Finite Group Databasebeta

← #25007067

Subgroups — #25007067

Order 11008.

444 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 71 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#19140165C211yesmaximal, characteristic
2#19134326C211yesmaximal, characteristic
3#19132926C211yesmaximal, characteristic
4#19132616C211yesmaximal, characteristic
5#19132596C211yesmaximal, characteristic
6#19132594C211yesmaximal, characteristic
7C43×#1351C211yesmaximal, characteristic
8C2×Q8×Dic43C411yescharacteristic, complemented
9C2×#13063281—21no—
10C2×#13063281C2211yescharacteristic
11#14582953—21no—
12#14582831C411yescharacteristic, complemented
13#14582824C2211yescharacteristic
14#14582818C411yescharacteristic, complemented
15#14582793—21no—
16#14582786—21no—
17#14582782—21no—
18#14582774—21no—
19#14582766C411yescharacteristic, complemented
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#393C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C23×Dic43D411yescharacteristic
28Q8×Dic43—41no—
29Q8×Dic43—41no—
30#13063281—24no—
31#13063281—41no—
32#13063281—41no—
33#13063281—42no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—41no—
39C2×Dic43⋊C4C2×C411yescharacteristic
40C2×Dic43⋊C4D411yescharacteristic
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43D411yescharacteristic
44C2×C4×Dic43—21no—
45C2×C4×Dic43—41no—
46C2×C4×Dic43C2×C411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48Dic43⋊C8—41no—
49C22⋊(C43⋊C8)—21no—
50#13063235—41no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C22×Q8×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C24×C43C2×D411yescharacteristic
65C2×Q8×C43—42no—
66C2×Q8×C43—41no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—41no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—22no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—41no—
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C2×C8×C43—41no—
85C22⋊C4×C43—22no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—42no—
88C22⋊C4×C43—41no—
89C22⋊Dic43—22no—
90C22⋊Dic43—41no—
91C22⋊Dic43—41no—
92C22⋊Dic43—41no—
93C22⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4⋊Dic43—41no—
96C4⋊Dic43—42no—
97C4⋊Dic43—41no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100Dic43⋊C4—44no—
101Dic43⋊C4—42no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—42no—
107C4×Dic43—44no—
108C2×C43⋊C8—41no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43C2×C22⋊C411yescharacteristic
114C23×C43AGL(1,ℤ/8)11yescharacteristic
115C23×C43#13711yescharacteristic
116Q8×C43—42no—
117Q8×C43—42no—
118C2×C4×C43—22no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×Dic43—22no—
132C2×Dic43—22no—
133C2×Dic43—22no—
134C2×Dic43—22no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—42no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C2×Dic43#9911yescharacteristic
153C2×Dic43#9911yescharacteristic
154C2×Dic43#10412yes—
155C8×C43—81no—
156C43⋊C8—81no—
157#11756—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—81no—
167C22×C43C2×#9911yescharacteristic
168C22×C43#41711yescharacteristic
169C22×C43C2×#10411yescharacteristic
170C4×C43—42no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—81no—
174C4×C43—82no—
175Dic43—21no—
176Dic43—21no—
177Dic43—22no—
178Dic43—41no—
179Dic43—41no—
180Dic43—81no—
181Dic43—82no—
182Dic43—81no—
183#2599—431no—
184#1740—431no—
185#1464—431no—
186#1351—431no—
187#1351D4311yescharacteristic
188#1344—431no—
189#1344—431no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—41no—
193C2×C43—41no—
194C2×C43#150411yescharacteristic
195C2×C43#212011yescharacteristic
196C2×C43#212911yescharacteristic
197C2×C4×Q8—431no—
198C2×#117—431no—
199C2×#117—861no—
200#432—861no—
201#398—431no—
202#397—431no—
203#395—431no—
204#393C2×D4311yescharacteristic
205#388—861no—
206#387—861no—
207#387—861no—
208#385—861no—
209#383—431no—
210#342—431no—
211#342—861no—
212#342C2×D4311yescharacteristic
213#324—861no—
214#323—431no—
215#323C2×D4311yescharacteristic
216C43#1175611yescharacteristic, complemented, Sylow
217C22×Q8C4×D4311yescharacteristic
218C23×C4—431no—
219C4×Q8—1721no—
220C4×Q8—1721no—
221#117—864no—
222#117—1721no—
223#117—1721no—
224#117—1722no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—1721no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—431no—
235C2×C22⋊C4—861no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4C22×D4311yescharacteristic
238C2×C42—431no—
239C2×C42—431no—
240C2×C42—861no—
241C2×C42—1721no—
242C4⋊C8—1721no—
243C22⋊C8—21no—
244C22⋊C8—861no—
245#97—1721no—
246#95—21no—
247#95—431no—
248#95—861no—
249#95—861no—
250#95—861no—
251#95—861no—
252#95—861no—
253#95C4×D4311yescharacteristic
254C24D4×D4311yescharacteristic
255C2×Q8—42no—
256C2×Q8—41no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—431no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—862no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—1721no—
272C22×C4C2×C4×D4311yescharacteristic
273C22×C4D4×D4311yescharacteristic
274C2×C8—41no—
275C2×C8—1721no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1722no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C4⋊C4—1722no—
283C4⋊C4—1724no—
284C22⋊C4—22no—
285C22⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—862no—
289C22⋊C4—1721no—
290C22⋊C4—1721no—
291C22⋊C4—1721no—
292C22⋊C4—1721no—
293C42—861no—
294C42—861no—
295C42—861no—
296C42—861no—
297C42—1722no—
298C42—1724no—
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23C22⋊C4×D4311yescharacteristic
304C23#1306335211yescharacteristic
305C23#1306335711yescharacteristic
306Q8—42no—
307Q8—42no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—432no—
324C2×C4—862no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—3441no—
335C2×C4—3441no—
336C2×C4—1722no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C8—81no—
346C8—3441no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—81no—
356C22#99×D4311yescharacteristic
357C22#1458289911yescharacteristic
358C22#104×D4311yescharacteristic
359C4—41no—
360C4—42no—
361C4—41no—
362C4—81no—
363C4—82no—
364C4—861no—
365C4—861no—
366C4—862no—
367C4—3441no—
368C4—3442no—
369C4—3441no—
370C4—1721no—
371C4—1721no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2#1913309811yescharacteristic
377C2#1913623311yescharacteristic
378C2#1913626811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1351C2
socleC22×C43C2×#99
prime radicalC24×C43C2×D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1351D43
hypocenterC43#11756
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
8. C2×Q8×Dic43C4semidirect
12. #14582831C4semidirect
14. #14582818C4semidirect
19. #14582766C4semidirect
216. C43#11756semidirect

Maximal subgroups

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

subgroupindex
#191401652
#191343262
#191329262
#191326162
#191325962
#191325942
C43×#13512
#1175643