharacteristic
95C22⋊Dic43—41no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43C22⋊C412yes—
102Dic43⋊C4—28no—
103Dic43⋊C4—22no—
104Dic43⋊C4—22no—
105Dic43⋊C4—41no—
106Dic43⋊C4—41no—
107C4×Dic43—28no—
108C4×Dic43—24no—
109C4×Dic43—22no—
110C4×Dic43—22no—
111C4×Dic43—21no—
112C4×Dic43—21no—
113C4×Dic43—21no—
114C4×Dic43—42no—
115C4×Dic43—44no—
116C4×Dic43—41no—
117C4×Dic43Q1612yescomplemented
118C2×C43⋊C8—41no—
119Dic172—44no—
120C23×C43#12011yescharacteristic
121C2×C4×C43—22no—
122C2×C4×C43—24no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12311yescharacteristic
132C2×C4×C43C2×Q1611yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C2×Dic43—22no—
137C2×Dic43—24no—
138C2×Dic43—22no—
139C2×Dic43—22no—
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—22no—
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148Dic86—24no—
149Dic86—22no—
150Dic86—42no—
151Dic86—81no—
152Dic86#10414yes—
153C8×C43—42no—
154C8×C43—81no—
155C43⋊C8—81no—
156#9232—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43#38611yescharacteristic
160C22×C43#45111yescharacteristic
161C22×C43#45211yescharacteristic
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—44no—
166C4×C43C2×#10412yes—
167C4×C43C4×Q1611yescharacteristic
168C4×C43#44111yescharacteristic
169C4×C43#46211yescharacteristic
170C4×C43#46411yescharacteristic
171Dic43—24no—
172Dic43—24no—
173Dic43—42no—
174Dic43—42no—
175Dic43—81no—
176Dic43—81no—
177#3104—431no—
178C42×Q8—431no—
179#1994—431no—
180#1503—431no—
181#1487—431no—
182#1303D4311yescharacteristic
183#1276—431no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43#187811yescharacteristic
187C2×C43#189611yescharacteristic
188C2×C43#190611yescharacteristic
189#533—431no—
190C2×C4×Q8—431no—
191C2×C4×Q8—861no—
192#484—861no—
193#477—432no—
194#462—432no—
195#451—861no—
196C4×Q16—862no—
197#431—431no—
198#431C2×D4311yescharacteristic
199#423C2×D4311yescharacteristic
200C4×C4⋊C4—861no—
201C4×C4⋊C4—861no—
202C4×C4⋊C4—862no—
203C4×C4⋊C4C2×D4311yescharacteristic
204C43—431no—
205C43—861no—
206#339—861no—
207#339—861no—
208#328—862no—
209Q8⋊C8—862no—
210C43#923211yescharacteristic, complemented, Sylow
211C22×Q8—431no—
212C2×Q16—862no—
213C2×M16—21no—
214C4⋊Q8—431no—
215C4⋊Q8—431no—
216#125—861no—
217C22⋊Q8—861no—
218C22⋊Q8—861no—
219C4×Q8—432no—
220C4×Q8—432no—
221C4×Q8—868no—
222C4×Q8—861no—
223C4×Q8—861no—
224C4×Q8—861no—
225C4×Q8—861no—
226#117—861no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—862no—
230C2×C4⋊C4—861no—
231C2×C42—21no—
232C2×C42—431no—
233C2×C42—431no—
234C2×C42—862no—
235C2×C42—861no—
236C2×C42—861no—
237C2×C42—862no—
238C2×C42—861no—
239C2×C42C22×D4311yescharacteristic
240#107—862no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—861no—
244C4⋊C8C4×D4312yes—
245#103—862no—
246#103—862no—
247C22⋊C8—21no—
248C22⋊C8—861no—
249C4×C8—21no—
250C4×C8—861no—
251#95—862no—
252#95D17212yes—
253C2×Q8—432no—
254C2×Q8—864no—
255C2×Q8—861no—
256C2×Q8—861no—
257C2×Q8—861no—
258C22×C4—22no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4C2×D17211yescharacteristic
264C22×C4D4×D4311yescharacteristic
265C22×C4D4×D4311yescharacteristic
266Q16—1724no—
267M16—41no—
268M16—41no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—1721no—
272C4⋊C4—24no—
273C4⋊C4—432no—
274C4⋊C4—868no—
275C4⋊C4—862no—
276C4⋊C4—862no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—1721no—
283C4⋊C4—1721no—
284C22⋊C4—1721no—
285C42—41no—
286C42—41no—
287C42—432no—
288C42—864no—
289C42—868no—
290C42—862no—
291C42—862no—
292C42—861no—
293C42—861no—
294C42—861no—
295C42—1722no—
296C42—1724no—
297C42—1721no—
298C42C2×C4×D4311yescharacteristic
299C42#1062189811yescharacteristic
300C42D4×D4311yescharacteristic
301C42#1062190211yescharacteristic
302C23#1306329511yescharacteristic
303Q8—434no—
304Q8—864no—
305Q8—862no—
306Q8—3441no—
307Q8—1722no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—862no—
314C2×C4—864no—
315C2×C4—862no—
316C2×C4—862no—
317C2×C4—862no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1722no—
324C2×C4—1721no—
325C2×C4C22⋊C4×D4311yescharacteristic
326C2×C4#1306328711yescharacteristic
327C2×C4C4×D17211yescharacteristic
328C2×C4#1306329811yescharacteristic
329C2×C4#1306330011yescharacteristic
330C2×C4#1306331011yescharacteristic
331C2×C4Q16×D4311yescharacteristic
332C2×C4#1306334411yescharacteristic
333C2×C4#1306335411yescharacteristic
334C2×C4#1306335411yescharacteristic
335C8—42no—
336C8—81no—
337C8—3441no—
338C22—21no—
339C22—21no—
340C22#1458277711yescharacteristic
341C22#1458305611yescharacteristic
342C22#1458306211yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—864no—
348C4—864no—
349C4—3441no—
350C4—3441no—
351C4—1722no—
352C4—1722no—
353C4#104×D4312yes—
354C4#1458299311yescharacteristic
355C4#1458300511yescharacteristic
356C4#1458310811yescharacteristic
357C4#1458312011yescharacteristic
358C2—21no—
359C2—21no—
360C2#1913493711yescharacteristic
361C2#1913503711yescharacteristic
362C2#1913509711yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#9232
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
12. #14583195C4semidirect
13. #14583110C4semidirect
117. C4×Dic43Q16semidirect
210. C43#9232semidirect

Maximal subgroups

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

subgroupindex
#191446352
C4×#130632902
#191355712
#191330932
#191330232
#191324272
C43×#13032
#923243