Finite Group Databasebeta

← #25006902

Subgroups — #25006902

Order 11008.

452 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 83 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#19137866C211yesmaximal, characteristic
2#19134332C211yesmaximal, characteristic
3#19132908C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132623C211yesmaximal, characteristic, complemented
6#19132621C211yesmaximal, characteristic, complemented
7C43×#1354C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×Q8×Dic43C411yescharacteristic
10C2×#13063283C2211yescharacteristic
11#14582949—21no—
12#14582838C2211yescharacteristic
13#14582836C411yescharacteristic
14#14582831—21no—
15#14582821—21no—
16#14582810C411yescharacteristic
17C4⋊C4×Dic43—21no—
18#14582750C411yescharacteristic
19#14582746—21no—
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⋊Dic43—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4C2×C411yescharacteristic
45C2×(C2×D43)⋊C4D411yescharacteristic
46C2×C4×Dic43—21no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43C2×C411yescharacteristic
49C2×C4×Dic43D411yescharacteristic
50Dic43⋊C8—41no—
51C22⋊(C43⋊C8)—21no—
52C8×Dic43—41no—
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—22no—
80C2×C4×D43SD1612yes—
81C2×C4×D43Q1612yes—
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—42no—
94C4⋊Dic43—42no—
95C4⋊Dic43—41no—
96Dic43⋊C4—42no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—41no—
102C4×Dic43—41no—
103C4×Dic43—42no—
104#10621877—22no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108#10621872—44no—
109C8×D43—44no—
110C23×C43C2×C22⋊C411yescharacteristic
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—41no—
114C22×D43—41no—
115C22×D43#10312yes—
116Q8×C43—42no—
117Q8×C43—42no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43C2×SD1611yescharacteristic
131C2×C4×C43C2×Q1611yescharacteristic
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43#9911yescharacteristic
143C2×Dic43#9911yescharacteristic
144C2×Dic43#10312yes—
145C2×Dic43#10412yes—
146C4×D43—22no—
147C4×D43—22no—
148C4×D43—22no—
149C4×D43—22no—
150C8×C43—42no—
151C8×C43—81no—
152C43⋊C8—42no—
153C43⋊C8—81no—
154#11721—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43C2×#9911yescharacteristic
158C22×C43C2×#10311yescharacteristic
159C22×C43C2×#10411yescharacteristic
160C2×D43—22no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—42no—
164C2×D43—81no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—42no—
168C4×C43—41no—
169C4×C43—42no—
170C4×C43—41no—
171Dic43—41no—
172Dic43—41no—
173Dic43—81no—
174Dic43—81no—
175Dic43#32812yes—
176Dic43#32812yes—
177#2396—431no—
178#1742—431no—
179#1458—431no—
180#1354—431no—
181#1354D4311yescharacteristic, complemented
182#1353—431no—
183#1353—431no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43C2×#32811yescharacteristic
187C2×C43#212011yescharacteristic
188C2×C43#213211yescharacteristic
189D43—42no—
190C22×M16—861no—
191C2×C4×Q8—431no—
192C2×#117—431no—
193#431—861no—
194#400—431no—
195#399—431no—
196#398—861no—
197#396—861no—
198#395C2×D4311yescharacteristic
199#393—431no—
200C4×C4⋊C4—431no—
201C4×C4⋊C4—861no—
202C4×C22⋊C4—861no—
203#343—431no—
204#343—861no—
205#343C2×D4311yescharacteristic
206#324—431no—
207#324C2×D4311yescharacteristic
208#323—861no—
209C43#1172111yescharacteristic, complemented, Sylow
210C22×Q8C4×D4311yescharacteristic
211C23×C4—431no—
212C2×M16—21no—
213C2×M16—864no—
214C2×M16—861no—
215C2×M16—1721no—
216C2×M16—1722no—
217C22×C8—1721no—
218C4×Q8—1721no—
219C4×Q8—1721no—
220#117—1721no—
221#117—1721no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4C22×D4311yescharacteristic
229C2×C22⋊C4—431no—
230C2×C22⋊C4—431no—
231C2×C22⋊C4—861no—
232C2×C22⋊C4—861no—
233C2×C42—431no—
234C2×C42—431no—
235C2×C42—861no—
236C2×C42—861no—
237C4⋊C8—1721no—
238C22⋊C8—21no—
239C22⋊C8—861no—
240C4×C8—1721no—
241#95—21no—
242#95—431no—
243#95—861no—
244#95—861no—
245#95—861no—
246#95C4×D4311yescharacteristic
247C24—431no—
248C2×Q8—42no—
249C2×Q8—41no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—431no—
253C22×C4—432no—
254C22×C4—432no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—862no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C2×C4×D4311yescharacteristic
263C22×C4D4×D4311yescharacteristic
264C22×C4D4×D4311yescharacteristic
265M16—22no—
266M16—41no—
267M16—862no—
268M16—1724no—
269M16—1721no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—1724no—
273C2×C8—1721no—
274C2×C8—1721no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1722no—
280C4⋊C4—1722no—
281C4⋊C4—1722no—
282C22⋊C4—1721no—
283C22⋊C4—1721no—
284C22⋊C4—1722no—
285C22⋊C4—1722no—
286C42—861no—
287C42—861no—
288C42—861no—
289C42—861no—
290C42—1721no—
291C42—1721no—
292C42—1722no—
293C23—432no—
294C23—861no—
295C23—861no—
296C23—1721no—
297C23—1721no—
298C23C22⋊C4×D4311yescharacteristic
299Q8—42no—
300Q8—42no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—432no—
316C2×C4—432no—
317C2×C4—862no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—862no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4SD16×D4311yescharacteristic
332C2×C4Q16×D4311yescharacteristic
333C8—42no—
334C8—81no—
335C8—3441no—
336C8—1722no—
337C22—21no—
338C22—21no—
339C22—862no—
340C22—3441no—
341C22—1722no—
342C22—1721no—
343C22—1721no—
344C22#99×D4311yescharacteristic
345C22#103×D4311yescharacteristic
346C22#104×D4311yescharacteristic
347C4—21no—
348C4—21no—
349C4—42no—
350C4—41no—
351C4—42no—
352C4—41no—
353C4—432no—
354C4—432no—
355C4—3441no—
356C4—3441no—
357C4—1721no—
358C4—1721no—
359C2—21no—
360C2—21no—
361C2—1722no—
362C2#328×D4311yescharacteristic
363C2#1913623311yescharacteristic
364C2#1913627911yescharacteristic
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#11721
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. #19132623C2semidirect
6. #19132621C2semidirect
7. C43×#1354C2semidirect
181. #1354D43semidirect
209. C43#11721semidirect

Maximal subgroups

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

subgroupindex
#191378662
#191343322
#191329082
#191326252
#191326232
#191326212
C43×#13542
#1172143