Finite Group Databasebeta

← #24992063

Subgroups — #24992063

Order 11008.

546 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#10621898C211yesmaximal, characteristic, complemented
2C4×#13063353C211yesmaximal, characteristic
3#19132983C211yesmaximal, characteristic, complemented
4C2×#14582628C211yesmaximal, characteristic, complemented
5#19132915C211yesmaximal, characteristic, complemented
6#19132446C211yesmaximal, characteristic, complemented
7C43×#1278C211yesmaximal, characteristic, complemented
8C2×#13063353C411yescharacteristic
9C4×#10621898C2211yescharacteristic
10C2×C4×D172C2211yescharacteristic
11C8×Dic86—21no—
12#14583012—21no—
13#14583001—21no—
14C4×#10621873—21no—
15C4×D344—21no—
16C8×D172—21no—
17C8×C22⋊D43—22no—
18#14582952C2211yescharacteristic
19#14582950—21no—
20#14582941C411yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22#14582905C411yescharacteristic
23#14582901C411yescharacteristic
24C4×C8×D43—21no—
25#14582631—21no—
26#14582628—21no—
27#14582628—21no—
28#14582628—21no—
29#14582622—22no—
30C43×#431C2211yescharacteristic
31C4×M16×C43C2211yescharacteristic
32C2×C4×C8×C43C2211yescharacteristic
33C2×#10621898C2×C411yescharacteristic
34C22×D172C2×C411yescharacteristic
35C22×C4×D43—21no—
36#13063353—22no—
37#13063353C814yescomplemented
38C2×#10621873—21no—
39C2×D344—21no—
40C22×C43⋊C8—21no—
41C2×C8×D43—22no—
42C4×Dic86D411yescharacteristic
43C4×Dic86D411yescharacteristic
44C4×D172—21no—
45C4×D172—21no—
46C4×D172—21no—
47C4×D172—21no—
48C4×D172D411yescharacteristic
49C4×D172D411yescharacteristic
50C4×C22⋊D43—21no—
51C4×C22⋊D43—21no—
52#13063284C2×C411yescharacteristic
53#13063282—21no—
54C2×C4⋊Dic43C2×C411yescharacteristic
55C2×(C2×D43)⋊C4—21no—
56C42×D43—21no—
57#13063259—21no—
58#13063257—21no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)—21no—
61C4⋊(C43⋊C8)—21no—
62Dic43⋊C8—22no—
63#13063250—21no—
64#13063247—21no—
65#13063247—21no—
66#13063247—21no—
67C22⋊(C43⋊C8)D412yes—
68(C2×D43)⋊C8—22no—
69C4×C43⋊C8—21no—
70C8×Dic43—22no—
71C2×M16×C43C2×C411yescharacteristic
72C2×M16×C43C2×C411yescharacteristic
73C22×C8×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77#97×C43—21no—
78C4×C8×C43—21no—
79C4×C8×C43—21no—
80C4×C8×C43—21no—
81C4×C8×C43D411yescharacteristic
82C4×C8×C43D411yescharacteristic
83C23×D43—21no—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C2×C22⋊D43—21no—
88C22×Dic43—21no—
89#10621898—21no—
90#10621898—21no—
91#10621898C2×C812yes—
92#10621898M1612yes—
93C2×D172—21no—
94C2×D172—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172C22⋊C411yescharacteristic
99C2×D172C2×C812yescomplemented
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105C2×C4×D43—81no—
106C2×C4×D43—81no—
107C2×Dic86C22⋊C411yescharacteristic
108M16×C43—21no—
109M16×C43—21no—
110M16×C43—21no—
111M16×C43C2×C812yescomplemented
112C2×C8×C43—21no—
113C2×C8×C43—21no—
114C2×C8×C43—21no—
115C2×C8×C43—21no—
116C2×C8×C43—42no—
117C2×C8×C43—41no—
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C22⋊Dic43—21no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—21no—
125(C2×D43)⋊C4—41no—
126(C2×D43)⋊C4—41no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43C22⋊C411yescharacteristic
130C4⋊Dic43C22⋊C411yescharacteristic
131Dic43⋊C4—21no—
132Dic43⋊C4—21no—
133C4×Dic43—21no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—41no—
138C2×C43⋊C8—81no—
139D344—24no—
140#10621873—24no—
141C8×D43—44no—
142C23×C43C4×D411yescharacteristic
143C22×D43—21no—
144C22×D43—22no—
145C22×D43—41no—
146C22×D43—41no—
147C22×D43—81no—
148C22×D43—81no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—41no—
152C2×C4×C43C2×C22⋊C411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×C4×C43C22×C811yescharacteristic
159C2×C4×C43C2×M1611yescharacteristic
160C2×C4×C43#13111yescharacteristic
161C2×C4×C43#13111yescharacteristic
162C22⋊D43—22no—
163C22⋊D43—22no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—41no—
168C2×Dic43—81no—
169D172—22no—
170D172—21no—
171D172—22no—
172D172—41no—
173D172—41no—
174D172C22⋊C812yes—
175C4×D43—22no—
176C4×D43—22no—
177C4×D43—42no—
178C4×D43—41no—
179C4×D43—41no—
180C4×D43—82no—
181C4×D43—81no—
182C4×D43—81no—
183Dic86—21no—
184Dic86C22⋊C812yes—
185C8×C43—22no—
186C8×C43—22no—
187C8×C43—41no—
188C8×C43—41no—
189C8×C43—81no—
190C43⋊C8—42no—
191C43⋊C8—81no—
192#9095—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43#38611yescharacteristic
196C22×C43C8×D411yescharacteristic
197C22×C43#43511yescharacteristic
198C2×D43—22no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—42no—
202C2×D43—82no—
203C2×D43—81no—
204C2×D43—81no—
205C2×D43—82no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43C2×C22⋊C811yescharacteristic
210C4×C43#40811yescharacteristic
211C4×C43C8×D411yescharacteristic
212C4×C43#43511yescharacteristic
213C4×C43#47111yescharacteristic
214C4×C43#47211yescharacteristic
215Dic43—22no—
216Dic43—41no—
217Dic43—41no—
218Dic43—81no—
219C8×#41—431no—
220C4×AGL(1,ℤ/8)—431no—
221#1477—431no—
222C2×D4⋊C8—431no—
223#1460—431no—
224#1283—431no—
225#1278D4311yescharacteristic, complemented
226C2×C43—21no—
227C2×C43—21no—
228C2×C43#186911yescharacteristic
229C2×C43#190611yescharacteristic
230C2×C43#190711yescharacteristic
231D43—42no—
232D43—82no—
233C2×AGL(1,ℤ/8)—431no—
234C4×#41—431no—
235C2×C4×D4—431no—
236C8×Q8—861no—
237#442—861no—
238#440—861no—
239C4×SD16—861no—
240C4×D8—861no—
241C8×D4—861no—
242C8×D4—862no—
243#431—431no—
244#431—861no—
245#431C2×D4311yescharacteristic
246#428—431no—
247C2×C4⋊C8—431no—
248#418—431no—
249#417—431no—
250C4×M16C2×D4311yescharacteristic
251C2×C4×C8—861no—
252C2×C4×C8C2×D4311yescharacteristic
253Q8⋊C8—861no—
254D4⋊C8—861no—
255D4⋊C8—861no—
256D4⋊C8—861no—
257#323—862no—
258C43#909511yescharacteristic, complemented, Sylow
259C2×#41—431no—
260C22×D4—431no—
261C23×C4—861no—
262AGL(1,ℤ/8)—434no—
263AGL(1,ℤ/8)—862no—
264C2×SD16—861no—
265C2×D8—861no—
266C2×M16C4×D4311yescharacteristic
267C2×M16C4×D4311yescharacteristic
268C22×C8—21no—
269C22×C8—862no—
270C22×C8—861no—
271C4×Q8—431no—
272C4×Q8—431no—
273C4×D4—431no—
274C4×D4—431no—
275C4×D4—861no—
276C4×D4—861no—
277C4×D4—861no—
278C4×D4—861no—
279C4×D4—861no—
280C4×D4—861no—
281#117—431no—
282#117—861no—
283C2×C4⋊C4—431no—
284C2×C22⋊C4—861no—
285C2×C42—861no—
286C2×C42C22×D4311yescharacteristic
287#107—861no—
288#106—861no—
289C4⋊C8—21no—
290C4⋊C8—862no—
291C4⋊C8—861no—
292C4⋊C8—861no—
293C4⋊C8—861no—
294#103—861no—
295#102—861no—
296#102—861no—
297#102—861no—
298C22⋊C8—21no—
299C22⋊C8—432no—
300C22⋊C8—862no—
301#97—21no—
302C4×C8—21no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—862no—
306C4×C8—861no—
307C4×C8D17211yescharacteristic
308C4×C8D17211yescharacteristic
309C24—861no—
310#41—432no—
311#41—432no—
312#41—861no—
313#41—861no—
314C2×Q8—431no—
315C2×D4—431no—
316C2×D4—432no—
317C2×D4—861no—
318C2×D4—861no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—861no—
322C2×D4—861no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—3441no—
328C22×C4—3441no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4C2×C4×D4311yescharacteristic
332C22×C4D4×D4311yescharacteristic
333C22×C4#1062190211yescharacteristic
334SD16—864no—
335D8—864no—
336M16—21no—
337M16—21no—
338M16—21no—
339M16C8×D4312yescomplemented
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—42no—
345C2×C8—41no—
346C2×C8—862no—
347C2×C8—3441no—
348C2×C8—1724no—
349C2×C8—1721no—
350C4⋊C4—431no—
351C4⋊C4—431no—
352C4⋊C4—861no—
353C4⋊C4—861no—
354C4⋊C4—861no—
355C4⋊C4—861no—
356C22⋊C4—861no—
357C22⋊C4—861no—
358C22⋊C4—861no—
359C22⋊C4—1721no—
360C22⋊C4—1721no—
361C42—861no—
362C42—861no—
363C42—861no—
364C42C2×D17211yescharacteristic
365C42#1062189811yescharacteristic
366C42D4×D4311yescharacteristic
367C42D4×D4311yescharacteristic
368C23—861no—
369C23—862no—
370C23—3441no—
371C23—3441no—
372C23—1721no—
373C23—1721no—
374C23#1306328711yescharacteristic
375Q8—432no—
376Q8—861no—
377D4—432no—
378D4—862no—
379D4—862no—
380D4—862no—
381D4—861no—
382D4—862no—
383D4—1721no—
384D4—1721no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—861no—
389C2×C4—862no—
390C2×C4—862no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—3442no—
394C2×C4—3441no—
395C2×C4—3441no—
396C2×C4—3441no—
397C2×C4—1722no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4C22⋊C4×D4311yescharacteristic
402C2×C4C4×D17211yescharacteristic
403C2×C4#1306329511yescharacteristic
404C2×C4#1306329811yescharacteristic
405C2×C4#1306330011yescharacteristic
406C2×C4#1306331011yescharacteristic
407C2×C4C2×C8×D4311yescharacteristic
408C2×C4M16×D4311yescharacteristic
409C2×C4#1306333111yescharacteristic
410C2×C4#1306333311yescharacteristic
411C8—22no—
412C8—22no—
413C8—41no—
414C8—41no—
415C8—81no—
416C8—3441no—
417C8—1722no—
418C22—21no—
419C22—21no—
420C22—862no—
421C22—3442no—
422C22—3442no—
423C22—3441no—
424C22—3441no—
425C22—1722no—
426C22—1721no—
427C22—1721no—
428C22#1458277711yescharacteristic
429C22#1458296411yescharacteristic
430C22#1458296911yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—862no—
435C4—3441no—
436C4—1721no—
437C4—1721no—
438C4C22⋊C8×D4311yescharacteristic
439C4#1458286411yescharacteristic
440C4C8×D17211yescharacteristic
441C4#1458297211yescharacteristic
442C4#1458316311yescharacteristic
443C4#1458317011yescharacteristic
444C2—21no—
445C2—21no—
446C2—3442no—
447C2—1722no—
448C2#1913488611yescharacteristic
449C2#1913509511yescharacteristic
450C2#1913510211yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1278C2
socleC22×C43#386
prime radicalC2×#13063353C4
cosocleC2×C42×C43C23
hypercenter#1278D43
hypocenterC43#9095
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
1. C8×#10621898C2semidirect
3. #19132983C2semidirect
4. C2×#14582628C2semidirect
5. #19132915C2semidirect
6. #19132446C2semidirect
7. C43×#1278C2semidirect
37. #13063353C8semidirect
99. C2×D172C2×C8semidirect
111. M16×C43C2×C8semidirect
225. #1278D43semidirect
258. C43#9095semidirect
339. M16C8×D43semidirect

Maximal subgroups

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

subgroupindex
C8×#106218982
C4×#130633532
#191329832
C2×#145826282
#191329152
#191324462
C43×#12782
#909543