Finite Group Databasebeta

← #24999307

Subgroups — #24999307

Order 11008.

588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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#19145743C211yesmaximal, characteristic
2#19145540C211yesmaximal, characteristic
3#19142993C211yesmaximal, characteristic
4#19133281C211yesmaximal, characteristic
5#19133277C211yesmaximal, characteristic
6#19132428C211yesmaximal, characteristic
7C43×#1994C211yesmaximal, characteristic
8C2×#13063325—22no—
9C2×#13063325C2211yescharacteristic
10C2×#13063325C2211yescharacteristic
11#14583302—21no—
12#14583278—21no—
13#14583251—21no—
14#14583249—21no—
15#14583232—22no—
16#14583194—22no—
17#14583109—22no—
18#14583054—22no—
19#14582952C2211yescharacteristic
20#14582952C2211yescharacteristic
21#14582769—22no—
22#14582769—22no—
23#14582647—22no—
24#14582644—22no—
25C43×#533C2211yescharacteristic
26C43×#423C2211yescharacteristic
27C43×C43C2211yescharacteristic
28C43×#339—22no—
29C22×Dic86—21no—
30C22×Dic86D412yes—
31C2×#10621885—24no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325—21no—
38#13063325—21no—
39#13063325—21no—
40#13063325—48no—
41C2×C4⋊Dic43—28no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43D412yes—
46#13063258—24no—
47C4⋊(C43⋊C8)D412yes—
48C4⋊(C43⋊C8)D412yes—
49#13063249—24no—
50#13063248—24no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C4×C43⋊C8—21no—
54C4×C43⋊C8—21no—
55C2×M16×C43—21no—
56C4⋊Q8×C43D411yescharacteristic
57C4⋊Q8×C43D411yescharacteristic
58#125×C43—21no—
59C22⋊Q8×C43—21no—
60C22⋊Q8×C43—21no—
61C4×Q8×C43—21no—
62C4×Q8×C43—21no—
63#117×C43—21no—
64C2×C42×C43—21no—
65C2×C42×C43—21no—
66C2×C42×C43D412yes—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C22×C4×C43—22no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—22no—
77C22×Dic43—22no—
78C2×Dic86—22no—
79C2×Dic86—22no—
80C2×Dic86—44no—
81C2×Dic86—44no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84M16×C43—42no—
85C2×C8×C43—41no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C42×C43—24no—
94C42×C43—24no—
95C42×C43—22no—
96C42×C43—41no—
97C42×C43Q1614yescomplemented
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43#4111yescharacteristic
102#10621885—84no—
103C4⋊Dic43—22no—
104C4⋊Dic43—22no—
105C4⋊Dic43—416no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—22no—
114C23×C43#12011yescharacteristic
115Q8×C43—42no—
116Q8×C43—42no—
117C2×C4×C43—24no—
118C2×C4×C43—24no—
119C2×C4×C43—24no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12711yescharacteristic
130C2×C4×C43C2×Q1612yes—
131C2×C4×C43#13712yes—
132C2×Dic43—44no—
133C2×Dic43—44no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136Dic86—44no—
137Dic86—82no—
138Dic86—82no—
139Dic86—82no—
140C8×C43—81no—
141C43⋊C8—42no—
142C43⋊C8—42no—
143#10293—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43#39211yescharacteristic
147C22×C43#45112yes—
148C4×C43—28no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—81no—
152C4×C43—81no—
153C4×C43#45312yes—
154C4×C43#45612yes—
155C4×C43#46212yes—
156C4×C43#49411yescharacteristic
157C4×C43#49711yescharacteristic
158Dic43—82no—
159Dic43—82no—
160#3230—431no—
161#3209—431no—
162#2868—431no—
163#1994D4311yescharacteristic
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—431no—
174C2×C4⋊Q8—862no—
175#500—861no—
176#494—861no—
177#487—861no—
178#487—861no—
179#484—862no—
180#477—862no—
181#462—862no—
182#451—862no—
183#431—431no—
184#431—431no—
185#423C2×D4311yescharacteristic
186#384—862no—
187#384—862no—
188C43C2×D4311yescharacteristic
189#339—22no—
190#333—862no—
191#332—862no—
192C43#1029311yescharacteristic, complemented, Sylow
193C22×Q8—432no—
194C22×Q8—861no—
195C2×Q16—864no—
196C2×M16—21no—
197C4⋊Q8—861no—
198C4⋊Q8—861no—
199C4⋊Q8—861no—
200C4⋊Q8—861no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8—861no—
204C4⋊Q8—861no—
205C4⋊Q8—1728no—
206C4⋊Q8D17211yescharacteristic
207C4⋊Q8D17211yescharacteristic
208#125—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C4×Q8—21no—
212C4×Q8—21no—
213#117—21no—
214C2×C4⋊C4—432no—
215C2×C4⋊C4—868no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42C22⋊D4312yes—
222C2×C42C22×D4311yescharacteristic
223#107—864no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—432no—
227C4⋊C8—432no—
228#103—864no—
229#103—864no—
230C22⋊C8—861no—
231C22⋊C8—861no—
232C4×C8—861no—
233C4×C8—861no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—862no—
237C2×Q8—862no—
238C2×Q8—1724no—
239C2×Q8—1724no—
240C2×Q8—1721no—
241C2×Q8—1721no—
242C22×C4—22no—
243C22×C4—862no—
244C22×C4—862no—
245C22×C4D4×D4311yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248Q16—3444no—
249M16—42no—
250C2×C8—41no—
251C2×C8—862no—
252C2×C8—862no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—862no—
260C4⋊C4—862no—
261C4⋊C4—17216no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C22⋊C4—41no—
269C42—24no—
270C42—24no—
271C42—22no—
272C42—41no—
273C42#1062188514yescomplemented
274C42C2×D17211yescharacteristic
275C42#1062189811yescharacteristic
276C42D4×D4311yescharacteristic
277C42D4×D4311yescharacteristic
278C23#1306329311yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—3442no—
282Q8—3442no—
283Q8—3442no—
284Q8—1724no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—1724no—
293C2×C4—1724no—
294C2×C4—1722no—
295C2×C4—1722no—
296C2×C4#1306329511yescharacteristic
297C2×C4#1306329511yescharacteristic
298C2×C4#1306329811yescharacteristic
299C2×C4#1306329811yescharacteristic
300C2×C4#1306329911yescharacteristic
301C2×C4#1306332111yescharacteristic
302C2×C4C2×#1062188512yes—
303C2×C4#1306335512yes—
304C8—81no—
305C8—1722no—
306C8—1722no—
307C22—21no—
308C22—21no—
309C22#1458280811yescharacteristic
310C22#1458305412yes—
311C4—28no—
312C4—21no—
313C4—21no—
314C4—81no—
315C4—81no—
316C4—3442no—
317C4—3442no—
318C4#1458306812yes—
319C4#1458308312yes—
320C4#1458310912yes—
321C4#1458327811yescharacteristic
322C4#1458329411yescharacteristic
323C2—22no—
324C2#1913560911yescharacteristic
325C2#1913563011yescharacteristic
326C2#1913569411yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1994C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1994D43
hypocenterC43#10293
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
97. C42×C43Q16semidirect
192. C43#10293semidirect
273. C42#10621885semidirect

Maximal subgroups

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

subgroupindex
#191457432
#191455402
#191429932
#191332812
#191332772
#191324282
C43×#19942
#1029343