Finite Group Databasebeta

← #25007102

Subgroups — #25007102

Order 11008.

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

normal subgroups only

This group has 428 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#19140167C211yesmaximal, characteristic
2#19134332C211yesmaximal, characteristic
3#19132928C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132602C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1354C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×Q8×Dic43C411yescharacteristic
10C2×#13063283C2211yescharacteristic
11#14582953—21no—
12#14582829C2211yescharacteristic
13#14582826C411yescharacteristic
14#14582810C411yescharacteristic
15#14582789—21no—
16#14582786—21no—
17#14582785—21no—
18#14582773—21no—
19#14582766C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582622—21no—
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43D411yescharacteristic
28C2×#10621877—21no—
29C2×#10621872—41no—
30M16×D43—24no—
31M16×D43—42no—
32C2×C8×D43—41no—
33Q8×Dic43—41no—
34Q8×Dic43—41no—
35#13063283—41no—
36#13063283—41no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4C2×C411yescharacteristic
44C2×(C2×D43)⋊C4D411yescharacteristic
45C2×C4×Dic43—21no—
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×M16×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C2×Q8×C43—42no—
66C2×Q8×C43—41no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—22no—
82M16×C43—22no—
83M16×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—42no—
88(C2×D43)⋊C4—41no—
89(C2×D43)⋊C4—41no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—42no—
92C4⋊Dic43—41no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4⋊Dic43—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—42no—
103#10621877—22no—
104#10621877—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107#10621872—44no—
108C8×D43—44no—
109C23×C43C2×C22⋊C411yescharacteristic
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—41no—
113C22×D43—41no—
114C22×D43#10412yes—
115Q8×C43—42no—
116Q8×C43—42no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—22no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
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×C43AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43#9911yescharacteristic
144C2×Dic43#9911yescharacteristic
145C4×D43—22no—
146C4×D43—22no—
147C4×D43—22no—
148C4×D43—22no—
149C8×C43—42no—
150C8×C43—81no—
151C43⋊C8—42no—
152C43⋊C8—81no—
153#11763—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43C2×#9911yescharacteristic
157C22×C43#41711yescharacteristic
158C22×C43C2×#10411yescharacteristic
159C2×D43—22no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—42no—
163C2×D43—81no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—42no—
168C4×C43—41no—
169C4×C43—81no—
170Dic43—21no—
171Dic43—21no—
172Dic43—41no—
173Dic43—41no—
174Dic43—81no—
175Dic43—81no—
176#2599—431no—
177#1742—431no—
178#1464—431no—
179#1354—431no—
180#1354D4311yescharacteristic, complemented
181#1346—431no—
182#1346—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43#150411yescharacteristic
186C2×C43#212011yescharacteristic
187C2×C43#213511yescharacteristic
188D43—42no—
189C22×M16—861no—
190C2×C4×Q8—431no—
191C2×#117—431no—
192#432—861no—
193#398—431no—
194#397—431no—
195#395C2×D4311yescharacteristic
196#393—431no—
197#388—861no—
198#387—861no—
199#387—861no—
200#385—861no—
201#383—431no—
202#343—431no—
203#343—861no—
204#343C2×D4311yescharacteristic
205#324—431no—
206#324C2×D4311yescharacteristic
207#323—861no—
208C43#1176311yescharacteristic, complemented, Sylow
209C22×Q8C4×D4311yescharacteristic
210C23×C4—431no—
211C2×M16—21no—
212C2×M16—864no—
213C2×M16—861no—
214C2×M16—1721no—
215C2×M16—1722no—
216C22×C8—1721no—
217C4×Q8—1721no—
218C4×Q8—1721no—
219#117—1721no—
220#117—1721no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4C22×D4311yescharacteristic
227C2×C22⋊C4—431no—
228C2×C22⋊C4—431no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C42—431no—
232C2×C42—431no—
233C2×C42—861no—
234C4⋊C8—1721no—
235C22⋊C8—21no—
236C22⋊C8—861no—
237#97—1721no—
238#95—21no—
239#95—431no—
240#95—861no—
241#95—861no—
242#95—861no—
243#95—861no—
244#95—861no—
245#95C4×D4311yescharacteristic
246C24—431no—
247C2×Q8—42no—
248C2×Q8—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—431no—
252C22×C4—431no—
253C22×C4—431no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—862no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4C2×C4×D4311yescharacteristic
262C22×C4D4×D4311yescharacteristic
263C22×C4D4×D4311yescharacteristic
264M16—22no—
265M16—41no—
266M16—862no—
267M16—1724no—
268M16—1721no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—1724no—
272C2×C8—1721no—
273C2×C8—1721no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C22⋊C4—1721no—
283C22⋊C4—1721no—
284C22⋊C4—1722no—
285C22⋊C4—1722no—
286C42—861no—
287C42—861no—
288C42—861no—
289C42—861no—
290C42—1722no—
291C23—432no—
292C23—861no—
293C23—861no—
294C23—1721no—
295C23—1721no—
296C23C22⋊C4×D4311yescharacteristic
297Q8—42no—
298Q8—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—862no—
314C2×C4—862no—
315C2×C4—862no—
316C2×C4—862no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4#1306335211yescharacteristic
330C2×C4#1306335711yescharacteristic
331C8—42no—
332C8—81no—
333C8—3441no—
334C8—1722no—
335C22—21no—
336C22—21no—
337C22—862no—
338C22—3441no—
339C22—1722no—
340C22—1721no—
341C22—1721no—
342C22#99×D4311yescharacteristic
343C22#1458289911yescharacteristic
344C22#104×D4311yescharacteristic
345C4—21no—
346C4—21no—
347C4—41no—
348C4—42no—
349C4—41no—
350C4—81no—
351C4—861no—
352C4—861no—
353C4—3441no—
354C4—3441no—
355C4—1721no—
356C4—1721no—
357C2—21no—
358C2—21no—
359C2—1722no—
360C2#1913309811yescharacteristic
361C2#1913623311yescharacteristic
362C2#1913628811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1354C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1354D43
hypocenterC43#11763
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #19132625C2semidirect
5. #19132602C2semidirect
6. #19132600C2semidirect
7. C43×#1354C2semidirect
180. #1354D43semidirect
208. C43#11763semidirect

Maximal subgroups

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

subgroupindex
#191401672
#191343322
#191329282
#191326252
#191326022
#191326002
C43×#13542
#1176343