Finite Group Databasebeta

← #25013423

Subgroups — #25013423

Order 11008.

472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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#19137769C211yesmaximal, characteristic
2#19134999C211yesmaximal, characteristic
3#19134812C212yesmaximal, complemented
4#19132721C212yesmaximal, complemented
5C2×C43×#355C211yesmaximal, characteristic
6#14583377C2211yescharacteristic
7#14582941—22no—
8#14582904—21no—
9C2×#13063244C2211yescharacteristic
10#14582806C2212yes—
11#14582792—22no—
12#14582779—21no—
13#14582774—22no—
14#14582765—21no—
15#14582660—22no—
16#14582659—21no—
17C2×#124×C43C2211yescharacteristic
18C2×#101×C43C2212yes—
19C43×#355C414yescomplemented
20C23×Dic43—21no—
21C2×#10621877—21no—
22Q8×Dic43—41no—
23Q8×Dic43—41no—
24#13063284—21no—
25#13063284—22no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43D412yes—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—22no—
31C2×C4×Dic43D412yes—
32#13063259—42no—
33#13063257—42no—
34#13063246—41no—
35#13063246—41no—
36#13063244—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C22×Q8×C43C2311yescharacteristic
41C22×D4×C43D411yescharacteristic
42C2×M16×C43—22no—
43#124×C43—22no—
44#124×C43C2×C412yes—
45#124×C43Q812yes—
46C2×C22⋊C4×C43—22no—
47C2×C42×C43D411yescharacteristic
48#101×C43—22no—
49#101×C43C2×C414yescomplemented
50C24×C43—21no—
51C2×Q8×C43—41no—
52C2×Q8×C43—41no—
53C2×Q8×C43C22×C411yescharacteristic
54C2×Q8×C43C2×Q811yescharacteristic
55C2×Q8×C43#4112yes—
56C2×D4×C43—21no—
57C2×D4×C43—41no—
58C2×D4×C43—41no—
59C2×D4×C43C4⋊C412yes—
60C22×C4×C43—21no—
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D412yes—
63C22×Dic43—22no—
64C22×Dic43—22no—
65C22×Dic43—82no—
66C22×Dic43—81no—
67M16×C43—24no—
68M16×C43—42no—
69C2×C8×C43—42no—
70C22⋊C4×C43—24no—
71C22⋊C4×C43—24no—
72C42×C43—21no—
73C42×C43C4⋊C412yes—
74C22⋊Dic43—41no—
75C22⋊Dic43—82no—
76C22⋊Dic43—81no—
77C4⋊Dic43—21no—
78C4⋊Dic43—21no—
79C4⋊Dic43—22no—
80C4⋊Dic43—22no—
81C4⋊Dic43—42no—
82C4⋊Dic43—81no—
83C4⋊Dic43—81no—
84C4×Dic43—41no—
85C4×Dic43—42no—
86C4×Dic43—42no—
87#10621877—41no—
88#10621877—41no—
89C2×C43⋊C8—41no—
90C23×C43—22no—
91C23×C43—42no—
92C23×C43—42no—
93C23×C43—41no—
94C23×C43—41no—
95C23×C43#12011yescharacteristic
96Q8×C43—41no—
97Q8×C43—41no—
98Q8×C43—42no—
99D4×C43—42no—
100D4×C43—81no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43C2×C4⋊C411yescharacteristic
109C2×C4×C43C4×D412yes—
110C2×C4×C43C22⋊Q812yes—
111C2×C4×C43#12311yescharacteristic
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116C2×Dic43—41no—
117C2×Dic43—41no—
118C2×Dic43—42no—
119C2×Dic43—42no—
120C2×Dic43—84no—
121C8×C43—44no—
122C43⋊C8—81no—
123#12970—431nomaximal, Sylow
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—44no—
127C22×C43—42no—
128C22×C43—82no—
129C22×C43—81no—
130C22×C43—81no—
131C22×C43#38511yescharacteristic
132C22×C43B(4,𝔽2)11yescharacteristic
133C22×C43#45811yescharacteristic
134C4×C43—21no—
135C4×C43—22no—
136C4×C43—21no—
137C4×C43—22no—
138C4×C43—42no—
139Dic43—82no—
140Dic43—81no—
141Dic43—82no—
142Dic43—81no—
143#2379—431no—
144C2×#355D4311yescharacteristic
145#1888—431no—
146#1857—432no—
147#1394—432no—
148C2×C43—21no—
149C2×C43—21no—
150C2×C43—82no—
151C2×C43#186711yescharacteristic
152C2×C43#220211yescharacteristic
153C2×C43#220311yescharacteristic
154C2×#124C2×D4311yescharacteristic
155#519—431no—
156#428—862no—
157#418—861no—
158C2×#101—431no—
159C2×#101C2×D4312yes—
160#391—432no—
161#388—862no—
162#386—861no—
163#385—862no—
164#382—861no—
165#355Dic4314yescomplemented
166#339—862no—
167#339—861no—
168C43#1297011yescharacteristic, complemented, Sylow
169C22×Q8C22×D4311yescharacteristic
170C22×D4D17211yescharacteristic
171C23×C4—861no—
172C2×M16—22no—
173C2×M16—861no—
174#124—22no—
175#124Dic8612yes—
176#124C2×Dic4312yes—
177C4×Q8—1721no—
178C4×Q8—1721no—
179#117—861no—
180#117—862no—
181C2×C4⋊C4—432no—
182C2×C4⋊C4—861no—
183C2×C4⋊C4—861no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—862no—
186C2×C22⋊C4—861no—
187C2×C42—432no—
188C2×C42D17211yescharacteristic
189#107—1722no—
190#106—1722no—
191#102—1721no—
192#102—1721no—
193#101—22no—
194#101—862no—
195#101C2×Dic4314yescomplemented
196#95—862no—
197#95—862no—
198#95—862no—
199C24—21no—
200C2×Q8—41no—
201C2×Q8—41no—
202C2×Q8C2×Dic8611yescharacteristic
203C2×Q8#1062190012yes—
204C2×Q8C22×Dic4311yescharacteristic
205C2×D4—21no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4C4⋊Dic4312yes—
209C22×C4—21no—
210C22×C4—862no—
211C22×C4—862no—
212C22×C4—3442no—
213C22×C4—3441no—
214C22×C4C2×D17211yescharacteristic
215C22×C4D4×D4312yes—
216M16—24no—
217M16—42no—
218M16—1721no—
219M16—1721no—
220C2×C8—42no—
221C2×C8—1721no—
222C4⋊C4—861no—
223C4⋊C4—861no—
224C4⋊C4—862no—
225C4⋊C4—862no—
226C4⋊C4—3441no—
227C4⋊C4—3441no—
228C4⋊C4—1722no—
229C22⋊C4—24no—
230C22⋊C4—24no—
231C22⋊C4—3442no—
232C22⋊C4—3441no—
233C22⋊C4—1721no—
234C42—21no—
235C42—1722no—
236C42—1722no—
237C42—1721no—
238C42C4⋊Dic4312yes—
239C23—22no—
240C23—42no—
241C23—42no—
242C23—41no—
243C23—41no—
244C23#1306329511yescharacteristic
245Q8—41no—
246Q8—42no—
247Q8—41no—
248D4—42no—
249D4—81no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—3444no—
258C2×C4—1722no—
259C2×C4—1722no—
260C2×C4—1722no—
261C2×C4—1722no—
262C2×C4—1721no—
263C2×C4—1721no—
264C2×C4—1722no—
265C2×C4—1722no—
266C2×C4C2×C4⋊Dic4311yescharacteristic
267C2×C4D4×Dic4312yes—
268C2×C4#1306330212yes—
269C2×C4#1306330911yescharacteristic
270C8—44no—
271C8—3441no—
272C22—21no—
273C22—21no—
274C22—44no—
275C22—42no—
276C22—82no—
277C22—81no—
278C22—81no—
279C22#1458277411yescharacteristic
280C22#1458308711yescharacteristic
281C22#1458309011yescharacteristic
282C4—22no—
283C4—21no—
284C4—21no—
285C4—22no—
286C4—42no—
287C4—3442no—
288C4—3442no—
289C4—3441no—
290C4—3441no—
291C2—21no—
292C2—21no—
293C2—82no—
294C2#1913487811yescharacteristic
295C2#1913661311yescharacteristic
296C2#1913661811yescharacteristic
subgroupG/H
centerC22#14583087
commutatorC2×Q8×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC2×C43×#355C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
cosocleC22×Q8×C43C23
hypercenterC2×#355D43
hypocenterC43#12970
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
3. #19134812C2semidirect
4. #19132721C2semidirect
19. C43×#355C4semidirect
49. #101×C43C2×C4semidirect
165. #355Dic43semidirect
168. C43#12970semidirect
195. #101C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191377692
#191349992
#191348122
#191327212
C2×C43×#3552
#1297043