Finite Group Databasebeta

← #25009605

Subgroups — #25009605

Order 11008.

386 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 57 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#19142666C211yesmaximal, characteristic
2#19135937C211yesmaximal, characteristic, complemented
3#19133603C211yesmaximal, characteristic, complemented
4#19132602C211yesmaximal, characteristic, complemented
5#19132598C211yesmaximal, characteristic
6#19132540C211yesmaximal, characteristic, complemented
7C43×#1599C211yesmaximal, characteristic
8C2×#13063318—21no—
9#14583227—21no—
10#14582942—21no—
11#14582833—21no—
12#14582829C2211yescharacteristic
13#14582822—21no—
14#14582822—21no—
15#14582822—21no—
16#14582813—21no—
17#14582768C2211yescharacteristic
18#14582668C2211yescharacteristic
19#14582658—21no—
20#14582636—21no—
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#450—21no—
24C43×#394C2211yescharacteristic
25C43×#328—21no—
26C43×#324C2211yescharacteristic
27C2×#10621877—21no—
28#13063318—42no—
29#13063318—42no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C4×Dic43D411yescharacteristic
43#13063258—41no—
44#13063256—41no—
45#13063256—41no—
46#13063249—41no—
47C22⋊(C43⋊C8)—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95D411yescharacteristic
51C22×D4×C43D411yescharacteristic
52C2×SD16×C43—41no—
53C4⋊Q8×C43—41no—
54#125×C43—41no—
55C22⋊Q8×C43—21no—
56C22⋊Q8×C43—21no—
57#117×C43—21no—
58C2×C4⋊C4×C43C2311yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61#102×C43—41no—
62C22⋊C8×C43—21no—
63#95×C43D411yescharacteristic
64C24×C43—21no—
65C2×Q8×C43—21no—
66C2×Q8×C43—21no—
67C2×D4×C43—41no—
68C2×D4×C43—81no—
69C22×C4×C43—21no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77SD16×C43—82no—
78C2×C8×C43—41no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—81no—
90C42×C43—41no—
91C22⋊Dic43—42no—
92C22⋊Dic43—42no—
93C22⋊Dic43—81no—
94C22⋊Dic43—81no—
95C4⋊Dic43—42no—
96C4⋊Dic43—41no—
97C4⋊Dic43—41no—
98Dic43⋊C4—42no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—81no—
102Dic43⋊C4—81no—
103Dic43⋊C4—81no—
104C4×Dic43—21no—
105C4×Dic43SD1612yescomplemented
106#10621877—22no—
107#10621877—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43#12011yescharacteristic
118Q8×C43—81no—
119Q8×C43—81no—
120D4×C43—42no—
121D4×C43—81no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43C2×SD1611yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C8×C43—81no—
148C43⋊C8—42no—
149C43⋊C8—81no—
150#12249—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—81no—
154C22×C43—81no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43—81no—
158C22×C43—81no—
159C22×C43—81no—
160C22×C43#45011yescharacteristic
161C22×C43#45611yescharacteristic
162C22×C43B(4,𝔽2)11yescharacteristic
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—81no—
168C4×C43—81no—
169C4×C43—81no—
170Dic43—42no—
171Dic43—81no—
172Dic43—81no—
173Dic43—81no—
174#2823—431no—
175#2060—431no—
176#1611—431no—
177#1599D4311yescharacteristic
178#1346—431no—
179#1345—431no—
180#1325—431no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—161no—
184C2×C43#160411yescharacteristic
185C2×C43#220011yescharacteristic
186C2×C43#220311yescharacteristic
187#544C2×D4311yescharacteristic
188C2×#126—861no—
189#483—861no—
190#450—21no—
191#428—861no—
192#398—431no—
193#398—861no—
194#396—861no—
195#396—861no—
196#396—861no—
197#394—861no—
198#394C2×D4311yescharacteristic
199#384—431no—
200#343—431no—
201#339—861no—
202#328—21no—
203#328—861no—
204#324—431no—
205#324C2×D4311yescharacteristic
206C43#1224911yescharacteristic, complemented, Sylow
207C22×D4C22⋊D4311yescharacteristic
208C2×SD16—41no—
209C2×M16—861no—
210C4⋊Q8—41no—
211#126—1722no—
212#126—1722no—
213#125—41no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216#117—21no—
217C2×C4⋊C4—431no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4C22×D4311yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—861no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C22⋊C4—861no—
232C2×C42—431no—
233#107—1721no—
234#106—1721no—
235#106—1721no—
236#103—1721no—
237#102—41no—
238C22⋊C8—21no—
239C22⋊C8—861no—
240#95—431no—
241#95—861no—
242#95—861no—
243#95C22⋊D4311yescharacteristic
244C24—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×D4—41no—
248C2×D4—81no—
249C22×C4—21no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4D4×D4311yescharacteristic
255C22×C4D4×D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257SD16—82no—
258M16—862no—
259M16—1721no—
260C2×C8—41no—
261C2×C8—1721no—
262C2×C8—1721no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—3441no—
271C4⋊C4—3441no—
272C4⋊C4—3441no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4—1722no—
276C4⋊C4—1722no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—81no—
283C22⋊C4—3441no—
284C22⋊C4—3441no—
285C22⋊C4—1722no—
286C22⋊C4—1722no—
287C42—41no—
288C42—432no—
289C42—861no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#1306329311yescharacteristic
298Q8—81no—
299Q8—81no—
300D4—42no—
301D4—81no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—862no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4SD16×D4311yescharacteristic
326C2×C4#1306335211yescharacteristic
327C8—81no—
328C8—3441no—
329C8—1722no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22#1458304811yescharacteristic
340C22#1458308011yescharacteristic
341C22#1458308511yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—3441no—
350C4—3441no—
351C4—3441no—
352C4—1722no—
353C2—21no—
354C2—21no—
355C2—161no—
356C2#1913356211yescharacteristic
357C2#1913660011yescharacteristic
358C2#1913661511yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1599C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
hypercenter#1599D43
hypocenterC43#12249
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1599

Complements

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

NH ≅ G/Ntype
2. #19135937C2semidirect
3. #19133603C2semidirect
4. #19132602C2semidirect
6. #19132540C2semidirect
105. C4×Dic43SD16semidirect
206. C43#12249semidirect

Maximal subgroups

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

subgroupindex
#191426662
#191359372
#191336032
#191326022
#191325982
#191325402
C43×#15992
#1224943