Finite Group Databasebeta

← #24984838

Subgroups — #24984838

Order 11008.

730 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 105 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#19137082C211yesmaximal, characteristic
2#19134287C212yesmaximal, complemented
3#19132420C212yesmaximal, complemented
4#19132416C211yesmaximal, characteristic, complemented
5C43×#1270C211yesmaximal, characteristic, complemented
6C22×#10621900C411yescharacteristic
7C22×#10621872—22no—
8C2×#13063283C411yescharacteristic
9C2×C42×D43C2211yescharacteristic
10#14582805C2211yescharacteristic
11#14582804C411yescharacteristic
12#14582802C411yescharacteristic
13#14582775—22no—
14C22⋊C4×Dic43—22no—
15#14582654C2212yes—
16#14582653—22no—
17C43×#390C2211yescharacteristic
18C43×#336C2212yes—
19C2×#10621900—22no—
20C2×#10621900—22no—
21C2×#10621900—42no—
22C2×#10621900—42no—
23C22×Dic86C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C23×Dic43—21no—
26C22×C4×D43C2×C411yescharacteristic
27C22×C4×D43D412yes—
28C2×#10621872—28no—
29C2×#10621872—44no—
30C2×#10621872—44no—
31C22×C43⋊C8—22no—
32#13063283—42no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×C22⋊Dic43—22no—
35C2×(C2×D43)⋊C4—21no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43C2×C411yescharacteristic
38C2×C4×Dic43D412yes—
39C42×D43—42no—
40C43⋊#95—22no—
41C43⋊#95—22no—
42C22×D4×C43C2×C411yescharacteristic
43C22×C8×C43—22no—
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C22⋊C4×C43—22no—
46C2×C42×C43C2311yescharacteristic
47C24×C43—21no—
48C23×D43C22⋊C411yescharacteristic
49C2×D4×C43—21no—
50C2×D4×C43—41no—
51C2×D4×C43—41no—
52C2×D4×C43M1612yescomplemented
53C22×C4×C43—21no—
54C22×C4×C43C22×C411yescharacteristic
55C22×C4×C43C2×D412yes—
56C2×C22⋊D43—24no—
57C2×C22⋊D43—42no—
58C2×C22⋊D43—42no—
59C22×Dic43—24no—
60C22×Dic43—21no—
61C22×Dic43—21no—
62C22×Dic43—42no—
63C22×Dic43—42no—
64C22×Dic43C22⋊C411yescharacteristic
65C22×Dic43C22⋊C412yes—
66#10621900—48no—
67#10621900—48no—
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—22no—
71C2×C4×D43—22no—
72C2×C4×D43—22no—
73C2×C4×D43—24no—
74C2×C4×D43—24no—
75C2×C4×D43—22no—
76C2×Dic86—21no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86M1612yescomplemented
80C2×C8×C43—24no—
81C2×C8×C43—42no—
82C2×C8×C43—42no—
83C4⋊C4×C43—41no—
84C22⋊C4×C43—42no—
85C22⋊C4×C43—42no—
86C42×C43—41no—
87C22⋊Dic43—44no—
88(C2×D43)⋊C4—42no—
89C4⋊Dic43—41no—
90C4×Dic43—41no—
91C4×Dic43—42no—
92C4×Dic43—42no—
93C2×C43⋊C8—24no—
94C2×C43⋊C8—42no—
95C2×C43⋊C8—42no—
96#10621872—416no—
97C23×C43—22no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43—42no—
101C23×C43—42no—
102C23×C43C2×C22⋊C411yescharacteristic
103C22×D43—21no—
104C22×D43—21no—
105C22×D43—22no—
106C22×D43—22no—
107C22×D43#9912yes—
108D4×C43—42no—
109D4×C43—42no—
110C2×C4×C43—22no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—22no—
114C2×C4×C43—41no—
115C2×C4×C43—42no—
116C2×C4×C43C2×M1611yescharacteristic
117C2×C4×C43C2×M1611yescharacteristic
118C2×C4×C43AGL(1,ℤ/8)12yes—
119C2×C4×C43#13712yes—
120C22⋊D43—48no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—48no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—42no—
131C2×Dic43#10012yes—
132C2×Dic43#10414yes—
133C4×D43—28no—
134C4×D43—28no—
135C4×D43—24no—
136C4×D43—24no—
137Dic86—42no—
138Dic86—42no—
139C8×C43—44no—
140C43⋊C8—44no—
141#7631—431nomaximal, Sylow
142C22×C43—42no—
143C22×C43—44no—
144C22×C43—81no—
145C22×C43—82no—
146C22×C43—81no—
147C22×C43#40711yescharacteristic
148C22×C43C2×#9911yescharacteristic
149C22×C43C2×#10011yescharacteristic
150C22×C43#41712yes—
151C22×C43C2×#10412yes—
152C2×D43—22no—
153C2×D43—24no—
154C2×D43—41no—
155C2×D43—42no—
156C2×D43—41no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—22no—
160C4×C43—22no—
161C4×C43—81no—
162Dic43—22no—
163Dic43—24no—
164Dic43—42no—
165Dic43—81no—
166#2297—431no—
167#1728—432no—
168#1272—432no—
169#1270—431no—
170#1270D4311yescharacteristic, complemented
171C2×C43—82no—
172C2×C43#146211yescharacteristic
173C2×C43#148912yes—
174C2×C43#150412yes—
175C2×C43#152511yescharacteristic
176C2×C43#156011yescharacteristic
177D43—42no—
178C22×#41—431no—
179C22×M16—862no—
180C2×#117—431no—
181C22×C42—431no—
182#391—431no—
183#391—431no—
184#390—431no—
185#390C2×D4311yescharacteristic
186#386—862no—
187C4×C22⋊C4—862no—
188#336—432no—
189#336—862no—
190#336C2×D4312yes—
191C43#763111yescharacteristic, complemented, Sylow
192C2×#41—862no—
193C2×#41—862no—
194C2×#41—1722no—
195C2×#41—1722no—
196C22×Q8—431no—
197C22×D4—861no—
198C22×D4C4×D4311yescharacteristic
199C23×C4—431no—
200C23×C4—432no—
201C23×C4—861no—
202C2×M16—868no—
203C2×M16—1724no—
204C2×M16—1724no—
205C22×C8—22no—
206C22×C8—862no—
207#117—1722no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4C4×D4311yescharacteristic
210C2×C22⋊C4—22no—
211C2×C22⋊C4—861no—
212C2×C22⋊C4—862no—
213C2×C42—431no—
214C2×C42—432no—
215C2×C42—861no—
216C2×C42—1722no—
217C2×C42C22×D4311yescharacteristic
218#95—862no—
219#95—862no—
220C24—21no—
221C24—431no—
222#41—1728no—
223#41—1728no—
224C2×Q8—432no—
225C2×Q8—861no—
226C2×Q8—1721no—
227C2×Q8—1721no—
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—864no—
232C2×D4—1722no—
233C2×D4—1722no—
234C2×D4#1062187212yescomplemented
235C22×C4—21no—
236C22×C4—432no—
237C22×C4—431no—
238C22×C4—862no—
239C22×C4—864no—
240C22×C4—864no—
241C22×C4—862no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—862no—
245C22×C4—862no—
246C22×C4—864no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—1722no—
250C22×C4—1722no—
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4D4×D4312yes—
253M16—17216no—
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—864no—
258C2×C8—1722no—
259C2×C8—1722no—
260C4⋊C4—41no—
261C4⋊C4—1721no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—1722no—
265C22⋊C4—1724no—
266C42—41no—
267C42—1722no—
268C42—1721no—
269C42—1722no—
270C23—22no—
271C23—41no—
272C23—41no—
273C23—42no—
274C23—42no—
275C23—432no—
276C23—861no—
277C23—861no—
278C23—862no—
279C23—862no—
280C23C22⋊C4×D4311yescharacteristic
281Q8—1722no—
282Q8—1722no—
283D4—42no—
284D4—42no—
285D4—1728no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—432no—
293C2×C4—434no—
294C2×C4—868no—
295C2×C4—864no—
296C2×C4—864no—
297C2×C4—868no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—862no—
301C2×C4—862no—
302C2×C4—862no—
303C2×C4—1728no—
304C2×C4—1721no—
305C2×C4—1722no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4M16×D4311yescharacteristic
309C2×C4C2×#1062187211yescharacteristic
310C2×C4#1306334912yes—
311C2×C4#1306335412yes—
312C8—44no—
313C8—1724no—
314C22—44no—
315C22—42no—
316C22—81no—
317C22—81no—
318C22—82no—
319C22—864no—
320C22—862no—
321C22—1721no—
322C22—1722no—
323C22—1721no—
324C22#1458286111yescharacteristic
325C22#99×D4311yescharacteristic
326C22#100×D4311yescharacteristic
327C22#1458289712yes—
328C22#104×D4312yes—
329C4—22no—
330C4—22no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4—864no—
335C4—862no—
336C4—3441no—
337C4—1722no—
338C2—82no—
339C2—1722no—
340C2#1913292011yescharacteristic
341C2#1913303112yes—
342C2#1913309612yes—
343C2#1913318511yescharacteristic
344C2#1913332711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#10621900C4
cosocleC2×C42×C43C23
hypercenter#1270D43
hypocenterC43#7631
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19134287C2semidirect
3. #19132420C2semidirect
4. #19132416C2semidirect
5. C43×#1270C2semidirect
52. C2×D4×C43M16semidirect
79. C2×Dic86M16semidirect
170. #1270D43semidirect
191. C43#7631semidirect
234. C2×D4#10621872semidirect

Maximal subgroups

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

subgroupindex
#191370822
#191342872
#191324202
#191324162
C43×#12702
#763143