Finite Group Databasebeta

← #24994389

Subgroups — #24994389

Order 11008.

576 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 115 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#19143624C211yesmaximal, characteristic
2#19138903C211yesmaximal, characteristic
3#19134679C212yesmaximal, complemented
4#19132462C212yesmaximal, complemented
5C43×#1799C211yesmaximal, characteristic
6C2×#13063306—21no—
7C22×C4⋊Dic43C2211yescharacteristic
8#14582971—24no—
9#14582956—21no—
10#14582863—21no—
11C2×C22⋊(C43⋊C8)C2212yes—
12#14582829C412yescomplemented
13#14582824C412yescomplemented
14#14582797—21no—
15#14582760—21no—
16#14582759—21no—
17#14582759C2211yescharacteristic
18#14582661—24no—
19C2×C4×D4×C43C2211yescharacteristic
20C2×#99×C43—21no—
21C43×#380C2212yes—
22C43×#342—21no—
23C23×Dic43—21no—
24C2×#10621877—22no—
25C22×C43⋊C8D414yes—
26#13063306—44no—
27C2×C4⋊Dic43—22no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43C2×C412yes—
32C2×Dic43⋊C4—22no—
33C2×C22⋊Dic43—22no—
34C2×C22⋊Dic43—21no—
35C4⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)—22no—
37C22⋊(C43⋊C8)—22no—
38C22⋊(C43⋊C8)—22no—
39#13063236—22no—
40C43⋊#95—22no—
41C43⋊#95—22no—
42C43⋊#95C2×C412yes—
43C22×D4×C43D411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C23×C4×C43C2311yescharacteristic
46C4×D4×C43—22no—
47C4×D4×C43—22no—
48C2×C4⋊C4×C43—22no—
49C2×C4⋊C4×C43C2×C411yescharacteristic
50C2×C22⋊C4×C43—22no—
51C2×C22⋊C4×C43C2×C411yescharacteristic
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54#99×C43—42no—
55#95×C43—22no—
56C24×C43C22⋊C411yescharacteristic
57C24×C43C2×D411yescharacteristic
58C2×D4×C43—22no—
59C2×D4×C43—21no—
60C2×D4×C43—22no—
61C2×D4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—42no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D412yes—
73C22×C4×C43#4112yes—
74C22×Dic43—22no—
75C22×Dic43—22no—
76C22×Dic43—42no—
77C22×Dic43—42no—
78C22×Dic43—41no—
79C22×Dic43—41no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—44no—
82C22⋊C4×C43—22no—
83C22⋊C4×C43—22no—
84C22⋊C4×C43—42no—
85C22⋊C4×C43—42no—
86C42×C43—21no—
87C42×C43—21no—
88C22⋊Dic43—44no—
89C22⋊Dic43—42no—
90C4⋊Dic43—24no—
91C4⋊Dic43—42no—
92C4⋊Dic43—41no—
93C4⋊Dic43—41no—
94Dic43⋊C4—44no—
95#10621877—82no—
96C2×C43⋊C8—24no—
97C2×C43⋊C8—44no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43—41no—
105C23×C43C2×C22⋊C411yescharacteristic
106C23×C43#12112yes—
107C23×C43AGL(1,ℤ/8)12yes—
108C23×C43AGL(1,ℤ/8)11yescharacteristic
109C23×C43#13711yescharacteristic
110D4×C43—42no—
111D4×C43—42no—
112C2×C4×C43—24no—
113C2×C4×C43—22no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—41no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—81no—
125C2×C4×C43—82no—
126C2×C4×C43—82no—
127C2×C4×C43—82no—
128C2×C4×C43C4×D412yes—
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12311yescharacteristic
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43—82no—
138C2×Dic43—82no—
139C43⋊C8—44no—
140#9474—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—22no—
143C22×C43—21no—
144C22×C43—22no—
145C22×C43—42no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—42no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—81no—
153C22×C43#38611yescharacteristic
154C22×C43#41711yescharacteristic
155C22×C43#41811yescharacteristic
156C22×C43#46812yes—
157C22×C43#46912yes—
158C4×C43—21no—
159C4×C43—22no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—162no—
164C4×C43#45812yes—
165Dic43—82no—
166Dic43—82no—
167#2973—431no—
168#2486—431no—
169#1823—432no—
170#1799D4311yescharacteristic
171#1289—432no—
172C2×C43—21no—
173C2×C43—22no—
174C2×C43—21no—
175C2×C43—22no—
176C2×C43—81no—
177C2×C43#189011yescharacteristic
178C2×C43#189511yescharacteristic
179C2×C43#190911yescharacteristic
180C2×#123—861no—
181C2×C4×D4C2×D4311yescharacteristic
182C22×C4⋊C4—431no—
183#435—864no—
184#432—861no—
185C2×#99—21no—
186#407—861no—
187C2×C22⋊C8—432no—
188#398—432no—
189#397—432no—
190#389—861no—
191#381—861no—
192#380—431no—
193#380—861no—
194#380C2×D4312yes—
195#342—21no—
196#340—864no—
197C43#947411yescharacteristic, complemented, Sylow
198C22×D4C22⋊D4311yescharacteristic
199C23×C4—861no—
200C23×C4D17211yescharacteristic
201C23×C4C22×D4311yescharacteristic
202C2×M16—862no—
203C22×C8—434no—
204#123—1724no—
205C4×D4—22no—
206C4×D4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—432no—
209C2×C4⋊C4—862no—
210C2×C4⋊C4—862no—
211C2×C4⋊C4—862no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4C4×D4311yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—862no—
217C2×C22⋊C4—861no—
218C2×C22⋊C4C4×D4311yescharacteristic
219C2×C22⋊C4C22⋊D4311yescharacteristic
220C2×C42D17211yescharacteristic
221C4⋊C8—862no—
222#99—42no—
223C22⋊C8—862no—
224C22⋊C8—862no—
225C22⋊C8—862no—
226#97—862no—
227#95—22no—
228#95—432no—
229#95—862no—
230#95—862no—
231C24(C2×D43)⋊C411yescharacteristic
232C24C2×C22⋊D4311yescharacteristic
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—21no—
236C2×D4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—862no—
243C22×C4—862no—
244C22×C4—1722no—
245C22×C4—1722no—
246C22×C4—1721no—
247C22×C4—1721no—
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4(C2×D43)⋊C411yescharacteristic
250C22×C4(C2×D43)⋊C411yescharacteristic
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4C2×D17211yescharacteristic
253C22×C4D4×D4312yes—
254C22×C4#1062190012yes—
255M16—3442no—
256C2×C8—864no—
257C2×C8—1724no—
258C4⋊C4—22no—
259C4⋊C4—44no—
260C4⋊C4—864no—
261C4⋊C4—1724no—
262C4⋊C4—1722no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—1724no—
270C22⋊C4—1722no—
271C42—21no—
272C42—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×(C2×D43)⋊C411yescharacteristic
281C23#1306329712yes—
282C23#1306335012yes—
283C23#1306335111yescharacteristic
284C23#1306335611yescharacteristic
285D4—42no—
286D4—42no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—3442no—
304C2×C4—3442no—
305C2×C4—1722no—
306C2×C4—1722no—
307C2×C4—1722no—
308C2×C4—1722no—
309C2×C4—1722no—
310C2×C4—1722no—
311C2×C4(C22⋊D43)⋊C412yes—
312C2×C4#1306329511yescharacteristic
313C2×C4#1306330911yescharacteristic
314C8—1724no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—22no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—42no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22#1458277611yescharacteristic
328C22#1458289811yescharacteristic
329C22#1458290311yescharacteristic
330C22#1458314712yes—
331C22#1458315012yes—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—162no—
338C4—3442no—
339C4—3442no—
340C4#1458309012yes—
341C2—22no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—81no—
346C2#1913500611yescharacteristic
347C2#1913503111yescharacteristic
348C2#1913511511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1799C2
socleC22×C43#386
prime radicalC22×D4×C43D4
cosocleC23×C4×C43C23
hypercenter#1799D43
hypocenterC43#9474
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #19134679C2semidirect
4. #19132462C2semidirect
12. #14582829C4semidirect
13. #14582824C4semidirect
197. C43#9474semidirect

Maximal subgroups

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

subgroupindex
#191436242
#191389032
#191346792
#191324622
C43×#17992
#947443