Finite Group Databasebeta

← #24986159

Subgroups — #24986159

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582950C211yesmaximal, characteristic
2C2×#14582921C211yesmaximal, characteristic
3#19136991C211yesmaximal, characteristic
4#19132436C211yesmaximal, characteristic, complemented
5#19132435C211yesmaximal, characteristic, complemented
6#19132434C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C2×C42×D43C2211yescharacteristic
10#14582950—22no—
11#14582950C414yescomplemented
12#14582921—22no—
13#14582921C414yescomplemented
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15C2×Dic43⋊C8—21no—
16C2×Dic43⋊C8—21no—
17C2×(C2×D43)⋊C8—21no—
18C2×C4×C43⋊C8C2211yescharacteristic
19#14582766—21no—
20#14582764C412yes—
21#14582761—21no—
22#14582756C412yes—
23C4×C4⋊Dic43C2211yescharacteristic
24C4×(C2×D43)⋊C4—21no—
25#14582745—21no—
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4×C8×C43C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C22×C4×D43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C22×C4×D43D411yescharacteristic
32C2×#10621872—24no—
33C2×#10621872—42no—
34C2×#10621872—42no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C2×C4⋊Dic43C2×C412yes—
38C2×(C2×D43)⋊C4—22no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43C2×C411yescharacteristic
41C2×C4×Dic43D411yescharacteristic
42C2×C4×Dic43D411yescharacteristic
43C42×D43C2×C412yes—
44C42×D43C2×C412yes—
45C42×D43D412yes—
46C42×D43Q812yes—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)C2×C412yes—
49Dic43⋊C8—24no—
50Dic43⋊C8—24no—
51(C2×D43)⋊C8—24no—
52C4×C43⋊C8—21no—
53C4×C43⋊C8C2×C412yes—
54C43⋊#95—21no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—22no—
58C22×C8×C43—21no—
59C22×C8×C43—21no—
60C2×C4⋊C4×C43C2×C412yes—
61C2×C42×C43—21no—
62C2×C42×C43C2311yescharacteristic
63C4⋊C8×C43—21no—
64C4⋊C8×C43C2×C412yes—
65C4×C8×C43—21no—
66C4×C8×C43C2×C412yes—
67#95×C43—21no—
68C23×D43C22⋊C411yescharacteristic
69C22×C4×C43—22no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—22no—
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C2×C4×D43—22no—
78C2×C4×D43—22no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—42no—
84C2×C4×D43C4212yes—
85C2×C4×D43C22⋊C412yes—
86C2×C4×D43C22⋊C412yes—
87C2×C4×D43C4⋊C412yes—
88C2×C4×D43C4⋊C412yes—
89C2×C4×D43C4⋊C412yes—
90C2×C8×C43—22no—
91C2×C8×C43—22no—
92C2×C8×C43—42no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C42×C43—41no—
98C42×C43—41no—
99C42×C43C22×C411yescharacteristic
100C42×C43C22×C411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×Q811yescharacteristic
103(C2×D43)⋊C4—44no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4×Dic43—41no—
107C4×Dic43—41no—
108C4×Dic43C4212yes—
109C4×Dic43C22⋊C412yes—
110C4×Dic43C22⋊C412yes—
111C4×Dic43C4⋊C412yes—
112C4×Dic43C4⋊C412yes—
113C4×Dic43C4⋊C412yes—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—42no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119#10621872—48no—
120C23×C43C2×C22⋊C411yescharacteristic
121C22×D43—22no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—22no—
125C22×D43#9512yes—
126C2×C4×C43—22no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43C2×C4211yescharacteristic
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C2×C4⋊C411yescharacteristic
134C2×C4×C43C2×C4⋊C411yescharacteristic
135C2×C4×C43C2×C4⋊C411yescharacteristic
136C2×C4×C43#13112yes—
137C2×C4×C43#13112yes—
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C2×Dic43—22no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—22no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43#9512yes—
150C2×Dic43#9512yes—
151C2×Dic43#9512yes—
152C4×D43—22no—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43—22no—
156C4×D43—24no—
157C4×D43—22no—
158C4×D43—22no—
159C4×D43—42no—
160C4×D43—42no—
161C8×C43—42no—
162C8×C43—42no—
163C43⋊C8—42no—
164C43⋊C8—42no—
165#7899—431nomaximal, Sylow
166C22×C43C2×#9511yescharacteristic
167C22×C43#40812yes—
168C22×C43#41711yescharacteristic
169C22×C43#41711yescharacteristic
170C22×C43#42112yes—
171C2×D43—22no—
172C2×D43—22no—
173C2×D43—22no—
174C2×D43—42no—
175C2×D43—42no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—82no—
179C4×C43#40511yescharacteristic
180C4×C43#40511yescharacteristic
181C4×C43#41811yescharacteristic
182C4×C43#41911yescharacteristic
183C4×C43#42412yes—
184C4×C43#42811yescharacteristic
185C4×C43#42811yescharacteristic
186Dic43—22no—
187Dic43—22no—
188Dic43—22no—
189Dic43—82no—
190C2×#431—431no—
191C2×#423—431no—
192#2283—431no—
193#1279—431no—
194#1279—431no—
195#1279—431no—
196#1279D4311yescharacteristic, complemented
197C2×C43#149512yes—
198C2×C43#149512yes—
199C2×C43#172911yescharacteristic
200C2×C43#173311yescharacteristic
201C2×C43#173611yescharacteristic
202D43—42no—
203C22×M16—861no—
204C22×C42—431no—
205#431—434no—
206#431—862no—
207#423—434no—
208#423—862no—
209C2×C4⋊C8—431no—
210C2×C4⋊C8—861no—
211C2×C4⋊C8—861no—
212C2×C4⋊C8C2×D4311yescharacteristic
213C2×C22⋊C8—861no—
214C2×C4×C8—431no—
215C2×C4×C8C2×D4311yescharacteristic
216#383—861no—
217#382—432no—
218#381—861no—
219#380—432no—
220C4×C4⋊C4—431no—
221C4×C4⋊C4C2×D4311yescharacteristic
222C4×C22⋊C4—861no—
223#376—861no—
224C43#789911yescharacteristic, complemented, Sylow
225C23×C4—431no—
226C23×C4—431no—
227C23×C4—431no—
228C2×M16—864no—
229C2×M16—1722no—
230C2×M16—1722no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—861no—
234C22×C8—861no—
235C2×C4⋊C4—432no—
236C2×C4⋊C4C4×D4312yes—
237C2×C22⋊C4—862no—
238C2×C42—21no—
239C2×C42—431no—
240C2×C42—431no—
241C2×C42—431no—
242C2×C42—432no—
243C2×C42—432no—
244C2×C42—432no—
245C2×C42—432no—
246C2×C42—861no—
247C2×C42C22×D4311yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—432no—
250C4⋊C8—864no—
251C4⋊C8—864no—
252C4⋊C8—861no—
253C4⋊C8C4×D4312yes—
254C22⋊C8—864no—
255C4×C8—21no—
256C4×C8—432no—
257C4×C8—861no—
258C4×C8C4×D4312yes—
259#95—21no—
260#95—862no—
261#95—862no—
262#95—862no—
263#95—861no—
264C24—431no—
265C22×C4—22no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—431no—
269C22×C4—432no—
270C22×C4—432no—
271C22×C4—432no—
272C22×C4—432no—
273C22×C4—432no—
274C22×C4—432no—
275C22×C4—862no—
276C22×C4—862no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—862no—
282C22×C4—1722no—
283C22×C4C2×C4×D4311yescharacteristic
284C22×C4D4×D4311yescharacteristic
285C22×C4D4×D4311yescharacteristic
286M16—1728no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—42no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—862no—
293C2×C8—862no—
294C2×C8—1722no—
295C2×C8—1721no—
296C2×C8—1721no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—862no—
300C4⋊C4—862no—
301C22⋊C4—1724no—
302C42—41no—
303C42—41no—
304C42—432no—
305C42—432no—
306C42—432no—
307C42—432no—
308C42—432no—
309C42—432no—
310C42—1721no—
311C42—1721no—
312C42C2×C4×D4311yescharacteristic
313C42C2×C4×D4311yescharacteristic
314C42D4×D4311yescharacteristic
315C42Q8×D4311yescharacteristic
316C23—432no—
317C23—862no—
318C23—861no—
319C23—861no—
320C23—862no—
321C23C22⋊C4×D4311yescharacteristic
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—432no—
327C2×C4—432no—
328C2×C4—432no—
329C2×C4—862no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—862no—
335C2×C4—862no—
336C2×C4—862no—
337C2×C4—864no—
338C2×C4—862no—
339C2×C4—862no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4C42×D4311yescharacteristic
346C2×C4C22⋊C4×D4311yescharacteristic
347C2×C4C22⋊C4×D4311yescharacteristic
348C2×C4C4⋊C4×D4311yescharacteristic
349C2×C4C4⋊C4×D4311yescharacteristic
350C2×C4C4⋊C4×D4311yescharacteristic
351C2×C4#1306333112yes—
352C2×C4#1306333312yes—
353C2×C4#1306334911yescharacteristic
354C2×C4#1306335211yescharacteristic
355C2×C4#1306335411yescharacteristic
356C2×C4#1306335711yescharacteristic
357C8—42no—
358C8—42no—
359C8—1722no—
360C8—1722no—
361C22—862no—
362C22—862no—
363C22—862no—
364C22—1722no—
365C22—1722no—
366C22#95×D4311yescharacteristic
367C22#1458286412yes—
368C22#1458289711yescharacteristic
369C22#1458289911yescharacteristic
370C22#1458291412yes—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—862no—
375C4—862no—
376C4—862no—
377C4—3442no—
378C4#1458285311yescharacteristic
379C4#1458285611yescharacteristic
380C4#1458290211yescharacteristic
381C4#1458290611yescharacteristic
382C4#1458292412yes—
383C4#1458293811yescharacteristic
384C4#1458294011yescharacteristic
385C2—1722no—
386C2#1913305712yes—
387C2#1913305912yes—
388C2#1913429011yescharacteristic
389C2#1913430311yescharacteristic
390C2#1913431311yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#7899
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #19132436C2semidirect
5. #19132435C2semidirect
6. #19132434C2semidirect
7. C43×#1279C2semidirect
11. #14582950C4semidirect
13. #14582921C4semidirect
196. #1279D43semidirect
224. C43#7899semidirect

Maximal subgroups

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

subgroupindex
C2×#145829502
C2×#145829212
#191369912
#191324362
#191324352
#191324342
C43×#12792
#789943