Finite Group Databasebeta

← #24991462

Subgroups — #24991462

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144627C211yesmaximal, characteristic
2M16×Dic86C211yesmaximal, characteristic, complemented
3#19135514C211yesmaximal, characteristic
4C4×#13063250C211yesmaximal, characteristic, complemented
5#19133047C211yesmaximal, characteristic
6#19132497C211yesmaximal, characteristic, complemented
7C43×#1278C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583218—21no—
11#14583185C411yescharacteristic, complemented
12#14583185C411yescharacteristic, complemented
13#14583100C411yescharacteristic, complemented
14#14583100C411yescharacteristic, complemented
15#14583040—21no—
16#14583029—21no—
17#14583027—22no—
18C8×Dic86—21no—
19C4×#10621873—21no—
20C4×#10621873—21no—
21#14582923C2211yescharacteristic
22#14582922—21no—
23C2×#13063251—21no—
24C2×#13063251—21no—
25C2×#13063250—21no—
26M16×Dic43—21no—
27C4×C4⋊Dic43C2211yescharacteristic
28#14582662—21no—
29#14582628—22no—
30C43×#431C2211yescharacteristic
31C4×M16×C43C2211yescharacteristic
32C2×C4×C8×C43C2211yescharacteristic
33C2×#10621898—21no—
34C22×Dic86D411yescharacteristic
35C2×#10621873—21no—
36C2×#10621873—21no—
37C2×#10621877—21no—
38#13063325C2×C411yescharacteristic
39#13063322C2×C411yescharacteristic
40#13063313—21no—
41#13063299—21no—
42#13063299—21no—
43C4×Dic86—21no—
44C4×Dic86—21no—
45C4×Dic86C2×C411yescharacteristic
46C4×Dic86C2×C411yescharacteristic
47C4×Dic86D411yescharacteristic
48C4×Dic86D411yescharacteristic
49C4×D172—21no—
50C4×D172—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43D411yescharacteristic
53C2×Dic43⋊C4—21no—
54C2×C4×Dic43—21no—
55C2×C4×Dic43—21no—
56#13063257—21no—
57#13063257—21no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)D412yes—
60Dic43⋊C8—22no—
61Dic43⋊C8—22no—
62#13063251—42no—
63#13063251—42no—
64#13063250—24no—
65#13063250—21no—
66#13063250—21no—
67#13063247—21no—
68#13063247—21no—
69#13063235—22no—
70C8×Dic43—22no—
71C43⋊#95—21no—
72C2×M16×C43D411yescharacteristic
73C2×M16×C43D411yescharacteristic
74C22×C8×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43C2×C411yescharacteristic
77C4⋊C8×C43C2×C411yescharacteristic
78C22⋊C8×C43—21no—
79#97×C43—21no—
80C4×C8×C43—21no—
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83C4×C8×C43—21no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C2×C22⋊D43—41no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—41no—
91#10621898—41no—
92#10621898—41no—
93#10621898—41no—
94#10621898—41no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—21no—
98C2×C4×D43—41no—
99C2×Dic86—22no—
100C2×Dic86—21no—
101C2×Dic86—21no—
102C2×Dic86—41no—
103C2×Dic86C22⋊C411yescharacteristic
104C2×Dic86C22⋊C411yescharacteristic
105M16×C43—21no—
106M16×C43—21no—
107M16×C43—21no—
108M16×C43SD1612yescomplemented
109C2×C8×C43—21no—
110C2×C8×C43—22no—
111C2×C8×C43—21no—
112C2×C8×C43—21no—
113C2×C8×C43—21no—
114C2×C8×C43—41no—
115C2×C8×C43—41no—
116C42×C43C22×C411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120(C2×D43)⋊C4—41no—
121(C2×D43)⋊C4—41no—
122C4⋊Dic43—21no—
123C4⋊Dic43—22no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—41no—
127C4⋊Dic43C22⋊C411yescharacteristic
128C4⋊Dic43C22⋊C411yescharacteristic
129Dic43⋊C4—21no—
130Dic43⋊C4—21no—
131Dic43⋊C4—21no—
132Dic43⋊C4—21no—
133C4×Dic43—21no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137C4×Dic43—41no—
138C4×Dic43—41no—
139#10621877—41no—
140#10621877—41no—
141C2×C43⋊C8—22no—
142#10621873—42no—
143#10621873—42no—
144C23×C43#12111yescharacteristic
145C22×D43—41no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—41no—
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12311yescharacteristic
155C2×C4×C43C2×SD1611yescharacteristic
156C2×C4×C43#13511yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43#13711yescharacteristic
159C22⋊D43—81no—
160C22⋊D43—81no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—42no—
166C2×Dic43—42no—
167C2×Dic43—41no—
168C2×Dic43—81no—
169C2×Dic43—81no—
170C2×Dic43—81no—
171D172—42no—
172D172—41no—
173D172—41no—
174D172—41no—
175D172—41no—
176C4×D43—81no—
177C4×D43—81no—
178Dic86—21no—
179Dic86—21no—
180Dic86—21no—
181Dic86—42no—
182Dic86—41no—
183Dic86—41no—
184Dic86#10412yescomplemented
185C8×C43—22no—
186C8×C43—42no—
187C8×C43—41no—
188C8×C43—41no—
189C8×C43—41no—
190C43⋊C8—42no—
191#8992—431nomaximal, Sylow
192C22×C43—21no—
193C22×C43—21no—
194C22×C43#38611yescharacteristic
195C22×C43#46011yescharacteristic
196C22×C43#46411yescharacteristic
197C2×D43—81no—
198C2×D43—81no—
199C2×D43—81no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43C2×#10411yescharacteristic
204C4×C43#42111yescharacteristic
205C4×C43C4×SD1611yescharacteristic
206C4×C43#44011yescharacteristic
207C4×C43#44811yescharacteristic
208C4×C43#44911yescharacteristic
209Dic43—22no—
210Dic43—41no—
211Dic43—41no—
212Dic43—41no—
213Dic43—82no—
214Dic43—81no—
215#3103—431no—
216Q8×M16—431no—
217#1980—431no—
218C4×#103—431no—
219#1492—431no—
220#1303—431no—
221#1278D4311yescharacteristic, complemented
222C2×C43—21no—
223C2×C43—21no—
224C2×C43#187111yescharacteristic
225C2×C43#188011yescharacteristic
226C2×C43#188111yescharacteristic
227D43—161no—
228#532—431no—
229C2×C4×Q8—431no—
230#481—861no—
231#475—431no—
232#475—431no—
233#460—431no—
234#460—431no—
235#448—861no—
236#446—861no—
237#446—862no—
238C8×Q8—861no—
239C4×SD16—861no—
240C4×SD16—861no—
241#431C2×D4311yescharacteristic
242#423—431no—
243#423—861no—
244C2×#104—861no—
245C2×#104—861no—
246C2×#103—861no—
247C4×M16—861no—
248C4×M16C2×D4311yescharacteristic
249C2×C4×C8C2×D4311yescharacteristic
250C4×C4⋊C4—431no—
251#340—861no—
252D4⋊C8—862no—
253C43#899211yescharacteristic, complemented, Sylow
254C2×#41—861no—
255C22×Q8—431no—
256C2×SD16—861no—
257C2×SD16—861no—
258C2×M16—861no—
259C2×M16D17211yescharacteristic
260C2×M16D17211yescharacteristic
261C22×C8—21no—
262C4⋊Q8—431no—
263#127—431no—
264#124—861no—
265#121—861no—
266#121—861no—
267C4×Q8—431no—
268C4×Q8—431no—
269C4×Q8—431no—
270C4×Q8—431no—
271C4×Q8—861no—
272C4×Q8—861no—
273C4×D4—861no—
274C4×D4—861no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4—861no—
278C2×C42—861no—
279C2×C42—861no—
280C2×C42C22×D4311yescharacteristic
281#106—861no—
282#106—861no—
283C4⋊C8—432no—
284C4⋊C8—862no—
285C4⋊C8—862no—
286C4⋊C8—861no—
287C4⋊C8C4×D4311yescharacteristic
288C4⋊C8C4×D4311yescharacteristic
289#104—1722no—
290#104—1722no—
291#103—861no—
292#103—861no—
293#103—864no—
294#102—861no—
295#102—861no—
296C22⋊C8—21no—
297#97—21no—
298#97—862no—
299C4×C8—21no—
300C4×C8—21no—
301C4×C8—21no—
302C4×C8—21no—
303C4×C8—862no—
304#95—861no—
305#41—1721no—
306#41—1721no—
307#41—1721no—
308#41—1721no—
309C2×Q8—431no—
310C2×Q8—431no—
311C2×Q8—862no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×Q8—1721no—
315C2×D4—861no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4—1721no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—1721no—
322C22×C4—1721no—
323C22×C4C2×D17211yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C22×C4#1062190211yescharacteristic
326SD16—1722no—
327SD16—1722no—
328M16—21no—
329M16—21no—
330M16—21no—
331M16—1721no—
332M16—1721no—
333M16#1062187312yescomplemented
334C2×C8—21no—
335C2×C8—22no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—862no—
342C4⋊C4—431no—
343C4⋊C4—431no—
344C4⋊C4—862no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—1721no—
353C22⋊C4—1721no—
354C22⋊C4—1721no—
355C42—861no—
356C42—861no—
357C42—861no—
358C42—861no—
359C42—1721no—
360C42—1721no—
361C42C2×C4×D4311yescharacteristic
362C42#1062189811yescharacteristic
363C42D4×D4311yescharacteristic
364C42D4×D4311yescharacteristic
365C23—1721no—
366C23#1306330011yescharacteristic
367Q8—432no—
368Q8—861no—
369Q8—861no—
370Q8—861no—
371Q8—1722no—
372Q8—1721no—
373Q8—1721no—
374D4—3441no—
375D4—3441no—
376D4—1722no—
377D4—1721no—
378D4—1721no—
379D4—1721no—
380D4—1721no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—3441no—
389C2×C4—3441no—
390C2×C4—3441no—
391C2×C4—3441no—
392C2×C4—3441no—
393C2×C4—1722no—
394C2×C4—1722no—
395C2×C4—1721no—
396C2×C4C22⋊C4×D4311yescharacteristic
397C2×C4#1306328711yescharacteristic
398C2×C4C4×D17211yescharacteristic
399C2×C4#1306329511yescharacteristic
400C2×C4#1306329811yescharacteristic
401C2×C4#1306331011yescharacteristic
402C2×C4C2×#1062187311yescharacteristic
403C2×C4#1306334711yescharacteristic
404C2×C4#1306335311yescharacteristic
405C2×C4#1306335811yescharacteristic
406C8—22no—
407C8—42no—
408C8—41no—
409C8—41no—
410C8—41no—
411C8—1722no—
412C22—21no—
413C22—21no—
414C22—3441no—
415C22—3441no—
416C22—3441no—
417C22#1458277711yescharacteristic
418C22#1458310011yescharacteristic
419C22#1458312211yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—862no—
424C4—3442no—
425C4—3441no—
426C4—1721no—
427C4—1721no—
428C4—1721no—
429C4#104×D4311yescharacteristic
430C4#1458291411yescharacteristic
431C4C4×#1062187311yescharacteristic
432C4#1458300111yescharacteristic
433C4#1458304011yescharacteristic
434C4#1458304611yescharacteristic
435C2—21no—
436C2—21no—
437C2—6881no—
438C2#1913489611yescharacteristic
439C2#1913494911yescharacteristic
440C2#1913495811yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1278C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1278D43
hypocenterC43#8992
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
2. M16×Dic86C2semidirect
4. C4×#13063250C2semidirect
6. #19132497C2semidirect
7. C43×#1278C2semidirect
11. #14583185C4semidirect
12. #14583185C4semidirect
13. #14583100C4semidirect
14. #14583100C4semidirect
108. M16×C43SD16semidirect
184. Dic86#104semidirect
221. #1278D43semidirect
253. C43#8992semidirect
333. M16#10621873semidirect

Maximal subgroups

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

subgroupindex
#191446272
M16×Dic862
#191355142
C4×#130632502
#191330472
#191324972
C43×#12782
#899243