Finite Group Databasebeta

← #24991601

Subgroups — #24991601

Order 11008.

836 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14582811C211yesmaximal, characteristic
2#19134529C212yesmaximal, complemented
3C2×#14582623C211yesmaximal, characteristic
4#19132473C212yesmaximal, complemented
5C43×#2312C211yesmaximal, characteristic
6C23×Dic86C2211yescharacteristic
7C22×C22⋊Dic43—21no—
8C2×#13063248—24no—
9C2×C22⋊(C43⋊C8)C2212yes—
10#14582811—22no—
11#14582811C414yescomplemented
12C2×C43⋊#95—21no—
13C2×C43⋊#95C2211yescharacteristic
14#14582623—22no—
15C22×C22⋊C4×C43C2211yescharacteristic
16C43×#388—24no—
17C43×#380C2212yes—
18C43×#379—21no—
19C4×C22⋊C4×C43—21no—
20C22×Dic86—22no—
21C22×Dic86—22no—
22C22×Dic86—21no—
23C22×Dic86—44no—
24C22×Dic86C2×C412yes—
25C23×Dic43—21no—
26C23×Dic43—21no—
27C22×C43⋊C8—22no—
28C2×C22⋊Dic43—24no—
29C2×C22⋊Dic43—44no—
30#13063248—48no—
31C22⋊(C43⋊C8)—22no—
32C22⋊(C43⋊C8)—22no—
33C43⋊#95—24no—
34C43⋊#95—21no—
35C43⋊#95C2×C412yes—
36C25×C43D411yescharacteristic
37C23×C4×C43D411yescharacteristic
38C23×C4×C43C2311yescharacteristic
39C2×C4⋊C4×C43D414yes—
40C2×C22⋊C4×C43—22no—
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—22no—
43C2×C22⋊C4×C43—22no—
44C2×C22⋊C4×C43—22no—
45C2×C22⋊C4×C43C2×C412yes—
46C2×C22⋊C4×C43D412yes—
47C2×C42×C43—22no—
48#95×C43—22no—
49#95×C43—22no—
50C24×C43—21no—
51C24×C43—22no—
52C24×C43—21no—
53C24×C43—22no—
54C24×C43—42no—
55C24×C43—42no—
56C24×C43C22⋊C412yes—
57C24×C43C2×D411yescharacteristic
58C22×C4×C43—21no—
59C22×C4×C43—24no—
60C22×C4×C43—21no—
61C22×C4×C43—42no—
62C22×C4×C43—42no—
63C22×C4×C43C22⋊C412yes—
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—42no—
72C22×Dic43—42no—
73C22×Dic43—42no—
74C22×Dic43—41no—
75C22×Dic43—41no—
76C22×Dic43—42no—
77C2×Dic86—28no—
78C2×Dic86—24no—
79C2×Dic86—44no—
80C2×Dic86—48no—
81C2×Dic86—44no—
82C2×Dic86—44no—
83C2×Dic86—42no—
84C4⋊C4×C43—44no—
85C22⋊C4×C43—24no—
86C22⋊C4×C43—24no—
87C22⋊C4×C43—42no—
88C22⋊C4×C43—42no—
89C22⋊C4×C43—82no—
90C22⋊C4×C43—82no—
91C42×C43—82no—
92C22⋊Dic43—48no—
93C2×C43⋊C8—44no—
94C2×C43⋊C8—42no—
95C23×C43—22no—
96C23×C43—22no—
97C23×C43—22no—
98C23×C43—22no—
99C23×C43—22no—
100C23×C43—42no—
101C23×C43—42no—
102C23×C43—48no—
103C23×C43—42no—
104C23×C43—42no—
105C23×C43—42no—
106C23×C43—42no—
107C23×C43—81no—
108C23×C43—81no—
109C23×C43—84no—
110C23×C43C2×C22⋊C411yescharacteristic
111C23×C43#12011yescharacteristic
112C23×C43#12311yescharacteristic
113C23×C43#13512yes—
114C23×C43#13712yes—
115C2×C4×C43—24no—
116C2×C4×C43—22no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—44no—
123C2×C4×C43—44no—
124C2×C4×C43—44no—
125C2×C4×C43—81no—
126C2×C4×C43C4×D412yes—
127C2×C4×C43#12112yes—
128C2×Dic43—24no—
129C2×Dic43—42no—
130C2×Dic43—44no—
131C2×Dic43—42no—
132C2×Dic43—44no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—84no—
137Dic86—28no—
138Dic86—48no—
139Dic86—44no—
140C43⋊C8—82no—
141#9016—431nomaximal, Sylow
142C22×C43—24no—
143C22×C43—24no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—44no—
149C22×C43—42no—
150C22×C43—42no—
151C22×C43—42no—
152C22×C43—82no—
153C22×C43—84no—
154C22×C43—84no—
155C22×C43#38611yescharacteristic
156C22×C43#41611yescharacteristic
157C22×C43#41911yescharacteristic
158C22×C43#45212yes—
159C22×C43#45512yes—
160C22×C43B(4,𝔽2)12yes—
161C22×C43#48512yes—
162C4×C43—22no—
163C4×C43—22no—
164C4×C43—42no—
165C4×C43—84no—
166Dic43—44no—
167Dic43—82no—
168C2×#393—431no—
169#2312D4311yescharacteristic
170#1787—432no—
171C2×#323—431no—
172#1294—432no—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43—22no—
176C2×C43—82no—
177C2×C43#160614yes—
178C2×C43#187311yescharacteristic
179C2×C43#188511yescharacteristic
180C2×C43#188911yescharacteristic
181C23×Q8—431no—
182C22×C22⋊C4—861no—
183C22×C22⋊C4C2×D4311yescharacteristic
184C2×#103—864no—
185C2×C22⋊C8—432no—
186#393—434no—
187#393—862no—
188#388—24no—
189#380C2×D4312yes—
190#379—21no—
191C4×C22⋊C4—21no—
192C2×#95—431no—
193C2×#95—861no—
194#323—862no—
195C43#901611yescharacteristic, complemented, Sylow
196C25C22⋊D4311yescharacteristic
197C22×Q8—432no—
198C22×Q8—861no—
199C22×Q8—862no—
200C22×Q8—862no—
201C22×Q8—1724no—
202C23×C4—861no—
203C23×C4—861no—
204C23×C4C22⋊D4311yescharacteristic
205C23×C4C22×D4311yescharacteristic
206C22×C8—862no—
207C2×C4⋊C4C22⋊D4314yes—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—864no—
214C2×C22⋊C4—1724no—
215C2×C22⋊C4C4×D4312yes—
216C2×C22⋊C4D17212yes—
217C2×C42—22no—
218#103—1728no—
219C22⋊C8—862no—
220C22⋊C8—862no—
221#95—22no—
222#95—22no—
223#95—432no—
224#95—864no—
225#95—861no—
226C24—21no—
227C24—22no—
228C24—21no—
229C24—22no—
230C24—42no—
231C24—42no—
232C24(C2×D43)⋊C412yes—
233C24C2×C22⋊D4311yescharacteristic
234C2×Q8—868no—
235C2×Q8—864no—
236C2×Q8—1724no—
237C2×Q8—1724no—
238C2×Q8—1724no—
239C2×Q8—1728no—
240C2×Q8—1722no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—24no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—864no—
247C22×C4—862no—
248C22×C4—862no—
249C22×C4—1722no—
250C22×C4—1722no—
251C22×C4—1722no—
252C22×C4—1722no—
253C22×C4—1721no—
254C22×C4—1721no—
255C22×C4(C2×D43)⋊C412yes—
256C22×C4C2×C4×D4311yescharacteristic
257C22×C4C2×D17211yescharacteristic
258C22×C4#1062189812yes—
259C22×C4C2×C22⋊D4312yes—
260C2×C8—1724no—
261C2×C8—1722no—
262C4⋊C4—44no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—82no—
268C22⋊C4—82no—
269C22⋊C4—1728no—
270C42—82no—
271C23—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—42no—
277C23—42no—
278C23—48no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—81no—
284C23—81no—
285C23—84no—
286C23C2×(C2×D43)⋊C411yescharacteristic
287C23#1306329411yescharacteristic
288C23#1306330811yescharacteristic
289C23#1306334512yes—
290C23#1306335512yes—
291Q8—868no—
292Q8—1728no—
293Q8—1724no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—81no—
305C2×C4—864no—
306C2×C4—3444no—
307C2×C4—1722no—
308C2×C4—1722no—
309C2×C4—1722no—
310C2×C4—1722no—
311C2×C4—1724no—
312C2×C4—1724no—
313C2×C4—1722no—
314C2×C4C4×C22⋊D4312yes—
315C2×C4#1306329912yes—
316C8—3442no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—24no—
322C22—24no—
323C22—44no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—82no—
328C22—84no—
329C22—84no—
330C22#1458277811yescharacteristic
331C22#1458289311yescharacteristic
332C22#1458290711yescharacteristic
333C22#1458306112yes—
334C22#1458307712yes—
335C22#1458308612yes—
336C22#1458324012yes—
337C4—22no—
338C4—22no—
339C4—42no—
340C4—84no—
341C4—3442no—
342C4—1724no—
343C2—21no—
344C2—21no—
345C2—22no—
346C2—82no—
347C2#1913357514yes—
348C2#1913490711yescharacteristic
349C2#1913498311yescharacteristic
350C2#1913500311yescharacteristic
subgroupG/H
centerC23#13063294
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2312C2
socleC23×C43#120
prime radicalC25×C43D4
cosocleC23×C4×C43C23
hypercenter#2312D43
hypocenterC43#9016
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #19134529C2semidirect
4. #19132473C2semidirect
11. #14582811C4semidirect
195. C43#9016semidirect

Maximal subgroups

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

subgroupindex
C2×#145828112
#191345292
C2×#145826232
#191324732
C43×#23122
#901643