Finite Group Databasebeta

← #24991654

Subgroups — #24991654

Order 11008.

660 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14582829C211yesmaximal, characteristic
2#19137213C211yesmaximal, characteristic
3#19134682C212yesmaximal
4#19132475C212yesmaximal
5C2×C43×#324C211yesmaximal, characteristic
6C2×#13063284—21no—
7C22×C4⋊Dic43C2211yescharacteristic
8C22×Dic43⋊C4—21no—
9#14582829—22no—
10#14582829C414yescomplemented
11#14582798—24no—
12#14582759—21no—
13#14582759C2212yes—
14C2×C43⋊#95—21no—
15C2×C43⋊#95C2211yescharacteristic
16#14582662—24no—
17C22×C4⋊C4×C43C2211yescharacteristic
18C2×C22⋊C8×C43C2212yes—
19C43×#324—22no—
20C23×Dic43—21no—
21C23×Dic43—21no—
22#13063284—42no—
23#13063284—42no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43—22no—
26C2×C4⋊Dic43—22no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43C2×C412yes—
30C2×C4⋊Dic43D414yes—
31C2×Dic43⋊C4—24no—
32C2×Dic43⋊C4—42no—
33C2×Dic43⋊C4—42no—
34C2×C22⋊Dic43—22no—
35C2×C4×Dic43—22no—
36C43⋊#95—22no—
37C43⋊#95—24no—
38C43⋊#95—22no—
39C43⋊#95—21no—
40C43⋊#95C2×C412yes—
41C23×C4×C43D411yescharacteristic
42C23×C4×C43D411yescharacteristic
43C23×C4×C43C2311yescharacteristic
44C22×C8×C43—22no—
45C2×C4⋊C4×C43—22no—
46C2×C4⋊C4×C43—22no—
47C2×C4⋊C4×C43C2×C412yes—
48C2×C4⋊C4×C43D412yes—
49C22⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C24×C43C2×D411yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43C22⋊C412yes—
61C22×C4×C43C22⋊C412yes—
62C22×C4×C43D812yes—
63C22×C4×C43SD1612yes—
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D412yes—
67C22×C4×C43#4112yes—
68C22×Dic43—24no—
69C22×Dic43—22no—
70C22×Dic43—22no—
71C22×Dic43—24no—
72C22×Dic43—42no—
73C22×Dic43—41no—
74C22×Dic43—41no—
75C22×Dic43—41no—
76C22×Dic43—41no—
77C22×Dic43—41no—
78C22×Dic43—41no—
79C22×Dic43—41no—
80C22×Dic43—41no—
81C2×C8×C43—44no—
82C2×C8×C43—42no—
83C4⋊C4×C43—24no—
84C4⋊C4×C43—24no—
85C22⋊Dic43—42no—
86C22⋊Dic43—42no—
87C4⋊Dic43—24no—
88C4⋊Dic43—44no—
89C4⋊Dic43—42no—
90C4⋊Dic43—44no—
91C4⋊Dic43—82no—
92Dic43⋊C4—48no—
93C4×Dic43—44no—
94C23×C43—22no—
95C23×C43—22no—
96C23×C43C2×C22⋊C411yescharacteristic
97C23×C43#12011yescharacteristic
98C23×C43#12311yescharacteristic
99C23×C43C2×D811yescharacteristic
100C23×C43C2×SD1611yescharacteristic
101C23×C43AGL(1,ℤ/8)11yescharacteristic
102C23×C43#13711yescharacteristic
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—24no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43—42no—
116C2×C4×C43—81no—
117C2×C4×C43#10214yes—
118C2×C4×C43C4×D412yes—
119C2×C4×C43#12112yes—
120C2×Dic43—24no—
121C2×Dic43—44no—
122C2×Dic43—44no—
123C2×Dic43—42no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—42no—
128C2×Dic43—44no—
129C2×Dic43—44no—
130C2×Dic43—44no—
131C2×Dic43—81no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43—81no—
135C8×C43—82no—
136#9027—431nomaximal, Sylow
137C22×C43—22no—
138C22×C43—22no—
139C22×C43—22no—
140C22×C43—22no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43#38611yescharacteristic
146C22×C43C2×#10211yescharacteristic
147C22×C43#41711yescharacteristic
148C22×C43#44711yescharacteristic
149C22×C43#44811yescharacteristic
150C22×C43#45612yes—
151C22×C43#45812yes—
152C22×C43#48011yescharacteristic
153C22×C43#48111yescharacteristic
154C4×C43—24no—
155C4×C43—22no—
156C4×C43—22no—
157C4×C43—42no—
158Dic43—44no—
159Dic43—84no—
160Dic43—82no—
161C2×#398—431no—
162#2316—431no—
163#1823—432no—
164C2×#324D4311yescharacteristic
165#1294—432no—
166C2×C43—21no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43—21no—
170C2×C43#161012yes—
171C2×C43#161112yes—
172C2×C43#187411yescharacteristic
173C2×C43#188611yescharacteristic
174C2×C43#189011yescharacteristic
175C2×#117—861no—
176C22×C4⋊C4—431no—
177C22×C4⋊C4—861no—
178C22×C4⋊C4C2×D4311yescharacteristic
179C2×C22⋊C8C2×D4312yes—
180#398—434no—
181#398—862no—
182#389—864no—
183#380—432no—
184#380—861no—
185C2×#95—431no—
186C2×#95—861no—
187#340—864no—
188#324—22no—
189C43#902711yescharacteristic, complemented, Sylow
190C23×C4—861no—
191C23×C4—861no—
192C23×C4D17211yescharacteristic
193C23×C4D17211yescharacteristic
194C23×C4C22×D4311yescharacteristic
195C22×C8—22no—
196#117—1722no—
197#117—1722no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—432no—
201C2×C4⋊C4—434no—
202C2×C4⋊C4—862no—
203C2×C4⋊C4—862no—
204C2×C4⋊C4—862no—
205C2×C4⋊C4—862no—
206C2×C4⋊C4—864no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—1722no—
209C2×C4⋊C4—1722no—
210C2×C4⋊C4C4×D4312yes—
211C2×C4⋊C4C22⋊D4312yes—
212C2×C22⋊C4—862no—
213C2×C42—862no—
214C22⋊C8—22no—
215C22⋊C8—22no—
216#95—432no—
217#95—862no—
218#95—864no—
219#95—862no—
220#95—861no—
221C24C2×D17211yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—864no—
231C22×C4—862no—
232C22×C4—862no—
233C22×C4—864no—
234C22×C4—1721no—
235C22×C4—1721no—
236C22×C4—1721no—
237C22×C4—1721no—
238C22×C4—1721no—
239C22×C4—1721no—
240C22×C4—1722no—
241C22×C4—1721no—
242C22×C4—1721no—
243C22×C4#1062187312yes—
244C22×C4D34412yes—
245C22×C4(C2×D43)⋊C412yes—
246C22×C4(C2×D43)⋊C412yes—
247C22×C4C2×C4×D4311yescharacteristic
248C22×C4D4×D4312yes—
249C22×C4#1062190012yes—
250C22×C4C2×C22⋊D4311yescharacteristic
251C2×C8—44no—
252C2×C8—42no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—864no—
256C4⋊C4—3442no—
257C4⋊C4—1724no—
258C4⋊C4—1724no—
259C4⋊C4—1728no—
260C4⋊C4—1722no—
261C22⋊C4—1722no—
262C22⋊C4—1722no—
263C42—1724no—
264C23—22no—
265C23—22no—
266C23C2×(C2×D43)⋊C411yescharacteristic
267C23#1306329511yescharacteristic
268C23#1306330911yescharacteristic
269C23C2×D34411yescharacteristic
270C23C2×#1062187311yescharacteristic
271C23#1306335311yescharacteristic
272C23#1306335811yescharacteristic
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—81no—
287C2×C4—864no—
288C2×C4—3441no—
289C2×C4—3441no—
290C2×C4—3441no—
291C2×C4—3441no—
292C2×C4—1724no—
293C2×C4—1724no—
294C2×C4—1722no—
295C2×C4—1722no—
296C2×C4—1722no—
297C2×C4—1724no—
298C2×C4—1722no—
299C2×C4—1724no—
300C2×C4—1724no—
301C2×C4—1722no—
302C2×C4#1306324714yes—
303C2×C4(C22⋊D43)⋊C412yes—
304C2×C4#1306329712yes—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22#1458277611yescharacteristic
315C22C2×#1306324711yescharacteristic
316C22#1458290111yescharacteristic
317C22#1458303511yescharacteristic
318C22#1458304011yescharacteristic
319C22#1458308412yes—
320C22#1458309012yes—
321C22#1458321311yescharacteristic
322C22#1458321811yescharacteristic
323C4—22no—
324C4—22no—
325C4—24no—
326C4—42no—
327C4—3444no—
328C4—3442no—
329C4—1724no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2#1913360012yes—
335C2#1913360512yes—
336C2#1913491011yescharacteristic
337C2#1913498611yescharacteristic
338C2#1913500611yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#324C2
socleC23×C43#120
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#324D43
hypocenterC43#9027
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
10. #14582829C4semidirect
189. C43#9027semidirect

Maximal subgroups

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

subgroupindex
C2×#145828292
#191372132
#191346822
#191324752
C2×C43×#3242
#902743