Finite Group Databasebeta

← #24998153

Subgroups — #24998153

Order 11008.

454 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 89 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#19145986C211yesmaximal, characteristic
2#19145739C211yesmaximal, characteristic
3#19135585C211yesmaximal, characteristic
4#19133189C211yesmaximal, characteristic
5#19133016C211yesmaximal, characteristic
6#19132485C211yesmaximal, characteristic
7C43×#3165C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583295—21no—
10#14583251—21no—
11#14583229—22no—
12#14583184—21no—
13#14583181—22no—
14#14583181—21no—
15#14583155—22no—
16#14583109—21no—
17#14583106—21no—
18#14582952C2211yescharacteristic
19#14582923C2211yescharacteristic
20C4×#10621877C2211yescharacteristic
21#14582668—22no—
22#14582640—22no—
23Q8⋊(C43⋊C8)—22no—
24C43×#533C2211yescharacteristic
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#501—22no—
27C43×#500—21no—
28C43×#498—21no—
29C43×#428—22no—
30C4×M16×C43C2211yescharacteristic
31C2×#10621885—22no—
32C2×#10621877—21no—
33C2×#10621877D412yes—
34#13063325D411yescharacteristic
35#13063325D411yescharacteristic
36#13063317—21no—
37#13063304—21no—
38#13063304—21no—
39C4×Dic86—21no—
40C4×Dic86—21no—
41#13063284—21no—
42#13063256—22no—
43#13063256—24no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)D412yes—
47#13063249—22no—
48#13063248—22no—
49#13063248—24no—
50C22⋊(C43⋊C8)—21no—
51#13063236—21no—
52C4×C43⋊C8—21no—
53C4×C43⋊C8—21no—
54C22×Q8×C43—21no—
55C2×M16×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43D411yescharacteristic
61C4⋊Q8×C43D411yescharacteristic
62#125×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67#117×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43D412yes—
70C2×C42×C43C2311yescharacteristic
71#107×C43—24no—
72#106×C43—24no—
73#97×C43D412yes—
74C4×C8×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C2×Q8×C43—82no—
80C22×C4×C43—22no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C2×Dic86—21no—
85C2×Dic86—21no—
86M16×C43—24no—
87C2×C8×C43—22no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C42×C43—41no—
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C22⋊Dic43—41no—
105#10621885—82no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112C4×Dic43—41no—
113#10621877—22no—
114#10621877—41no—
115#10621877—42no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8—22no—
118C2×C43⋊C8—41no—
119C23×C43#12111yescharacteristic
120Q8×C43—41no—
121Q8×C43—41no—
122Q8×C43—42no—
123Q8×C43—82no—
124Q8×C43—82no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—82no—
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12011yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12711yescharacteristic
139C2×Dic43—41no—
140C2×Dic43—41no—
141Dic86—41no—
142Dic86—41no—
143Dic86—42no—
144C8×C43—24no—
145C43⋊C8—42no—
146C43⋊C8—42no—
147C43⋊C8—42no—
148#10119—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43#39211yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—81no—
157C4×C43—82no—
158C4×C43—81no—
159C4×C43#45511yescharacteristic
160C4×C43#45611yescharacteristic
161C4×C43#45612yes—
162C4×C43#47112yes—
163Dic43—81no—
164Dic43—81no—
165#3255—431no—
166#3229—431no—
167#3165D4311yescharacteristic
168#1997—431no—
169#1526—431no—
170#1485—431no—
171#1299—431no—
172C2×C43—41no—
173C2×C43#200511yescharacteristic
174C2×C43#200711yescharacteristic
175C2×C43#201911yescharacteristic
176#533—431no—
177#533C2×D4311yescharacteristic
178C2×C4⋊Q8C2×D4311yescharacteristic
179#501—22no—
180#500—21no—
181#498—21no—
182#498—861no—
183#487—861no—
184#483—862no—
185#475—862no—
186#475—861no—
187#475—861no—
188#470—862no—
189#462—861no—
190#462—861no—
191#431—431no—
192#428—22no—
193#423—431no—
194C4×M16—431no—
195C4×M16C2×D4311yescharacteristic
196#343—862no—
197#330—862no—
198Q8⋊C8—862no—
199C43#1011911yescharacteristic, complemented, Sylow
200C22×Q8—21no—
201C2×Q16—862no—
202C2×M16—21no—
203C2×M16—432no—
204C2×M16—861no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—431no—
210C4⋊Q8—431no—
211C4⋊Q8C22⋊D4311yescharacteristic
212C4⋊Q8C22⋊D4311yescharacteristic
213#125—21no—
214#125—861no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—861no—
218C22⋊Q8—861no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—861no—
222C4×Q8—861no—
223#117—21no—
224#117—861no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D4312yes—
227C2×C42C22×D4311yescharacteristic
228#107—24no—
229#106—24no—
230#106—862no—
231#106—864no—
232C4⋊C8—432no—
233C4⋊C8—861no—
234C4⋊C8—861no—
235#103—862no—
236#103—864no—
237#103—862no—
238C22⋊C8—861no—
239#97—861no—
240#97C22⋊D4312yes—
241C4×C8—21no—
242C4×C8—861no—
243C4×C8—861no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—82no—
249C2×Q8—861no—
250C2×Q8—861no—
251C22×C4—22no—
252C22×C4D4×D4311yescharacteristic
253C22×C4#1062190011yescharacteristic
254C22×C4C2×C22⋊D4311yescharacteristic
255Q16—3442no—
256M16—24no—
257M16—862no—
258M16—1721no—
259M16—1722no—
260C2×C8—22no—
261C2×C8—862no—
262C2×C8—862no—
263C2×C8—1721no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C22⋊C4—41no—
281C22⋊C4—1721no—
282C42—41no—
283C42—1721no—
284C42D4×D4311yescharacteristic
285C42D4×D4311yescharacteristic
286C42C2×C22⋊D4311yescharacteristic
287C42C2×C22⋊D4311yescharacteristic
288C23#1306329711yescharacteristic
289Q8—41no—
290Q8—41no—
291Q8—42no—
292Q8—82no—
293Q8—82no—
294Q8—1721no—
295Q8—1721no—
296Q8—1722no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4#1306329311yescharacteristic
308C2×C4#1306329311yescharacteristic
309C2×C4#1306329411yescharacteristic
310C2×C4#1306329611yescharacteristic
311C2×C4#1306329711yescharacteristic
312C2×C4#1306332111yescharacteristic
313C8—24no—
314C8—1722no—
315C8—1722no—
316C8—1722no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22#1458280711yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—82no—
326C4—81no—
327C4—3441no—
328C4—3441no—
329C4#1458307511yescharacteristic
330C4#1458308011yescharacteristic
331C4#1458308112yes—
332C4#1458316012yes—
333C2—41no—
334C2#1913563111yescharacteristic
335C2#1913564011yescharacteristic
336C2#1913570911yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3165C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#3165D43
hypocenterC43#10119
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
199. C43#10119semidirect

Maximal subgroups

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

subgroupindex
#191459862
#191457392
#191355852
#191331892
#191330162
#191324852
C43×#31652
#1011943