Finite Group Databasebeta

← #25006238

Subgroups — #25006238

Order 11008.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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#19139585C211yesmaximal, characteristic
2#19132937C211yesmaximal, characteristic
3#19132917C211yesmaximal, characteristic
4#19132529C211yesmaximal, characteristic
5#19132528C211yesmaximal, characteristic
6#19132528C211yesmaximal, characteristic
7C43×#1319C211yesmaximal, characteristic
8C2×#13063325C411yescharacteristic
9C2×#13063323C411yescharacteristic
10C2×#13063323C411yescharacteristic
11C2×#13063290C2211yescharacteristic
12#14582953—21no—
13#14582949—21no—
14#14582833—21no—
15#14582833—21no—
16#14582804C2211yescharacteristic
17#14582796—21no—
18#14582796—21no—
19C4×Dic43⋊C4C411yescharacteristic
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22#14582624—21no—
23#14582624—21no—
24C43×#391C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×Dic86C2×C411yescharacteristic
29#13063325—42no—
30#13063323—41no—
31#13063323—41no—
32#13063323—42no—
33#13063290—41no—
34#13063290—41no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4D411yescharacteristic
43C2×Dic43⋊C4D411yescharacteristic
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43C2×C411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48Dic43⋊C8—41no—
49Dic43⋊C8—41no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52#13063235—41no—
53C8×Dic43—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C22×Q8×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43C2311yescharacteristic
59C2×C42×C43C2×C411yescharacteristic
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—21no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C22×Dic43C22⋊C411yescharacteristic
78C22×Dic43C22⋊C411yescharacteristic
79C2×Dic86—21no—
80C2×Dic86—21no—
81C2×Dic86—22no—
82C2×Dic86—21no—
83C2×Dic86—21no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87C2×C8×C43—41no—
88C2×C8×C43—41no—
89C4⋊C4×C43—41no—
90C42×C43—41no—
91C4⋊Dic43—42no—
92C4⋊Dic43—42no—
93Dic43⋊C4—24no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—42no—
97Dic43⋊C4—42no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100Dic43⋊C4—42no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43C2×C22⋊C411yescharacteristic
111Q8×C43—81no—
112Q8×C43—81no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—22no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43#13111yescharacteristic
126C2×C4×C43#13111yescharacteristic
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—22no—
130C2×Dic43—22no—
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#9911yescharacteristic
142C2×Dic43#9911yescharacteristic
143C2×Dic43#10012yes—
144Dic86—42no—
145Dic86—42no—
146Dic86—81no—
147Dic86—81no—
148C8×C43—81no—
149C8×C43—81no—
150C43⋊C8—81no—
151C43⋊C8—81no—
152#11568—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43#40811yescharacteristic
156C22×C43C2×#9911yescharacteristic
157C22×C43C2×#10011yescharacteristic
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—42no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—81no—
164Dic43—21no—
165Dic43—22no—
166Dic43—42no—
167Dic43—41no—
168Dic43—41no—
169Dic43—81no—
170Dic43#35612yes—
171#2546—431no—
172#1467—431no—
173#1461—431no—
174#1319—431no—
175#1319—431no—
176#1319—431no—
177#1319D4311yescharacteristic
178C2×C43—21no—
179C2×C43—21no—
180C2×C43#147111yescharacteristic
181C2×C43#212911yescharacteristic
182C2×C43C2×#35611yescharacteristic
183C2×C4⋊Q8—431no—
184C2×C4⋊Q8—431no—
185C2×C4⋊Q8—431no—
186C2×C4×Q8—431no—
187#432—861no—
188#431—861no—
189#398—861no—
190#398—861no—
191#391—431no—
192#391C2×D4311yescharacteristic
193#389—861no—
194#389—861no—
195C4×C4⋊C4—431no—
196#324—431no—
197#324—431no—
198#324—861no—
199#324—861no—
200#324C2×D4311yescharacteristic
201#324C2×D4311yescharacteristic
202C43#1156811yescharacteristic, complemented, Sylow
203C22×Q8—431no—
204C22×Q8—431no—
205C22×Q8C4×D4311yescharacteristic
206C4⋊Q8—1722no—
207C4⋊Q8—1721no—
208C4⋊Q8—1721no—
209C4⋊Q8—1722no—
210C4×Q8—1721no—
211C4×Q8—1721no—
212C2×C4⋊C4—431no—
213C2×C4⋊C4—431no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C22×D4311yescharacteristic
222C2×C42—431no—
223C2×C42—431no—
224C2×C42—431no—
225C2×C42—431no—
226C2×C42C4×D4311yescharacteristic
227C4⋊C8—1721no—
228C4⋊C8—1721no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231C22⋊C8—861no—
232C22⋊C8—861no—
233#97—1721no—
234C4×C8—1721no—
235#95—21no—
236#95—21no—
237#95—861no—
238#95—861no—
239#95—861no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—862no—
245C2×Q8—861no—
246C2×Q8—861no—
247C2×Q8—861no—
248C2×Q8—861no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—431no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4C2×C4×D4311yescharacteristic
261C22×C4D4×D4311yescharacteristic
262C22×C4D4×D4311yescharacteristic
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—1721no—
266C2×C8—1721no—
267C4⋊C4—41no—
268C4⋊C4—864no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1722no—
274C4⋊C4—1722no—
275C4⋊C4—1722no—
276C4⋊C4—1722no—
277C4⋊C4—1722no—
278C42—41no—
279C42—861no—
280C42—861no—
281C42—861no—
282C42—861no—
283C42—861no—
284C42—861no—
285C42—1721no—
286C23C22⋊C4×D4311yescharacteristic
287Q8—81no—
288Q8—81no—
289Q8—3441no—
290Q8—3441no—
291Q8—1722no—
292Q8—1722no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—431no—
306C2×C4—431no—
307C2×C4—432no—
308C2×C4—862no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—862no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4#1306333111yescharacteristic
323C2×C4#1306333311yescharacteristic
324C8—81no—
325C8—81no—
326C8—3441no—
327C8—3441no—
328C22—21no—
329C22—21no—
330C22#1458286411yescharacteristic
331C22#99×D4311yescharacteristic
332C22#100×D4311yescharacteristic
333C4—21no—
334C4—21no—
335C4—42no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—432no—
340C4—861no—
341C4—862no—
342C4—3441no—
343C4—1722no—
344C4—1721no—
345C4—1721no—
346C2—21no—
347C2—21no—
348C2#1913295311yescharacteristic
349C2#1913626811yescharacteristic
350C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1319D43
hypocenterC43#11568
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
202. C43#11568semidirect

Maximal subgroups

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

subgroupindex
#191395852
#191329372
#191329172
#191325292
#191325282
C43×#13192
#1156843