Finite Group Databasebeta

← #14761617

Subgroups — #14761617

Order 2816.

738 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
1#13078398C211yesmaximal, characteristic
2#13077551C211yesmaximal, characteristic, complemented
3C4×#66960C211yesmaximal, characteristic
4#13069391C211yesmaximal, characteristic, complemented
5#13069218C212yesmaximal, complemented
6#13068892C212yesmaximal
7#13068637C211yesmaximal, characteristic
8#13068499C212yesmaximal, complemented
9#13068485C211yesmaximal, characteristic, complemented
10#13068457C212yesmaximal
11C11×#1986C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66960C2211yescharacteristic
14C2×#66960C2211yescharacteristic
15C4×#4339C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17C4×C11×C4⋊C4C2211yescharacteristic
18C2×#66886C2212yes—
19#10622735C2211yescharacteristic
20#10622735C2211yescharacteristic
21#10622707C411yescharacteristic, complemented
22#10622704C411yescharacteristic, complemented
23#10622700C411yescharacteristic, complemented
24#10622697C411yescharacteristic, complemented
25#10622679C412yescomplemented
26#10622676C412yescomplemented
27#10622637—21no—
28#10622637—21no—
29Q8×C11⋊C8—21no—
30Q8×C11⋊C8—21no—
31#10622615C2212yes—
32#10622612C2212yes—
33#10622611C2212yes—
34#10622610C2212yes—
35C2×#66869C2212yes—
36#10622537C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×#66867C2212yes—
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622321—21no—
41#10622321—21no—
42C4×#4313—21no—
43C4×C8×D11—21no—
44C11×#339C2212yes—
45C11×#339C2212yes—
46#10622196C2212yes—
47#10622162C2212yes—
48#10622161C2212yes—
49C2×#4339C2311yescharacteristic
50C2×C11×M16C2311yescharacteristic
51C2×C11×M16C2311yescharacteristic
52C11×C4⋊Q8C2×C411yescharacteristic
53C11×C4⋊Q8C2×C411yescharacteristic
54C11×#125C2×C412yes—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C11×#117C2312yes—
60C2×C11×C4⋊C4—21no—
61C2×C42×C11C2312yes—
62C2×C42×C11C2311yescharacteristic
63C4×C22⋊D11—21no—
64C4×C22⋊D11—21no—
65#66979C2311yescharacteristic
66C2×#4318C2312yes—
67C22×C11⋊C8C2312yes—
68C22×C11⋊C8C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70#66960—22no—
71#66960—22no—
72#66960—22no—
73#66960Q814yescomplemented
74C2×#4313—21no—
75C2×#4313—21no—
76C2×C8×D11—21no—
77C2×C8×D11—21no—
78C4×D44C2×C411yescharacteristic
79C4×D44C2×C411yescharacteristic
80#66925—21no—
81C42×D11—21no—
82C4×Dic22C2×C411yescharacteristic
83C4×Dic22C2×C411yescharacteristic
84C11×#97—21no—
85C4×C8×C11—21no—
86C11×#95—21no—
87#66886—24no—
88#66879—21no—
89#66879—21no—
90C8×Dic11—21no—
91C8×Dic11—21no—
92#66874C2×C412yes—
93#66874C2×C412yes—
94#66873C2×C412yes—
95#66873C2×C412yes—
96#66872C2×C412yes—
97#66872C2×C412yes—
98#66871C2×C412yes—
99#66871C2×C412yes—
100#66869—24no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)—22no—
105C4⋊(C11⋊C8)C2×C412yes—
106C4⋊(C11⋊C8)C2×C411yescharacteristic
107C4⋊(C11⋊C8)C2×C411yescharacteristic
108#66867—22no—
109#66867—24no—
110C4×C11⋊C8—22no—
111C4×C11⋊C8D411yescharacteristic
112C4×C11⋊C8D411yescharacteristic
113C4×C11⋊C8D411yescharacteristic
114C4×C11⋊C8D411yescharacteristic
115#21628—111nomaximal, Sylow
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—21no—
123#4339—21no—
124#4339—21no—
125#4339C2×Q812yes—
126#4339#4112yes—
127C2×D44C22×C411yescharacteristic
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×Dic22C22×C411yescharacteristic
132C11×M16—21no—
133C11×M16—21no—
134C11×M16C2×Q812yes—
135C11×M16#4112yes—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4C22×C412yes—
144C11×C4⋊C4C22×C412yes—
145C11×C22⋊C4—22no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11C22×C411yescharacteristic
150C42×C11C22×C411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C22⋊Dic11—21no—
154(C2×D11)⋊C4—21no—
155(C2×D11)⋊C4—21no—
156C4⋊Dic11C22×C411yescharacteristic
157C4⋊Dic11C22×C411yescharacteristic
158Dic11⋊C4—21no—
159Dic11⋊C4—21no—
160C4×Dic11—21no—
161C4×Dic11—21no—
162C4×Dic11—21no—
163#4318—22no—
164#4318—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8C22×C412yes—
171C2×C11⋊C8C22×C412yes—
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176C2×C11⋊C8C2×Q812yes—
177C2×C11⋊C8#4112yes—
178#4313—24no—
179#4313—24no—
180C8×D11—24no—
181C8×D11—24no—
182#3076—111no—
183#2960—111no—
184C4×#131—111no—
185#1986D1111yescharacteristic, complemented
186#1950—111no—
187#1922—112no—
188#1866—112no—
189#1806—111no—
190#1773—112no—
191#1770—111no—
192#1765—112no—
193C23×C11C2×#4111yescharacteristic
194C22×D11—21no—
195Q8×C11—42no—
196Q8×C11—42no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11C4×D411yescharacteristic
205C2×C4×C11C4×D411yescharacteristic
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×Q811yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C22⋊D11—22no—
215C22⋊D11—22no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219D44—21no—
220D44C4×Q812yes—
221C4×D11—22no—
222C4×D11—22no—
223C4×D11—42no—
224C4×D11—42no—
225Dic22—21no—
226Dic22C4×Q812yes—
227C8×C11—22no—
228C8×C11—22no—
229C11⋊C8—22no—
230C11⋊C8—22no—
231C11⋊C8—21no—
232C11⋊C8—21no—
233C11⋊C8—42no—
234C11⋊C8C22⋊Q812yes—
235C11⋊C8C22⋊Q812yes—
236C2×#131—111no—
237C2×#131—111no—
238#533C2×D1111yescharacteristic
239C4×#41—111no—
240#479—112no—
241#478—112no—
242#477—111no—
243#476—111no—
244#475—111no—
245#474—111no—
246#446—221no—
247#446—221no—
248C8×Q8—221no—
249C8×Q8—221no—
250C2×#108—112no—
251#427—112no—
252#424—112no—
253#423—111no—
254C2×C4⋊C8—111no—
255C2×#104—112no—
256#416—112no—
257#405—111no—
258#405—111no—
259#405—112no—
260#405—221no—
261#405—221no—
262C4×M16—221no—
263C4×M16C2×D1111yescharacteristic
264C2×#97—112no—
265C2×C4×C8—111no—
266C2×C4×C8—221no—
267C4×C4⋊C4C2×D1111yescharacteristic
268#341—112no—
269#339—112no—
270#339C2×D1112yes—
271#339C2×D1112yes—
272#336—112no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11C2×C4×D411yescharacteristic
276C22×C11#52911yescharacteristic
277C22×C11#53311yescharacteristic
278C2×D11—22no—
279C2×D11—41no—
280C2×D11—41no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—82no—
287C4×C11#44412yes—
288C4×C11C2×C4×Q811yescharacteristic
289C4×C11C4×#4111yescharacteristic
290C4×C11C2×C22⋊Q811yescharacteristic
291C4×C11#52511yescharacteristic
292Dic11—22no—
293Dic11—41no—
294Dic11—41no—
295C2×#41—111no—
296#131—114no—
297#131—222no—
298#131—222no—
299#131—222no—
300C2×M16—112no—
301C2×M16—221no—
302C2×M16—221no—
303C2×M16C22×D1111yescharacteristic
304C2×M16C22×D1111yescharacteristic
305C22×C8—111no—
306C22×C8—111no—
307C22×C8—112no—
308C22×C8—221no—
309C22×C8—221no—
310C4⋊Q8C4×D1111yescharacteristic
311C4⋊Q8C4×D1111yescharacteristic
312#125C4×D1112yes—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—111no—
318C4×Q8—111no—
319C4×D4—111no—
320C4×D4—111no—
321C4×D4—221no—
322C4×D4—221no—
323#117—111no—
324#117—221no—
325#117C22×D1112yes—
326C2×C4⋊C4—21no—
327C2×C42—221no—
328C2×C42C22×D1112yes—
329C2×C42C22×D1111yescharacteristic
330#108—224no—
331#107—112no—
332#107—112no—
333#106—112no—
334#106—112no—
335C4⋊C8—111no—
336C4⋊C8—111no—
337C4⋊C8—112no—
338C4⋊C8—222no—
339C4⋊C8—222no—
340C4⋊C8—221no—
341C4⋊C8—221no—
342#104—224no—
343#103—112no—
344#103—112no—
345#102—112no—
346#102—112no—
347#97—21no—
348#97—224no—
349#97—222no—
350#97—221no—
351#97—221no—
352C4×C8—21no—
353C4×C8—111no—
354C4×C8—111no—
355C4×C8—111no—
356C4×C8—111no—
357C4×C8—222no—
358C4×C8—221no—
359C4×C8—221no—
360#95—21no—
361C2×C11—21no—
362C2×C11—21no—
363C2×C11C4×C22⋊Q811yescharacteristic
364C2×C11C2×#44411yescharacteristic
365C2×C11#295511yescharacteristic
366D11—42no—
367#41—112no—
368#41—112no—
369#41—221no—
370#41—221no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—111no—
374C2×D4—111no—
375C2×D4—221no—
376C22×C4—22no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4#434111yescharacteristic
381C22×C4#434111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383M16—21no—
384M16—21no—
385M16—224no—
386M16—224no—
387M16—222no—
388M16—222no—
389M16Q8×D1112yes—
390M16#434312yes—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—111no—
394C2×C8—111no—
395C2×C8—112no—
396C2×C8—112no—
397C2×C8—112no—
398C2×C8—112no—
399C2×C8—111no—
400C2×C8—111no—
401C2×C8—224no—
402C2×C8—224no—
403C2×C8—222no—
404C2×C8—221no—
405C2×C8—222no—
406C2×C8—221no—
407C2×C8—222no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—42no—
413C4⋊C4—111no—
414C4⋊C4—111no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4C2×C4×D1112yes—
418C4⋊C4C2×C4×D1112yes—
419C22⋊C4—22no—
420C22⋊C4—221no—
421C22⋊C4—221no—
422C22⋊C4—221no—
423C42—22no—
424C42—22no—
425C42—22no—
426C42—221no—
427C42—221no—
428C42—221no—
429C42C2×C4×D1111yescharacteristic
430C42C2×C4×D1111yescharacteristic
431C42D4×D1111yescharacteristic
432C42D4×D1111yescharacteristic
433C11#2162811yescharacteristic, complemented, Sylow
434C23—221no—
435C23C2×#434111yescharacteristic
436Q8—42no—
437Q8—42no—
438Q8—112no—
439Q8—221no—
440D4—112no—
441D4—222no—
442D4—222no—
443D4—221no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—221no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4(C22⋊D11)⋊C411yescharacteristic
459C2×C4(C22⋊D11)⋊C411yescharacteristic
460C2×C4(C22⋊D11)⋊C411yescharacteristic
461C2×C4(C22⋊D11)⋊C411yescharacteristic
462C2×C4C22×C4×D1111yescharacteristic
463C2×C4C2×D4×D1111yescharacteristic
464C2×C4C2×Q8×D1111yescharacteristic
465C2×C4C2×#434311yescharacteristic
466C2×C4#41×D1111yescharacteristic
467C2×C4#41×D1111yescharacteristic
468C8—22no—
469C8—22no—
470C8—112no—
471C8—112no—
472C8—222no—
473C8—222no—
474C8—221no—
475C8—221no—
476C8—442no—
477C22—21no—
478C22—21no—
479C22—222no—
480C22—441no—
481C22—441no—
482C22C2×(C22⋊D11)⋊C411yescharacteristic
483C22#1062321111yescharacteristic
484C22#1062325911yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—42no—
490C4—82no—
491C4—222no—
492C4—441no—
493C4—441no—
494C4#1062243612yes—
495C4C4×Q8×D1111yescharacteristic
496C4C4×#434311yescharacteristic
497C4D11×C22⋊Q811yescharacteristic
498C4#1062315811yescharacteristic
499C2—21no—
500C2—21no—
501C2—442no—
502C2#1307115411yescharacteristic
503C2C2×#1062243611yescharacteristic
504C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1986C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#1986D11
hypocenterC11#21628
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #13077551C2semidirect
4. #13069391C2semidirect
5. #13069218C2semidirect
8. #13068499C2semidirect
9. #13068485C2semidirect
11. C11×#1986C2semidirect
21. #10622707C4semidirect
22. #10622704C4semidirect
23. #10622700C4semidirect
24. #10622697C4semidirect
25. #10622679C4semidirect
26. #10622676C4semidirect
73. #66960Q8semidirect
185. #1986D11semidirect
433. C11#21628semidirect

Maximal subgroups

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

subgroupindex
#130783982
#130775512
C4×#669602
#130693912
#130692182
#130688922
#130686372
#130684992
#130684852
#130684572
C11×#19862
#2162811