Finite Group Databasebeta

← #25251007

Subgroups — #25251007

Order 11008.

674 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#19147729C211yesmaximal, characteristic
2C2×#14583339C211yesmaximal, characteristic, complemented
3#19145089C211yesmaximal, characteristic, complemented
4#19136676C214yesmaximal, complemented
5#19136664C214yesmaximal, complemented
6#19136361C211yesmaximal, characteristic, complemented
7#19136342C211yesmaximal, characteristic, complemented
8C2×#14582714C211yesmaximal, characteristic, complemented
9C43×#2957C211yesmaximal, characteristic, complemented
10C2×#13063358—21no—
11C2×#13063347C2211yescharacteristic
12C22×Dic172C2211yescharacteristic
13#14583475—21no—
14#14583340—21no—
15#14583339—22no—
16#14583339C2214yes—
17#14583339C2212yes—
18#14583335—21no—
19#14583334C2212yes—
20#14583329—22no—
21C2×#13063271—21no—
22C2×#13063269—21no—
23C2×#13063265C2211yescharacteristic
24C2×#13063265C2211yescharacteristic
25#14583293—22no—
26#14583283C2212yescomplemented
27#14583279C2212yescomplemented
28#14582720C2214yescomplemented
29#14582714C2214yescomplemented
30#14582714C2212yescomplemented
31#14582711C2212yescomplemented
32C2×#135×C43C2211yescharacteristic
33C43×#568—21no—
34C43×#444—22no—
35C43×#443C2214yes—
36C2×#108×C43C2211yescharacteristic
37C43×#421—21no—
38C43×#405C2211yescharacteristic
39C2×#10621898—21no—
40C22×Dic86—21no—
41#13063358—42no—
42#13063358—42no—
43#13063347—21no—
44#13063347—21no—
45#13063347—21no—
46#13063347—21no—
47C2×Dic172—21no—
48C2×Dic172—21no—
49C2×Dic172—21no—
50C2×Dic172—21no—
51C2×Dic172—21no—
52C2×Dic172—22no—
53C2×Dic172C2312yes—
54C2×Dic172C2311yescharacteristic
55C2×#10621873—21no—
56C2×#10621873—22no—
57C2×D344C2311yescharacteristic
58#13063325—22no—
59#13063313—22no—
60#13063309—42no—
61#13063305—42no—
62#13063271—24no—
63#13063271—22no—
64#13063269—24no—
65#13063269—22no—
66#13063268—22no—
67#13063266—22no—
68#13063265—21no—
69#13063265—21no—
70#13063265C2312yes—
71#13063265C2312yes—
72C2×C43⋊C16—21no—
73C2×C43⋊C16—21no—
74C2×#41×C43—21no—
75#135×C43—21no—
76#135×C43—21no—
77#135×C43D412yes—
78#135×C43C2312yes—
79C2×Q16×C43D411yescharacteristic
80C2×SD16×C43—21no—
81C2×D8×C43D411yescharacteristic
82#131×C43—24no—
83#131×C43—42no—
84C2×M16×C43—21no—
85C2×M16×C43—42no—
86C2×M16×C43D411yescharacteristic
87C22×C8×C43C2311yescharacteristic
88#117×C43D411yescharacteristic
89#108×C43—21no—
90#108×C43C2312yes—
91#104×C43—24no—
92#97×C43D412yes—
93C4×C8×C43C2312yes—
94#41×C43—22no—
95#41×C43—22no—
96#41×C43—41no—
97#41×C43—41no—
98C2×Q8×C43—21no—
99C2×D4×C43—21no—
100C2×D4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43C2×D411yescharacteristic
103C2×C22⋊D43—41no—
104C22×Dic43—41no—
105#10621898—41no—
106#10621898—41no—
107#10621898—41no—
108#10621898—41no—
109C2×D172—21no—
110C2×C4×D43—41no—
111C2×Dic86—22no—
112C2×Dic86—21no—
113C2×Dic86—41no—
114C2×Dic86—41no—
115C2×Dic86—41no—
116C2×Dic86—41no—
117C2×Dic86—41no—
118Q16×C43—21no—
119Q16×C43C2×D412yes—
120SD16×C43—22no—
121SD16×C43—22no—
122D8×C43—21no—
123D8×C43C2×D412yes—
124M16×C43—22no—
125M16×C43—41no—
126M16×C43—44no—
127M16×C43D812yes—
128M16×C43D812yes—
129C2×C8×C43—41no—
130C2×C8×C43—44no—
131C2×C8×C43C2×D411yescharacteristic
132C2×C8×C43C2×D411yescharacteristic
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2×D412yes—
135C2×C8×C43#4111yescharacteristic
136C2×C8×C43#4111yescharacteristic
137C2×C8×C43C2411yescharacteristic
138C4⋊C4×C43—21no—
139C22⋊C4×C43—21no—
140C42×C43C2×D412yes—
141(C2×D43)⋊C4—44no—
142C4⋊Dic43—44no—
143Dic172—22no—
144Dic172—21no—
145Dic172—22no—
146Dic172—21no—
147Dic172—41no—
148Dic172—41no—
149Dic172—44no—
150D344—21no—
151D344—21no—
152#10621873—41no—
153#10621873—41no—
154#10621873—44no—
155C43⋊C16—22no—
156C43⋊C16—22no—
157C23×C43—41no—
158C23×C43AGL(1,ℤ/8)11yescharacteristic
159C22×D43—41no—
160Q8×C43—22no—
161Q8×C43—41no—
162D4×C43—22no—
163D4×C43—42no—
164D4×C43—42no—
165D4×C43—41no—
166C2×C4×C43—22no—
167C2×C4×C43—41no—
168C2×C4×C43—42no—
169C2×C4×C43—42no—
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43C2×D811yescharacteristic
173C2×C4×C43C2×D811yescharacteristic
174C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C43C22×D411yescharacteristic
176C22⋊D43—81no—
177C22⋊D43—81no—
178C2×Dic43—41no—
179C2×Dic43—42no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182D172—41no—
183D172—41no—
184C4×D43—81no—
185C4×D43—81no—
186Dic86—41no—
187Dic86—42no—
188Dic86—42no—
189Dic86—41no—
190Dic86—81no—
191Dic86—81no—
192C8×C43—42no—
193C8×C43#12111yescharacteristic
194C8×C43#12111yescharacteristic
195C8×C43C2×D814yes—
196C8×C43C22×D411yescharacteristic
197C8×C43C2×#4111yescharacteristic
198#33596—431nomaximal, Sylow
199C22×C43—41no—
200C22×C43—42no—
201C22×C43—161no—
202C22×C43#45911yescharacteristic
203C22×C43#45911yescharacteristic
204C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
205C2×D43—82no—
206C2×D43—81no—
207C4×C43—42no—
208C4×C43—42no—
209C4×C43#45911yescharacteristic
210C4×C43#45911yescharacteristic
211C4×C43C2×#12111yescharacteristic
212C4×C43C22×D811yescharacteristic
213Dic43—82no—
214Dic43—81no—
215#3414—431no—
216C2×#510—431no—
217#3156—431no—
218#2957D4311yescharacteristic, complemented
219#2214—434no—
220#2212—434no—
221#2153—431no—
222#2148—431no—
223C2×#362—431no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43—21no—
227C2×C43—82no—
228C2×C43C2×#45911yescharacteristic
229D43—161no—
230C2×#137—861no—
231C2×#135—431no—
232C2×#135C2×D4311yescharacteristic
233C22×Q16—431no—
234#568—21no—
235#536—861no—
236#510—434no—
237#510—432no—
238#510—862no—
239#510—861no—
240#509—432no—
241#509—861no—
242#508—862no—
243C2×Q32—861no—
244C2×SD32—861no—
245C2×M32—431no—
246C2×M32—431no—
247#497—862no—
248#495—432no—
249#494—432no—
250#444—22no—
251#443C2×D4314yes—
252C2×#108C2×D4311yescharacteristic
253#421—21no—
254#405C2×D4311yescharacteristic
255#364—434no—
256#362—434no—
257#362—432no—
258#361—432no—
259C43#3359611yescharacteristic, complemented, Sylow
260C2×#41—21no—
261C2×#41—861no—
262C22×Q8—861no—
263#137—1722no—
264#137—1722no—
265#135—21no—
266#135—21no—
267#135—861no—
268#135—861no—
269#135—861no—
270#135—861no—
271#135D17212yes—
272#135C22×D4312yes—
273C2×Q16—432no—
274C2×Q16—431no—
275C2×Q16—861no—
276C2×Q16—861no—
277C2×Q16—861no—
278C2×Q16—861no—
279C2×Q16—861no—
280C2×Q16—862no—
281C2×Q16D17211yescharacteristic
282C2×SD16—21no—
283C2×SD16—861no—
284C2×SD16—862no—
285C2×D8—431no—
286C2×D8D17211yescharacteristic
287#131—24no—
288#131—42no—
289C2×M16—21no—
290C2×M16—42no—
291C2×M16C22⋊D4311yescharacteristic
292C22×C8C22×D4311yescharacteristic
293C4⋊Q8—862no—
294#124—862no—
295#123—1722no—
296C22⋊Q8—1722no—
297#117C22⋊D4311yescharacteristic
298Q32—864no—
299Q32—862no—
300SD32—862no—
301SD32—864no—
302SD32—862no—
303D16—862no—
304M32—432no—
305M32—432no—
306M32—861no—
307M32—861no—
308C2×C16—861no—
309C2×C16—861no—
310#108—21no—
311#108C22×D4312yes—
312#104—24no—
313#97C22⋊D4312yes—
314C4×C8C22×D4312yes—
315#41—22no—
316#41—22no—
317#41—41no—
318#41—41no—
319#41—1721no—
320#41—1721no—
321#41—1721no—
322#41—1721no—
323C2×Q8—21no—
324C2×Q8—862no—
325C2×Q8—861no—
326C2×Q8—1721no—
327C2×Q8—1721no—
328C2×Q8—1721no—
329C2×Q8—1721no—
330C2×Q8—1721no—
331C2×D4—21no—
332C2×D4—41no—
333C2×D4—861no—
334C2×D4—1721no—
335C22×C4—41no—
336C22×C4—1721no—
337C22×C4—1721no—
338C22×C4C2×C22⋊D4311yescharacteristic
339Q16—21no—
340Q16—862no—
341Q16—861no—
342Q16—862no—
343Q16—861no—
344Q16—1721no—
345Q16—1721no—
346Q16—1724no—
347Q16C2×D17212yes—
348SD16—22no—
349SD16—22no—
350SD16—1721no—
351SD16—1721no—
352SD16—1724no—
353D8—21no—
354D8—861no—
355D8—861no—
356D8C2×D17212yes—
357M16—22no—
358M16—41no—
359M16—44no—
360M16#1062188212yes—
361M16#1062188212yes—
362C2×C8—41no—
363C2×C8—44no—
364C2×C8C2×D17211yescharacteristic
365C2×C8C2×D17211yescharacteristic
366C2×C8#1062189811yescharacteristic
367C2×C8#1062189811yescharacteristic
368C2×C8C2×C22⋊D4311yescharacteristic
369C2×C8C2×C22⋊D4312yes—
370C2×C8C23×D4311yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—1724no—
373C22⋊C4—21no—
374C22⋊C4—1724no—
375C42C2×C22⋊D4312yes—
376C16—862no—
377C16—862no—
378C23—41no—
379C23—1721no—
380C23#1306335011yescharacteristic
381Q8—22no—
382Q8—41no—
383Q8—3441no—
384Q8—3441no—
385Q8—1721no—
386Q8—1722no—
387Q8—1722no—
388Q8—1721no—
389D4—22no—
390D4—42no—
391D4—42no—
392D4—41no—
393D4—3441no—
394D4—3441no—
395D4—1721no—
396D4—1721no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—3441no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—1722no—
406C2×C4—1721no—
407C2×C4#1306329911yescharacteristic
408C2×C4#1306329911yescharacteristic
409C2×C4C2×#1062188211yescharacteristic
410C2×C4C2×#1062188211yescharacteristic
411C2×C4#1306335011yescharacteristic
412C2×C4C22×C22⋊D4311yescharacteristic
413C8—42no—
414C8#1306329911yescharacteristic
415C8#1306329911yescharacteristic
416C8C2×#1062188214yes—
417C8C22×D17211yescharacteristic
418C8C2×#1062189811yescharacteristic
419C22—41no—
420C22—42no—
421C22—161no—
422C22—3442no—
423C22—3441no—
424C22#1458309411yescharacteristic
425C22#1458309411yescharacteristic
426C22C2×#1306335011yescharacteristic
427C4—42no—
428C4—42no—
429C4—3441no—
430C4—3442no—
431C4#1458309411yescharacteristic
432C4#1458309411yescharacteristic
433C4C2×#1306329911yescharacteristic
434C4C22×#1062188211yescharacteristic
435C2—21no—
436C2—21no—
437C2—21no—
438C2—82no—
439C2—6881no—
440C2C2×#1458309411yescharacteristic
subgroupG/H
centerC2C2×#14583094
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2957C2
socleC2×C43C2×#459
prime radical#19147729C2
hypercenter#2957D43
hypocenterC43#33596
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. C2×#14583339C2semidirect
3. #19145089C2semidirect
4. #19136676C2semidirect
5. #19136664C2semidirect
6. #19136361C2semidirect
7. #19136342C2semidirect
8. C2×#14582714C2semidirect
9. C43×#2957C2semidirect
26. #14583283C22semidirect
27. #14583279C22semidirect
28. #14582720C22semidirect
29. #14582714C22semidirect
30. #14582714C22semidirect
31. #14582711C22semidirect
218. #2957D43semidirect
259. C43#33596semidirect

Maximal subgroups

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

subgroupindex
#191477292
C2×#145833392
#191450892
#191366762
#191366642
#191363612
#191363422
C2×#145827142
C43×#29572
#3359643