Finite Group Databasebeta

← #25009639

Subgroups — #25009639

Order 11008.

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

normal subgroups only

This group has 388 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#19135948C211yesmaximal, characteristic
2#19133619C211yesmaximal, characteristic
3#19133551C211yesmaximal, characteristic
4#19132619C211yesmaximal, characteristic
5#19132616C211yesmaximal, characteristic
6#19132543C211yesmaximal, characteristic
7C43×#2742C211yesmaximal, characteristic
8#14583525C2211yescharacteristic
9#14583234—21no—
10#14583055—21no—
11#14582772—21no—
12#14582666C2211yescharacteristic
13#14582665—21no—
14#14582635—21no—
15#14582635—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C43×#400—21no—
19C43×#399C2211yescharacteristic
20C43×#395—21no—
21C43×#393C2211yescharacteristic
22C43×#389—21no—
23C43×#388—21no—
24C43×#387—21no—
25C43×#385C2211yescharacteristic
26C43×#380—21no—
27C2×#10621885—41no—
28#13063304—21no—
29#13063304—21no—
30#13063302—41no—
31#13063302—41no—
32C2×Dic43⋊C4—41no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35#13063258—41no—
36#13063249—41no—
37#13063248—41no—
38C22⋊(C43⋊C8)—21no—
39C22⋊(C43⋊C8)—21no—
40C43⋊#95—41no—
41C22×Q8×C43D411yescharacteristic
42C23×C4×C43D411yescharacteristic
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C22⋊C4×C43C2311yescharacteristic
53C2×C42×C43—21no—
54#95×C43—21no—
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43D411yescharacteristic
61#95×C43D411yescharacteristic
62C24×C43C2×D411yescharacteristic
63C2×Q8×C43—41no—
64C2×Q8×C43—81no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—41no—
72C22×C4×C43—42no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—41no—
78C2×Dic86—21no—
79C2×Dic86—21no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—42no—
82C4⋊C4×C43—42no—
83C4⋊C4×C43—81no—
84C4⋊C4×C43—81no—
85C4⋊C4×C43—81no—
86C22⋊C4×C43—21no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—81no—
89C22⋊C4×C43—81no—
90C22⋊C4×C43Q1612yescomplemented
91C42×C43—81no—
92C22⋊Dic43—22no—
93C22⋊Dic43—41no—
94C22⋊Dic43—41no—
95C22⋊Dic43—41no—
96#10621885—82no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—82no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43#12011yescharacteristic
109C23×C43C2×Q1611yescharacteristic
110C23×C43#13711yescharacteristic
111Q8×C43—42no—
112Q8×C43—81no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—42no—
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×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—81no—
137C2×Dic43—42no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144Dic86—81no—
145Dic86—81no—
146C43⋊C8—81no—
147C43⋊C8—81no—
148#12254—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—81no—
158C22×C43#45111yescharacteristic
159C22×C43#45611yescharacteristic
160C22×C43B(4,𝔽2)11yescharacteristic
161C4×C43—42no—
162C4×C43—41no—
163C4×C43—42no—
164C4×C43—41no—
165C4×C43—81no—
166C4×C43—81no—
167C4×C43—81no—
168C4×C43—81no—
169Dic43—82no—
170Dic43—81no—
171Dic43—81no—
172#2742D4311yescharacteristic
173#2062—431no—
174#1614—431no—
175#1602—431no—
176#1352—431no—
177#1351—431no—
178#1326—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—41no—
182C2×C43—41no—
183C2×C43#160511yescharacteristic
184C2×C43#219711yescharacteristic
185C2×C43#220011yescharacteristic
186#543—431no—
187#484—861no—
188#451—861no—
189#400—21no—
190#399C2×D4311yescharacteristic
191#395—21no—
192#393C2×D4311yescharacteristic
193#389—21no—
194#388—21no—
195#387—21no—
196#385—861no—
197#385C2×D4311yescharacteristic
198#380—21no—
199#342—431no—
200#342—861no—
201#328—861no—
202#328—861no—
203#323—431no—
204#323—431no—
205C43#1225411yescharacteristic, complemented, Sylow
206C22×Q8C22⋊D4311yescharacteristic
207C23×C4C22⋊D4311yescharacteristic
208C2×Q16—1721no—
209C22⋊Q8—861no—
210C22⋊Q8—861no—
211C22⋊Q8—1721no—
212C22⋊Q8—1721no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—1721no—
219C2×C4⋊C4C22⋊D4311yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—861no—
223C2×C22⋊C4—861no—
224C2×C22⋊C4C22⋊D4311yescharacteristic
225C2×C22⋊C4C22×D4311yescharacteristic
226C2×C42—21no—
227#107—1721no—
228#103—1721no—
229#103—1721no—
230C22⋊C8—861no—
231C22⋊C8—861no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—1721no—
239#95C22⋊D4311yescharacteristic
240#95C22⋊D4311yescharacteristic
241C24C2×C22⋊D4311yescharacteristic
242C2×Q8—41no—
243C2×Q8—81no—
244C2×Q8—861no—
245C2×Q8—861no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—42no—
253C22×C4—41no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—1721no—
257C22×C4C2×C22⋊D4311yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259Q16—3442no—
260C2×C8—1721no—
261C2×C8—1721no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—3442no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C22⋊C4—21no—
274C22⋊C4—41no—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C22⋊C4—862no—
278C22⋊C4—1721no—
279C22⋊C4—1721no—
280C22⋊C4—1721no—
281C22⋊C4#1062188512yescomplemented
282C42—81no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23#1306329411yescharacteristic
288C23C2×#1062188511yescharacteristic
289C23#1306335611yescharacteristic
290Q8—42no—
291Q8—81no—
292Q8—3441no—
293Q8—3441no—
294C2×C4—22no—
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—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—1722no—
323C2×C4—1721no—
324C2×C4—1721no—
325C8—3441no—
326C8—3441no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22#1458305511yescharacteristic
337C22#1458308211yescharacteristic
338C22#1458308611yescharacteristic
339C4—42no—
340C4—41no—
341C4—42no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—3442no—
348C4—3441no—
349C4—3441no—
350C2—21no—
351C2—21no—
352C2—41no—
353C2—41no—
354C2#1913356911yescharacteristic
355C2#1913658511yescharacteristic
356C2#1913660211yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2742C2
socleC22×C43B(4,𝔽2)
prime radicalC24×C43C2×D4
hypercenter#2742D43
hypocenterC43#12254
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2742

Complements

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

NH ≅ G/Ntype
90. C22⋊C4×C43Q16semidirect
205. C43#12254semidirect
281. C22⋊C4#10621885semidirect

Maximal subgroups

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

subgroupindex
#191359482
#191336192
#191335512
#191326192
#191326162
#191325432
C43×#27422
#1225443