Finite Group Databasebeta

← #25014186

Subgroups — #25014186

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143056C211yesmaximal, characteristic
2#19136270C211yesmaximal, characteristic, complemented
3#19136249C211yesmaximal, characteristic, complemented
4#19134565C211yesmaximal, characteristic
5#19132724C211yesmaximal, characteristic, complemented
6#19132716C211yesmaximal, characteristic, complemented
7C43×#3009C211yesmaximal, characteristic
8#14583374—21no—
9#14582916—21no—
10#14582904—21no—
11#14582883C2211yescharacteristic
12#14582873—21no—
13#14582873C2211yescharacteristic
14#14582873C2211yescharacteristic
15#14582873C2211yescharacteristic
16C2×#13063240—22no—
17C2×#13063240—22no—
18#14582694—22no—
19#14582689—22no—
20C2×H(5,𝔽2)×C43C2211yescharacteristic
21C2×#137×C43C411yescharacteristic, complemented
22C22×SD16×C43C411yescharacteristic, complemented
23C43×#536C2211yescharacteristic
24C43×#452—21no—
25C43×#452—21no—
26C43×#450—21no—
27C43×#450—21no—
28C43×#418C411yescharacteristic, complemented
29C43×#416C411yescharacteristic, complemented
30C43×#408C2211yescharacteristic
31C2×#10621877—21no—
32D4×Dic43—42no—
33D4×Dic43—42no—
34#13063284—21no—
35#13063284—21no—
36#13063284—21no—
37C2×C22⋊Dic43—24no—
38#13063252—42no—
39#13063246—42no—
40#13063244—21no—
41#13063242—21no—
42#13063240—24no—
43#13063240—21no—
44#13063240—21no—
45#13063240—21no—
46#13063240—21no—
47#13063240D412yes—
48#13063240D412yes—
49H(5,𝔽2)×C43—42no—
50H(5,𝔽2)×C43—42no—
51C2×#41×C43—21no—
52C2×#41×C43C2×C411yescharacteristic
53C2×#41×C43D411yescharacteristic
54C2×#41×C43D411yescharacteristic
55C2×#41×C43C2311yescharacteristic
56C22×Q8×C43C2×C411yescharacteristic, complemented
57C22×D4×C43—21no—
58C22×D4×C43—21no—
59C22×D4×C43—21no—
60C22×D4×C43C2×C411yescharacteristic
61C22×D4×C43D411yescharacteristic
62C22×D4×C43D411yescharacteristic
63#137×C43—42no—
64C2×Q16×C43—21no—
65C2×SD16×C43—21no—
66C2×SD16×C43—21no—
67C2×SD16×C43—21no—
68C2×SD16×C43—42no—
69C2×M16×C43C2×C411yescharacteristic, complemented
70C22×C8×C43C2×C411yescharacteristic, complemented
71C4⋊Q8×C43—21no—
72#124×C43—21no—
73#123×C43—21no—
74#123×C43—21no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43—21no—
77#117×C43C2×C411yescharacteristic, complemented
78#103×C43—21no—
79#102×C43—21no—
80#102×C43—21no—
81#102×C43—21no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43—21no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—21no—
87#41×C43—22no—
88#41×C43—22no—
89#41×C43—41no—
90#41×C43—41no—
91#41×C43—41no—
92#41×C43—41no—
93#41×C43—41no—
94#41×C43—41no—
95#41×C43—44no—
96C2×Q8×C43—21no—
97C2×Q8×C43—21no—
98C2×Q8×C43—41no—
99C2×Q8×C43—41no—
100C2×Q8×C43C22⋊C411yescharacteristic
101C2×Q8×C43#4111yescharacteristic
102C2×D4×C43—22no—
103C2×D4×C43—22no—
104C2×D4×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—44no—
113C2×D4×C43—44no—
114C2×D4×C43—41no—
115C2×D4×C43—41no—
116C2×D4×C43—44no—
117C2×D4×C43C22⋊C411yescharacteristic
118C2×D4×C43C22⋊C411yescharacteristic
119C2×D4×C43C22⋊C411yescharacteristic
120C2×D4×C43C2×D411yescharacteristic
121C2×D4×C43C2×D411yescharacteristic
122C2×D4×C43#4111yescharacteristic
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×Dic43—44no—
131Q16×C43—42no—
132SD16×C43—42no—
133SD16×C43—42no—
134SD16×C43—42no—
135M16×C43—41no—
136C2×C8×C43—21no—
137C2×C8×C43—21no—
138C2×C8×C43—41no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43—41no—
142C22⋊C4×C43—21no—
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C42×C43—21no—
146C22⋊Dic43—22no—
147C22⋊Dic43—22no—
148C22⋊Dic43—44no—
149C22⋊Dic43—41no—
150C4⋊Dic43—41no—
151C4⋊Dic43—41no—
152C4⋊Dic43—41no—
153C4×Dic43—41no—
154C4×Dic43—41no—
155C4×Dic43—41no—
156#10621877—41no—
157#10621877—41no—
158C2×C43⋊C8—41no—
159C23×C43—24no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—21no—
163C23×C43—42no—
164C23×C43—42no—
165C23×C43—161no—
166C23×C43—161no—
167C23×C43—161no—
168C23×C43C4×D411yescharacteristic
169C23×C43#12011yescharacteristic
170C23×C43#12111yescharacteristic
171Q8×C43—21no—
172Q8×C43—21no—
173Q8×C43—41no—
174Q8×C43—41no—
175Q8×C43—41no—
176Q8×C43—81no—
177D4×C43—24no—
178D4×C43—21no—
179D4×C43—21no—
180D4×C43—21no—
181D4×C43—21no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—42no—
186D4×C43—42no—
187D4×C43—42no—
188D4×C43—42no—
189D4×C43—42no—
190D4×C43#9912yes—
191D4×C43#9912yes—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—81no—
205C2×C4×C43C2×C22⋊C411yescharacteristic
206C2×C4×C43C4×D411yescharacteristic
207C2×C4×C43#12111yescharacteristic
208C2×C4×C43#12311yescharacteristic
209C2×Dic43—42no—
210C2×Dic43—42no—
211C2×Dic43—81no—
212C2×Dic43—164no—
213C8×C43—41no—
214C8×C43—41no—
215C43⋊C8—81no—
216#13100—431nomaximal, Sylow
217C22×C43—21no—
218C22×C43—22no—
219C22×C43—22no—
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—41no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43—41no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43—84no—
230C22×C43—162no—
231C22×C43—162no—
232C22×C43#38611yescharacteristic
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—41no—
237C4×C43—81no—
238C4×C43—81no—
239C4×C43C2×#9911yescharacteristic
240C4×C43C2×#9911yescharacteristic
241Dic43—82no—
242Dic43—82no—
243Dic43—161no—
244#3009D4311yescharacteristic
245#2883—431no—
246#2129—431no—
247#2123—431no—
248#1795—431no—
249#1395—431no—
250#1391—431no—
251C2×C43—21no—
252C2×C43—41no—
253C2×C43—41no—
254C2×C43—41no—
255C2×C43—42no—
256C2×C43—42no—
257C2×C43—81no—
258C2×C43#189811yescharacteristic
259C2×H(5,𝔽2)C2×D4311yescharacteristic
260C2×#137Dic4311yescharacteristic, complemented
261C22×SD16Dic4311yescharacteristic, complemented
262#536C2×D4311yescharacteristic
263#518—861no—
264#452—21no—
265#452—21no—
266#450—21no—
267#450—21no—
268#421—861no—
269#418—861no—
270#418Dic4311yescharacteristic, complemented
271#416Dic4311yescharacteristic, complemented
272#413—431no—
273#410—431no—
274#410—431no—
275#410—431no—
276#410—861no—
277C2×#99—862no—
278C2×#99—862no—
279#408C2×D4311yescharacteristic
280#354—862no—
281#352—862no—
282C43#1310011yescharacteristic, complemented, Sylow
283H(5,𝔽2)—42no—
284H(5,𝔽2)—42no—
285C2×#41—21no—
286C2×#41C2×Dic4311yescharacteristic
287C2×#41C22⋊D4311yescharacteristic
288C2×#41C22⋊D4311yescharacteristic
289C2×#41C22×D4311yescharacteristic
290C22×Q8C2×Dic4311yescharacteristic, complemented
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4C2×Dic4311yescharacteristic
295C22×D4C22⋊D4311yescharacteristic
296C22×D4C22⋊D4311yescharacteristic
297#137—42no—
298C2×Q16—21no—
299C2×SD16—21no—
300C2×SD16—21no—
301C2×SD16—21no—
302C2×SD16—42no—
303C2×M16—861no—
304C2×M16C2×Dic4311yescharacteristic, complemented
305C22×C8C2×Dic4311yescharacteristic, complemented
306C4⋊Q8—21no—
307#124—21no—
308#123—21no—
309#123—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C4×D4—1722no—
313C4×D4—1722no—
314#117—861no—
315#117—861no—
316#117—861no—
317#117C2×Dic4311yescharacteristic, complemented
318C2×C22⋊C4—864no—
319#104—1722no—
320#103—21no—
321#102—21no—
322#102—21no—
323#102—21no—
324#102—1722no—
325#101—861no—
326#100—861no—
327#99—432no—
328#99—432no—
329#99—864no—
330#99—861no—
331#99—861no—
332#99—861no—
333#99—861no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336C24—21no—
337C24—21no—
338C24—21no—
339#41—22no—
340#41—22no—
341#41—41no—
342#41—41no—
343#41—41no—
344#41—41no—
345#41—41no—
346#41—41no—
347#41—44no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8C22⋊Dic4311yescharacteristic
353C2×Q8#1062190011yescharacteristic
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—44no—
367C2×D4—44no—
368C2×D4—44no—
369C2×D4C22⋊Dic4311yescharacteristic
370C2×D4C22⋊Dic4311yescharacteristic
371C2×D4C22⋊Dic4311yescharacteristic
372C2×D4D4×D4311yescharacteristic
373C2×D4D4×D4311yescharacteristic
374C2×D4#1062190011yescharacteristic
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—1724no—
380C22×C4C22×Dic4311yescharacteristic
381C22×C4C2×C22⋊D4311yescharacteristic
382C22×C4C2×C22⋊D4311yescharacteristic
383Q16—42no—
384SD16—42no—
385SD16—42no—
386SD16—42no—
387M16—41no—
388M16—1721no—
389M16—1721no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—41no—
393C2×C8—1721no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—1721no—
398C4⋊C4—1721no—
399C4⋊C4—1721no—
400C22⋊C4—21no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—862no—
404C22⋊C4—862no—
405C22⋊C4—1721no—
406C22⋊C4—1724no—
407C42—21no—
408C42—1721no—
409C42—1721no—
410C42—1721no—
411C23—24no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—42no—
416C23—42no—
417C23—161no—
418C23—161no—
419C23—161no—
420C23D4×Dic4311yescharacteristic
421C23#1306329311yescharacteristic
422C23#1306329711yescharacteristic
423Q8—21no—
424Q8—21no—
425Q8—41no—
426Q8—41no—
427Q8—41no—
428Q8—81no—
429D4—24no—
430D4—21no—
431D4—21no—
432D4—21no—
433D4—21no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—42no—
441D4—42no—
442D4#1306324012yes—
443D4#1306324012yes—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—81no—
457C2×C4—3441no—
458C2×C4—1722no—
459C2×C4—1722no—
460C2×C4—6884no—
461C2×C4C2×C22⋊Dic4311yescharacteristic
462C2×C4D4×Dic4311yescharacteristic
463C2×C4#1306329711yescharacteristic
464C2×C4#1306330611yescharacteristic
465C8—41no—
466C8—41no—
467C8—3441no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—22no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—84no—
481C22—162no—
482C22—162no—
483C22#1458277911yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—41no—
488C4—81no—
489C4—81no—
490C4—3442no—
491C4—3442no—
492C4—6881no—
493C4C2×#1306324011yescharacteristic
494C4C2×#1306324011yescharacteristic
495C2—21no—
496C2—41no—
497C2—41no—
498C2—41no—
499C2—42no—
500C2—42no—
501C2—81no—
502C2#1913504911yescharacteristic
subgroupG/H
centerC2#19135049
commutatorC22×C4×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#3009C2
socleC2×C43#1898
prime radicalC2×H(5,𝔽2)×C43C22
cosocleC2×#41×C43C23
hypercenter#3009D43
hypocenterC43#13100
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×H(5,𝔽2) ◁ #3009

Complements

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

NH ≅ G/Ntype
2. #19136270C2semidirect
3. #19136249C2semidirect
5. #19132724C2semidirect
6. #19132716C2semidirect
21. C2×#137×C43C4semidirect
22. C22×SD16×C43C4semidirect
28. C43×#418C4semidirect
29. C43×#416C4semidirect
56. C22×Q8×C43C2×C4semidirect
69. C2×M16×C43C2×C4semidirect
70. C22×C8×C43C2×C4semidirect
77. #117×C43C2×C4semidirect
260. C2×#137Dic43semidirect
261. C22×SD16Dic43semidirect
270. #418Dic43semidirect
271. #416Dic43semidirect
282. C43#13100semidirect
290. C22×Q8C2×Dic43semidirect
304. C2×M16C2×Dic43semidirect
305. C22×C8C2×Dic43semidirect
317. #117C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191430562
#191362702
#191362492
#191345652
#191327242
#191327162
C43×#30092
#1310043