Finite Group Databasebeta

← #25000267

Subgroups — #25000267

Order 11008.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#14583191C211yesmaximal, characteristic
2#19134588C211yesmaximal, characteristic
3#19133370C211yesmaximal, characteristic
4#19133280C211yesmaximal, characteristic
5#19132989C211yesmaximal, characteristic
6#19132490C211yesmaximal, characteristic
7C43×#1548C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583191—22no—
10#14583191—22no—
11#14582952C2211yescharacteristic
12C2×#13063258—21no—
13#14582923C2211yescharacteristic
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15C2×#13063248—21no—
16C2×#13063243—21no—
17#14582667—21no—
18#14582652—22no—
19#14582645—22no—
20#14582629—22no—
21C2×C4⋊Q8×C43C2211yescharacteristic
22C43×#431C2211yescharacteristic
23C43×#423C2211yescharacteristic
24C43×#333—22no—
25C22×Dic86D411yescharacteristic
26C2×#10621877—21no—
27C22×C43⋊C8—21no—
28C4×Dic86—21no—
29C4×Dic86—21no—
30C4×Dic86—21no—
31C4×Dic86—21no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×C4×Dic43—21no—
35#13063258—24no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)D412yes—
41#13063248—24no—
42#13063243—42no—
43C22⋊(C43⋊C8)—21no—
44C4×C43⋊C8—21no—
45C22×Q8×C43—21no—
46C2×M16×C43—21no—
47C4⋊Q8×C43—21no—
48C4⋊Q8×C43—21no—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43D412yes—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C42×C43C2311yescharacteristic
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56C4⋊C8×C43D412yes—
57C22⋊C8×C43—21no—
58C4×C8×C43—21no—
59C2×Q8×C43—22no—
60C2×Q8×C43—41no—
61C2×Q8×C43—82no—
62C22×C4×C43—41no—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43#4111yescharacteristic
65C22×C4×C43#4111yescharacteristic
66C22×Dic43—21no—
67C22×Dic43—21no—
68C2×Dic86—21no—
69C2×Dic86—21no—
70C2×Dic86—21no—
71C2×Dic86—21no—
72C2×Dic86—21no—
73C2×Dic86Q1612yes—
74M16×C43—41no—
75M16×C43—41no—
76C2×C8×C43—22no—
77C2×C8×C43—41no—
78C4⋊C4×C43—22no—
79C4⋊C4×C43—22no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C42×C43C2×D411yescharacteristic
83C42×C43C2×D411yescharacteristic
84C42×C43C2×D411yescharacteristic
85C42×C43#4111yescharacteristic
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90C4×Dic43—41no—
91C4×Dic43—41no—
92#10621877—41no—
93#10621877—41no—
94C2×C43⋊C8—22no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C23×C43#12311yescharacteristic
100Q8×C43—82no—
101Q8×C43—82no—
102C2×C4×C43—22no—
103C2×C4×C43—41no—
104C2×C4×C43—42no—
105C2×C4×C43—82no—
106C2×C4×C43#12011yescharacteristic
107C2×C4×C43#12111yescharacteristic
108C2×C4×C43#12111yescharacteristic
109C2×C4×C43#12111yescharacteristic
110C2×C4×C43#12311yescharacteristic
111C2×C4×C43#12411yescharacteristic
112C2×C4×C43C2×Q1611yescharacteristic
113C2×C4×C43#13511yescharacteristic
114C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C43#13711yescharacteristic
116C2×Dic43—22no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—81no—
121Dic86—22no—
122Dic86—22no—
123Dic86—41no—
124Dic86—41no—
125C8×C43—42no—
126C8×C43—81no—
127C43⋊C8—42no—
128C43⋊C8—81no—
129C43⋊C8—81no—
130#10455—431nomaximal, Sylow
131C22×C43—21no—
132C22×C43—21no—
133C22×C43#39411yescharacteristic
134C22×C43#48411yescharacteristic
135C22×C43#48511yescharacteristic
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—21no—
139C4×C43—82no—
140C4×C43#44911yescharacteristic
141C4×C43#45111yescharacteristic
142C4×C43#46711yescharacteristic
143C4×C43#46811yescharacteristic
144C4×C43#47312yes—
145Dic43—42no—
146Dic43—81no—
147C2×#477—431no—
148#1801—431no—
149#1571—431no—
150#1549—431no—
151#1548D4311yescharacteristic
152#1479—431no—
153#1301—431no—
154C2×C43—21no—
155C2×C43—21no—
156C2×C43#203611yescharacteristic
157C2×C43#204711yescharacteristic
158C2×C43#204811yescharacteristic
159C2×C4⋊Q8C2×D4311yescharacteristic
160C2×C4×Q8—431no—
161#477—862no—
162#477—862no—
163#431—431no—
164#431C2×D4311yescharacteristic
165C2×#107—861no—
166#423—431no—
167#423C2×D4311yescharacteristic
168C2×C4⋊C8—431no—
169C2×#103—861no—
170C2×#101—861no—
171#343—861no—
172#335—862no—
173#333—22no—
174#332—862no—
175Q8⋊C8—862no—
176C43#1045511yescharacteristic, complemented, Sylow
177C22×Q8—21no—
178C22×Q8—431no—
179C2×M16—21no—
180C2×M16—861no—
181C22×C8—861no—
182C4⋊Q8—21no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8D17212yes—
186C4×Q8—861no—
187C4×Q8—861no—
188C4×Q8—861no—
189C4×Q8—861no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—861no—
194C2×C42—861no—
195C2×C42C22×D4311yescharacteristic
196#107—864no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—432no—
200C4⋊C8—861no—
201C4⋊C8—861no—
202C4⋊C8—861no—
203C4⋊C8—861no—
204C4⋊C8C22⋊D4312yes—
205#103—864no—
206#101—1722no—
207C22⋊C8—21no—
208C22⋊C8—861no—
209C4×C8—21no—
210C4×C8—861no—
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—82no—
214C2×Q8—432no—
215C2×Q8—861no—
216C2×Q8—861no—
217C2×Q8—861no—
218C2×Q8—861no—
219C2×Q8—861no—
220C22×C4—41no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4#1062189811yescharacteristic
224C22×C4D4×D4311yescharacteristic
225C22×C4#1062190011yescharacteristic
226M16—41no—
227M16—41no—
228M16—1721no—
229M16—1721no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—862no—
233C2×C8—1721no—
234C2×C8—1721no—
235C2×C8—1721no—
236C2×C8—1721no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4—1721no—
244C4⋊C4—1721no—
245C42—1721no—
246C42—1721no—
247C42C2×D17211yescharacteristic
248C42D4×D4311yescharacteristic
249C42#1062190011yescharacteristic
250C42C2×C22⋊D4311yescharacteristic
251C23#1306330711yescharacteristic
252Q8—82no—
253Q8—82no—
254Q8—862no—
255Q8—862no—
256Q8—1721no—
257Q8—1721no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—862no—
263C2×C4—3441no—
264C2×C4—1721no—
265C2×C4—1721no—
266C2×C4—1721no—
267C2×C4#1306329511yescharacteristic
268C2×C4#1306329611yescharacteristic
269C2×C4#1306329711yescharacteristic
270C2×C4#1306329911yescharacteristic
271C2×C4#1306330911yescharacteristic
272C2×C4#1306331111yescharacteristic
273C2×C4Q16×D4311yescharacteristic
274C2×C4#1306334811yescharacteristic
275C2×C4#1306335211yescharacteristic
276C2×C4#1306335411yescharacteristic
277C8—42no—
278C8—81no—
279C8—3441no—
280C8—3441no—
281C8—1722no—
282C22—21no—
283C22—21no—
284C22#1458281511yescharacteristic
285C22#1458323311yescharacteristic
286C22#1458323911yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—82no—
291C4—3441no—
292C4—1722no—
293C4#1458304711yescharacteristic
294C4#1458305611yescharacteristic
295C4#1458313711yescharacteristic
296C4#1458314211yescharacteristic
297C4#1458317212yes—
298C2—21no—
299C2—21no—
300C2#1913579711yescharacteristic
301C2#1913586211yescharacteristic
302C2#1913586711yescharacteristic
subgroupG/H
centerC22#14582815
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1548C2
socleC22×C43#394
prime radicalC23×C43#123
hypercenter#1548D43
hypocenterC43#10455
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
176. C43#10455semidirect

Maximal subgroups

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

subgroupindex
C2×#145831912
#191345882
#191333702
#191332802
#191329892
#191324902
C43×#15482
#1045543