Finite Group Databasebeta

← #25000373

Subgroups — #25000373

Order 11008.

366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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#19144400C211yesmaximal, characteristic
2#19133365C211yesmaximal, characteristic
3#19133253C211yesmaximal, characteristic
4#19133158C211yesmaximal, characteristic
5#19132919C211yesmaximal, characteristic
6#19132453C211yesmaximal, characteristic
7C43×#1805C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583206—22no—
10#14583194—21no—
11#14583184—21no—
12#14582952C2211yescharacteristic
13#14582952C2211yescharacteristic
14#14582939—21no—
15#14582923C2211yescharacteristic
16#14582908—21no—
17#14582649—22no—
18#14582647—21no—
19#14582644—21no—
20#14582635—22no—
21#14582625—22no—
22C2×C4×Q8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×#103×C43—21no—
25C43×#382C2211yescharacteristic
26C43×#340—21no—
27C2×#10621877—21no—
28#13063325D411yescharacteristic
29#13063325D411yescharacteristic
30#13063317—21no—
31#13063304—21no—
32#13063304—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35#13063284—21no—
36#13063258—22no—
37#13063256—22no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)D412yes—
42#13063249—22no—
43#13063249—22no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)D412yes—
46C4×C43⋊C8—21no—
47C4×C43⋊C8—21no—
48C22×Q8×C43D411yescharacteristic
49C22×C8×C43—21no—
50C4×Q8×C43—21no—
51C4×Q8×C43—21no—
52C4×Q8×C43—21no—
53C4×Q8×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43—21no—
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61#103×C43—42no—
62#95×C43—21no—
63#95×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—21no—
66C2×Q8×C43—21no—
67C2×Q8×C43—21no—
68C2×Q8×C43—21no—
69C2×Q8×C43SD1612yes—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—41no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C2×Dic86—21no—
77C2×Dic86—21no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C42×C43—41no—
88C42×C43—41no—
89C42×C43C2×D411yescharacteristic
90C42×C43C2×D411yescharacteristic
91C42×C43#4111yescharacteristic
92C42×C43#4111yescharacteristic
93C22⋊Dic43—41no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100C4×Dic43—41no—
101#10621877—41no—
102#10621877—41no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8—22no—
105C2×C43⋊C8—41no—
106C23×C43#12111yescharacteristic
107Q8×C43—22no—
108Q8×C43—22no—
109Q8×C43—41no—
110Q8×C43—41no—
111C2×C4×C43—22no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43#12011yescharacteristic
122C2×C4×C43#12111yescharacteristic
123C2×C4×C43#12111yescharacteristic
124C2×C4×C43#12311yescharacteristic
125C2×C4×C43#12311yescharacteristic
126C2×C4×C43#12411yescharacteristic
127C2×C4×C43C2×SD1611yescharacteristic
128C2×C4×C43#13511yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C2×Dic43—41no—
132C2×Dic43—41no—
133Dic86—81no—
134Dic86—81no—
135C8×C43—81no—
136C43⋊C8—42no—
137C43⋊C8—42no—
138C43⋊C8—81no—
139#10470—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43#39411yescharacteristic
143C22×C43#46511yescharacteristic
144C22×C43#47011yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—42no—
150C4×C43—81no—
151C4×C43—161no—
152C4×C43#44811yescharacteristic
153C4×C43#45211yescharacteristic
154C4×C43#48311yescharacteristic
155C4×C43#48511yescharacteristic
156Dic43—81no—
157Dic43—81no—
158#3078—431no—
159#1805D4311yescharacteristic
160#1570—431no—
161#1542—431no—
162#1518—431no—
163#1461—431no—
164#1286—431no—
165C2×C43—21no—
166C2×C43—21no—
167C2×C43#203511yescharacteristic
168C2×C43#204911yescharacteristic
169C2×C43#205311yescharacteristic
170#533—431no—
171C2×C4×Q8C2×D4311yescharacteristic
172#479—862no—
173#477—861no—
174#475—861no—
175#431—431no—
176#431—431no—
177#428—861no—
178#423—431no—
179C2×C4⋊C8C2×D4311yescharacteristic
180#419—861no—
181C2×#103—21no—
182#382C2×D4311yescharacteristic
183#340—21no—
184#334—862no—
185#333—861no—
186#332—861no—
187#328—862no—
188#324—862no—
189C43#1047011yescharacteristic, complemented, Sylow
190C22×Q8C22⋊D4311yescharacteristic
191C2×M16—861no—
192C22×C8—21no—
193C4⋊Q8—431no—
194C4⋊Q8—431no—
195#125—861no—
196C22⋊Q8—861no—
197C22⋊Q8—861no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—861no—
203C4×Q8—861no—
204#117—861no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C22⋊D4311yescharacteristic
208C2×C42—21no—
209C2×C42C22×D4311yescharacteristic
210#107—862no—
211#106—862no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—432no—
215C4⋊C8—861no—
216C4⋊C8—861no—
217C4⋊C8—861no—
218#103—42no—
219#103—862no—
220#103—862no—
221C22⋊C8—432no—
222C22⋊C8—861no—
223C4×C8—861no—
224C4×C8—861no—
225#95—21no—
226#95—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—861no—
233C2×Q8—861no—
234C2×Q8#1062188312yes—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4D4×D4311yescharacteristic
239C22×C4#1062190011yescharacteristic
240C22×C4C2×C22⋊D4311yescharacteristic
241M16—1721no—
242M16—1721no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—862no—
247C2×C8—862no—
248C2×C8—1721no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C22⋊C4—1721no—
262C42—41no—
263C42—41no—
264C42—1721no—
265C42#1062189811yescharacteristic
266C42#1062189811yescharacteristic
267C42D4×D4311yescharacteristic
268C42D4×D4311yescharacteristic
269C23#1306329711yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274Q8—3441no—
275Q8—3441no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4#1306329311yescharacteristic
289C2×C4#1306329811yescharacteristic
290C2×C4#1306329811yescharacteristic
291C2×C4#1306330711yescharacteristic
292C2×C4#1306330811yescharacteristic
293C2×C4#1306331111yescharacteristic
294C2×C4C2×#1062188311yescharacteristic
295C2×C4#1306334511yescharacteristic
296C2×C4#1306335511yescharacteristic
297C2×C4#1306335611yescharacteristic
298C8—81no—
299C8—3441no—
300C8—1722no—
301C8—1722no—
302C22—21no—
303C22—21no—
304C22#1458281411yescharacteristic
305C22#1458312611yescharacteristic
306C22#1458315511yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—161no—
314C4—3441no—
315C4—3441no—
316C4#1458303711yescharacteristic
317C4#1458305911yescharacteristic
318C4#1458322911yescharacteristic
319C4#1458324011yescharacteristic
320C2—21no—
321C2—21no—
322C2#1913579111yescharacteristic
323C2#1913587311yescharacteristic
324C2#1913589911yescharacteristic
subgroupG/H
centerC22#14582814
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1805C2
socleC22×C43#394
prime radicalC23×C43#121
hypercenter#1805D43
hypocenterC43#10470
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
189. C43#10470semidirect

Maximal subgroups

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

subgroupindex
#191444002
#191333652
#191332532
#191331582
#191329192
#191324532
C43×#18052
#1047043