Finite Group Databasebeta

← #14761614

Subgroups — #14761614

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#13078404C211yesmaximal, characteristic
2#13077550C211yesmaximal, characteristic, complemented
3#13069560C211yesmaximal, characteristic, complemented
4#13069391C211yesmaximal, characteristic, complemented
5#13069215C212yesmaximal, complemented
6#13068891C212yesmaximal
7#13068636C211yesmaximal, characteristic
8#13068501C212yesmaximal, complemented
9#13068483C211yesmaximal, characteristic, complemented
10#13068458C212yesmaximal
11C4×C11×#131C211yesmaximal, characteristic
12C2×C11×#131C2211yescharacteristic
13C2×C11×#131C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#405—21no—
17C11×#405—21no—
18C11×#405C2211yescharacteristic
19C11×#405C2211yescharacteristic
20C4×C11×M16—21no—
21C4×C11×M16C2211yescharacteristic
22C2×C4×C8×C11—21no—
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66901C2212yes—
25#10622846C2212yes—
26C2×#66886C2212yes—
27#10622715C2212yes—
28#10622714C2212yes—
29C2×#66879C2212yes—
30#10622635C412yescomplemented
31#10622634C411yescharacteristic, complemented
32#10622633C411yescharacteristic, complemented
33#10622622C412yescomplemented
34#10622621C411yescharacteristic, complemented
35#10622620C411yescharacteristic, complemented
36#10622611C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38#10622537C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622292—21no—
41#10622292—21no—
42C8×Dic22—21no—
43C8×Dic22—21no—
44#10622196C2212yes—
45#10622193C2212yes—
46#10622193C2212yes—
47#10622188C2212yes—
48#10622170C2212yes—
49C2×C11×#41C2311yescharacteristic
50C11×#131—22no—
51C11×#131—22no—
52C11×#131—22no—
53C11×#131Q814yescomplemented
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16C2311yescharacteristic
57C2×C11×M16C2311yescharacteristic
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C4×Q8×C11C2×C411yescharacteristic
63C4×Q8×C11C2×C411yescharacteristic
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11C2×C411yescharacteristic
67C4×D4×C11C2×C411yescharacteristic
68C11×#117—21no—
69C11×#117C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72#66979C2312yes—
73C2×C4⋊Dic11—21no—
74#66977—21no—
75#66977—21no—
76C2×C4×Dic11C2312yes—
77C2×#4318C2312yes—
78C22×C11⋊C8C2312yes—
79#66923C2×C412yes—
80#66922C2×C411yescharacteristic
81#66922C2×C411yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×#97—21no—
85C11×#97—21no—
86C11×#97—21no—
87C4×C8×C11—21no—
88C4×C8×C11—21no—
89C4×C8×C11—21no—
90C4×C8×C11D411yescharacteristic
91C4×C8×C11D411yescharacteristic
92C4×C8×C11D411yescharacteristic
93C4×C8×C11D411yescharacteristic
94#66901—24no—
95#66899C2×C412yes—
96#66899C2×C412yes—
97#66896C2×C412yes—
98#66896C2×C412yes—
99C11⋊#95—21no—
100#66886—24no—
101#66879—22no—
102#66879—24no—
103Dic11⋊C8—22no—
104Dic11⋊C8—22no—
105C8×Dic11—22no—
106#66872C2×C412yes—
107#66872C2×C412yes—
108#66871C2×C412yes—
109#66871C2×C412yes—
110C4⋊(C11⋊C8)—21no—
111C4⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)C2×C411yescharacteristic
113C4⋊(C11⋊C8)C2×C411yescharacteristic
114C4⋊(C11⋊C8)C2×C412yes—
115#21628—111nomaximal, Sylow
116C11×#41—21no—
117C11×#41—21no—
118C11×#41C2×Q812yes—
119C11×#41#4112yes—
120C2×Q8×C11C22×C411yescharacteristic
121C2×D4×C11—21no—
122C2×D4×C11C22×C411yescharacteristic
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11#4111yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—22no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C11×M16—24no—
133C11×M16—24no—
134C11×M16—21no—
135C11×M16—21no—
136C11×M16C2×Q812yes—
137C11×M16#4112yes—
138C2×C8×C11—24no—
139C2×C8×C11—24no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2×Q812yes—
149C2×C8×C11#4112yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4C22×C411yescharacteristic
153C11×C4⋊C4C22×C411yescharacteristic
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11C22×C411yescharacteristic
161C42×C11C22×C411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C22⋊Dic11—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—42no—
168C4⋊Dic11C22×C412yes—
169C4⋊Dic11C22×C412yes—
170Dic11⋊C4—22no—
171Dic11⋊C4—22no—
172C4×Dic11—22no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175#4318—22no—
176#4318—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8C22×C412yes—
181C2×C11⋊C8C22×C412yes—
182#3076—111no—
183#2960—111no—
184C4×#131D1111yescharacteristic
185#1986—111no—
186#1950—111no—
187#1922—112no—
188#1866—112no—
189#1806—111no—
190#1773—112no—
191#1770—111no—
192#1765—112no—
193C23×C11—21no—
194C23×C11C2×#4111yescharacteristic
195Q8×C11—21no—
196Q8×C11C4×Q812yes—
197D4×C11—22no—
198D4×C11—22no—
199D4×C11—21no—
200D4×C11C4×Q812yes—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11C4×D411yescharacteristic
211C2×C4×C11C4×D411yescharacteristic
212C2×C4×C11C4×D411yescharacteristic
213C2×C4×C11C4×D411yescharacteristic
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×Q811yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225Dic22—42no—
226Dic22—42no—
227C8×C11—22no—
228C8×C11—21no—
229C8×C11—22no—
230C8×C11—21no—
231C8×C11C22⋊Q812yes—
232C8×C11C22⋊Q812yes—
233C11⋊C8—22no—
234C11⋊C8—22no—
235C11⋊C8—42no—
236C2×#131C2×D1111yescharacteristic
237C2×#131C2×D1111yescharacteristic
238#533—111no—
239C4×#41C2×D1111yescharacteristic
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—21no—
258#405—21no—
259#405—112no—
260#405C2×D1111yescharacteristic
261#405C2×D1111yescharacteristic
262C4×M16—21no—
263C4×M16C2×D1111yescharacteristic
264C2×#97—112no—
265C2×C4×C8—21no—
266C2×C4×C8C2×D1111yescharacteristic
267C4×C4⋊C4—111no—
268#341—112no—
269#339—112no—
270#339—112no—
271#339—112no—
272#336—112no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—22no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11C2×C4×D411yescharacteristic
279C22×C11#52911yescharacteristic
280C22×C11#53311yescharacteristic
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—22no—
285C4×C11—41no—
286C4×C11—41no—
287C4×C11#44412yes—
288C4×C11C2×C4×Q811yescharacteristic
289C4×C11C4×#4111yescharacteristic
290C4×C11C2×C22⋊Q811yescharacteristic
291C4×C11#52511yescharacteristic
292Dic11—42no—
293Dic11—42no—
294Dic11—82no—
295C2×#41C22×D1111yescharacteristic
296#131—22no—
297#131—22no—
298#131—22no—
299#131Dic2214yescomplemented
300C2×M16—21no—
301C2×M16—21no—
302C2×M16—112no—
303C2×M16C22×D1111yescharacteristic
304C2×M16C22×D1111yescharacteristic
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—112no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310C4⋊Q8—111no—
311C4⋊Q8—111no—
312#125—112no—
313C22⋊Q8—221no—
314C22⋊Q8—221no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×Q8C4×D1111yescharacteristic
318C4×Q8C4×D1111yescharacteristic
319C4×D4—21no—
320C4×D4—21no—
321C4×D4C4×D1111yescharacteristic
322C4×D4C4×D1111yescharacteristic
323#117—21no—
324#117—112no—
325#117C22×D1111yescharacteristic
326C2×C4⋊C4—221no—
327C2×C42—21no—
328C2×C42—112no—
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—21no—
349#97—21no—
350#97—224no—
351#97—222no—
352C4×C8—21no—
353C4×C8—21no—
354C4×C8—21no—
355C4×C8—222no—
356C4×C8C22⋊D1111yescharacteristic
357C4×C8C22⋊D1111yescharacteristic
358C4×C8C22⋊D1111yescharacteristic
359C4×C8C22⋊D1111yescharacteristic
360#95—221no—
361C2×C11—21no—
362C2×C11—21no—
363C2×C11—42no—
364C2×C11C4×C22⋊Q811yescharacteristic
365C2×C11C2×#44411yescharacteristic
366C2×C11#295511yescharacteristic
367#41—21no—
368#41—21no—
369#41C2×Dic2212yes—
370#41#433912yes—
371C2×Q8—221no—
372C2×Q8—221no—
373C2×Q8C2×C4×D1111yescharacteristic
374C2×D4—21no—
375C2×D4C2×C4×D1111yescharacteristic
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—222no—
380C22×C4#433911yescharacteristic
381C22×C4#433911yescharacteristic
382C22×C4C23×D1111yescharacteristic
383M16—24no—
384M16—21no—
385M16—21no—
386M16—24no—
387M16—222no—
388M16—222no—
389M16C2×Dic2212yes—
390M16#433912yes—
391C2×C8—24no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—24no—
397C2×C8—112no—
398C2×C8—112no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8C2×Dic2212yes—
403C2×C8#433912yes—
404C2×C8C2×C22⋊D1111yescharacteristic
405C2×C8C2×C22⋊D1111yescharacteristic
406C2×C8C2×C22⋊D1111yescharacteristic
407C2×C8C2×C22⋊D1111yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—112no—
411C4⋊C4—112no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—442no—
417C4⋊C4C2×C4×D1111yescharacteristic
418C4⋊C4C2×C4×D1111yescharacteristic
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—222no—
423C42—21no—
424C42—21no—
425C42—21no—
426C42—222no—
427C42—222no—
428C42—222no—
429C42C2×C4×D1111yescharacteristic
430C42C2×C4×D1111yescharacteristic
431C42C2×C22⋊D1111yescharacteristic
432C42C2×C22⋊D1111yescharacteristic
433C11#2162811yescharacteristic, complemented, Sylow
434C23—21no—
435C23C2×#433911yescharacteristic
436Q8—21no—
437Q8—442no—
438Q8—442no—
439Q8C4×Dic2212yes—
440D4—22no—
441D4—22no—
442D4—21no—
443D4C4×Dic2212yes—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4C4×C22⋊D1111yescharacteristic
459C2×C4C4×C22⋊D1111yescharacteristic
460C2×C4C4×C22⋊D1111yescharacteristic
461C2×C4C4×C22⋊D1111yescharacteristic
462C2×C4C22×Dic2211yescharacteristic
463C2×C4C22×C4×D1111yescharacteristic
464C2×C4C2×#433911yescharacteristic
465C2×C4C2×#433911yescharacteristic
466C2×C4C2×#433911yescharacteristic
467C2×C4C22×C22⋊D1111yescharacteristic
468C8—22no—
469C8—21no—
470C8—22no—
471C8—21no—
472C8—222no—
473C8—222no—
474C8—442no—
475C8#6697712yes—
476C8#6697712yes—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—41no—
481C22—41no—
482C22#1062300111yescharacteristic
483C22#1062301011yescharacteristic
484C22C2×C4×C22⋊D1111yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—22no—
489C4—41no—
490C4—41no—
491C4—442no—
492C4—442no—
493C4—882no—
494C4#1062275812yes—
495C4C2×C4×Dic2211yescharacteristic
496C4C4×#433911yescharacteristic
497C4C2×#6697711yescharacteristic
498C4#1062332211yescharacteristic
499C2—21no—
500C2—21no—
501C2—42no—
502C2C4×#6697711yescharacteristic
503C2C2×#1062275811yescharacteristic
504C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#131C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenterC4×#131D11
hypocenterC11#21628
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #13077550C2semidirect
3. #13069560C2semidirect
4. #13069391C2semidirect
5. #13069215C2semidirect
8. #13068501C2semidirect
9. #13068483C2semidirect
30. #10622635C4semidirect
31. #10622634C4semidirect
32. #10622633C4semidirect
33. #10622622C4semidirect
34. #10622621C4semidirect
35. #10622620C4semidirect
53. C11×#131Q8semidirect
299. #131Dic22semidirect
433. C11#21628semidirect

Maximal subgroups

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

subgroupindex
#130784042
#130775502
#130695602
#130693912
#130692152
#130688912
#130686362
#130685012
#130684832
#130684582
C4×C11×#1312
#2162811