Finite Group Databasebeta

← #25006187

Subgroups — #25006187

Order 11008.

366 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 69 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#19139051C211yesmaximal, characteristic
2#19132928C211yesmaximal, characteristic
3#19132908C211yesmaximal, characteristic
4#19132539C211yesmaximal, characteristic, complemented
5#19132528C211yesmaximal, characteristic, complemented
6#19132528C211yesmaximal, characteristic, complemented
7C43×#1324C211yesmaximal, characteristic, complemented
8C2×#13063305C411yescharacteristic
9C2×#13063283C2211yescharacteristic
10#14582953—21no—
11#14582949—21no—
12#14582828—21no—
13#14582828—21no—
14#14582805C411yescharacteristic
15#14582804C2211yescharacteristic
16#14582786—21no—
17#14582786—21no—
18#14582768C411yescharacteristic
19C4×(C2×D43)⋊C4C411yescharacteristic
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22#14582622—21no—
23#14582622—21no—
24C43×#382C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×C4×D43C2×C411yescharacteristic
29#13063305—41no—
30#13063305—41no—
31#13063283—41no—
32#13063283—41no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4D411yescharacteristic
40C2×(C2×D43)⋊C4D411yescharacteristic
41C2×C4×Dic43C2×C411yescharacteristic
42C2×C4×Dic43D411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44Dic43⋊C8—41no—
45Dic43⋊C8—41no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48#13063235—41no—
49C8×Dic43—41no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C42×C43C2×C411yescharacteristic
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62C23×D43C22⋊C411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—41no—
78C2×Dic86—21no—
79C2×Dic86—21no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C42×C43—21no—
87C42×C43—21no—
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—
95Dic43⋊C4—42no—
96Dic43⋊C4—42no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C22×D43—21no—
106C22×D43—21no—
107C22×D43—21no—
108C22×D43—41no—
109C22×D43—41no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43#13111yescharacteristic
123C2×C4×C43#13111yescharacteristic
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—22no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43#9911yescharacteristic
137C2×Dic43#9911yescharacteristic
138C4×D43—41no—
139C4×D43—41no—
140C4×D43—41no—
141C4×D43—41no—
142Dic86—81no—
143Dic86—81no—
144C8×C43—81no—
145C8×C43—81no—
146C43⋊C8—81no—
147C43⋊C8—81no—
148#11556—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43#40811yescharacteristic
152C22×C43C2×#9911yescharacteristic
153C22×C43#41311yescharacteristic
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—81no—
158C2×D43—81no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—81no—
164C4×C43—81no—
165Dic43—21no—
166Dic43—21no—
167Dic43—42no—
168Dic43—41no—
169Dic43—41no—
170Dic43—81no—
171#2499—431no—
172#1464—431no—
173#1458—431no—
174#1324—431no—
175#1324D4311yescharacteristic, complemented
176#1319—431no—
177#1319—431no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43#146811yescharacteristic
181C2×C43#212911yescharacteristic
182C2×C43#213211yescharacteristic
183D43—81no—
184C2×C22⋊Q8—431no—
185C2×#117—431no—
186#432—861no—
187#431—861no—
188#397—861no—
189#397—861no—
190#391—431no—
191#391—431no—
192#387—861no—
193#387—861no—
194#384—431no—
195#382C2×D4311yescharacteristic
196C4×C22⋊C4—431no—
197#324—431no—
198#324—431no—
199#324C2×D4311yescharacteristic
200#324C2×D4311yescharacteristic
201#323—861no—
202#323—861no—
203C43#1155611yescharacteristic, complemented, Sylow
204C22×Q8—431no—
205C23×C4—431no—
206C22⋊Q8—1721no—
207C22⋊Q8—1721no—
208#117—1721no—
209#117—1721no—
210C2×C4⋊C4—431no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4C4×D4311yescharacteristic
215C2×C4⋊C4C22×D4311yescharacteristic
216C2×C22⋊C4—431no—
217C2×C22⋊C4—431no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4—861no—
220C2×C42—431no—
221C2×C42—431no—
222C2×C42—431no—
223C2×C42C4×D4311yescharacteristic
224C4⋊C8—1721no—
225C4⋊C8—1721no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8—861no—
229C22⋊C8—861no—
230#97—1721no—
231C4×C8—1721no—
232#95—21no—
233#95—21no—
234#95—861no—
235#95—861no—
236#95—861no—
237#95—861no—
238#95—861no—
239C24—431no—
240C2×Q8—861no—
241C2×Q8—861no—
242C2×Q8—1721no—
243C2×Q8—1721no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—431no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—1721no—
256C22×C4C2×C4×D4311yescharacteristic
257C22×C4D4×D4311yescharacteristic
258C22×C4D4×D4311yescharacteristic
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—1721no—
262C2×C8—1721no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1722no—
269C4⋊C4—1722no—
270C22⋊C4—1721no—
271C22⋊C4—1721no—
272C22⋊C4—1722no—
273C22⋊C4—1722no—
274C42—21no—
275C42—21no—
276C42—861no—
277C42—861no—
278C42—861no—
279C42—861no—
280C42—1721no—
281C23—861no—
282C23—861no—
283C23—861no—
284C23—1721no—
285C23—1721no—
286C23C22⋊C4×D4311yescharacteristic
287Q8—3441no—
288Q8—3441no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—431no—
302C2×C4—431no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—862no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4#1306333111yescharacteristic
320C2×C4#1306333311yescharacteristic
321C8—81no—
322C8—81no—
323C8—3441no—
324C8—3441no—
325C22—21no—
326C22—21no—
327C22—3441no—
328C22—3441no—
329C22—1721no—
330C22—1721no—
331C22—1721no—
332C22#1458286411yescharacteristic
333C22#99×D4311yescharacteristic
334C22#1458288211yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—861no—
342C4—861no—
343C4—3441no—
344C4—1722no—
345C4—1721no—
346C4—1721no—
347C2—21no—
348C2—21no—
349C2—3441no—
350C2#1913294211yescharacteristic
351C2#1913626811yescharacteristic
352C2#1913627711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1324D43
hypocenterC43#11556
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
4. #19132539C2semidirect
5. #19132528C2semidirect
6. #19132528C2semidirect
7. C43×#1324C2semidirect
175. #1324D43semidirect
203. C43#11556semidirect

Maximal subgroups

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

subgroupindex
#191390512
#191329282
#191329082
#191325392
#191325282
C43×#13242
#1155643