Finite Group Databasebeta

← #24993132

Subgroups — #24993132

Order 11008.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145739C211yesmaximal, characteristic
2#19143538C211yesmaximal, characteristic
3#19135440C211yesmaximal, characteristic
4#19133283C211yesmaximal, characteristic
5#19132492C211yesmaximal, characteristic
6#19132445C211yesmaximal, characteristic
7C2×C43×#332C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583295—21no—
10#14583251—21no—
11#14583229C414yes—
12#14583181—22no—
13#14583028—22no—
14#14583026—21no—
15#14583023—21no—
16#14582952C2211yescharacteristic
17#14582925—21no—
18#14582923C2211yescharacteristic
19C2×#13063244—21no—
20C2×#13063244—21no—
21#14582854—21no—
22C4×#10621877C2211yescharacteristic
23#14582647—21no—
24#14582646—21no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C43×#332—21no—
29C43×#332—21no—
30C2×#10621877—21no—
31C2×#10621877D411yescharacteristic
32C2×#10621877D411yescharacteristic
33#13063325D411yescharacteristic
34#13063325D411yescharacteristic
35#13063317—21no—
36#13063304—21no—
37#13063304C2×C412yes—
38C4×Dic86—21no—
39C4×Dic86D412yes—
40#13063284—21no—
41#13063256—24no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45Dic43⋊C8—22no—
46Dic43⋊C8—22no—
47#13063248—24no—
48#13063244—42no—
49#13063244—42no—
50C22⋊(C43⋊C8)C2×C412yes—
51#13063236—21no—
52#13063235—22no—
53C4×C43⋊C8—21no—
54C4×C43⋊C8—21no—
55C8×Dic43—22no—
56C22×Q8×C43—21no—
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43C2×C412yes—
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C4⋊C8×C43D411yescharacteristic
70C4⋊C8×C43D411yescharacteristic
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43—41no—
74C2×Q8×C43—41no—
75C2×Q8×C43—41no—
76C2×Q8×C43—41no—
77C22×C4×C43—22no—
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C2×Dic86—21no—
82C2×Dic86C22⋊C412yes—
83C2×C8×C43—21no—
84C2×C8×C43—21no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C2×C8×C43—81no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C42×C43C2×D411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43#4111yescharacteristic
97C22⋊Dic43—22no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43C22⋊C412yes—
102Dic43⋊C4—22no—
103Dic43⋊C4—22no—
104C4×Dic43—22no—
105#10621877—21no—
106#10621877—21no—
107#10621877—21no—
108#10621877—41no—
109#10621877—41no—
110#10621877SD1612yes—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—21no—
114C2×C43⋊C8—41no—
115C23×C43C4×D411yescharacteristic
116Q8×C43—81no—
117Q8×C43—81no—
118Q8×C43—81no—
119Q8×C43—81no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—41no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43#12011yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12311yescharacteristic
132C2×C4×C43C2×SD1611yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C2×Dic43—22no—
137C2×Dic43—22no—
138Dic86—41no—
139Dic86—41no—
140Dic86—42no—
141C8×C43—41no—
142C8×C43—41no—
143C8×C43—81no—
144C43⋊C8—22no—
145C43⋊C8—42no—
146C43⋊C8—41no—
147C43⋊C8—81no—
148#9272—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43#38611yescharacteristic
152C22×C43C4×SD1611yescharacteristic
153C22×C43#44011yescharacteristic
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—82no—
158C4×C43#44811yescharacteristic
159C4×C43#44911yescharacteristic
160C4×C43#46011yescharacteristic
161C4×C43#46411yescharacteristic
162C4×C43#47111yescharacteristic
163C4×C43#47311yescharacteristic
164Dic43—42no—
165Dic43—42no—
166#3229—431no—
167#2962—431no—
168#1966—431no—
169#1550—431no—
170C2×#332D4311yescharacteristic
171#1301—431no—
172#1283—431no—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43#188011yescharacteristic
176C2×C43#190811yescharacteristic
177C2×C43#191511yescharacteristic
178#533—431no—
179C2×C4⋊Q8C2×D4311yescharacteristic
180#498—861no—
181#487—861no—
182#483—434no—
183#475—862no—
184#446—862no—
185#446—861no—
186C8×Q8—861no—
187#431—431no—
188#424—861no—
189#423—431no—
190C2×C4⋊C8C2×D4311yescharacteristic
191C2×C4⋊C8C2×D4311yescharacteristic
192C2×#101—861no—
193C2×#101—861no—
194#405—861no—
195C4×M16—431no—
196#333—861no—
197#332—21no—
198#332—21no—
199#332—861no—
200C43#927211yescharacteristic, complemented, Sylow
201C22×Q8—21no—
202C2×M16—431no—
203C2×M16—431no—
204C2×M16—861no—
205C22×C8—21no—
206C22×C8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—431no—
212C4⋊Q8—431no—
213#125—861no—
214C22⋊Q8—432no—
215C22⋊Q8—861no—
216C4×Q8—432no—
217C4×Q8—861no—
218#117—861no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C4×D4312yes—
221C2×C42C22×D4311yescharacteristic
222#106—864no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—862no—
227C4⋊C8—862no—
228C4⋊C8—861no—
229C4⋊C8—861no—
230C4⋊C8—861no—
231C4⋊C8C22⋊D4311yescharacteristic
232C4⋊C8C22⋊D4311yescharacteristic
233#103—864no—
234#101—1722no—
235#101—1722no—
236C22⋊C8—432no—
237#97—862no—
238#97—861no—
239C4×C8—862no—
240C4×C8—861no—
241C4×C8—861no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—432no—
249C2×Q8—861no—
250C22×C4—22no—
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253C22×C4#1062190011yescharacteristic
254M16—432no—
255M16—861no—
256M16—861no—
257M16—861no—
258M16—1721no—
259M16—1721no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—81no—
266C2×C8—861no—
267C2×C8—862no—
268C2×C8—861no—
269C2×C8—1721no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—432no—
275C4⋊C4—862no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—862no—
280C22⋊C4—862no—
281C42—862no—
282C42#1062189811yescharacteristic
283C42D4×D4311yescharacteristic
284C42D4×D4311yescharacteristic
285C42C2×C22⋊D4311yescharacteristic
286C23(C22⋊D43)⋊C411yescharacteristic
287Q8—81no—
288Q8—81no—
289Q8—81no—
290Q8—81no—
291Q8—1722no—
292Q8—1721no—
293Q8—1721no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—862no—
301C2×C4—862no—
302C2×C4C22⋊C4×D4311yescharacteristic
303C2×C4C4×C22⋊D4311yescharacteristic
304C2×C4#1306329311yescharacteristic
305C2×C4#1306329611yescharacteristic
306C2×C4#1306329811yescharacteristic
307C2×C4#1306330711yescharacteristic
308C2×C4SD16×D4311yescharacteristic
309C2×C4#1306334411yescharacteristic
310C2×C4#1306334911yescharacteristic
311C2×C4#1306335411yescharacteristic
312C8—41no—
313C8—41no—
314C8—81no—
315C8—862no—
316C8—3441no—
317C8—1722no—
318C8—1721no—
319C22—21no—
320C22—21no—
321C22#1458277511yescharacteristic
322C22#1458299011yescharacteristic
323C22#1458299611yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—1722no—
329C4—1722no—
330C4#1458303611yescharacteristic
331C4#1458304111yescharacteristic
332C4#1458309811yescharacteristic
333C4#1458312011yescharacteristic
334C4#1458315911yescharacteristic
335C4#1458317111yescharacteristic
336C2—21no—
337C2—21no—
338C2#1913494711yescharacteristic
339C2#1913511311yescharacteristic
340C2#1913514411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socleC22×C43#386
prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenterC2×#332D43
hypocenterC43#9272
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
200. C43#9272semidirect

Maximal subgroups

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

subgroupindex
#191457392
#191435382
#191354402
#191332832
#191324922
#191324452
C2×C43×#3322
#927243