Finite Group Databasebeta

← #24998159

Subgroups — #24998159

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#19145989C211yesmaximal, characteristic
2#19145741C211yesmaximal, characteristic
3#19145141C211yesmaximal, characteristic
4#19135583C211yesmaximal, characteristic
5#19133189C211yesmaximal, characteristic
6#19133015C211yesmaximal, characteristic
7C43×#1299C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583456C2211yescharacteristic
10C2×#13063325C2211yescharacteristic
11#14583308—22no—
12#14583304—21no—
13#14583297—21no—
14#14583297—21no—
15#14583250—21no—
16#14583230—22no—
17#14583185—21no—
18#14583185—21no—
19#14583185—22no—
20#14583157—22no—
21#14583110—21no—
22#14583110—21no—
23#14582941—22no—
24C4×#10621877C2211yescharacteristic
25#14582667—22no—
26#14582640—22no—
27#14582629—22no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C4×M16×C43C2211yescharacteristic
31C22×Dic86—21no—
32C2×Dic172—22no—
33C2×#10621877—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325—21no—
38#13063325D411yescharacteristic
39#13063325D411yescharacteristic
40#13063325D411yescharacteristic
41#13063325D411yescharacteristic
42#13063317—21no—
43#13063317—21no—
44#13063304—21no—
45#13063304—21no—
46#13063304—21no—
47#13063304—21no—
48C4×Dic86—21no—
49C4×Dic86—21no—
50C4×Dic86—21no—
51C4×Dic86—21no—
52#13063284—21no—
53#13063284—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D412yes—
56#13063259—24no—
57#13063257—24no—
58#13063257—24no—
59#13063257—22no—
60#13063250—22no—
61#13063250—22no—
62#13063250—24no—
63#13063236—21no—
64C4×C43⋊C8—21no—
65C2×M16×C43—21no—
66C2×M16×C43D412yes—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43D412yes—
71C22⋊C8×C43—21no—
72#97×C43D412yes—
73C4×C8×C43—21no—
74C4×C8×C43—21no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×Dic43—22no—
79C2×Dic86—21no—
80C2×Dic86—21no—
81C2×Dic86—21no—
82C2×Dic86—21no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×Dic86—82no—
86M16×C43—24no—
87M16×C43—42no—
88C2×C8×C43—22no—
89C2×C8×C43—22no—
90C2×C8×C43—22no—
91C42×C43C2×D411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C22⋊Dic43—41no—
96C22⋊Dic43—41no—
97C4⋊Dic43—22no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—22no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113C4×Dic43—41no—
114C4×Dic43—41no—
115#10621877—22no—
116#10621877—41no—
117C2×C43⋊C8—41no—
118Dic172—82no—
119C23×C43#12111yescharacteristic
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43#12011yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12711yescharacteristic
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—42no—
135C2×Dic43—82no—
136Dic86—41no—
137Dic86—41no—
138Dic86—42no—
139Dic86—41no—
140Dic86—41no—
141Dic86—42no—
142Dic86—82no—
143Dic86—82no—
144C8×C43—24no—
145C8×C43—42no—
146C8×C43—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#45511yescharacteristic
157C4×C43#45612yes—
158C4×C43#45611yescharacteristic
159C4×C43#47112yes—
160Dic43—81no—
161Dic43—81no—
162Dic43—81no—
163Dic43—81no—
164Dic43—82no—
165#3255—431no—
166#3229—431no—
167#3165—431no—
168#1997—431no—
169#1526—431no—
170#1485—431no—
171#1299D4311yescharacteristic
172C2×C43—41no—
173C2×C43#200511yescharacteristic
174C2×C43#200711yescharacteristic
175C2×C43#201911yescharacteristic
176#533—431no—
177#533—431no—
178C2×C4⋊Q8—431no—
179#501—862no—
180#500—861no—
181#498—861no—
182#498—861no—
183#487—861no—
184#483—862no—
185#475—861no—
186#475—861no—
187#475—862no—
188#470—862no—
189#462—861no—
190#462—861no—
191#431C2×D4311yescharacteristic
192#428—862no—
193#423C2×D4311yescharacteristic
194C4×M16—431no—
195C4×M16C2×D4311yescharacteristic
196#343—862no—
197#330—862no—
198Q8⋊C8—862no—
199C43#1011911yescharacteristic, complemented, Sylow
200C22×Q8—861no—
201C2×Q16—862no—
202C2×M16—21no—
203C2×M16—861no—
204C2×M16D17212yes—
205C4⋊Q8—431no—
206C4⋊Q8—431no—
207C4⋊Q8—431no—
208C4⋊Q8—431no—
209C4⋊Q8—861no—
210C4⋊Q8—861no—
211C4⋊Q8—861no—
212C4⋊Q8—861no—
213#125—861no—
214#125—861no—
215C22⋊Q8—861no—
216C22⋊Q8—861no—
217C22⋊Q8—861no—
218C22⋊Q8—861no—
219C4×Q8—861no—
220C4×Q8—861no—
221C4×Q8—861no—
222C4×Q8—861no—
223#117—861no—
224#117—861no—
225C2×C4⋊C4—432no—
226C2×C4⋊C4—861no—
227C2×C42C22×D4311yescharacteristic
228#107—864no—
229#106—864no—
230#106—862no—
231#106—864no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8D17212yes—
235#103—862no—
236#103—862no—
237#103—864no—
238C22⋊C8—21no—
239#97—861no—
240#97D17212yes—
241C4×C8—21no—
242C4×C8—21no—
243C4×C8—861no—
244C2×Q8—861no—
245C2×Q8—861no—
246C2×Q8—861no—
247C2×Q8—861no—
248C2×Q8—3442no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C22×C4—862no—
252C22×C4C2×D17211yescharacteristic
253C22×C4D4×D4311yescharacteristic
254C22×C4#1062190211yescharacteristic
255Q16—3442no—
256M16—24no—
257M16—42no—
258M16—862no—
259M16—1721no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—1721no—
264C4⋊C4—862no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—862no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—1721no—
275C4⋊C4—1721no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C22⋊C4—1721no—
281C22⋊C4—1721no—
282C42—1721no—
283C42—1721no—
284C42C2×D17211yescharacteristic
285C42C2×D17211yescharacteristic
286C42D4×D4311yescharacteristic
287C42D4×D4311yescharacteristic
288C23#1306330011yescharacteristic
289Q8—3442no—
290Q8—3442no—
291Q8—1721no—
292Q8—1721no—
293Q8—1722no—
294Q8—1721no—
295Q8—1721no—
296Q8—1722no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—3442no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1722no—
307C2×C4#1306329511yescharacteristic
308C2×C4#1306329511yescharacteristic
309C2×C4#1306329511yescharacteristic
310C2×C4#1306330011yescharacteristic
311C2×C4#1306330011yescharacteristic
312C2×C4#1306332211yescharacteristic
313C8—24no—
314C8—42no—
315C8—42no—
316C8—1722no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22#1458280911yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—3441no—
325C4—3441no—
326C4—3441no—
327C4—3442no—
328C4—3441no—
329C4#1458307911yescharacteristic
330C4#1458308312yes—
331C4#1458308411yescharacteristic
332C4#1458316312yes—
333C2—41no—
334C2#1913563411yescharacteristic
335C2#1913564411yescharacteristic
336C2#1913571211yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1299C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#1299D43
hypocenterC43#10119
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1299

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
#191459892
#191457412
#191451412
#191355832
#191331892
#191330152
C43×#12992
#1011943