Finite Group Databasebeta

← #24985114

Subgroups — #24985114

Order 11008.

556 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 107 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#19142926C211yesmaximal, characteristic
2#19134663C211yesmaximal, characteristic, complemented
3#19132417C212yesmaximal, complemented
4#19132415C212yesmaximal, complemented
5C43×#1728C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063299C411yescharacteristic
8C2×C22⋊(C43⋊C8)—21no—
9#14582801C411yescharacteristic
10#14582801C2211yescharacteristic
11#14582797C411yescharacteristic
12#14582797C2211yescharacteristic
13#14582790—21no—
14#14582790—21no—
15#14582778—21no—
16#14582759C411yescharacteristic
17#14582654—21no—
18#14582654C2212yes—
19C22×M16×C43—21no—
20C22×C42×C43C2211yescharacteristic
21C43×#336—21no—
22C43×#336C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C43⋊C8—22no—
26#13063308—44no—
27#13063299—42no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C22⋊(C43⋊C8)—42no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C23×C4×C43C2×C411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C2×M16×C43—24no—
47C2×M16×C43—42no—
48C2×M16×C43—42no—
49C22×C8×C43—22no—
50C2×C42×C43—42no—
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43C2311yescharacteristic
55C24×C43C22⋊C411yescharacteristic
56C23×D43—21no—
57C22×C4×C43—22no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43—22no—
65C22×C4×C43—41no—
66C22×C4×C43—41no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C2×C22⋊D43—42no—
74C2×C22⋊D43—42no—
75C2×C22⋊D43—42no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×D172—22no—
80C2×D172—41no—
81C2×D172—41no—
82M16×C43—48no—
83C2×C8×C43—24no—
84C2×C8×C43—42no—
85C2×C8×C43—42no—
86C42×C43—41no—
87C42×C43—41no—
88C42×C43—41no—
89C42×C43—41no—
90C22⋊Dic43—42no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—42no—
96(C2×D43)⋊C4—41no—
97C4⋊Dic43—22no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100Dic43⋊C4—42no—
101Dic43⋊C4—42no—
102C2×C43⋊C8—42no—
103C2×C43⋊C8—42no—
104C2×C43⋊C8—42no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43#9912yes—
112C23×C43C2×C22⋊C411yescharacteristic
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C2×C4×C43—24no—
121C2×C4×C43—24no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—44no—
137C2×C4×C43—44no—
138C2×C4×C43#10412yes—
139C2×C4×C43#13112yes—
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)12yes—
142C2×C4×C43#13711yescharacteristic
143C22⋊D43—84no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153D172—82no—
154C8×C43—44no—
155C43⋊C8—82no—
156#7694—431nomaximal, Sylow
157C22×C43—22no—
158C22×C43—22no—
159C22×C43—22no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43#40811yescharacteristic
165C22×C43C2×#9911yescharacteristic
166C22×C43#41311yescharacteristic
167C22×C43#41711yescharacteristic
168C22×C43#41811yescharacteristic
169C22×C43C2×#10411yescharacteristic
170C22×C43#42111yescharacteristic
171C2×D43—81no—
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43—22no—
179C4×C43—21no—
180C4×C43—22no—
181C4×C43—21no—
182C4×C43—22no—
183C4×C43—41no—
184C4×C43—41no—
185Dic43—81no—
186Dic43—81no—
187Dic43—81no—
188#2854—431no—
189#1817—431no—
190#1728D4311yescharacteristic, complemented
191#1271—432no—
192#1270—432no—
193C2×C43—42no—
194C2×C43#146811yescharacteristic
195C2×C43#148411yescharacteristic
196C2×C43#149511yescharacteristic
197C2×C43#150411yescharacteristic
198C2×C43#151011yescharacteristic
199C2×C43#152911yescharacteristic
200C2×C43#155711yescharacteristic
201D43—161no—
202C22×M16—21no—
203C2×#123—861no—
204C2×#121—431no—
205C22×C42C2×D4311yescharacteristic
206C2×C22⋊C8—861no—
207#390—431no—
208#390—431no—
209#389—431no—
210#389—431no—
211#388—861no—
212#388—861no—
213#386—861no—
214#380—431no—
215#336—21no—
216#336—432no—
217#336—861no—
218#336C2×D4312yes—
219C43#769411yescharacteristic, complemented, Sylow
220C22×D4—431no—
221C22×D4—861no—
222C23×C4C4×D4311yescharacteristic
223C23×C4D17211yescharacteristic
224C23×C4C22⋊D4311yescharacteristic
225C2×M16—24no—
226C2×M16—42no—
227C2×M16—42no—
228C22×C8—22no—
229C22×C8—862no—
230#123—1724no—
231#121—1722no—
232C2×C4⋊C4—431no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—861no—
237C2×C22⋊C4—861no—
238C2×C22⋊C4—861no—
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C42—42no—
244C2×C42C4×D4311yescharacteristic
245C2×C42D17211yescharacteristic
246C2×C42C22⋊D4311yescharacteristic
247C2×C42C22×D4311yescharacteristic
248C22⋊C8—1722no—
249#95—861no—
250#95—861no—
251#95—861no—
252C24—861no—
253C24(C2×D43)⋊C411yescharacteristic
254C2×D4—862no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1722no—
258C2×D4—1722no—
259C2×D4—1722no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4(C2×D43)⋊C411yescharacteristic
274C22×C4(C2×D43)⋊C411yescharacteristic
275C22×C4(C2×D43)⋊C411yescharacteristic
276C22×C4C2×C4×D4311yescharacteristic
277C22×C4C2×D17211yescharacteristic
278C22×C4C2×C22⋊D4311yescharacteristic
279M16—48no—
280C2×C8—24no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—1722no—
284C2×C8—1722no—
285C2×C8—1722no—
286C4⋊C4—862no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1722no—
290C4⋊C4—1722no—
291C22⋊C4—1722no—
292C22⋊C4—1722no—
293C22⋊C4—1722no—
294C22⋊C4—1722no—
295C22⋊C4—1721no—
296C22⋊C4—1722no—
297C22⋊C4—1721no—
298C42—41no—
299C42—41no—
300C42—41no—
301C42—41no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—1721no—
309C23—1721no—
310C23—1721no—
311C23—1721no—
312C23—1721no—
313C23—1721no—
314C23—1721no—
315C23#1306323912yes—
316C23C2×(C2×D43)⋊C411yescharacteristic
317D4—3442no—
318D4—3444no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4#1306325312yes—
347C2×C4#1306333312yes—
348C2×C4#1306335111yescharacteristic
349C2×C4#1306335312yes—
350C2×C4#1306335611yescharacteristic
351C8—44no—
352C8—3442no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22—3441no—
364C22—3441no—
365C22—3441no—
366C22—3441no—
367C22#1458286711yescharacteristic
368C22C2×#1306323911yescharacteristic
369C22#1458288111yescharacteristic
370C22#1458289811yescharacteristic
371C22#1458290511yescharacteristic
372C22C2×#1306325311yescharacteristic
373C22#1458291511yescharacteristic
374C4—22no—
375C4—21no—
376C4—22no—
377C4—21no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—3441no—
382C4—3441no—
383C4—3441no—
384C2—42no—
385C2—6881no—
386C2#1913294411yescharacteristic
387C2#1913301311yescharacteristic
388C2#1913305811yescharacteristic
389C2#1913309711yescharacteristic
390C2#1913312511yescharacteristic
391C2#1913320011yescharacteristic
392C2#1913331511yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1728C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C4
cosocleC2×C42×C43C23
hypercenter#1728D43
hypocenterC43#7694
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
2. #19134663C2semidirect
3. #19132417C2semidirect
4. #19132415C2semidirect
5. C43×#1728C2semidirect
190. #1728D43semidirect
219. C43#7694semidirect

Maximal subgroups

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

subgroupindex
#191429262
#191346632
#191324172
#191324152
C43×#17282
#769443