Finite Group Databasebeta

← #24993499

Subgroups — #24993499

Order 11008.

536 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 111 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#19144725C211yesmaximal, characteristic
2#19135538C211yesmaximal, characteristic
3#19133106C211yesmaximal, characteristic
4#19133042C211yesmaximal, characteristic
5#19132488C211yesmaximal, characteristic
6#19132451C211yesmaximal, characteristic
7C43×#2276C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583229—21no—
10#14583184C412yescomplemented
11#14583109C412yescomplemented
12#14583055—21no—
13#14583004—22no—
14#14582956C2211yescharacteristic
15#14582956C2211yescharacteristic
16C4×#10621877C2211yescharacteristic
17#14582659—22no—
18#14582635—21no—
19#14582635—21no—
20Q8⋊(C43⋊C8)—22no—
21C2×C4×Q8×C43—21no—
22C2×C4×Q8×C43C2211yescharacteristic
23C4×C4⋊C4×C43—21no—
24C4×C4⋊C4×C43—22no—
25C4×C4⋊C4×C43—21no—
26C4×C4⋊C4×C43C2211yescharacteristic
27C43×#376—21no—
28C43×#376C2211yescharacteristic
29C2×#10621885—22no—
30C2×#10621877—21no—
31#13063325C2×C411yescharacteristic
32#13063325C2×C411yescharacteristic
33#13063317—21no—
34#13063304—21no—
35#13063304—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38#13063284—21no—
39#13063256—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)C2×C412yes—
42#13063249—22no—
43#13063248—22no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46#13063236—21no—
47#13063236—21no—
48#13063236—21no—
49C4×C43⋊C8—21no—
50C22×Q8×C43D411yescharacteristic
51C4×Q8×C43—28no—
52C4×Q8×C43—21no—
53C4×Q8×C43—21no—
54C4×Q8×C43C2×C412yes—
55C4×Q8×C43D412yes—
56C2×C4⋊C4×C43—22no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43D411yescharacteristic
60C2×C42×C43—22no—
61C2×C42×C43—21no—
62C2×C42×C43—21no—
63C2×C42×C43—22no—
64C2×C42×C43D412yes—
65C2×C42×C43C2311yescharacteristic
66#95×C43—22no—
67#95×C43—21no—
68#95×C43—21no—
69#95×C43D411yescharacteristic
70#95×C43D411yescharacteristic
71C2×Q8×C43—24no—
72C2×Q8×C43—21no—
73C2×Q8×C43C22⋊C412yes—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—22no—
78C22×C4×C43—21no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C2×Dic86—21no—
83C2×Dic86—21no—
84C4⋊C4×C43—28no—
85C4⋊C4×C43—24no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43C22⋊C412yes—
90C42×C43—28no—
91C42×C43—24no—
92C42×C43—22no—
93C42×C43—22no—
94C42×C43—42no—
95C42×C43—82no—
96C42×C43C22×C411yescharacteristic
97C42×C43C2×D411yescharacteristic
98C42×C43#4111yescharacteristic
99C42×C43#4111yescharacteristic
100C22⋊Dic43—41no—
101#10621885—44no—
102C4⋊Dic43—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106Dic43⋊C4—41no—
107Dic43⋊C4—41no—
108C4×Dic43—41no—
109#10621877—22no—
110#10621877—41no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C23×C43#12011yescharacteristic
115Q8×C43—24no—
116Q8×C43—22no—
117Q8×C43#10414yes—
118C2×C4×C43—24no—
119C2×C4×C43—22no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—24no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12311yescharacteristic
142C2×Dic43—41no—
143C2×Dic43—41no—
144Dic86—42no—
145Dic86—81no—
146C43⋊C8—42no—
147C43⋊C8—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—24no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—44no—
162C4×C43—42no—
163C4×C43—42no—
164C4×C43—42no—
165C4×C43C2×#10412yes—
166Dic43—81no—
167Dic43—81no—
168#3113—431no—
169#2276D4311yescharacteristic
170#1986—431no—
171#1506—431no—
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#533—431no—
181C2×C4×Q8—21no—
182C2×C4×Q8C2×D4311yescharacteristic
183#483—861no—
184#475—432no—
185#462—432no—
186#451—861no—
187#441—862no—
188#432—431no—
189#432—431no—
190C4×M16—431no—
191C4×C4⋊C4—21no—
192C4×C4⋊C4—22no—
193C4×C4⋊C4—21no—
194C4×C4⋊C4C2×D4311yescharacteristic
195#376—21no—
196#376C2×D4311yescharacteristic
197#339—862no—
198#328—861no—
199#328—861no—
200Q8⋊C8—862no—
201C43#932411yescharacteristic, complemented, Sylow
202C22×Q8C22⋊D4311yescharacteristic
203C2×Q16—862no—
204C2×M16—861no—
205C4⋊Q8—431no—
206C4⋊Q8—431no—
207#125—861no—
208C22⋊Q8—861no—
209C22⋊Q8—861no—
210C4×Q8—28no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—861no—
214C4×Q8—861no—
215C4×Q8C4×D4312yes—
216C4×Q8D17212yes—
217#117—861no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C22⋊D4311yescharacteristic
222C2×C42—22no—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42—22no—
226C2×C42C22⋊D4312yes—
227C2×C42C22×D4311yescharacteristic
228#106—862no—
229C4⋊C8—432no—
230C4⋊C8—861no—
231#103—862no—
232#103—862no—
233C22⋊C8—861no—
234C22⋊C8—861no—
235#97—861no—
236#97—861no—
237#97—861no—
238C4×C8—861no—
239#95—22no—
240#95—21no—
241#95—21no—
242#95C22⋊D4311yescharacteristic
243#95C22⋊D4311yescharacteristic
244C2×Q8—24no—
245C2×Q8—21no—
246C2×Q8—861no—
247C2×Q8—861no—
248C2×Q8(C2×D43)⋊C412yes—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4C2×C22⋊D4311yescharacteristic
255C22×C4C2×C22⋊D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257Q16—1724no—
258M16—862no—
259M16—1721no—
260C2×C8—862no—
261C2×C8—1721no—
262C2×C8—1721no—
263C4⋊C4—28no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C4⋊C4(C2×D43)⋊C412yes—
275C22⋊C4—1721no—
276C42—28no—
277C42—24no—
278C42—22no—
279C42—22no—
280C42—42no—
281C42—82no—
282C42—1721no—
283C42C2×C4×D4311yescharacteristic
284C42C2×D17211yescharacteristic
285C42#1062189811yescharacteristic
286C42#1062189811yescharacteristic
287C23#1306329411yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—3441no—
291Q8—1722no—
292Q8#1306325314yes—
293C2×C4—24no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4C2×(C2×D43)⋊C411yescharacteristic
314C2×C4C4×C22⋊D4311yescharacteristic
315C2×C4C4×C22⋊D4311yescharacteristic
316C2×C4#1306329911yescharacteristic
317C2×C4#1306329911yescharacteristic
318C2×C4#1306330811yescharacteristic
319C8—3441no—
320C8—1722no—
321C8—1722no—
322C22—21no—
323C22—21no—
324C22#1458277811yescharacteristic
325C22#1458307711yescharacteristic
326C22#1458308211yescharacteristic
327C4—24no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—44no—
334C4—42no—
335C4—42no—
336C4—42no—
337C4—3441no—
338C4—3441no—
339C4C2×#1306325312yes—
340C2—21no—
341C2—21no—
342C2#1913496411yescharacteristic
343C2#1913503811yescharacteristic
344C2#1913508911yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2276C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#2276D43
hypocenterC43#9324
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2276

Complements

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

NH ≅ G/Ntype
10. #14583184C4semidirect
11. #14583109C4semidirect
201. C43#9324semidirect

Maximal subgroups

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

subgroupindex
#191447252
#191355382
#191331062
#191330422
#191324882
#191324512
C43×#22762
#932443