Finite Group Databasebeta

← #24991236

Subgroups — #24991236

Order 11008.

540 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143708C211yesmaximal, characteristic, complemented
2C4×#13063353C211yesmaximal, characteristic
3#19135389C211yesmaximal, characteristic, complemented
4#19132985C211yesmaximal, characteristic, complemented
5#19132978C211yesmaximal, characteristic, complemented
6#19132446C211yesmaximal, characteristic, complemented
7C43×#1278C211yesmaximal, characteristic, complemented
8C2×#13063353C411yescharacteristic
9C4×#10621898C2211yescharacteristic
10C2×C4×D172C2211yescharacteristic
11#14583029—21no—
12#14583012—21no—
13#14583001—21no—
14C4×#10621873—21no—
15C4×D344—21no—
16#14582978—21no—
17#14582967—22no—
18#14582955—21no—
19#14582952C2211yescharacteristic
20#14582941C411yescharacteristic
21#14582921—21no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23#14582905C411yescharacteristic
24#14582901C411yescharacteristic
25C2×(C2×D43)⋊C8—22no—
26#14582631—21no—
27#14582628—21no—
28#14582626—21no—
29#14582626—21no—
30C43×#431C2211yescharacteristic
31C4×M16×C43C2211yescharacteristic
32C2×C4×C8×C43C2211yescharacteristic
33C2×#10621898C2×C411yescharacteristic
34C22×D172C2×C411yescharacteristic
35C22×C4×D43—21no—
36#13063353—22no—
37#13063353—22no—
38C2×#10621873—21no—
39C2×D344—21no—
40C2×#10621872—22no—
41C22×C43⋊C8D412yes—
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)—21no—
68(C2×D43)⋊C8—22no—
69(C2×D43)⋊C8—44no—
70#13063235—22no—
71C4×C43⋊C8—21no—
72C2×M16×C43C2×C411yescharacteristic
73C2×M16×C43C2×C411yescharacteristic
74C22×C8×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43D411yescharacteristic
77C4⋊C8×C43D411yescharacteristic
78C22⋊C8×C43—21no—
79#97×C43—21no—
80C4×C8×C43—21no—
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83C4×C8×C43—21no—
84C23×D43—21no—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C2×C22⋊D43—21no—
89C22×Dic43—21no—
90#10621898—21no—
91#10621898—21no—
92#10621898—21no—
93#10621898—21no—
94C2×D172—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172C22⋊C411yescharacteristic
100C2×D172M1612yescomplemented
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—21no—
104C2×C4×D43—42no—
105C2×C4×D43—42no—
106C2×C4×D43—41no—
107C2×C4×D43—41no—
108C2×Dic86C22⋊C411yescharacteristic
109M16×C43—21no—
110M16×C43—21no—
111M16×C43—21no—
112M16×C43M1612yescomplemented
113C2×C8×C43—21no—
114C2×C8×C43—22no—
115C2×C8×C43—21no—
116C2×C8×C43—21no—
117C2×C8×C43—21no—
118C2×C8×C43—41no—
119C2×C8×C43—41no—
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4111yescharacteristic
124C22⋊Dic43—21no—
125(C2×D43)⋊C4—21no—
126(C2×D43)⋊C4—21no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—41no—
129C4⋊Dic43—21no—
130C4⋊Dic43—21no—
131C4⋊Dic43C22⋊C411yescharacteristic
132C4⋊Dic43C22⋊C411yescharacteristic
133Dic43⋊C4—21no—
134Dic43⋊C4—21no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C2×C43⋊C8—22no—
139C2×C43⋊C8—42no—
140C2×C43⋊C8—41no—
141D344—24no—
142#10621873—24no—
143#10621872—82no—
144C23×C43C4×D411yescharacteristic
145C22×D43—21no—
146C22×D43—22no—
147C22×D43—42no—
148C22×D43—42no—
149C22×D43—41no—
150C22×D43—41no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—41no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12311yescharacteristic
160C2×C4×C43C2×M1611yescharacteristic
161C2×C4×C43C2×M1611yescharacteristic
162C2×C4×C43#13111yescharacteristic
163C2×C4×C43#13111yescharacteristic
164C22⋊D43—41no—
165C22⋊D43—41no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171D172—22no—
172D172—21no—
173D172—21no—
174D172—22no—
175D172—41no—
176D172—41no—
177C4×D43—41no—
178C4×D43—41no—
179C4×D43—41no—
180C4×D43—41no—
181C4×D43—81no—
182C4×D43—82no—
183C4×D43—81no—
184C4×D43—81no—
185Dic86—21no—
186Dic86—21no—
187C8×C43—22no—
188C8×C43—42no—
189C8×C43—41no—
190C8×C43—41no—
191C8×C43—41no—
192C43⋊C8—42no—
193C43⋊C8—81no—
194#8956—431nomaximal, Sylow
195C22×C43—21no—
196C22×C43—21no—
197C22×C43#38611yescharacteristic
198C22×C43#43511yescharacteristic
199C22×C43#43611yescharacteristic
200C2×D43—44no—
201C2×D43—42no—
202C2×D43—41no—
203C2×D43—41no—
204C2×D43—41no—
205C2×D43—82no—
206C2×D43—81no—
207C2×D43—81no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43#40711yescharacteristic
212C4×C43#40811yescharacteristic
213C4×C43#43511yescharacteristic
214C4×C43#43611yescharacteristic
215C4×C43#45311yescharacteristic
216C4×C43#45411yescharacteristic
217Dic43—41no—
218Dic43—41no—
219Dic43—41no—
220Dic43—81no—
221#2989—431no—
222C4×AGL(1,ℤ/8)—431no—
223#1954—431no—
224#1478—431no—
225#1476—431no—
226#1283—431no—
227#1278D4311yescharacteristic, complemented
228C2×C43—21no—
229C2×C43—21no—
230C2×C43#187011yescharacteristic
231C2×C43#188111yescharacteristic
232C2×C43#188311yescharacteristic
233D43—81no—
234D43—82no—
235C2×AGL(1,ℤ/8)—431no—
236C4×#41—431no—
237C2×C4×D4—431no—
238#446—861no—
239#442—861no—
240#440—861no—
241C4×SD16—861no—
242C4×D8—861no—
243#436—861no—
244#435—862no—
245#432—861no—
246#431—431no—
247#431C2×D4311yescharacteristic
248#428—431no—
249#423—861no—
250C2×C4⋊C8—431no—
251#418—431no—
252#417—431no—
253C2×C22⋊C8—862no—
254C4×M16C2×D4311yescharacteristic
255C2×C4×C8C2×D4311yescharacteristic
256Q8⋊C8—861no—
257D4⋊C8—861no—
258D4⋊C8—861no—
259D4⋊C8—861no—
260C43#895611yescharacteristic, complemented, Sylow
261C2×#41—431no—
262C22×D4—431no—
263C23×C4—861no—
264AGL(1,ℤ/8)—862no—
265AGL(1,ℤ/8)—862no—
266C2×SD16—861no—
267C2×D8—861no—
268C2×M16—862no—
269C2×M16C4×D4311yescharacteristic
270C2×M16C4×D4311yescharacteristic
271C22×C8—21no—
272C22×C8—432no—
273C4×Q8—431no—
274C4×Q8—431no—
275C4×D4—431no—
276C4×D4—431no—
277C4×D4—861no—
278C4×D4—861no—
279C4×D4—861no—
280C4×D4—861no—
281C4×D4—861no—
282C4×D4—861no—
283#117—431no—
284#117—861no—
285C2×C4⋊C4—431no—
286C2×C22⋊C4—861no—
287C2×C42—861no—
288C2×C42C22×D4311yescharacteristic
289#107—861no—
290#106—861no—
291C4⋊C8—862no—
292C4⋊C8—861no—
293C4⋊C8—861no—
294C4⋊C8—861no—
295C4⋊C8D17211yescharacteristic
296C4⋊C8D17211yescharacteristic
297#103—861no—
298#102—861no—
299#102—861no—
300#102—861no—
301C22⋊C8—21no—
302C22⋊C8—862no—
303C22⋊C8—861no—
304C22⋊C8—1724no—
305#97—21no—
306#97—862no—
307C4×C8—21no—
308C4×C8—21no—
309C4×C8—21no—
310C4×C8—21no—
311C4×C8—861no—
312C24—861no—
313#41—861no—
314#41—861no—
315#41—861no—
316#41—861no—
317C2×Q8—431no—
318C2×D4—431no—
319C2×D4—432no—
320C2×D4—861no—
321C2×D4—861no—
322C2×D4—861no—
323C2×D4—861no—
324C2×D4—861no—
325C2×D4—861no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—1722no—
331C22×C4—1722no—
332C22×C4—1721no—
333C22×C4—1721no—
334C22×C4C2×C4×D4311yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4#1062190211yescharacteristic
337SD16—864no—
338D8—864no—
339M16—21no—
340M16—21no—
341M16—21no—
342M16—3442no—
343M16#1062187212yescomplemented
344C2×C8—21no—
345C2×C8—22no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—862no—
352C2×C8—1721no—
353C2×C8—1722no—
354C4⋊C4—431no—
355C4⋊C4—431no—
356C4⋊C4—861no—
357C4⋊C4—861no—
358C4⋊C4—861no—
359C4⋊C4—861no—
360C22⋊C4—861no—
361C22⋊C4—861no—
362C22⋊C4—861no—
363C22⋊C4—1721no—
364C22⋊C4—1721no—
365C42—861no—
366C42—861no—
367C42—861no—
368C42C2×D17211yescharacteristic
369C42#1062189811yescharacteristic
370C42D4×D4311yescharacteristic
371C42D4×D4311yescharacteristic
372C23—862no—
373C23—861no—
374C23—1722no—
375C23—1722no—
376C23—1721no—
377C23—1721no—
378C23#1306328711yescharacteristic
379Q8—861no—
380Q8—861no—
381D4—861no—
382D4—862no—
383D4—861no—
384D4—862no—
385D4—1721no—
386D4—1721no—
387D4—1721no—
388D4—1721no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—861no—
395C2×C4—3442no—
396C2×C4—3441no—
397C2×C4—3441no—
398C2×C4—3441no—
399C2×C4—1722no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4C22⋊C4×D4311yescharacteristic
406C2×C4C4×D17211yescharacteristic
407C2×C4#1306329511yescharacteristic
408C2×C4#1306329811yescharacteristic
409C2×C4#1306330011yescharacteristic
410C2×C4#1306331011yescharacteristic
411C2×C4M16×D4311yescharacteristic
412C2×C4C2×#1062187211yescharacteristic
413C2×C4#1306333111yescharacteristic
414C2×C4#1306333311yescharacteristic
415C8—22no—
416C8—42no—
417C8—41no—
418C8—41no—
419C8—41no—
420C8—3441no—
421C8—1722no—
422C22—21no—
423C22—21no—
424C22—3442no—
425C22—3441no—
426C22—3441no—
427C22—1724no—
428C22—1721no—
429C22—1722no—
430C22—1721no—
431C22—1721no—
432C22#1458277711yescharacteristic
433C22#1458296911yescharacteristic
434C22#1458297611yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—3441no—
439C4—1721no—
440C4—1721no—
441C4—1721no—
442C4#1458286111yescharacteristic
443C4#1458286411yescharacteristic
444C4#1458297211yescharacteristic
445C4#1458297811yescharacteristic
446C4#1458306811yescharacteristic
447C4#1458307311yescharacteristic
448C2—21no—
449C2—21no—
450C2—3442no—
451C2—3441no—
452C2#1913489111yescharacteristic
453C2#1913495811yescharacteristic
454C2#1913497211yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1278C2
socleC22×C43#386
prime radicalC2×#13063353C4
cosocleC2×C42×C43C23
hypercenter#1278D43
hypocenterC43#8956
LCSG ▷ C22×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. #19143708C2semidirect
3. #19135389C2semidirect
4. #19132985C2semidirect
5. #19132978C2semidirect
6. #19132446C2semidirect
7. C43×#1278C2semidirect
100. C2×D172M16semidirect
112. M16×C43M16semidirect
227. #1278D43semidirect
260. C43#8956semidirect
343. M16#10621872semidirect

Maximal subgroups

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

subgroupindex
#191437082
C4×#130633532
#191353892
#191329852
#191329782
#191324462
C43×#12782
#895643