Finite Group Databasebeta

← #25251172

Subgroups — #25251172

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583329C211yesmaximal, characteristic, complemented
2C2×#14583316C211yesmaximal, characteristic, complemented
3#19144315C211yesmaximal, characteristic, complemented
4#19136727C212yesmaximal, complemented
5#19136723C212yesmaximal, complemented
6#19136718C212yesmaximal, complemented
7#19136713C212yesmaximal, complemented
8C2×#14582728C211yesmaximal, characteristic, complemented
9#19136344C211yesmaximal, characteristic, complemented
10#19136342C211yesmaximal, characteristic, complemented
11C43×#3067C211yesmaximal, characteristic, complemented
12#14583697—21no—
13C2×#13063347C2211yescharacteristic
14#14583329—21no—
15#14583329—21no—
16#14583329—21no—
17#14583329—21no—
18C2×#13063271C2211yescharacteristic, complemented
19C2×#13063269C2211yescharacteristic, complemented
20C2×#13063268C2211yescharacteristic, complemented
21C2×#13063266C2211yescharacteristic, complemented
22#14583316—21no—
23#14583316—21no—
24#14583316C2212yes—
25#14583316C2212yes—
26C2×#13063265—21no—
27C2×#13063265C2211yescharacteristic
28C22×C43⋊C16—21no—
29C22×C43⋊C16C2211yescharacteristic
30#14583174C2212yes—
31#14583169C2212yes—
32#14583162—22no—
33C2×#13063261C2211yescharacteristic
34#14582881—21no—
35#14582728C2212yescomplemented
36#14582728C2212yescomplemented
37#14582715C2212yescomplemented
38#14582714C2212yescomplemented
39#14582712C2212yescomplemented
40#14582711C2212yescomplemented
41C43×#575—21no—
42C2×#135×C43C2211yescharacteristic
43C2×#131×C43C2211yescharacteristic
44C43×#473C2212yes—
45C43×#472C2212yes—
46C43×#471—22no—
47C2×#108×C43C2211yescharacteristic
48C43×#413—21no—
49C2×#10621898—21no—
50#13063356—41no—
51#13063355—22no—
52#13063351—41no—
53#13063350—22no—
54#13063347—21no—
55#13063347—21no—
56#13063347—21no—
57#13063347—21no—
58#13063345—42no—
59C2×Dic172C2311yescharacteristic
60C2×#10621873—21no—
61C2×D344C2311yescharacteristic
62C2×#10621877—21no—
63#13063271—21no—
64#13063271—21no—
65#13063269—21no—
66#13063269—21no—
67#13063268—21no—
68#13063268—21no—
69#13063266—21no—
70#13063266—21no—
71#13063265—21no—
72#13063265—22no—
73#13063265—22no—
74#13063265C2312yes—
75C2×C43⋊C16—21no—
76C2×C43⋊C16—22no—
77C2×C43⋊C16—22no—
78C2×C43⋊C16D411yescharacteristic
79C2×C43⋊C16D411yescharacteristic
80C2×C43⋊C16D411yescharacteristic
81C2×C43⋊C16D411yescharacteristic
82C2×C43⋊C16C2311yescharacteristic
83C2×C43⋊C16C2311yescharacteristic
84#13063261—21no—
85#13063261C2312yes—
86#13063243—22no—
87#13063241—22no—
88C2×#41×C43—21no—
89C2×#41×C43D411yescharacteristic
90#137×C43—22no—
91#137×C43—41no—
92AGL(1,ℤ/8)×C43—22no—
93AGL(1,ℤ/8)×C43—41no—
94#135×C43—21no—
95#135×C43—21no—
96#135×C43—21no—
97#135×C43—21no—
98#135×C43—42no—
99C2×Q16×C43C2311yescharacteristic
100C2×SD16×C43—21no—
101C2×D8×C43C2311yescharacteristic
102#131×C43—21no—
103#131×C43—21no—
104#131×C43D412yes—
105#131×C43C2312yes—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43D411yescharacteristic
109C22×C8×C43—21no—
110C22×C8×C43C2311yescharacteristic
111#108×C43—21no—
112#108×C43C2312yes—
113#101×C43—22no—
114#100×C43—22no—
115#41×C43—21no—
116#41×C43—21no—
117#41×C43—41no—
118#41×C43—41no—
119#41×C43—41no—
120#41×C43—41no—
121#41×C43D812yes—
122#41×C43C2×D412yes—
123C2×Q8×C43—21no—
124C2×Q8×C43D811yescharacteristic
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—41no—
128C2×D4×C43D811yescharacteristic
129C22×C4×C43—21no—
130C22×C4×C43—41no—
131C22×C4×C43C2×D411yescharacteristic
132C2×C22⋊D43—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137C2×D172—21no—
138C2×C4×D43—41no—
139C2×Dic86—21no—
140Q16×C43—21no—
141Q16×C43—21no—
142Q16×C43—42no—
143SD16×C43—42no—
144SD16×C43—42no—
145SD16×C43—41no—
146SD16×C43—41no—
147D8×C43—21no—
148D8×C43—21no—
149D8×C43—42no—
150M16×C43—21no—
151M16×C43—22no—
152M16×C43—22no—
153M16×C43—22no—
154M16×C43—41no—
155M16×C43C2×D412yes—
156C2×C8×C43—21no—
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C2×C8×C43—41no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43#4111yescharacteristic
164C2×C8×C43#4111yescharacteristic
165C2×C8×C43C2411yescharacteristic
166#10621885—42no—
167#10621884—42no—
168#10621883—42no—
169#10621882—42no—
170#10621877—22no—
171#10621877—41no—
172C2×C43⋊C8—41no—
173Dic172—21no—
174Dic172—21no—
175D344—21no—
176D344—21no—
177#10621873—41no—
178#10621873—41no—
179C43⋊C16—22no—
180C43⋊C16C2×D411yescharacteristic
181C43⋊C16C2×D411yescharacteristic
182C43⋊C16C2×D411yescharacteristic
183C43⋊C16C2×D411yescharacteristic
184C23×C43—21no—
185C23×C43—41no—
186C23×C43#13511yescharacteristic
187C22×D43—41no—
188Q8×C43—21no—
189Q8×C43—41no—
190Q8×C43—41no—
191Q8×C43C2×D812yes—
192D4×C43—22no—
193D4×C43—22no—
194D4×C43—21no—
195D4×C43—41no—
196D4×C43—41no—
197D4×C43—81no—
198D4×C43—81no—
199D4×C43C2×D812yes—
200C2×C4×C43—21no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—41no—
204C2×C4×C43—81no—
205C2×C4×C43—81no—
206C2×C4×C43#12111yescharacteristic
207C2×C4×C43#12111yescharacteristic
208C2×C4×C43C2×D811yescharacteristic
209C2×C4×C43C2×D811yescharacteristic
210C2×C4×C43#13511yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C22⋊D43—81no—
213C22⋊D43—81no—
214C2×Dic43—41no—
215D172—41no—
216D172—41no—
217C4×D43—81no—
218C4×D43—81no—
219Dic86—41no—
220Dic86—41no—
221C8×C43—22no—
222C8×C43—42no—
223C8×C43#12111yescharacteristic
224C8×C43#12111yescharacteristic
225C8×C43C22×D411yescharacteristic
226C8×C43C2×#4111yescharacteristic
227C43⋊C8—42no—
228#33617—431nomaximal, Sylow
229C22×C43—22no—
230C22×C43—41no—
231C22×C43—42no—
232C22×C43—81no—
233C22×C43—161no—
234C22×C43#46611yescharacteristic
235C22×C43#46611yescharacteristic
236C22×C43C2×#13511yescharacteristic
237C2×D43—81no—
238C2×D43—161no—
239C4×C43—22no—
240C4×C43—81no—
241C4×C43#46611yescharacteristic
242C4×C43#46611yescharacteristic
243C4×C43C2×#12111yescharacteristic
244C4×C43C22×D811yescharacteristic
245Dic43—81no—
246C2×#508—431no—
247C2×#504—431no—
248#3067—431no—
249#3067D4311yescharacteristic, complemented
250#2223—432no—
251#2223—432no—
252#2222—432no—
253#2221—432no—
254C2×#368—431no—
255#2148—431no—
256#2148—431no—
257C2×C43—21no—
258C2×C43—21no—
259C2×C43—21no—
260C2×C43—42no—
261C2×C43—161no—
262C2×C43C2×#46611yescharacteristic
263D43—161no—
264#575—21no—
265#575—861no—
266C2×#135—431no—
267C2×#135C2×D4311yescharacteristic
268C2×#131C2×D4311yescharacteristic
269#508—861no—
270#508—861no—
271#508—861no—
272#508—861no—
273C2×Q32—431no—
274C2×SD32—431no—
275C2×SD32—431no—
276C2×D16—431no—
277#504—432no—
278#504—432no—
279#504—861no—
280#504—861no—
281C2×M32—431no—
282C2×M32—861no—
283C22×C16—431no—
284C22×C16—861no—
285#473—432no—
286#473C2×D4312yes—
287#472—432no—
288#472C2×D4312yes—
289#471—22no—
290#471—862no—
291C2×#108—431no—
292C2×#108C2×D4311yescharacteristic
293#413—21no—
294#413—861no—
295#368—432no—
296#368—432no—
297#362—432no—
298#362—432no—
299#361—432no—
300#361—432no—
301C43#3361711yescharacteristic, complemented, Sylow
302C2×#41—21no—
303C2×#41—861no—
304C2×#41C22⋊D4311yescharacteristic
305#137—22no—
306#137—41no—
307#137—862no—
308#137—1721no—
309AGL(1,ℤ/8)—22no—
310AGL(1,ℤ/8)—41no—
311AGL(1,ℤ/8)—862no—
312AGL(1,ℤ/8)—1721no—
313#135—21no—
314#135—21no—
315#135—21no—
316#135—21no—
317#135—42no—
318#135—861no—
319#135—861no—
320#135—861no—
321#135—861no—
322#135—1722no—
323C2×Q16—431no—
324C2×Q16C22×D4311yescharacteristic
325C2×SD16—21no—
326C2×SD16—861no—
327C2×D8—431no—
328C2×D8C22×D4311yescharacteristic
329#131—21no—
330#131—21no—
331#131C22⋊D4312yes—
332#131C22×D4312yes—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—861no—
336C2×M16C22⋊D4311yescharacteristic
337C22×C8—21no—
338C22×C8C22×D4311yescharacteristic
339Q32—861no—
340Q32—861no—
341SD32—861no—
342SD32—861no—
343SD32—861no—
344SD32—861no—
345D16—861no—
346D16—861no—
347M32—432no—
348M32—862no—
349M32—862no—
350M32—861no—
351C2×C16—431no—
352C2×C16—431no—
353C2×C16—431no—
354C2×C16—431no—
355C2×C16—431no—
356C2×C16—431no—
357C2×C16—862no—
358C2×C16—862no—
359C2×C16—861no—
360#108—21no—
361#108—432no—
362#108—861no—
363#108C22×D4312yes—
364#101—22no—
365#101—862no—
366#100—22no—
367#100—862no—
368#41—21no—
369#41—21no—
370#41—41no—
371#41—41no—
372#41—41no—
373#41—41no—
374#41—1721no—
375#41—1721no—
376#41—1721no—
377#41—1721no—
378#41#1062188212yes—
379#41C2×C22⋊D4312yes—
380C2×Q8—21no—
381C2×Q8—861no—
382C2×Q8#1062188211yescharacteristic
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—861no—
387C2×D4—1721no—
388C2×D4#1062188211yescharacteristic
389C22×C4—21no—
390C22×C4—41no—
391C22×C4—1721no—
392C22×C4C2×C22⋊D4311yescharacteristic
393Q16—21no—
394Q16—21no—
395Q16—42no—
396Q16—861no—
397Q16—861no—
398Q16—1722no—
399SD16—42no—
400SD16—42no—
401SD16—41no—
402SD16—41no—
403SD16—1722no—
404SD16—1722no—
405SD16—1721no—
406SD16—1721no—
407D8—21no—
408D8—21no—
409D8—42no—
410D8—861no—
411D8—861no—
412D8—1722no—
413M16—21no—
414M16—22no—
415M16—22no—
416M16—22no—
417M16—41no—
418M16—862no—
419M16—1721no—
420M16C2×C22⋊D4312yes—
421C2×C8—21no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—41no—
425C2×C8—1721no—
426C2×C8D4×D4311yescharacteristic
427C2×C8D4×D4311yescharacteristic
428C2×C8#1062190011yescharacteristic
429C2×C8#1062190011yescharacteristic
430C2×C8C2×C22⋊D4311yescharacteristic
431C2×C8C23×D4311yescharacteristic
432C16—431no—
433C16—431no—
434C16—431no—
435C16—431no—
436C16—862no—
437C23—21no—
438C23—41no—
439C23—1721no—
440C23#1306334511yescharacteristic
441Q8—21no—
442Q8—41no—
443Q8—41no—
444Q8—1721no—
445Q8—1721no—
446Q8C2×#1062188212yes—
447D4—22no—
448D4—22no—
449D4—21no—
450D4—41no—
451D4—41no—
452D4—81no—
453D4—81no—
454D4—3441no—
455D4—3441no—
456D4—1721no—
457D4—1721no—
458D4C2×#1062188212yes—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—3441no—
466C2×C4—3441no—
467C2×C4—1721no—
468C2×C4#1306329711yescharacteristic
469C2×C4#1306329711yescharacteristic
470C2×C4C2×#1062188211yescharacteristic
471C2×C4C2×#1062188211yescharacteristic
472C2×C4#1306334511yescharacteristic
473C2×C4C22×C22⋊D4311yescharacteristic
474C8—22no—
475C8—42no—
476C8—1722no—
477C8#1306329711yescharacteristic
478C8#1306329711yescharacteristic
479C8C2×D4×D4311yescharacteristic
480C8C2×#1062190011yescharacteristic
481C22—22no—
482C22—41no—
483C22—42no—
484C22—81no—
485C22—161no—
486C22—3441no—
487C22—6881no—
488C22#1458313311yescharacteristic
489C22#1458313311yescharacteristic
490C22C2×#1306334511yescharacteristic
491C4—22no—
492C4—81no—
493C4—3441no—
494C4#1458313311yescharacteristic
495C4#1458313311yescharacteristic
496C4C2×#1306329711yescharacteristic
497C4C22×#1062188211yescharacteristic
498C2—21no—
499C2—21no—
500C2—21no—
501C2—42no—
502C2—161no—
503C2—6881no—
504C2C2×#1458313311yescharacteristic
subgroupG/H
centerC4#14583133
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3067C2
socleC2×C43C2×#466
hypercenter#3067D43
hypocenterC43#33617
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. C2×#14583329C2semidirect
2. C2×#14583316C2semidirect
3. #19144315C2semidirect
4. #19136727C2semidirect
5. #19136723C2semidirect
6. #19136718C2semidirect
7. #19136713C2semidirect
8. C2×#14582728C2semidirect
9. #19136344C2semidirect
10. #19136342C2semidirect
11. C43×#3067C2semidirect
18. C2×#13063271C22semidirect
19. C2×#13063269C22semidirect
20. C2×#13063268C22semidirect
21. C2×#13063266C22semidirect
35. #14582728C22semidirect
36. #14582728C22semidirect
37. #14582715C22semidirect
38. #14582714C22semidirect
39. #14582712C22semidirect
40. #14582711C22semidirect
249. #3067D43semidirect
301. C43#33617semidirect

Maximal subgroups

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

subgroupindex
C2×#145833292
C2×#145833162
#191443152
#191367272
#191367232
#191367182
#191367132
C2×#145827282
#191363442
#191363422
C43×#30672
#3361743