Finite Group Databasebeta

← #24998014

Subgroups — #24998014

Order 11008.

474 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144977C211yesmaximal, characteristic
2#19140716C211yesmaximal, characteristic
3#19133320C211yesmaximal, characteristic
4#19133197C211yesmaximal, characteristic
5#19133107C211yesmaximal, characteristic
6#19132487C211yesmaximal, characteristic
7C43×#3236C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583269—22no—
10#14583251—21no—
11#14583251—21no—
12#14582956C2211yescharacteristic
13#14582907—22no—
14C4×#10621877C2211yescharacteristic
15#14582829—22no—
16#14582819—22no—
17#14582768—21no—
18#14582764—21no—
19#14582745C2211yescharacteristic
20#14582647—22no—
21#14582641—22no—
22#14582636—22no—
23C43×#533C2211yescharacteristic
24C2×#125×C43C2211yescharacteristic
25C43×#501—21no—
26C43×#491—21no—
27C43×#484—21no—
28C43×#483—21no—
29C43×#479—22no—
30C43×#432C2211yescharacteristic
31C22×Dic86D412yes—
32C2×#10621877—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×Dic43⋊C4—24no—
40C2×C4×Dic43—21no—
41C4⋊(C43⋊C8)—21no—
42#13063248—24no—
43#13063248—24no—
44C22⋊(C43⋊C8)—21no—
45#13063236—21no—
46#13063236D412yes—
47C4×C43⋊C8—21no—
48C43⋊#95—24no—
49C43⋊#95—21no—
50C43⋊#95D412yes—
51C4⋊Q8×C43D411yescharacteristic
52C4⋊Q8×C43D411yescharacteristic
53#125×C43—21no—
54#125×C43—21no—
55#125×C43—21no—
56#125×C43—21no—
57#125×C43—21no—
58C22⋊Q8×C43—21no—
59C22⋊Q8×C43—21no—
60C4×Q8×C43—21no—
61C4×Q8×C43—21no—
62#117×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C42×C43C2311yescharacteristic
68#107×C43—22no—
69#106×C43—22no—
70C4⋊C8×C43D412yes—
71#103×C43—22no—
72#103×C43—22no—
73C22⋊C8×C43—21no—
74#97×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—22no—
83C22×Dic43—22no—
84C2×Dic86—22no—
85C2×Dic86—22no—
86C2×Dic86—44no—
87C2×C8×C43—22no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—41no—
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43#4111yescharacteristic
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112Dic43⋊C4—84no—
113C4×Dic43—24no—
114#10621877—42no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—41no—
117C23×C43#12011yescharacteristic
118Q8×C43—42no—
119Q8×C43—81no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
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—42no—
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12711yescharacteristic
135C2×Dic43—24no—
136C2×Dic43—42no—
137C2×Dic43—42no—
138C2×Dic43—42no—
139C2×Dic43—44no—
140Dic86—44no—
141Dic86—82no—
142C8×C43—42no—
143C43⋊C8—42no—
144C43⋊C8—81no—
145#10099—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43#39211yescharacteristic
149C22×C43#45512yes—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—81no—
156C4×C43—81no—
157C4×C43—81no—
158C4×C43—81no—
159C4×C43#45612yes—
160Dic43—44no—
161Dic43—82no—
162#3236D4311yescharacteristic
163#3139—431no—
164#2660—431no—
165#1558—431no—
166#1528—431no—
167#1506—431no—
168#1300—431no—
169C2×C43—22no—
170C2×C43#200411yescharacteristic
171C2×C43#200511yescharacteristic
172C2×C43#200911yescharacteristic
173#533C2×D4311yescharacteristic
174C2×C4⋊Q8—431no—
175C2×#125C2×D4311yescharacteristic
176#501—21no—
177#491—21no—
178#491—862no—
179#487—861no—
180#487—861no—
181#484—21no—
182#483—21no—
183#479—22no—
184#432—431no—
185#432C2×D4311yescharacteristic
186#419—862no—
187C4×M16—431no—
188#398—862no—
189#395—862no—
190#384—861no—
191#382—861no—
192#376—431no—
193#333—862no—
194#330—862no—
195#328—862no—
196C43#1009911yescharacteristic, complemented, Sylow
197C22×Q8—432no—
198C2×M16—861no—
199C4⋊Q8—861no—
200C4⋊Q8—861no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8C22⋊D4311yescharacteristic
204C4⋊Q8C22⋊D4311yescharacteristic
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209#125—21no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214#117—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—864no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4C22⋊D4311yescharacteristic
221C2×C4⋊C4C22⋊D4311yescharacteristic
222C2×C42—861no—
223C2×C42C22×D4311yescharacteristic
224#107—22no—
225#106—22no—
226C4⋊C8—861no—
227C4⋊C8C22⋊D4312yes—
228#103—22no—
229#103—22no—
230#103—864no—
231#103—864no—
232C22⋊C8—21no—
233C22⋊C8—861no—
234#97—21no—
235#97—432no—
236#97—861no—
237C4×C8—861no—
238#95—432no—
239#95—864no—
240#95—861no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—862no—
244C2×Q8—862no—
245C2×Q8—1724no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—862no—
249C22×C4—862no—
250C22×C4D4×D4311yescharacteristic
251C22×C4D4×D4311yescharacteristic
252C22×C4C2×C22⋊D4311yescharacteristic
253M16—1722no—
254C2×C8—22no—
255C2×C8—862no—
256C2×C8—1721no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—3444no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4—1721no—
276C22⋊C4—41no—
277C42—41no—
278C42—864no—
279C42D4×D4311yescharacteristic
280C42#1062190011yescharacteristic
281C42C2×C22⋊D4311yescharacteristic
282C42C2×C22⋊D4311yescharacteristic
283C23#1306329311yescharacteristic
284Q8—42no—
285Q8—81no—
286Q8—3442no—
287Q8—1724no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—864no—
298C2×C4—1722no—
299C2×C4—1724no—
300C2×C4—1722no—
301C2×C4—1722no—
302C2×C4#1306329311yescharacteristic
303C2×C4#1306329411yescharacteristic
304C2×C4#1306329611yescharacteristic
305C2×C4#1306329711yescharacteristic
306C2×C4#1306329711yescharacteristic
307C2×C4#1306332111yescharacteristic
308C8—42no—
309C8—3441no—
310C8—1722no—
311C22—21no—
312C22—21no—
313C22#1458280711yescharacteristic
314C22#1458307512yes—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—81no—
324C4—3442no—
325C4—1724no—
326C4#1458308212yes—
327C2—22no—
328C2#1913562111yescharacteristic
329C2#1913562911yescharacteristic
330C2#1913565211yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3236C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#3236D43
hypocenterC43#10099
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
196. C43#10099semidirect

Maximal subgroups

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

subgroupindex
#191449772
#191407162
#191333202
#191331972
#191331072
#191324872
C43×#32362
#1009943