Finite Group Databasebeta

← #24993496

Subgroups — #24993496

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#19144721C211yesmaximal, characteristic
2#19136958C211yesmaximal, characteristic
3#19135540C211yesmaximal, characteristic
4#19133041C211yesmaximal, characteristic
5#19132488C211yesmaximal, characteristic
6#19132450C211yesmaximal, characteristic
7C43×#1506C211yesmaximal, characteristic
8C2×C4×Dic86—21no—
9C2×C4×Dic86C2211yescharacteristic
10#14583227—21no—
11#14583181C412yescomplemented
12#14583106C412yescomplemented
13#14583054—21no—
14#14583004—22no—
15#14582956C2211yescharacteristic
16C4×#10621877C2211yescharacteristic
17C4×C4⋊Dic43—21no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582750—22no—
20#14582750—21no—
21#14582744—21no—
22#14582658—22no—
23#14582629—22no—
24C43×#533C2211yescharacteristic
25C43×#432C2211yescharacteristic
26C43×#376C2211yescharacteristic
27C43×#328—21no—
28C43×#328—21no—
29C22×Dic86D411yescharacteristic
30C2×#10621885—22no—
31C2×#10621877—21no—
32C4×Dic86—28no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C4×Dic86C2×C412yes—
36C4×Dic86D412yes—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43D411yescharacteristic
39C2×Dic43⋊C4—22no—
40C2×Dic43⋊C4—21no—
41C2×C4×Dic43—22no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—22no—
44C2×C4×Dic43D412yes—
45#13063256—22no—
46C4⋊(C43⋊C8)C2×C412yes—
47#13063249—22no—
48#13063248—22no—
49C22⋊(C43⋊C8)—21no—
50#13063236—21no—
51#13063236—21no—
52C4×C43⋊C8—21no—
53C43⋊#95—22no—
54C43⋊#95—21no—
55C4⋊Q8×C43C2×C411yescharacteristic
56C4⋊Q8×C43C2×C411yescharacteristic
57#125×C43—21no—
58C22⋊Q8×C43—21no—
59C22⋊Q8×C43—21no—
60C4×Q8×C43—21no—
61C4×Q8×C43—21no—
62#117×C43—21no—
63C2×C42×C43—21no—
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67#97×C43—21no—
68#95×C43—21no—
69#95×C43D411yescharacteristic
70#95×C43D411yescharacteristic
71C2×Q8×C43—21no—
72C2×Q8×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—22no—
81C2×Dic86—21no—
82C2×Dic86—24no—
83C2×Dic86C22⋊C412yes—
84C2×C8×C43—41no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C42×C43—24no—
93C42×C43—41no—
94C42×C43C22×C411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43#4111yescharacteristic
97C42×C43#4111yescharacteristic
98#10621885—44no—
99C4⋊Dic43—24no—
100C4⋊Dic43—21no—
101C4⋊Dic43C22⋊C412yes—
102Dic43⋊C4—28no—
103Dic43⋊C4—22no—
104Dic43⋊C4—22no—
105C4×Dic43—28no—
106C4×Dic43—22no—
107C4×Dic43—22no—
108C4×Dic43—42no—
109C4×Dic43—82no—
110#10621877—22no—
111#10621877—41no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—41no—
114C23×C43#12011yescharacteristic
115Q8×C43—42no—
116Q8×C43—81no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12311yescharacteristic
135C2×Dic43—24no—
136C2×Dic43—22no—
137C2×Dic43—24no—
138C2×Dic43—22no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143Dic86—24no—
144Dic86—22no—
145Dic86#10414yes—
146C8×C43—81no—
147C43⋊C8—42no—
148C43⋊C8—42no—
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×C43—81no—
163C4×C43—81no—
164C4×C43C2×#10412yes—
165Dic43—24no—
166Dic43—44no—
167Dic43—42no—
168#3113—431no—
169#2276—431no—
170#1986—431no—
171#1506D4311yescharacteristic
172#1491—431no—
173#1300—431no—
174#1285—431no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43#188211yescharacteristic
178C2×C43#189611yescharacteristic
179C2×C43#190511yescharacteristic
180#533C2×D4311yescharacteristic
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×M16—431no—
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—21no—
199#328—21no—
200Q8⋊C8—862no—
201C43#932411yescharacteristic, complemented, Sylow
202C22×Q8—431no—
203C2×Q16—862no—
204C2×M16—861no—
205C4⋊Q8C4×D4311yescharacteristic
206C4⋊Q8C4×D4311yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—432no—
213C4×Q8—432no—
214C4×Q8—868no—
215C4×Q8—861no—
216C4×Q8—861no—
217#117—21no—
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—21no—
230C4⋊C8—432no—
231#103—862no—
232#103—862no—
233C22⋊C8—21no—
234C22⋊C8—861no—
235#97—21no—
236#97—861no—
237#97—861no—
238C4×C8—861no—
239#95—21no—
240#95—862no—
241#95—861no—
242#95C22⋊D4311yescharacteristic
243#95C22⋊D4311yescharacteristic
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—432no—
247C2×Q8—864no—
248C2×Q8—861no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—861no—
252C22×C4—862no—
253C22×C4—861no—
254C22×C4D4×D4311yescharacteristic
255C22×C4D4×D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257Q16—1724no—
258M16—862no—
259M16—1721no—
260C2×C8—41no—
261C2×C8—862no—
262C2×C8—1721no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—432no—
270C4⋊C4—868no—
271C4⋊C4—864no—
272C4⋊C4—862no—
273C4⋊C4—862no—
274C4⋊C4—861no—
275C22⋊C4—41no—
276C42—24no—
277C42—41no—
278C42—868no—
279C42—862no—
280C42—862no—
281C42—3442no—
282C42—1722no—
283C42C2×C4×D4311yescharacteristic
284C42#1062189811yescharacteristic
285C42D4×D4311yescharacteristic
286C42#1062190011yescharacteristic
287C23#1306329311yescharacteristic
288Q8—42no—
289Q8—81no—
290Q8—434no—
291Q8—864no—
292Q8—862no—
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—41no—
304C2×C4—41no—
305C2×C4—864no—
306C2×C4—862no—
307C2×C4—864no—
308C2×C4—862no—
309C2×C4—1722no—
310C2×C4—1721no—
311C2×C4—1722no—
312C2×C4—1721no—
313C2×C4C22⋊C4×D4311yescharacteristic
314C2×C4(C22⋊D43)⋊C411yescharacteristic
315C2×C4C4×C22⋊D4311yescharacteristic
316C2×C4#1306329611yescharacteristic
317C2×C4#1306329811yescharacteristic
318C2×C4#1306330711yescharacteristic
319C8—81no—
320C8—1722no—
321C8—1722no—
322C22—21no—
323C22—21no—
324C22#1458277511yescharacteristic
325C22#1458307511yescharacteristic
326C22#1458308011yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—42no—
333C4—42no—
334C4—81no—
335C4—81no—
336C4—864no—
337C4—1724no—
338C4—1722no—
339C4#104×D4312yes—
340C2—21no—
341C2—21no—
342C2#1913496111yescharacteristic
343C2#1913503511yescharacteristic
344C2#1913509211yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1506C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1506D43
hypocenterC43#9324
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
11. #14583181C4semidirect
12. #14583106C4semidirect
201. C43#9324semidirect

Maximal subgroups

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

subgroupindex
#191447212
#191369582
#191355402
#191330412
#191324882
#191324502
C43×#15062
#932443