Finite Group Databasebeta

← #25009359

Subgroups — #25009359

Order 11008.

414 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135756C211yesmaximal, characteristic, complemented
2#19133602C211yesmaximal, characteristic, complemented
3#19133534C211yesmaximal, characteristic
4#19132601C211yesmaximal, characteristic, complemented
5#19132598C211yesmaximal, characteristic
6#19132529C211yesmaximal, characteristic, complemented
7C43×#2728C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583229—21no—
10#14583050—21no—
11#14582908—21no—
12#14582668C2211yescharacteristic
13#14582659—21no—
14#14582635—21no—
15#14582635—21no—
16#14582625C2211yescharacteristic
17#14582625C2211yescharacteristic
18C2×C22⋊Q8×C43—21no—
19C43×#400—21no—
20C43×#398C2211yescharacteristic
21C43×#397—21no—
22C43×#394C2211yescharacteristic
23C43×#391C2211yescharacteristic
24C43×#388—21no—
25C43×#386—21no—
26C43×#385—21no—
27C2×#10621883—41no—
28C2×#10621877—21no—
29#13063324—41no—
30#13063316—41no—
31#13063304—21no—
32#13063304—21no—
33#13063284—21no—
34#13063256—41no—
35#13063249—41no—
36#13063249—41no—
37#13063248—41no—
38#13063246—41no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C22×Q8×C43D411yescharacteristic
42C22×D4×C43D411yescharacteristic
43C23×C4×C43—21no—
44C22⋊Q8×C43—42no—
45C22⋊Q8×C43—42no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C42×C43D411yescharacteristic
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43D411yescharacteristic
63#95×C43D411yescharacteristic
64C24×C43—21no—
65C2×Q8×C43—21no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43SD1612yescomplemented
69C2×D4×C43—42no—
70C2×D4×C43—41no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—42no—
77C22×C4×C43—81no—
78C22×C4×C43—81no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C2×Dic86—21no—
83C2×Dic86—21no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—42no—
87C4⋊C4×C43—42no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C22⋊C4×C43—42no—
91C22⋊C4×C43—42no—
92C22⋊C4×C43—42no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—81no—
96C42×C43—41no—
97C22⋊Dic43—41no—
98#10621883—82no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105C4×Dic43—41no—
106#10621877—41no—
107#10621877—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C23×C43—22no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43#12011yescharacteristic
119Q8×C43—42no—
120Q8×C43—81no—
121D4×C43—42no—
122D4×C43—81no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—22no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—84no—
145C2×C4×C43C2×SD1611yescharacteristic
146C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
147C2×Dic43—41no—
148C2×Dic43—41no—
149Dic86—81no—
150Dic86—81no—
151C43⋊C8—81no—
152C43⋊C8—81no—
153C43⋊C8—81no—
154#12210—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—42no—
158C22×C43—42no—
159C22×C43—42no—
160C22×C43—81no—
161C22×C43—81no—
162C22×C43—81no—
163C22×C43—81no—
164C22×C43#45011yescharacteristic
165C22×C43#45511yescharacteristic
166C22×C43B(4,𝔽2)11yescharacteristic
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—42no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—81no—
173C4×C43—81no—
174C4×C43—81no—
175C4×C43—81no—
176Dic43—81no—
177Dic43—81no—
178#2728D4311yescharacteristic
179#2028—431no—
180#1611—431no—
181#1599—431no—
182#1346—431no—
183#1345—431no—
184#1319—431no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43—82no—
188C2×C43#160111yescharacteristic
189C2×C43#219711yescharacteristic
190C2×C43#220311yescharacteristic
191#544—431no—
192C2×C22⋊Q8—21no—
193#483—861no—
194#450—861no—
195#419—861no—
196#400—21no—
197#398C2×D4311yescharacteristic
198#397—21no—
199#394C2×D4311yescharacteristic
200#391C2×D4311yescharacteristic
201#388—21no—
202#386—21no—
203#385—21no—
204#343—431no—
205#339—861no—
206#328—861no—
207#328—861no—
208#324—431no—
209#324—431no—
210C43#1221011yescharacteristic, complemented, Sylow
211C22×Q8C22⋊D4311yescharacteristic
212C22×D4C22⋊D4311yescharacteristic
213C23×C4—21no—
214C2×SD16—1721no—
215C2×M16—861no—
216C4⋊Q8—1721no—
217#125—1721no—
218C22⋊Q8—42no—
219C22⋊Q8—42no—
220C22⋊Q8—861no—
221C22⋊Q8—861no—
222#117—861no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D4311yescharacteristic
227C2×C4⋊C4C22×D4311yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42C22⋊D4311yescharacteristic
234#106—1721no—
235#103—1721no—
236#103—1721no—
237#103—1721no—
238#102—1721no—
239C22⋊C8—861no—
240C22⋊C8—861no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95C22⋊D4311yescharacteristic
247#95C22⋊D4311yescharacteristic
248C24—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—861no—
253C2×Q8—861no—
254C2×Q8#1062188312yescomplemented
255C2×D4—41no—
256C2×D4—42no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4C2×C22⋊D4311yescharacteristic
266C22×C4C2×C22⋊D4311yescharacteristic
267C22×C4C2×C22⋊D4311yescharacteristic
268SD16—3442no—
269M16—1721no—
270M16—1721no—
271C2×C8—1721no—
272C2×C8—1721no—
273C2×C8—1721no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—81no—
292C22⋊C4—1721no—
293C42—41no—
294C42—1721no—
295C23—22no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23#1306329411yescharacteristic
303Q8—42no—
304Q8—81no—
305Q8—3441no—
306Q8—3441no—
307D4—42no—
308D4—81no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—84no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4C2×#1062188311yescharacteristic
334C2×C4#1306335111yescharacteristic
335C8—3441no—
336C8—3441no—
337C8—3441no—
338C22—21no—
339C22—21no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22#1458305011yescharacteristic
348C22#1458307711yescharacteristic
349C22#1458308611yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—42no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—81no—
359C4—3441no—
360C4—3441no—
361C2—21no—
362C2—21no—
363C2—82no—
364C2#1913354711yescharacteristic
365C2#1913658511yescharacteristic
366C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2728C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
hypercenter#2728D43
hypocenterC43#12210
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2728

Complements

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

NH ≅ G/Ntype
1. #19135756C2semidirect
2. #19133602C2semidirect
4. #19132601C2semidirect
6. #19132529C2semidirect
68. C2×Q8×C43SD16semidirect
210. C43#12210semidirect
254. C2×Q8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191357562
#191336022
#191335342
#191326012
#191325982
#191325292
C43×#27282
#1221043