Finite Group Databasebeta

← #72269608

Subgroups — #72269608

Order 7040.

2928 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72269581C213yesmaximal, complemented
2#72269577C213yesmaximal, complemented
3#72269567C211yesmaximal, characteristic, complemented
4#72269562C211yesmaximal, characteristic, complemented
5#72269557C211yesmaximal, characteristic, complemented
6#72269550C213yesmaximal, complemented
7#72269539C213yesmaximal, complemented
8C11⋊C5×#576C211yesmaximal, characteristic, complemented
9#72269513C211yesmaximal, characteristic, complemented
10#72254693C211yesmaximal, characteristic, complemented
11#72254638C213yesmaximal, complemented
12#72254632C213yesmaximal, complemented
13H(5,𝔽2)×AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
14C2×#66964⋊C5C213yesmaximal, complemented
15AGL(1,ℤ/8)×AGL(1,𝔽11)C213yesmaximal, complemented
16H(5,𝔽2)×C11⋊C5C2211yescharacteristic, complemented
17H(5,𝔽2)×C11⋊C5C2211yescharacteristic, complemented
18#67043⋊C5—21no—
19#67043⋊C5C2213yescomplemented
20#67043⋊C5C2211yescharacteristic, complemented
21#67042⋊C5—21no—
22#67042⋊C5C2213yescomplemented
23#67042⋊C5C2211yescharacteristic, complemented
24#41×AGL(1,𝔽11)—21no—
25#41×AGL(1,𝔽11)—21no—
26#41×AGL(1,𝔽11)C2211yescharacteristic
27#41×AGL(1,𝔽11)C2213yescomplemented
28#41×AGL(1,𝔽11)C2213yescomplemented
29#67037⋊C5—23no—
30#67037⋊C5—23no—
31#67037⋊C5C2213yescomplemented
32#67037⋊C5C2213yescomplemented
33C2×#4341⋊C5—23no—
34C2×#4341⋊C5C2213yescomplemented
35C2×D4×AGL(1,𝔽11)—23no—
36C2×D4×AGL(1,𝔽11)C2213yescomplemented
37AGL(1,ℤ/8)×C11⋊C5C2213yescomplemented
38AGL(1,ℤ/8)×C11⋊C5C2213yescomplemented
39#135×C11⋊C5C2213yescomplemented
40C2×D8×C11⋊C5C2213yescomplemented
41#131×C11⋊C5C2211yescharacteristic, complemented
42#67004⋊C5C2213yescomplemented
43#67003⋊C5C2213yescomplemented
44#67003⋊C5C2213yescomplemented
45#67002⋊C5C2213yescomplemented
46#67001⋊C5C2211yescharacteristic, complemented
47C2×#4324⋊C5C2213yescomplemented
48#66985⋊C5C2213yescomplemented
49#66985⋊C5C2213yescomplemented
50C2×#4323⋊C5C2213yescomplemented
51#66971⋊C5C2211yescharacteristic, complemented
52#66971⋊C5C2213yescomplemented
53#66969⋊C5C2216yescomplemented
54#66968⋊C5C2213yescomplemented
55#66968⋊C5C2213yescomplemented
56#66967⋊C5C2213yescomplemented
57#66967⋊C5C2213yescomplemented
58SD16×AGL(1,𝔽11)C2216yescomplemented
59#66965⋊C5C2216yescomplemented
60#66964⋊C5C2216yescomplemented
61#66964⋊C5C2213yescomplemented
62#66964⋊C5C2216yescomplemented
63#66964⋊C5C2216yescomplemented
64#66964⋊C5C2213yescomplemented
65D8×AGL(1,𝔽11)C2216yescomplemented
66#66962⋊C5C2213yescomplemented
67#66961⋊C5C2213yescomplemented
68#66960⋊C5C2213yescomplemented
69M16×AGL(1,𝔽11)C2213yescomplemented
70#66957⋊C5C2213yescomplemented
71C2×#4314⋊C5C2213yescomplemented
72#66954⋊C5C2213yescomplemented
73C2×#4313⋊C5C2213yescomplemented
74#13083391C511yesmaximal, characteristic, complemented, Hall
75C23×AGL(1,𝔽11)—23no—
76#41×C11⋊C5—21no—
77#41×C11⋊C5—21no—
78#41×C11⋊C5C2313yes—
79#41×C11⋊C5C2311yescharacteristic
80#41×C11⋊C5C2313yescomplemented
81C2×D4×C11⋊C5—23no—
82C2×D4×C11⋊C5—23no—
83C2×D4×C11⋊C5C2313yes—
84C2×D4×C11⋊C5C2313yescomplemented
85C2×C22⋊AGL(1,𝔽11)—23no—
86C2×C22⋊AGL(1,𝔽11)—26no—
87C2×C22⋊AGL(1,𝔽11)—26no—
88C2×C22⋊AGL(1,𝔽11)—23no—
89C22×Dic11⋊C5—23no—
90#4343⋊C5—21no—
91#4343⋊C5D411yescharacteristic
92#4343⋊C5C2311yescharacteristic
93#4343⋊C5C2313yes—
94Q8×AGL(1,𝔽11)—21no—
95Q8×AGL(1,𝔽11)D411yescharacteristic
96Q8×AGL(1,𝔽11)C2311yescharacteristic
97Q8×AGL(1,𝔽11)C2313yescomplemented
98#4341⋊C5—23no—
99#4341⋊C5—26no—
100#4341⋊C5—23no—
101#4341⋊C5—23no—
102#4341⋊C5—23no—
103#4341⋊C5—23no—
104#4341⋊C5—23no—
105#4341⋊C5—23no—
106#4341⋊C5D413yes—
107#4341⋊C5C2313yes—
108#4341⋊C5C2313yes—
109#4341⋊C5C2316yescomplemented
110D4×AGL(1,𝔽11)—23no—
111D4×AGL(1,𝔽11)—23no—
112D4×AGL(1,𝔽11)—23no—
113D4×AGL(1,𝔽11)—26no—
114D4×AGL(1,𝔽11)—23no—
115D4×AGL(1,𝔽11)—23no—
116D4×AGL(1,𝔽11)—23no—
117D4×AGL(1,𝔽11)—23no—
118D4×AGL(1,𝔽11)D413yes—
119D4×AGL(1,𝔽11)C2316yes—
120D4×AGL(1,𝔽11)C2313yes—
121D4×AGL(1,𝔽11)C2313yescomplemented
122#4339⋊C5—23no—
123#4339⋊C5—23no—
124#4339⋊C5—23no—
125#4339⋊C5—23no—
126#4339⋊C5C2313yes—
127#4339⋊C5C2313yes—
128#4339⋊C5C2313yescomplemented
129C2×C4⋊AGL(1,𝔽11)—23no—
130C2×C4⋊AGL(1,𝔽11)C2313yes—
131C2×C4×AGL(1,𝔽11)—23no—
132C2×C4×AGL(1,𝔽11)—23no—
133C2×C4×AGL(1,𝔽11)C2313yes—
134C2×(C11⋊C5)⋊Q8—23no—
135C2×(C11⋊C5)⋊Q8C2313yescomplemented
136Q16×C11⋊C5C2311yescharacteristic, complemented
137SD16×C11⋊C5C2313yescomplemented
138SD16×C11⋊C5C2313yescomplemented
139D8×C11⋊C5C2316yescomplemented
140D8×C11⋊C5C2313yescomplemented
141M16×C11⋊C5C2313yescomplemented
142C2×C8×C11⋊C5C2313yescomplemented
143#4326⋊C5C2311yescharacteristic, complemented
144#4326⋊C5C2313yescomplemented
145#4325⋊C5C2313yescomplemented
146#4325⋊C5C2311yescharacteristic, complemented
147#4324⋊C5C2313yescomplemented
148#4324⋊C5C2316yescomplemented
149#4324⋊C5C2313yescomplemented
150#4323⋊C5C2313yescomplemented
151#4323⋊C5C2316yescomplemented
152#4323⋊C5C2313yescomplemented
153#4318⋊C5C2313yescomplemented
154C2×(C11⋊C5)⋊C8C2313yescomplemented
155Dic44⋊C5C2313yescomplemented
156D88⋊C5C2313yescomplemented
157#4314⋊C5C2313yescomplemented
158#4314⋊C5C2316yescomplemented
159#4314⋊C5C2311yescharacteristic, complemented
160#4313⋊C5C2311yescharacteristic
161#4313⋊C5C2313yes—
162#4313⋊C5C2313yescomplemented
163#4313⋊C5C2313yescomplemented
164C8×AGL(1,𝔽11)C2316yescomplemented
165#10623455C2×C511yescharacteristic, complemented
166D11×H(5,𝔽2)C2×C511yescharacteristic, complemented
167C11×#576C2×C511yescharacteristic, complemented
168#10623367C2×C511yescharacteristic, complemented
169#10623366C2×C511yescharacteristic, complemented
170#10623306C2×C513yescomplemented
171#10623305C2×C513yescomplemented
172#10623304C2×C513yescomplemented
173D11×AGL(1,ℤ/8)C2×C513yescomplemented
174#10623301C2×C513yescomplemented
175#10623299C2×C513yescomplemented
176#10623288C2×C513yescomplemented
177C2×#66964C2×C513yescomplemented
178#10623282C2×C511yescharacteristic, complemented
179#10623281C2×C511yescharacteristic, complemented
180C5×#3585—111nomaximal, Hall
181C23×C11⋊C5—23no—
182C23×C11⋊C5—23no—
183C22×AGL(1,𝔽11)—23no—
184C22×AGL(1,𝔽11)—23no—
185C22×AGL(1,𝔽11)—23no—
186C22×AGL(1,𝔽11)—26no—
187C22×AGL(1,𝔽11)—86no—
188C22×AGL(1,𝔽11)C2×D413yes—
189Q8×C11⋊C5C2×D411yescharacteristic
190Q8×C11⋊C5C2411yescharacteristic
191Q8×C11⋊C5C2411yescharacteristic
192D4×C11⋊C5—23no—
193D4×C11⋊C5—23no—
194D4×C11⋊C5—23no—
195D4×C11⋊C5—23no—
196D4×C11⋊C5C2×D413yes—
197D4×C11⋊C5C2413yes—
198D4×C11⋊C5C2413yes—
199C2×C4×C11⋊C5—23no—
200C2×C4×C11⋊C5—23no—
201C2×C4×C11⋊C5C2413yes—
202C22⋊AGL(1,𝔽11)—23no—
203C22⋊AGL(1,𝔽11)—23no—
204C22⋊AGL(1,𝔽11)—23no—
205C22⋊AGL(1,𝔽11)—23no—
206C22⋊AGL(1,𝔽11)—26no—
207C22⋊AGL(1,𝔽11)—26no—
208C22⋊AGL(1,𝔽11)—23no—
209C22⋊AGL(1,𝔽11)—23no—
210C22⋊AGL(1,𝔽11)C2×D416yes—
211C2×Dic11⋊C5—23no—
212C2×Dic11⋊C5—26no—
213C2×Dic11⋊C5—23no—
214C2×Dic11⋊C5—23no—
215C2×Dic11⋊C5C2×D413yes—
216C4⋊AGL(1,𝔽11)—23no—
217C4⋊AGL(1,𝔽11)—21no—
218C4⋊AGL(1,𝔽11)—23no—
219C4⋊AGL(1,𝔽11)C2×D413yes—
220C4⋊AGL(1,𝔽11)C2413yes—
221C4⋊AGL(1,𝔽11)C2411yescharacteristic
222C4×AGL(1,𝔽11)—21no—
223C4×AGL(1,𝔽11)—23no—
224C4×AGL(1,𝔽11)—23no—
225C4×AGL(1,𝔽11)—23no—
226C4×AGL(1,𝔽11)—21no—
227C4×AGL(1,𝔽11)—23no—
228C4×AGL(1,𝔽11)C2×D413yes—
229C4×AGL(1,𝔽11)C2×D413yes—
230C4×AGL(1,𝔽11)C2413yes—
231C4×AGL(1,𝔽11)C2411yescharacteristic
232(C11⋊C5)⋊Q8—23no—
233(C11⋊C5)⋊Q8—23no—
234(C11⋊C5)⋊Q8—21no—
235(C11⋊C5)⋊Q8C2×D413yes—
236(C11⋊C5)⋊Q8C2413yes—
237(C11⋊C5)⋊Q8C2411yescharacteristic
238C8×C11⋊C5C2413yes—
239C8×C11⋊C5C2411yescharacteristic
240(C11⋊C5)⋊C8C2413yes—
241(C11⋊C5)⋊C8C2411yescharacteristic
242C11×H(5,𝔽2)C22×C511yescharacteristic, complemented
243C11×H(5,𝔽2)C22×C511yescharacteristic, complemented
244#67043—21no—
245#67043C22×C513yescomplemented
246#67043C22×C511yescharacteristic, complemented
247#67042—21no—
248#67042C22×C513yescomplemented
249#67042C22×C511yescharacteristic, complemented
250#41×D11—21no—
251#41×D11—21no—
252#41×D11C22×C511yescharacteristic
253#41×D11C22×C513yescomplemented
254#41×D11C22×C513yescomplemented
255#67037—23no—
256#67037—23no—
257#67037C22×C513yescomplemented
258#67037C22×C513yescomplemented
259C2×#4341—23no—
260C2×#4341C22×C513yescomplemented
261C2×D4×D11—23no—
262C2×D4×D11C22×C513yescomplemented
263C11×AGL(1,ℤ/8)C22×C513yescomplemented
264C11×AGL(1,ℤ/8)C22×C513yescomplemented
265C11×#135C22×C513yescomplemented
266C2×C11×D8C22×C513yescomplemented
267C11×#131C22×C511yescharacteristic, complemented
268#67004C22×C513yescomplemented
269#67003C22×C513yescomplemented
270#67003C22×C513yescomplemented
271#67002C22×C513yescomplemented
272#67001C22×C511yescharacteristic, complemented
273C2×#4324C22×C513yescomplemented
274#66985C22×C513yescomplemented
275#66985C22×C513yescomplemented
276C2×#4323C22×C513yescomplemented
277#66971C22×C511yescharacteristic, complemented
278#66971C22×C513yescomplemented
279#66969C22×C516yescomplemented
280#66968C22×C513yescomplemented
281#66968C22×C513yescomplemented
282#66967C22×C513yescomplemented
283#66967C22×C513yescomplemented
284SD16×D11C22×C516yescomplemented
285#66965C22×C516yescomplemented
286#66964C22×C513yescomplemented
287#66964C22×C516yescomplemented
288#66964C22×C516yescomplemented
289#66964C22×C516yescomplemented
290#66964C22×C513yescomplemented
291D8×D11C22×C516yescomplemented
292#66962C22×C513yescomplemented
293#66961C22×C513yescomplemented
294#66960C22×C513yescomplemented
295M16×D11C22×C513yescomplemented
296#66957C22×C513yescomplemented
297C2×#4314C22×C513yescomplemented
298#66954C22×C513yescomplemented
299C2×#4313C22×C513yescomplemented
300C5×#585—111no—
301C2×C5×H(5,𝔽2)—111no—
302C5×#577—111no—
303C5×#577—113no—
304C5×#577—113no—
305C5×#577—111no—
306C5×#576—111no—
307C5×#576—113no—
308C5×#576—113no—
309C5×#576—221no—
310C5×#575—113no—
311C5×#575—113no—
312C2×C5×AGL(1,ℤ/8)—113no—
313C2×C5×AGL(1,ℤ/8)—113no—
314C5×#568—111no—
315C22×C11⋊C5—23no—
316C22×C11⋊C5—23no—
317C22×C11⋊C5—83no—
318C22×C11⋊C5—83no—
319C22×C11⋊C5C22×D413yes—
320C2×AGL(1,𝔽11)—21no—
321C2×AGL(1,𝔽11)—23no—
322C2×AGL(1,𝔽11)—43no—
323C2×AGL(1,𝔽11)—46no—
324C2×AGL(1,𝔽11)—83no—
325C2×AGL(1,𝔽11)—86no—
326C2×AGL(1,𝔽11)—83no—
327C2×AGL(1,𝔽11)C22×D411yescharacteristic
328C2×AGL(1,𝔽11)C22×D413yes—
329C4×C11⋊C5—21no—
330C4×C11⋊C5—21no—
331C4×C11⋊C5C22×D413yes—
332C4×C11⋊C5C2511yescharacteristic
333Dic11⋊C5—23no—
334Dic11⋊C5—21no—
335Dic11⋊C5C22×D413yes—
336Dic11⋊C5C22×D411yescharacteristic
337C23×D11—23no—
338C11×#41—21no—
339C11×#41—21no—
340C11×#41C23×C513yes—
341C11×#41C23×C511yescharacteristic
342C11×#41C23×C513yescomplemented
343C2×D4×C11—23no—
344C2×D4×C11—23no—
345C2×D4×C11C23×C513yes—
346C2×D4×C11C23×C513yescomplemented
347C2×C22⋊D11—26no—
348C2×C22⋊D11—26no—
349C2×C22⋊D11—23no—
350C2×C22⋊D11—23no—
351C22×Dic11—23no—
352#4343—21no—
353#4343C5×D411yescharacteristic
354#4343C23×C511yescharacteristic
355#4343C23×C513yes—
356Q8×D11—21no—
357Q8×D11C5×D411yescharacteristic
358Q8×D11C23×C511yescharacteristic
359Q8×D11C23×C513yescomplemented
360#4341—26no—
361#4341—23no—
362#4341—23no—
363#4341—23no—
364#4341—23no—
365#4341—23no—
366#4341—23no—
367#4341—23no—
368#4341C5×D413yes—
369#4341C23×C513yes—
370#4341C23×C513yes—
371#4341C23×C516yescomplemented
372D4×D11—26no—
373D4×D11—23no—
374D4×D11—23no—
375D4×D11—23no—
376D4×D11—23no—
377D4×D11—23no—
378D4×D11—23no—
379D4×D11—23no—
380D4×D11C5×D413yes—
381D4×D11C23×C516yes—
382D4×D11C23×C513yes—
383D4×D11C23×C513yescomplemented
384#4339—23no—
385#4339—23no—
386#4339—23no—
387#4339—23no—
388#4339C23×C513yes—
389#4339C23×C513yes—
390#4339C23×C513yescomplemented
391C2×D44—23no—
392C2×D44C23×C513yes—
393C2×C4×D11—23no—
394C2×C4×D11—23no—
395C2×C4×D11C23×C513yes—
396C2×Dic22—23no—
397C2×Dic22C23×C513yescomplemented
398C11×Q16C23×C511yescharacteristic, complemented
399C11×SD16C23×C513yescomplemented
400C11×SD16C23×C513yescomplemented
401C11×D8C23×C516yescomplemented
402C11×D8C23×C513yescomplemented
403C11×M16C23×C513yescomplemented
404C2×C8×C11C23×C513yescomplemented
405#4326C23×C511yescharacteristic, complemented
406#4326C23×C513yescomplemented
407#4325C23×C513yescomplemented
408#4325C23×C511yescharacteristic, complemented
409#4324C23×C513yescomplemented
410#4324C23×C516yescomplemented
411#4324C23×C513yescomplemented
412#4323C23×C513yescomplemented
413#4323C23×C516yescomplemented
414#4323C23×C513yescomplemented
415#4318C23×C513yescomplemented
416C2×C11⋊C8C23×C513yescomplemented
417Dic44C23×C513yescomplemented
418D88C23×C513yescomplemented
419#4314C23×C513yescomplemented
420#4314C23×C516yescomplemented
421#4314C23×C511yescharacteristic, complemented
422#4313C23×C511yescharacteristic
423#4313C23×C513yes—
424#4313C23×C513yescomplemented
425#4313C23×C513yescomplemented
426C8×D11C23×C516yescomplemented
427C5×2−1+4—111no—
428C5×2−1+4—113no—
429C5×2−1+4—221no—
430C5×H(5,𝔽2)—113no—
431C5×H(5,𝔽2)—111no—
432C5×H(5,𝔽2)—113no—
433C5×H(5,𝔽2)—113no—
434C5×H(5,𝔽2)—223no—
435C5×H(5,𝔽2)—221no—
436C5×H(5,𝔽2)—223no—
437C5×H(5,𝔽2)—221no—
438C5×H(5,𝔽2)—221no—
439C2×C5×#41—111no—
440C2×C5×#41—113no—
441C2×C5×#41—113no—
442C2×C5×#41—113no—
443C2×C5×#41—221no—
444C2×C5×#41—221no—
445C2×C5×#41—223no—
446C22×C5×D4—113no—
447C22×C5×D4—223no—
448C5×#137—113no—
449C5×#137—111no—
450C5×#137—113no—
451C5×#137—113no—
452C5×#137—113no—
453C5×#137—113no—
454C5×AGL(1,ℤ/8)—113no—
455C5×AGL(1,ℤ/8)—113no—
456C5×AGL(1,ℤ/8)—113no—
457C5×AGL(1,ℤ/8)—113no—
458C5×AGL(1,ℤ/8)—113no—
459C5×AGL(1,ℤ/8)—116no—
460C5×AGL(1,ℤ/8)—113no—
461C5×AGL(1,ℤ/8)—116no—
462C5×AGL(1,ℤ/8)—116no—
463C5×AGL(1,ℤ/8)—113no—
464C5×AGL(1,ℤ/8)—113no—
465C5×AGL(1,ℤ/8)—223no—
466C5×AGL(1,ℤ/8)—223no—
467C5×#135—113no—
468C5×#135—113no—
469C5×#135—116no—
470C5×#135—116no—
471C5×#135—113no—
472C5×#135—223no—
473C2×C5×SD16—113no—
474C2×C5×SD16—116no—
475C2×C5×SD16—113no—
476C2×C5×D8—113no—
477C2×C5×D8—116no—
478C2×C5×D8—223no—
479C5×#131—111no—
480C5×#131—113no—
481C5×#131—113no—
482C5×#131—221no—
483C2×C5×M16—113no—
484C2×C5×M16—113no—
485#3585—111noSylow
486C2×C11⋊C5—23no—
487C2×C11⋊C5—43no—
488C2×C11⋊C5—43no—
489C2×C11⋊C5C23×D411yescharacteristic
490AGL(1,𝔽11)—21no—
491AGL(1,𝔽11)—23no—
492AGL(1,𝔽11)—43no—
493AGL(1,𝔽11)—41no—
494C23×C11—23no—
495C23×C11—23no—
496C22×D11—23no—
497C22×D11—23no—
498C22×D11—23no—
499C22×D11—26no—
500C22×D11—86no—
501C22×D11C2×C5×D413yes—
502Q8×C11C2×C5×D411yescharacteristic
503Q8×C11C24×C511yescharacteristic
504Q8×C11C24×C511yescharacteristic
505D4×C11—23no—
506D4×C11—23no—
507D4×C11—23no—
508D4×C11—23no—
509D4×C11C2×C5×D413yes—
510D4×C11C24×C513yes—
511D4×C11C24×C513yes—
512C2×C4×C11—23no—
513C2×C4×C11—23no—
514C2×C4×C11C24×C513yes—
515C22⋊D11—23no—
516C22⋊D11—23no—
517C22⋊D11—23no—
518C22⋊D11—23no—
519C22⋊D11—26no—
520C22⋊D11—26no—
521C22⋊D11—23no—
522C22⋊D11—23no—
523C22⋊D11C2×C5×D416yes—
524C2×Dic11—23no—
525C2×Dic11—26no—
526C2×Dic11—23no—
527C2×Dic11—23no—
528C2×Dic11C2×C5×D413yes—
529D44—23no—
530D44—21no—
531D44—23no—
532D44C2×C5×D413yes—
533D44C24×C513yes—
534D44C24×C511yescharacteristic
535C4×D11—21no—
536C4×D11—23no—
537C4×D11—23no—
538C4×D11—23no—
539C4×D11—21no—
540C4×D11—23no—
541C4×D11C2×C5×D413yes—
542C4×D11C2×C5×D413yes—
543C4×D11C24×C513yes—
544C4×D11C24×C511yescharacteristic
545Dic22—23no—
546Dic22—23no—
547Dic22—21no—
548Dic22C2×C5×D413yes—
549Dic22C24×C513yes—
550Dic22C24×C511yescharacteristic
551C8×C11C24×C513yes—
552C8×C11C24×C511yescharacteristic
553C11⋊C8C24×C513yes—
554C11⋊C8C24×C511yescharacteristic
555C24×C5—223no—
556C5×#41—111no—
557C5×#41—113no—
558C5×#41—113no—
559C5×#41—113no—
560C5×#41—111no—
561C5×#41—116no—
562C5×#41—113no—
563C5×#41—113no—
564C5×#41—113no—
565C5×#41—113no—
566C5×#41—223no—
567C5×#41—223no—
568C5×#41—223no—
569C5×#41—223no—
570C5×#41—223no—
571C5×#41—223no—
572C5×#41—226no—
573C5×#41—221no—
574C5×#41—223no—
575C5×#41—223no—
576C5×#41—223no—
577C5×#41—223no—
578C5×#41—223no—
579C5×#41—223no—
580C5×#41—221no—
581C5×#41—223no—
582C5×#41—441no—
583C5×#41—441no—
584C2×C5×Q8—111no—
585C2×C5×Q8—113no—
586C2×C5×Q8—111no—
587C2×C5×Q8—113no—
588C2×C5×Q8—221no—
589C2×C5×Q8—223no—
590C2×C5×D4—113no—
591C2×C5×D4—113no—
592C2×C5×D4—116no—
593C2×C5×D4—113no—
594C2×C5×D4—113no—
595C2×C5×D4—223no—
596C2×C5×D4—223no—
597C2×C5×D4—223no—
598C2×C5×D4—226no—
599C2×C5×D4—226no—
600C2×C5×D4—226no—
601C2×C5×D4—223no—
602C2×C5×D4—223no—
603C2×C5×D4—223no—
604C2×C5×D4—223no—
605C2×C5×D4—223no—
606C2×C5×D4—223no—
607C2×C5×D4—223no—
608C2×C5×D4—223no—
609C2×C5×D4—223no—
610C2×C5×D4—443no—
611C2×C5×D4—443no—
612C22×C4×C5—113no—
613C22×C4×C5—223no—
614C22×C4×C5—223no—
615C22×C4×C5—223no—
616C5×Q16—113no—
617C5×Q16—111no—
618C5×Q16—113no—
619C5×Q16—221no—
620C5×SD16—113no—
621C5×SD16—111no—
622C5×SD16—113no—
623C5×SD16—116no—
624C5×SD16—113no—
625C5×SD16—116no—
626C5×SD16—113no—
627C5×SD16—111no—
628C5×SD16—223no—
629C5×SD16—223no—
630C5×D8—113no—
631C5×D8—113no—
632C5×D8—116no—
633C5×D8—113no—
634C5×D8—226no—
635C5×D8—223no—
636C5×M16—113no—
637C5×M16—113no—
638C5×M16—111no—
639C5×M16—113no—
640C5×M16—113no—
641C5×M16—223no—
642C2×C5×C8—113no—
643C2×C5×C8—116no—
644C2×C5×C8—223no—
645#585—111no—
646C2×H(5,𝔽2)—111no—
647#577—111no—
648#577—113no—
649#577—113no—
650#577—111no—
651#576—111no—
652#576—113no—
653#576—113no—
654#576AGL(1,𝔽11)11yescharacteristic, complemented
655#575—113no—
656#575—113no—
657C2×AGL(1,ℤ/8)—113no—
658C2×AGL(1,ℤ/8)—113no—
659#568—111no—
660C11⋊C5#358511yescharacteristic, complemented, Hall
661C22×C11—23no—
662C22×C11—23no—
663C22×C11—83no—
664C22×C11—83no—
665C22×C11C22×C5×D413yes—
666C2×D11—23no—
667C2×D11—21no—
668C2×D11—43no—
669C2×D11—46no—
670C2×D11—86no—
671C2×D11—83no—
672C2×D11—83no—
673C2×D11C22×C5×D411yescharacteristic
674C2×D11C22×C5×D413yes—
675C4×C11—21no—
676C4×C11—21no—
677C4×C11C22×C5×D413yes—
678C4×C11C25×C511yescharacteristic
679Dic11—23no—
680Dic11—21no—
681Dic11C22×C5×D413yes—
682Dic11C22×C5×D411yescharacteristic
683C23×C5—113no—
684C23×C5—223no—
685C23×C5—223no—
686C23×C5—226no—
687C23×C5—223no—
688C23×C5—443no—
689C23×C5—443no—
690C23×C5—886no—
691C5×Q8—113no—
692C5×Q8—113no—
693C5×Q8—111no—
694C5×Q8—223no—
695C5×Q8—221no—
696C5×Q8—223no—
697C5×Q8—221no—
698C5×Q8—221no—
699C5×Q8—221no—
700C5×D4—116no—
701C5×D4—113no—
702C5×D4—111no—
703C5×D4—113no—
704C5×D4—223no—
705C5×D4—226no—
706C5×D4—223no—
707C5×D4—223no—
708C5×D4—223no—
709C5×D4—226no—
710C5×D4—223no—
711C5×D4—223no—
712C5×D4—223no—
713C5×D4—223no—
714C5×D4—221no—
715C5×D4—223no—
716C5×D4—223no—
717C5×D4—223no—
718C5×D4—443no—
719C5×D4—443no—
720C5×D4—443no—
721C5×D4—443no—
722C2×C4×C5—113no—
723C2×C4×C5—113no—
724C2×C4×C5—113no—
725C2×C4×C5—113no—
726C2×C4×C5—111no—
727C2×C4×C5—223no—
728C2×C4×C5—223no—
729C2×C4×C5—226no—
730C2×C4×C5—221no—
731C2×C4×C5—223no—
732C2×C4×C5—223no—
733C2×C4×C5—223no—
734C2×C4×C5—223no—
735C2×C4×C5—221no—
736C2×C4×C5—223no—
737C2×C4×C5—223no—
738C2×C4×C5—443no—
739C2×C4×C5—443no—
740C5×C8—113no—
741C5×C8—111no—
742C5×C8—223no—
743C5×C8—221no—
7442−1+4—111no—
7452−1+4—113no—
7462−1+4—221no—
747H(5,𝔽2)—113no—
748H(5,𝔽2)—111no—
749H(5,𝔽2)—113no—
750H(5,𝔽2)—113no—
751H(5,𝔽2)—223no—
752H(5,𝔽2)—223no—
753H(5,𝔽2)—221no—
754H(5,𝔽2)C2×AGL(1,𝔽11)11yescharacteristic, complemented
755H(5,𝔽2)C2×AGL(1,𝔽11)11yescharacteristic, complemented
756C2×#41—111no—
757C2×#41—113no—
758C2×#41—113no—
759C2×#41—113no—
760C2×#41—223no—
761C2×#41—221no—
762C2×#41—221no—
763C22×D4—113no—
764C22×D4—223no—
765#137—113no—
766#137—111no—
767#137—113no—
768#137—113no—
769#137—113no—
770#137—113no—
771AGL(1,ℤ/8)—113no—
772AGL(1,ℤ/8)—113no—
773AGL(1,ℤ/8)—113no—
774AGL(1,ℤ/8)—113no—
775AGL(1,ℤ/8)—113no—
776AGL(1,ℤ/8)—116no—
777AGL(1,ℤ/8)—113no—
778AGL(1,ℤ/8)—116no—
779AGL(1,ℤ/8)—116no—
780AGL(1,ℤ/8)—113no—
781AGL(1,ℤ/8)—113no—
782AGL(1,ℤ/8)C2×AGL(1,𝔽11)13yescomplemented
783AGL(1,ℤ/8)C2×AGL(1,𝔽11)13yescomplemented
784#135—113no—
785#135—113no—
786#135—116no—
787#135—116no—
788#135—113no—
789#135C2×AGL(1,𝔽11)13yescomplemented
790C2×SD16—113no—
791C2×SD16—116no—
792C2×SD16—113no—
793C2×D8—113no—
794C2×D8—116no—
795C2×D8C2×AGL(1,𝔽11)13yescomplemented
796#131—111no—
797#131—113no—
798#131—113no—
799#131C2×AGL(1,𝔽11)11yescharacteristic, complemented
800C2×M16—113no—
801C2×M16—113no—
802C2×C11—23no—
803C2×C11—43no—
804C2×C11—43no—
805C2×C11C23×C5×D411yescharacteristic
806D11—21no—
807D11—23no—
808D11—43no—
809D11—41no—
810C22×C5—111no—
811C22×C5—113no—
812C22×C5—221no—
813C22×C5—223no—
814C22×C5—223no—
815C22×C5—443no—
816C22×C5—443no—
817C22×C5—443no—
818C22×C5—446no—
819C22×C5—886no—
820C22×C5—883no—
821C22×C5—883no—
822C22×C5—1763no—
823C22×C5—1763no—
824C4×C5—111no—
825C4×C5—113no—
826C4×C5—221no—
827C4×C5—223no—
828C4×C5—223no—
829C4×C5—221no—
830C4×C5—441no—
831C4×C5—441no—
832C24—223no—
833#41—21no—
834#41—21no—
835#41—111no—
836#41—113no—
837#41—113no—
838#41—113no—
839#41—111no—
840#41—116no—
841#41—113no—
842#41—113no—
843#41—113no—
844#41—113no—
845#41—223no—
846#41—223no—
847#41—223no—
848#41—223no—
849#41—223no—
850#41—223no—
851#41—223no—
852#41—223no—
853#41—226no—
854#41—223no—
855#41—223no—
856#41—221no—
857#41—223no—
858#41C22×AGL(1,𝔽11)13yes—
859#41C22×AGL(1,𝔽11)11yescharacteristic
860#41C22×AGL(1,𝔽11)13yescomplemented
861C2×Q8—111no—
862C2×Q8—113no—
863C2×Q8—111no—
864C2×Q8—113no—
865C2×Q8—223no—
866C2×Q8—221no—
867C2×D4—23no—
868C2×D4—23no—
869C2×D4—113no—
870C2×D4—113no—
871C2×D4—116no—
872C2×D4—113no—
873C2×D4—113no—
874C2×D4—223no—
875C2×D4—223no—
876C2×D4—223no—
877C2×D4—223no—
878C2×D4—226no—
879C2×D4—223no—
880C2×D4—223no—
881C2×D4—223no—
882C2×D4—223no—
883C2×D4—226no—
884C2×D4—226no—
885C2×D4—223no—
886C2×D4—223no—
887C2×D4C22×AGL(1,𝔽11)13yes—
888C2×D4C22×AGL(1,𝔽11)13yescomplemented
889C22×C4—113no—
890C22×C4—223no—
891C22×C4—223no—
892C22×C4—223no—
893Q16—113no—
894Q16—111no—
895Q16—113no—
896Q16C22×AGL(1,𝔽11)11yescharacteristic, complemented
897SD16—113no—
898SD16—111no—
899SD16—113no—
900SD16—116no—
901SD16—113no—
902SD16—116no—
903SD16—113no—
904SD16—111no—
905SD16C22×AGL(1,𝔽11)13yescomplemented
906SD16C22×AGL(1,𝔽11)13yescomplemented
907D8—113no—
908D8—113no—
909D8—116no—
910D8—113no—
911D8C22×AGL(1,𝔽11)16yescomplemented
912D8C22×AGL(1,𝔽11)13yescomplemented
913M16—113no—
914M16—113no—
915M16—111no—
916M16—113no—
917M16—113no—
918M16C22×AGL(1,𝔽11)13yescomplemented
919C2×C8—113no—
920C2×C8—116no—
921C2×C8C22×AGL(1,𝔽11)13yescomplemented
922C11C5×#358511yescharacteristic, complemented, Sylow
923C2×C5—221no—
924C2×C5—223no—
925C2×C5—221no—
926C2×C5—443no—
927C2×C5—443no—
928C2×C5—441no—
929C2×C5—883no—
930C2×C5—883no—
931C23—23no—
932C23—23no—
933C23—113no—
934C23—223no—
935C23—223no—
936C23—226no—
937C23—223no—
938C23—886no—
939Q8—113no—
940Q8—113no—
941Q8—111no—
942Q8—223no—
943Q8—221no—
944Q8—223no—
945Q8D4×AGL(1,𝔽11)11yescharacteristic
946Q8C23×AGL(1,𝔽11)11yescharacteristic
947Q8C23×AGL(1,𝔽11)11yescharacteristic
948D4—23no—
949D4—23no—
950D4—23no—
951D4—23no—
952D4—116no—
953D4—113no—
954D4—111no—
955D4—113no—
956D4—223no—
957D4—221no—
958D4—223no—
959D4—226no—
960D4—223no—
961D4—223no—
962D4—223no—
963D4—226no—
964D4—223no—
965D4—223no—
966D4—223no—
967D4D4×AGL(1,𝔽11)13yes—
968D4C23×AGL(1,𝔽11)13yes—
969D4C23×AGL(1,𝔽11)13yes—
970C2×C4—23no—
971C2×C4—23no—
972C2×C4—113no—
973C2×C4—113no—
974C2×C4—113no—
975C2×C4—113no—
976C2×C4—111no—
977C2×C4—221no—
978C2×C4—223no—
979C2×C4—221no—
980C2×C4—223no—
981C2×C4—223no—
982C2×C4—223no—
983C2×C4—226no—
984C2×C4—223no—
985C2×C4—223no—
986C2×C4—223no—
987C2×C4C23×AGL(1,𝔽11)13yes—
988C8—111no—
989C8—113no—
990C8C23×AGL(1,𝔽11)13yes—
991C8C23×AGL(1,𝔽11)11yescharacteristic
992C5—221noSylow
993C22—23no—
994C22—23no—
995C22—83no—
996C22—83no—
997C22—111no—
998C22—113no—
999C22—221no—
1000C22—223no—
1001C22—443no—
1002C22—446no—
1003C22—883no—
1004C22—886no—
1005C22—883no—
1006C22C2×D4×AGL(1,𝔽11)13yes—
1007C4—21no—
1008C4—21no—
1009C4—111no—
1010C4—113no—
1011C4—221no—
1012C4—223no—
1013C4C2×D4×AGL(1,𝔽11)13yes—
1014C4C24×AGL(1,𝔽11)11yescharacteristic
1015C2—23no—
1016C2—43no—
1017C2—43no—
1018C2—221no—
1019C2—223no—
1020C2—443no—
1021C2—441no—
1022C2C22×D4×AGL(1,𝔽11)11yescharacteristic
subgroupG/H
centerC2C22×D4×AGL(1,𝔽11)
commutator, cosocleC4×C11C25×C5
FrattiniC4C24×AGL(1,𝔽11)
FittingC11×#576C2×C5
socleC2×C11C23×C5×D4
hypercenter#576AGL(1,𝔽11)
hypocenterC11C5×#3585
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ #41 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #72269581C2semidirect
2. #72269577C2semidirect
3. #72269567C2semidirect
4. #72269562C2semidirect
5. #72269557C2semidirect
6. #72269550C2semidirect
7. #72269539C2semidirect
8. C11⋊C5×#576C2semidirect
9. #72269513C2semidirect
10. #72254693C2semidirect
11. #72254638C2semidirect
12. #72254632C2semidirect
13. H(5,𝔽2)×AGL(1,𝔽11)C2semidirect
14. C2×#66964⋊C5C2semidirect
15. AGL(1,ℤ/8)×AGL(1,𝔽11)C2semidirect
16. H(5,𝔽2)×C11⋊C5C22semidirect
17. H(5,𝔽2)×C11⋊C5C22semidirect
19. #67043⋊C5C22semidirect
20. #67043⋊C5C22semidirect
22. #67042⋊C5C22semidirect
23. #67042⋊C5C22semidirect
27. #41×AGL(1,𝔽11)C22semidirect
28. #41×AGL(1,𝔽11)C22semidirect
31. #67037⋊C5C22semidirect
32. #67037⋊C5C22semidirect
34. C2×#4341⋊C5C22semidirect
36. C2×D4×AGL(1,𝔽11)C22semidirect
37. AGL(1,ℤ/8)×C11⋊C5C22semidirect
38. AGL(1,ℤ/8)×C11⋊C5C22semidirect
39. #135×C11⋊C5C22semidirect
40. C2×D8×C11⋊C5C22semidirect
41. #131×C11⋊C5C22semidirect
42. #67004⋊C5C22semidirect
43. #67003⋊C5C22semidirect
44. #67003⋊C5C22semidirect
45. #67002⋊C5C22semidirect
46. #67001⋊C5C22semidirect
47. C2×#4324⋊C5C22semidirect
48. #66985⋊C5C22semidirect
49. #66985⋊C5C22semidirect
50. C2×#4323⋊C5C22semidirect
51. #66971⋊C5C22semidirect
52. #66971⋊C5C22semidirect
53. #66969⋊C5C22semidirect
54. #66968⋊C5C22semidirect
55. #66968⋊C5C22semidirect
56. #66967⋊C5C22semidirect
57. #66967⋊C5C22semidirect
58. SD16×AGL(1,𝔽11)C22semidirect
59. #66965⋊C5C22semidirect
60. #66964⋊C5C22semidirect
61. #66964⋊C5C22semidirect
62. #66964⋊C5C22semidirect
63. #66964⋊C5C22semidirect
64. #66964⋊C5C22semidirect
65. D8×AGL(1,𝔽11)C22semidirect
66. #66962⋊C5C22semidirect
67. #66961⋊C5C22semidirect
68. #66960⋊C5C22semidirect
69. M16×AGL(1,𝔽11)C22semidirect
70. #66957⋊C5C22semidirect
71. C2×#4314⋊C5C22semidirect
72. #66954⋊C5C22semidirect
73. C2×#4313⋊C5C22semidirect
74. #13083391C5semidirect
80. #41×C11⋊C5C23semidirect
84. C2×D4×C11⋊C5C23semidirect
97. Q8×AGL(1,𝔽11)C23semidirect
109. #4341⋊C5C23semidirect
121. D4×AGL(1,𝔽11)C23semidirect
128. #4339⋊C5C23semidirect
135. C2×(C11⋊C5)⋊Q8C23semidirect
136. Q16×C11⋊C5C23semidirect
137. SD16×C11⋊C5C23semidirect
138. SD16×C11⋊C5C23semidirect
139. D8×C11⋊C5C23semidirect
140. D8×C11⋊C5C23semidirect
141. M16×C11⋊C5C23semidirect
142. C2×C8×C11⋊C5C23semidirect
143. #4326⋊C5C23semidirect
144. #4326⋊C5C23semidirect
145. #4325⋊C5C23semidirect
146. #4325⋊C5C23semidirect
147. #4324⋊C5C23semidirect
148. #4324⋊C5C23semidirect
149. #4324⋊C5C23semidirect
150. #4323⋊C5C23semidirect
151. #4323⋊C5C23semidirect
152. #4323⋊C5C23semidirect
153. #4318⋊C5C23semidirect
154. C2×(C11⋊C5)⋊C8C23semidirect
155. Dic44⋊C5C23semidirect
156. D88⋊C5C23semidirect
157. #4314⋊C5C23semidirect
158. #4314⋊C5C23semidirect
159. #4314⋊C5C23semidirect
162. #4313⋊C5C23semidirect
163. #4313⋊C5C23semidirect
164. C8×AGL(1,𝔽11)C23semidirect
165. #10623455C2×C5semidirect
166. D11×H(5,𝔽2)C2×C5semidirect
167. C11×#576C2×C5semidirect
168. #10623367C2×C5semidirect
169. #10623366C2×C5semidirect
170. #10623306C2×C5semidirect
171. #10623305C2×C5semidirect
172. #10623304C2×C5semidirect
173. D11×AGL(1,ℤ/8)C2×C5semidirect
174. #10623301C2×C5semidirect
175. #10623299C2×C5semidirect
176. #10623288C2×C5semidirect
177. C2×#66964C2×C5semidirect
178. #10623282C2×C5semidirect
179. #10623281C2×C5semidirect
242. C11×H(5,𝔽2)C22×C5semidirect
243. C11×H(5,𝔽2)C22×C5semidirect
245. #67043C22×C5semidirect
246. #67043C22×C5semidirect
248. #67042C22×C5semidirect
249. #67042C22×C5semidirect
253. #41×D11C22×C5semidirect
254. #41×D11C22×C5semidirect
257. #67037C22×C5semidirect
258. #67037C22×C5semidirect
260. C2×#4341C22×C5semidirect
262. C2×D4×D11C22×C5semidirect
263. C11×AGL(1,ℤ/8)C22×C5semidirect
264. C11×AGL(1,ℤ/8)C22×C5semidirect
265. C11×#135C22×C5semidirect
266. C2×C11×D8C22×C5semidirect
267. C11×#131C22×C5semidirect
268. #67004C22×C5semidirect
269. #67003C22×C5semidirect
270. #67003C22×C5semidirect
271. #67002C22×C5semidirect
272. #67001C22×C5semidirect
273. C2×#4324C22×C5semidirect
274. #66985C22×C5semidirect
275. #66985C22×C5semidirect
276. C2×#4323C22×C5semidirect
277. #66971C22×C5semidirect
278. #66971C22×C5semidirect
279. #66969C22×C5semidirect
280. #66968C22×C5semidirect
281. #66968C22×C5semidirect
282. #66967C22×C5semidirect
283. #66967C22×C5semidirect
284. SD16×D11C22×C5semidirect
285. #66965C22×C5semidirect
286. #66964C22×C5semidirect
287. #66964C22×C5semidirect
288. #66964C22×C5semidirect
289. #66964C22×C5semidirect
290. #66964C22×C5semidirect
291. D8×D11C22×C5semidirect
292. #66962C22×C5semidirect
293. #66961C22×C5semidirect
294. #66960C22×C5semidirect
295. M16×D11C22×C5semidirect
296. #66957C22×C5semidirect
297. C2×#4314C22×C5semidirect
298. #66954C22×C5semidirect
299. C2×#4313C22×C5semidirect
342. C11×#41C23×C5semidirect
346. C2×D4×C11C23×C5semidirect
359. Q8×D11C23×C5semidirect
371. #4341C23×C5semidirect
383. D4×D11C23×C5semidirect
390. #4339C23×C5semidirect
397. C2×Dic22C23×C5semidirect
398. C11×Q16C23×C5semidirect
399. C11×SD16C23×C5semidirect
400. C11×SD16C23×C5semidirect
401. C11×D8C23×C5semidirect
402. C11×D8C23×C5semidirect
403. C11×M16C23×C5semidirect
404. C2×C8×C11C23×C5semidirect
405. #4326C23×C5semidirect
406. #4326C23×C5semidirect
407. #4325C23×C5semidirect
408. #4325C23×C5semidirect
409. #4324C23×C5semidirect
410. #4324C23×C5semidirect
411. #4324C23×C5semidirect
412. #4323C23×C5semidirect
413. #4323C23×C5semidirect
414. #4323C23×C5semidirect
415. #4318C23×C5semidirect
416. C2×C11⋊C8C23×C5semidirect
417. Dic44C23×C5semidirect
418. D88C23×C5semidirect
419. #4314C23×C5semidirect
420. #4314C23×C5semidirect
421. #4314C23×C5semidirect
424. #4313C23×C5semidirect
425. #4313C23×C5semidirect
426. C8×D11C23×C5semidirect
654. #576AGL(1,𝔽11)semidirect
660. C11⋊C5#3585semidirect
754. H(5,𝔽2)C2×AGL(1,𝔽11)semidirect
755. H(5,𝔽2)C2×AGL(1,𝔽11)semidirect
782. AGL(1,ℤ/8)C2×AGL(1,𝔽11)semidirect
783. AGL(1,ℤ/8)C2×AGL(1,𝔽11)semidirect
789. #135C2×AGL(1,𝔽11)semidirect
795. C2×D8C2×AGL(1,𝔽11)semidirect
799. #131C2×AGL(1,𝔽11)semidirect
860. #41C22×AGL(1,𝔽11)semidirect
888. C2×D4C22×AGL(1,𝔽11)semidirect
896. Q16C22×AGL(1,𝔽11)semidirect
905. SD16C22×AGL(1,𝔽11)semidirect
906. SD16C22×AGL(1,𝔽11)semidirect
911. D8C22×AGL(1,𝔽11)semidirect
912. D8C22×AGL(1,𝔽11)semidirect
918. M16C22×AGL(1,𝔽11)semidirect
921. C2×C8C22×AGL(1,𝔽11)semidirect
922. C11C5×#3585semidirect

Maximal subgroups

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

subgroupindex
#722695812
#722695772
#722695672
#722695622
#722695572
#722695502
#722695392
C11⋊C5×#5762
#722695132
#722546932
#722546382
#722546322
H(5,𝔽2)×AGL(1,𝔽11)2
C2×#66964⋊C52
AGL(1,ℤ/8)×AGL(1,𝔽11)2
#130833915
C5×#358511