Finite Group Databasebeta

← #25012428

Subgroups — #25012428

Order 11008.

768 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#14583649C211yesmaximal, characteristic
2C2×#14582694C211yesmaximal, characteristic
3C2×#14582690C212yesmaximal
4#19135008C212yesmaximal
5C43×#1885C211yesmaximal, characteristic
6#14583649—24no—
7#14583649—22no—
8#14583649C414yescomplemented
9C2×#13063323—21no—
10C2×#13063318—22no—
11C2×#13063317—21no—
12C2×#13063306C2212yes—
13C2×#13063302—22no—
14C2×#13063240C2212yes—
15#14582760—22no—
16#14582694—22no—
17#14582690—24no—
18#14582666—22no—
19C2×#124×C43C2211yescharacteristic
20C43×#518C2211yescharacteristic
21C43×#419—21no—
22C2×#100×C43C2211yescharacteristic
23C43×#339—21no—
24C22×Dic86—21no—
25C23×Dic43D412yes—
26#13063323—24no—
27#13063323—24no—
28#13063318—28no—
29#13063318—28no—
30#13063317—24no—
31#13063317—24no—
32#13063306—22no—
33#13063306—22no—
34#13063306C2×C414yes—
35#13063306D414yes—
36#13063302—28no—
37#13063302—28no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×Dic43⋊C4—22no—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—22no—
43C2×C22⋊Dic43—22no—
44C2×C22⋊Dic43—22no—
45C2×C22⋊Dic43D412yes—
46C2×C4×Dic43—21no—
47#13063240—22no—
48#13063240—22no—
49C43⋊#95—44no—
50C22×Q8×C43D411yescharacteristic
51C22×D4×C43C2311yescharacteristic
52C2×M16×C43—21no—
53#124×C43—22no—
54#124×C43C2×C412yes—
55#124×C43D412yes—
56C4×D4×C43—42no—
57#117×C43—21no—
58C2×C22⋊C4×C43—22no—
59C2×C22⋊C4×C43—22no—
60C2×C42×C43D411yescharacteristic
61#103×C43—42no—
62#100×C43—22no—
63C24×C43C2×D412yes—
64C2×Q8×C43—21no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43C22⋊C412yes—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43C22×C411yescharacteristic
71C2×D4×C43C2×D412yes—
72C2×D4×C43C2×D411yescharacteristic
73C22×C4×C43—24no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43C2×D411yescharacteristic
77C22×Dic43—22no—
78C22×Dic43—22no—
79C22×Dic43—22no—
80C22×Dic43—42no—
81C22×Dic43—42no—
82C22×Dic43—42no—
83C22×Dic43C22⋊C414yes—
84C2×Dic86—24no—
85C2×Dic86—81no—
86C2×Dic86—81no—
87M16×C43—41no—
88M16×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—22no—
91C22⋊C4×C43—24no—
92C22⋊C4×C43—24no—
93C22⋊C4×C43—42no—
94C22⋊C4×C43—41no—
95C42×C43—21no—
96C42×C43—41no—
97C42×C43C22⋊C412yes—
98C22⋊Dic43—24no—
99C22⋊Dic43—24no—
100C22⋊Dic43—22no—
101C22⋊Dic43—42no—
102C22⋊Dic43—42no—
103C22⋊Dic43C22⋊C414yes—
104C4⋊Dic43—24no—
105C4⋊Dic43—24no—
106Dic43⋊C4—28no—
107Dic43⋊C4—28no—
108Dic43⋊C4—24no—
109Dic43⋊C4—24no—
110C4×Dic43—24no—
111C23×C43—22no—
112C23×C43—22no—
113C23×C43—44no—
114C23×C43C2×C22⋊C412yes—
115C23×C43#12011yescharacteristic
116C23×C43#12012yes—
117Q8×C43—42no—
118Q8×C43—81no—
119D4×C43—41no—
120D4×C43—41no—
121D4×C43—42no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—42no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—84no—
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43#12011yescharacteristic
133C2×Dic43—24no—
134C2×Dic43—24no—
135C2×Dic43—44no—
136C2×Dic43—42no—
137C2×Dic43—42no—
138C2×Dic43—44no—
139C2×Dic43—82no—
140C2×Dic43—82no—
141C2×Dic43—84no—
142Dic86—84no—
143C8×C43—81no—
144#12764—431nomaximal, Sylow
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—22no—
148C22×C43—42no—
149C22×C43—42no—
150C22×C43—44no—
151C22×C43—82no—
152C22×C43#37911yescharacteristic
153C22×C43B(4,𝔽2)11yescharacteristic
154C22×C43#45811yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—42no—
158C4×C43—42no—
159C4×C43—82no—
160Dic43—44no—
161Dic43—44no—
162Dic43—162no—
163C2×#563—431no—
164C2×#354—431no—
165C2×#352—432no—
166#1890—432no—
167#1885D4311yescharacteristic
168C2×C43—21no—
169C2×C43—21no—
170C2×C43—42no—
171C2×C43—42no—
172C2×C43#179011yescharacteristic
173C2×C43#220112yes—
174#563—434no—
175#563—864no—
176#563—862no—
177C2×C4⋊Q8—861no—
178C2×#126—862no—
179C2×#125—861no—
180C2×#124C2×D4311yescharacteristic
181C2×#123—432no—
182C2×C22⋊Q8—862no—
183#518C2×D4311yescharacteristic
184#419—21no—
185C2×#100C2×D4311yescharacteristic
186C2×#99—432no—
187#381—862no—
188#354—862no—
189#352—864no—
190#342—862no—
191#339—21no—
192C43#1276411yescharacteristic, complemented, Sylow
193C22×Q8—861no—
194C22×Q8C22⋊D4311yescharacteristic
195C22×D4C22×D4311yescharacteristic
196C23×C4—432no—
197C2×M16—21no—
198C4⋊Q8—864no—
199C4⋊Q8—864no—
200#126—868no—
201#126—868no—
202#125—864no—
203#125—864no—
204#124—22no—
205#124C4×D4312yes—
206#124D17212yes—
207#123—434no—
208#123—434no—
209#123—862no—
210#123—862no—
211C22⋊Q8—868no—
212C22⋊Q8—868no—
213C4×D4—42no—
214#117—21no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—862no—
217C2×C4⋊C4—862no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—862no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—432no—
223C2×C22⋊C4—862no—
224C2×C22⋊C4—862no—
225C2×C42—861no—
226C2×C42C22⋊D4311yescharacteristic
227#103—42no—
228#100—22no—
229#99—862no—
230#99—862no—
231#95—1724no—
232C24D4×D4312yes—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—864no—
237C2×Q8—3441no—
238C2×Q8—3441no—
239C2×Q8(C2×D43)⋊C412yes—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4C2×C4×D4311yescharacteristic
243C2×D4C2×D17211yescharacteristic
244C2×D4D4×D4312yes—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—24no—
248C22×C4—434no—
249C22×C4—862no—
250C22×C4—862no—
251C22×C4—862no—
252C22×C4—1722no—
253C22×C4—1722no—
254C22×C4—1722no—
255C22×C4C2×C22⋊D4311yescharacteristic
256M16—41no—
257M16—41no—
258C2×C8—41no—
259C4⋊C4—22no—
260C4⋊C4—864no—
261C4⋊C4—868no—
262C4⋊C4—868no—
263C4⋊C4—864no—
264C4⋊C4—864no—
265C4⋊C4—864no—
266C22⋊C4—24no—
267C22⋊C4—24no—
268C22⋊C4—42no—
269C22⋊C4—41no—
270C22⋊C4—434no—
271C22⋊C4—864no—
272C22⋊C4—862no—
273C22⋊C4—864no—
274C22⋊C4—1722no—
275C22⋊C4—1722no—
276C42—21no—
277C42—41no—
278C42—864no—
279C42(C2×D43)⋊C412yes—
280C23—22no—
281C23—22no—
282C23—44no—
283C23C22⋊C4×D4312yes—
284C23#1306329311yescharacteristic
285C23#1306329512yes—
286Q8—42no—
287Q8—81no—
288Q8—3444no—
289D4—41no—
290D4—41no—
291D4—42no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—84no—
301C2×C4—864no—
302C2×C4—864no—
303C2×C4—3442no—
304C2×C4—3442no—
305C2×C4—3444no—
306C2×C4—1724no—
307C2×C4—1722no—
308C2×C4—1722no—
309C2×C4—1724no—
310C2×C4C2×(C2×D43)⋊C411yescharacteristic
311C2×C4#1306329311yescharacteristic
312C8—81no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—42no—
317C22—42no—
318C22—44no—
319C22—82no—
320C22#1458275411yescharacteristic
321C22#1458308511yescharacteristic
322C22#1458308811yescharacteristic
323C4—21no—
324C4—21no—
325C4—42no—
326C4—42no—
327C4—82no—
328C4—1724no—
329C4—1724no—
330C4—6882no—
331C2—21no—
332C2—21no—
333C2—42no—
334C2—42no—
335C2#1913454211yescharacteristic
336C2#1913660712yes—
subgroupG/H
centerC22#14583085
commutatorC2×D4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1885C2
socleC22×C43B(4,𝔽2)
prime radical, cosocleC22×D4×C43C23
hypercenter#1885D43
hypocenterC43#12764
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1885

Complements

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

NH ≅ G/Ntype
8. #14583649C4semidirect
192. C43#12764semidirect

Maximal subgroups

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

subgroupindex
C2×#145836492
C2×#145826942
C2×#145826902
#191350082
C43×#18852
#1276443