Finite Group Databasebeta

← #24999306

Subgroups — #24999306

Order 11008.

588 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 109 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#19145540C211yesmaximal, characteristic
2#19142991C211yesmaximal, characteristic
3#19135573C211yesmaximal, characteristic
4#19133280C211yesmaximal, characteristic
5#19133275C211yesmaximal, characteristic
6#19132427C211yesmaximal, characteristic
7C43×#3230C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×#13063323—22no—
10#14583278—21no—
11#14583251—21no—
12#14583109—22no—
13#14583054—22no—
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16#14582768—22no—
17#14582768—22no—
18C42×Dic43C2211yescharacteristic
19#14582658—22no—
20#14582647—22no—
21#14582645—22no—
22C43×#533C2211yescharacteristic
23C2×C4⋊Q8×C43C2211yescharacteristic
24C43×#500—21no—
25C43×#487—21no—
26C43×#484—22no—
27C43×#477—22no—
28C43×#431C2211yescharacteristic
29C22×Dic86D412yes—
30C2×#10621885—24no—
31C2×#10621877—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063323—48no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×Dic43⋊C4—28no—
40C2×C4×Dic43—21no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43D412yes—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)D412yes—
46#13063248—24no—
47C22⋊(C43⋊C8)—21no—
48C4×C43⋊C8—21no—
49C22×Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43D411yescharacteristic
55C4⋊Q8×C43D411yescharacteristic
56#125×C43—21no—
57C22⋊Q8×C43—21no—
58C22⋊Q8×C43—21no—
59C4×Q8×C43—21no—
60C4×Q8×C43—21no—
61#117×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43D412yes—
64C2×C42×C43C2311yescharacteristic
65#107×C43—24no—
66C4⋊C8×C43D412yes—
67#103×C43—24no—
68C22⋊C8×C43—21no—
69C4×C8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—44no—
73C2×Q8×C43—41no—
74C2×Q8×C43—41no—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×Dic43—22no—
80C22×Dic43—22no—
81C2×Dic86—22no—
82C2×Dic86—22no—
83C2×Dic86—44no—
84C2×C8×C43—22no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C42×C43—41no—
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43#4111yescharacteristic
101#10621885—84no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104C4⋊Dic43—41no—
105C4⋊Dic43—41no—
106Dic43⋊C4—416no—
107C4×Dic43—24no—
108C4×Dic43—24no—
109C4×Dic43—22no—
110C4×Dic43Q1614yescomplemented
111#10621877—42no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—41no—
114C23×C43#12011yescharacteristic
115Q8×C43—42no—
116Q8×C43—42no—
117Q8×C43—82no—
118Q8×C43—82no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—44no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43#12011yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12711yescharacteristic
131C2×C4×C43C2×Q1612yes—
132C2×C4×C43#13712yes—
133C2×Dic43—24no—
134C2×Dic43—24no—
135C2×Dic43—24no—
136C2×Dic43—44no—
137C2×Dic43—42no—
138Dic86—44no—
139Dic86—82no—
140C8×C43—42no—
141C43⋊C8—42no—
142C43⋊C8—81no—
143#10293—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43#39211yescharacteristic
147C22×C43#45112yes—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—82no—
151C4×C43—81no—
152C4×C43—81no—
153C4×C43#45312yes—
154C4×C43#45612yes—
155C4×C43#46212yes—
156C4×C43#49411yescharacteristic
157C4×C43#49711yescharacteristic
158Dic43—28no—
159Dic43—82no—
160#3230D4311yescharacteristic
161#3209—431no—
162#2868—431no—
163#1994—431no—
164#1549—431no—
165#1548—431no—
166#1276—431no—
167C2×C43—22no—
168C2×C43#200211yescharacteristic
169C2×C43#200511yescharacteristic
170C2×C43#201611yescharacteristic
171#533C2×D4311yescharacteristic
172C2×C4⋊Q8—431no—
173C2×C4⋊Q8—862no—
174C2×C4⋊Q8C2×D4311yescharacteristic
175#500—21no—
176#494—861no—
177#487—21no—
178#487—861no—
179#484—22no—
180#477—22no—
181#462—862no—
182#451—862no—
183#431—431no—
184#431C2×D4311yescharacteristic
185#423—431no—
186#384—862no—
187#384—862no—
188C43—431no—
189#339—862no—
190#333—862no—
191#332—862no—
192C43#1029311yescharacteristic, complemented, Sylow
193C22×Q8—21no—
194C22×Q8—432no—
195C2×Q16—864no—
196C2×M16—861no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8—861no—
204C4⋊Q8—861no—
205C4⋊Q8—1728no—
206C4⋊Q8C22⋊D4311yescharacteristic
207C4⋊Q8C22⋊D4311yescharacteristic
208#125—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C4×Q8—21no—
212C4×Q8—21no—
213#117—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—868no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4C22⋊D4312yes—
219C2×C42—432no—
220C2×C42—861no—
221C2×C42—861no—
222C2×C42C22×D4311yescharacteristic
223#107—24no—
224C4⋊C8—432no—
225C4⋊C8—861no—
226C4⋊C8—861no—
227C4⋊C8C22⋊D4312yes—
228#103—24no—
229#103—864no—
230C22⋊C8—21no—
231C22⋊C8—861no—
232C4×C8—21no—
233C4×C8—861no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—44no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—862no—
240C2×Q8—862no—
241C2×Q8—1724no—
242C22×C4—22no—
243C22×C4—862no—
244C22×C4—862no—
245C22×C4D4×D4311yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248Q16—3444no—
249M16—1722no—
250C2×C8—22no—
251C2×C8—862no—
252C2×C8—1721no—
253C4⋊C4—21no—
254C4⋊C4—22no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—17216no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C22⋊C4—41no—
269C42—41no—
270C42—434no—
271C42—864no—
272C42—864no—
273C42—862no—
274C42D4×D4311yescharacteristic
275C42#1062190011yescharacteristic
276C42C2×C22⋊D4311yescharacteristic
277C42C2×C22⋊D4311yescharacteristic
278C23#1306329311yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—82no—
282Q8—82no—
283Q8—3442no—
284Q8—1724no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—44no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—864no—
292C2×C4—864no—
293C2×C4—864no—
294C2×C4—1724no—
295C2×C4—1722no—
296C2×C4#1306329311yescharacteristic
297C2×C4#1306329411yescharacteristic
298C2×C4#1306329611yescharacteristic
299C2×C4#1306329711yescharacteristic
300C2×C4#1306329711yescharacteristic
301C2×C4#1306332111yescharacteristic
302C2×C4Q16×D4312yes—
303C2×C4#1306335712yes—
304C8—42no—
305C8—3441no—
306C8—1722no—
307C22—21no—
308C22—21no—
309C22#1458280711yescharacteristic
310C22#1458305312yes—
311C4—21no—
312C4—21no—
313C4—82no—
314C4—81no—
315C4—81no—
316C4—868no—
317C4—3442no—
318C4#1458306512yes—
319C4#1458308212yes—
320C4#1458310712yes—
321C4#1458327711yescharacteristic
322C4#1458329211yescharacteristic
323C2—22no—
324C2#1913560711yescharacteristic
325C2#1913562911yescharacteristic
326C2#1913569311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3230C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#3230D43
hypocenterC43#10293
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
110. C4×Dic43Q16semidirect
192. C43#10293semidirect

Maximal subgroups

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

subgroupindex
#191455402
#191429912
#191355732
#191332802
#191332752
#191324272
C43×#32302
#1029343