Finite Group Databasebeta

← #24984830

Subgroups — #24984830

Order 11008.

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

normal subgroups only

This group has 658 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#391×D43C211yesmaximal, characteristic
2#19134356C212yesmaximal
3#19132421C211yesmaximal, characteristic, complemented
4#19132420C212yesmaximal, complemented
5C43×#1272C211yesmaximal, characteristic, complemented
6C22×Q8×D43C411yescharacteristic
7C2×C4⋊C4×D43C411yescharacteristic
8C2×C42×D43C2211yescharacteristic
9C2×(C2×D43)⋊C8—22no—
10C2×#13063235—22no—
11#14582806C411yescharacteristic
12#14582805C2211yescharacteristic
13#14582804C411yescharacteristic
14#14582803—22no—
15#95×D43—22no—
16#14582654C2212yes—
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C22×Dic86C2×C411yescharacteristic
21C2×Q8×D43—22no—
22C2×Q8×D43—22no—
23C2×Q8×D43—42no—
24C2×Q8×D43—42no—
25C22×C4×D43—21no—
26C22×C4×D43—21no—
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D412yes—
29C22×C43⋊C8—22no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C4⋊C4×D43—42no—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43D412yes—
35C42×D43—42no—
36(C2×D43)⋊C8—28no—
37#13063235—44no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C22×Q8×C43C2×C411yescharacteristic
42C22×C8×C43—22no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C42×C43C2311yescharacteristic
45#95×C43—22no—
46C23×D43C22⋊C411yescharacteristic
47C2×Q8×C43—21no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43M1612yes—
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43C22×C411yescharacteristic
54C22×C4×C43C2×D412yes—
55C22×Dic43—21no—
56C22×Dic43—21no—
57C22×Dic43C22⋊C412yes—
58C22×Dic43C22⋊C411yescharacteristic
59Q8×D43—48no—
60Q8×D43—48no—
61C2×C4×D43—21no—
62C2×C4×D43—21no—
63C2×C4×D43—22no—
64C2×C4×D43—24no—
65C2×C4×D43—22no—
66C2×C4×D43—22no—
67C2×C4×D43—22no—
68C2×C4×D43—24no—
69C2×C4×D43—42no—
70C2×C4×D43—42no—
71C2×C4×D43—42no—
72C2×C4×D43—42no—
73C2×C4×D43—44no—
74C2×Dic86—24no—
75C2×Dic86—21no—
76C2×Dic86—42no—
77C2×Dic86—42no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86M1612yes—
81C2×C8×C43—24no—
82C2×C8×C43—42no—
83C2×C8×C43—42no—
84C4⋊C4×C43—41no—
85C42×C43—41no—
86C4⋊Dic43—41no—
87Dic43⋊C4—42no—
88C4×Dic43—24no—
89C4×Dic43—41no—
90C2×C43⋊C8—24no—
91C2×C43⋊C8—42no—
92C2×C43⋊C8—42no—
93C23×C43C2×C22⋊C411yescharacteristic
94C22×D43—21no—
95C22×D43—21no—
96C22×D43—22no—
97C22×D43#10012yes—
98C22×D43#10414yes—
99Q8×C43—42no—
100Q8×C43—42no—
101C2×C4×C43—22no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—42no—
110C2×C4×C43C2×M1611yescharacteristic
111C2×C4×C43C2×M1611yescharacteristic
112C2×C4×C43#13712yes—
113C2×C4×C43#13712yes—
114C2×Dic43—21no—
115C2×Dic43—21no—
116C2×Dic43—22no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—22no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—42no—
124C2×Dic43#9912yes—
125C4×D43—24no—
126C4×D43—24no—
127C4×D43—44no—
128C4×D43—44no—
129C4×D43—48no—
130C4×D43—84no—
131Dic86—48no—
132Dic86—42no—
133Dic86—42no—
134C8×C43—44no—
135C43⋊C8—44no—
136#7629—431nomaximal, Sylow
137C22×C43#40711yescharacteristic
138C22×C43C2×#9911yescharacteristic
139C22×C43C2×#10011yescharacteristic
140C22×C43#41912yes—
141C22×C43C2×#10412yes—
142C2×D43—22no—
143C2×D43—22no—
144C2×D43—24no—
145C2×D43—24no—
146C2×D43#32914yes—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—22no—
150C4×C43—22no—
151C4×C43—42no—
152C4×C43—81no—
153Dic43—22no—
154Dic43—42no—
155Dic43—42no—
156Dic43—81no—
157C2×#391—431no—
158#1749—432no—
159#1272—431no—
160#1272—432no—
161#1272D4311yescharacteristic, complemented
162C2×C43#146211yescharacteristic
163C2×C43#149112yes—
164C2×C43#150812yes—
165C2×C43C2×#32911yescharacteristic
166C2×C43#155811yescharacteristic
167D43—24no—
168C23×Q8—431no—
169C22×C4⋊C4—431no—
170C22×C42—431no—
171C2×C22⋊C8—862no—
172C2×#97—862no—
173#391—431no—
174#391—431no—
175#391—431no—
176#391—862no—
177#391C2×D4311yescharacteristic
178C2×#95—862no—
179#336—432no—
180#336C2×D4312yes—
181C43#762911yescharacteristic, complemented, Sylow
182C22×Q8—431no—
183C22×Q8—861no—
184C22×Q8—862no—
185C22×Q8—862no—
186C22×Q8—1722no—
187C22×Q8—1722no—
188C22×Q8C4×D4311yescharacteristic
189C23×C4—431no—
190C23×C4—432no—
191C23×C4—861no—
192C23×C4—861no—
193C22×C8—22no—
194C22×C8—862no—
195C2×C4⋊C4—431no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4—1722no—
198C2×C4⋊C4C4×D4311yescharacteristic
199C2×C42—432no—
200C2×C42—431no—
201C2×C42—1722no—
202C2×C42C22×D4311yescharacteristic
203C22⋊C8—868no—
204#97—1724no—
205#95—22no—
206#95—862no—
207#95—862no—
208#95—862no—
209C24—431no—
210C2×Q8—21no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—432no—
214C2×Q8—864no—
215C2×Q8—861no—
216C2×Q8—1721no—
217C2×Q8—1721no—
218C2×Q8—1722no—
219C2×Q8—1722no—
220C2×Q8—1728no—
221C2×Q8—1728no—
222C2×Q8#1062187212yes—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—431no—
226C22×C4—432no—
227C22×C4—862no—
228C22×C4—862no—
229C22×C4—864no—
230C22×C4—864no—
231C22×C4—861no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—862no—
235C22×C4—862no—
236C22×C4—861no—
237C22×C4—1722no—
238C22×C4—1722no—
239C22×C4—1724no—
240C22×C4—1722no—
241C22×C4—1722no—
242C22×C4C2×C4×D4311yescharacteristic
243C22×C4D4×D4312yes—
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—864no—
248C2×C8—1722no—
249C2×C8—1722no—
250C4⋊C4—41no—
251C4⋊C4—1721no—
252C4⋊C4—1722no—
253C42—41no—
254C42—864no—
255C42—1721no—
256C23—432no—
257C23—434no—
258C23—861no—
259C23—861no—
260C23—862no—
261C23C22⋊C4×D4311yescharacteristic
262Q8—42no—
263Q8—42no—
264Q8—1722no—
265Q8—1722no—
266Q8—1728no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—432no—
277C2×C4—864no—
278C2×C4—864no—
279C2×C4—861no—
280C2×C4—861no—
281C2×C4—862no—
282C2×C4—862no—
283C2×C4—862no—
284C2×C4—862no—
285C2×C4—3444no—
286C2×C4—1724no—
287C2×C4—1724no—
288C2×C4—1728no—
289C2×C4—1721no—
290C2×C4—1722no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4M16×D4311yescharacteristic
294C2×C4C2×#1062187211yescharacteristic
295C2×C4#1306335412yes—
296C2×C4#1306335712yes—
297C8—44no—
298C8—1724no—
299C22—434no—
300C22—864no—
301C22—862no—
302C22—864no—
303C22—862no—
304C22#1458286111yescharacteristic
305C22#99×D4311yescharacteristic
306C22#100×D4311yescharacteristic
307C22#1458290612yes—
308C22#104×D4312yes—
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—862no—
316C4—3441no—
317C4—1722no—
318C4—1722no—
319C2—864no—
320C2#1913292011yescharacteristic
321C2#1913304012yes—
322C2#1913311312yes—
323C2#329×D4311yescharacteristic
324C2#1913331911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7629
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
3. #19132421C2semidirect
4. #19132420C2semidirect
5. C43×#1272C2semidirect
161. #1272D43semidirect
181. C43#7629semidirect

Maximal subgroups

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

subgroupindex
#391×D432
#191343562
#191324212
#191324202
C43×#12722
#762943