Finite Group Databasebeta

← #14908348

Subgroups — #14908348

Order 2816.

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×#10622807C211yesmaximal, characteristic, complemented
2C2×#10622753C211yesmaximal, characteristic, complemented
3#13078336C211yesmaximal, characteristic, complemented
4#13070748C212yesmaximal, complemented
5#13070744C212yesmaximal, complemented
6#13070739C212yesmaximal, complemented
7#13070734C212yesmaximal, complemented
8C2×#10622131C211yesmaximal, characteristic, complemented
9#13070365C211yesmaximal, characteristic, complemented
10#13070363C211yesmaximal, characteristic, complemented
11C11×#3067C211yesmaximal, characteristic, complemented
12C11×#575—21no—
13C2×C11×#135C2211yescharacteristic
14C2×C11×#131C2211yescharacteristic
15#10623353—21no—
16C2×#66957C2211yescharacteristic
17C11×#473C2212yes—
18C11×#472C2212yes—
19C11×#471—22no—
20C2×C11×#108C2211yescharacteristic
21C11×#413—21no—
22#10622807—21no—
23#10622807—21no—
24#10622807—21no—
25#10622807—21no—
26C2×#66893C2211yescharacteristic, complemented
27C2×#66892C2211yescharacteristic, complemented
28C2×#66891C2211yescharacteristic, complemented
29C2×#66890C2211yescharacteristic, complemented
30#10622756C2212yes—
31#10622755C2212yes—
32#10622754—22no—
33#10622753—21no—
34#10622753—21no—
35#10622753C2212yes—
36#10622753C2212yes—
37#10622745—21no—
38C2×#66883C2211yescharacteristic
39C2×#66876—21no—
40C2×#66876C2211yescharacteristic
41C22×C11⋊C16—21no—
42C22×C11⋊C16C2211yescharacteristic
43#10622203C2212yescomplemented
44#10622201C2212yescomplemented
45#10622134C2212yescomplemented
46#10622133C2212yescomplemented
47#10622131C2212yescomplemented
48#10622131C2212yescomplemented
49C2×C11×#41—21no—
50C2×C11×#41D411yescharacteristic
51C2×#4339—21no—
52C11×#137—22no—
53C11×#137—41no—
54C11×AGL(1,ℤ/8)—22no—
55C11×AGL(1,ℤ/8)—41no—
56C11×#135—21no—
57C11×#135—21no—
58C11×#135—21no—
59C11×#135—21no—
60C11×#135—42no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C11×#131—21no—
65C11×#131—21no—
66C11×#131D412yes—
67C11×#131C2312yes—
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16D411yescharacteristic
71C22×C8×C11—21no—
72C22×C8×C11C2311yescharacteristic
73#67004—22no—
74#67003—42no—
75#67002—22no—
76#66995—41no—
77#66985—41no—
78C2×#4318—21no—
79C2×Dic44C2311yescharacteristic
80#66957—21no—
81#66957—21no—
82#66957—21no—
83#66957—21no—
84C2×D88C2311yescharacteristic
85C2×#4314—21no—
86C11×#108—21no—
87C11×#108C2312yes—
88C11×#101—22no—
89C11×#100—22no—
90#66893—21no—
91#66893—21no—
92#66892—21no—
93#66892—21no—
94#66891—21no—
95#66891—21no—
96#66890—21no—
97#66890—21no—
98#66888—22no—
99#66887—22no—
100#66883—21no—
101#66883C2312yes—
102#66876—21no—
103#66876—22no—
104#66876—22no—
105#66876C2312yes—
106C2×C11⋊C16—21no—
107C2×C11⋊C16—22no—
108C2×C11⋊C16—22no—
109C2×C11⋊C16D411yescharacteristic
110C2×C11⋊C16D411yescharacteristic
111C2×C11⋊C16D411yescharacteristic
112C2×C11⋊C16D411yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114C2×C11⋊C16C2311yescharacteristic
115#33617—111nomaximal, Sylow
116C11×#41—21no—
117C11×#41—21no—
118C11×#41—41no—
119C11×#41—41no—
120C11×#41—41no—
121C11×#41—41no—
122C11×#41D812yes—
123C11×#41C2×D412yes—
124C2×Q8×C11—21no—
125C2×Q8×C11D811yescharacteristic
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11D811yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C2×C22⋊D11—41no—
134#4339—41no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138C2×D44—21no—
139C2×C4×D11—41no—
140C2×Dic22—21no—
141C11×Q16—21no—
142C11×Q16—21no—
143C11×Q16—42no—
144C11×SD16—41no—
145C11×SD16—41no—
146C11×SD16—42no—
147C11×SD16—42no—
148C11×D8—21no—
149C11×D8—21no—
150C11×D8—42no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—21no—
154C11×M16—22no—
155C11×M16—41no—
156C11×M16C2×D412yes—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—21no—
160C2×C8×C11—41no—
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11#4111yescharacteristic
165C2×C8×C11#4111yescharacteristic
166C2×C8×C11C2411yescharacteristic
167#4326—42no—
168#4325—42no—
169#4324—42no—
170#4323—42no—
171#4318—22no—
172#4318—41no—
173C2×C11⋊C8—41no—
174Dic44—21no—
175Dic44—21no—
176D88—21no—
177D88—21no—
178#4314—41no—
179#4314—41no—
180C11⋊C16—22no—
181C11⋊C16C2×D411yescharacteristic
182C11⋊C16C2×D411yescharacteristic
183C11⋊C16C2×D411yescharacteristic
184C11⋊C16C2×D411yescharacteristic
185C2×#508—111no—
186C2×#504—111no—
187#3067—111no—
188#3067D1111yescharacteristic, complemented
189#2223—112no—
190#2223—112no—
191#2222—112no—
192#2221—112no—
193C2×#368—111no—
194#2148—111no—
195#2148—111no—
196C23×C11—21no—
197C23×C11—41no—
198C23×C11#13511yescharacteristic
199C22×D11—41no—
200Q8×C11—21no—
201Q8×C11—41no—
202Q8×C11—41no—
203Q8×C11C2×D812yes—
204D4×C11—22no—
205D4×C11—22no—
206D4×C11—21no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—81no—
210D4×C11—81no—
211D4×C11C2×D812yes—
212C2×C4×C11—21no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—41no—
216C2×C4×C11—81no—
217C2×C4×C11—81no—
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11C2×D811yescharacteristic
221C2×C4×C11C2×D811yescharacteristic
222C2×C4×C11#13511yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C22⋊D11—81no—
225C22⋊D11—81no—
226C2×Dic11—41no—
227D44—41no—
228D44—41no—
229C4×D11—81no—
230C4×D11—81no—
231Dic22—41no—
232Dic22—41no—
233C8×C11—22no—
234C8×C11—42no—
235C8×C11#12111yescharacteristic
236C8×C11#12111yescharacteristic
237C8×C11C22×D411yescharacteristic
238C8×C11C2×#4111yescharacteristic
239C11⋊C8—42no—
240#575—21no—
241#575—221no—
242C2×#135—111no—
243C2×#135C2×D1111yescharacteristic
244C2×#131C2×D1111yescharacteristic
245#508—221no—
246#508—221no—
247#508—221no—
248#508—221no—
249C2×Q32—111no—
250C2×SD32—111no—
251C2×SD32—111no—
252C2×D16—111no—
253#504—112no—
254#504—112no—
255#504—221no—
256#504—221no—
257C2×M32—111no—
258C2×M32—221no—
259C22×C16—111no—
260C22×C16—221no—
261#473—112no—
262#473C2×D1112yes—
263#472—112no—
264#472C2×D1112yes—
265#471—22no—
266#471—222no—
267C2×#108—111no—
268C2×#108C2×D1111yescharacteristic
269#413—21no—
270#413—221no—
271#368—112no—
272#368—112no—
273#362—112no—
274#362—112no—
275#361—112no—
276#361—112no—
277C22×C11—22no—
278C22×C11—41no—
279C22×C11—42no—
280C22×C11—81no—
281C22×C11—161no—
282C22×C11#46611yescharacteristic
283C22×C11#46611yescharacteristic
284C22×C11C2×#13511yescharacteristic
285C2×D11—81no—
286C2×D11—161no—
287C4×C11—22no—
288C4×C11—81no—
289C4×C11#46611yescharacteristic
290C4×C11#46611yescharacteristic
291C4×C11C2×#12111yescharacteristic
292C4×C11C22×D811yescharacteristic
293Dic11—81no—
294C2×#41—21no—
295C2×#41—221no—
296C2×#41C22⋊D1111yescharacteristic
297#137—22no—
298#137—41no—
299#137—222no—
300#137—441no—
301AGL(1,ℤ/8)—22no—
302AGL(1,ℤ/8)—41no—
303AGL(1,ℤ/8)—222no—
304AGL(1,ℤ/8)—441no—
305#135—21no—
306#135—21no—
307#135—21no—
308#135—21no—
309#135—42no—
310#135—221no—
311#135—221no—
312#135—221no—
313#135—221no—
314#135—442no—
315C2×Q16—111no—
316C2×Q16C22×D1111yescharacteristic
317C2×SD16—21no—
318C2×SD16—221no—
319C2×D8—111no—
320C2×D8C22×D1111yescharacteristic
321#131—21no—
322#131—21no—
323#131C22⋊D1112yes—
324#131C22×D1112yes—
325C2×M16—21no—
326C2×M16—21no—
327C2×M16—221no—
328C2×M16C22⋊D1111yescharacteristic
329C22×C8—21no—
330C22×C8C22×D1111yescharacteristic
331Q32—221no—
332Q32—221no—
333SD32—221no—
334SD32—221no—
335SD32—221no—
336SD32—221no—
337D16—221no—
338D16—221no—
339M32—112no—
340M32—222no—
341M32—222no—
342M32—221no—
343C2×C16—111no—
344C2×C16—111no—
345C2×C16—111no—
346C2×C16—111no—
347C2×C16—111no—
348C2×C16—111no—
349C2×C16—222no—
350C2×C16—222no—
351C2×C16—221no—
352#108—21no—
353#108—112no—
354#108—221no—
355#108C22×D1112yes—
356#101—22no—
357#101—222no—
358#100—22no—
359#100—222no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—21no—
363C2×C11—42no—
364C2×C11—161no—
365C2×C11C2×#46611yescharacteristic
366D11—161no—
367#41—21no—
368#41—21no—
369#41—41no—
370#41—41no—
371#41—41no—
372#41—41no—
373#41—441no—
374#41—441no—
375#41—441no—
376#41—441no—
377#41#432312yes—
378#41C2×C22⋊D1112yes—
379C2×Q8—21no—
380C2×Q8—221no—
381C2×Q8#432311yescharacteristic
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—41no—
385C2×D4—221no—
386C2×D4—441no—
387C2×D4#432311yescharacteristic
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—441no—
391C22×C4C2×C22⋊D1111yescharacteristic
392Q16—21no—
393Q16—21no—
394Q16—42no—
395Q16—221no—
396Q16—221no—
397Q16—442no—
398SD16—42no—
399SD16—42no—
400SD16—41no—
401SD16—41no—
402SD16—442no—
403SD16—442no—
404SD16—441no—
405SD16—441no—
406D8—21no—
407D8—21no—
408D8—42no—
409D8—221no—
410D8—221no—
411D8—442no—
412M16—21no—
413M16—22no—
414M16—22no—
415M16—22no—
416M16—41no—
417M16—222no—
418M16—441no—
419M16C2×C22⋊D1112yes—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—41no—
424C2×C8—441no—
425C2×C8D4×D1111yescharacteristic
426C2×C8D4×D1111yescharacteristic
427C2×C8#434111yescharacteristic
428C2×C8#434111yescharacteristic
429C2×C8C2×C22⋊D1111yescharacteristic
430C2×C8C23×D1111yescharacteristic
431C16—111no—
432C16—111no—
433C16—111no—
434C16—111no—
435C16—222no—
436C11#3361711yescharacteristic, complemented, Sylow
437C23—21no—
438C23—41no—
439C23—441no—
440C23#6700311yescharacteristic
441Q8—21no—
442Q8—41no—
443Q8—41no—
444Q8—441no—
445Q8—441no—
446Q8C2×#432312yes—
447D4—22no—
448D4—22no—
449D4—21no—
450D4—41no—
451D4—41no—
452D4—81no—
453D4—81no—
454D4—441no—
455D4—441no—
456D4—881no—
457D4—881no—
458D4C2×#432312yes—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—441no—
466C2×C4—881no—
467C2×C4—881no—
468C2×C4C2×#432311yescharacteristic
469C2×C4C2×#432311yescharacteristic
470C2×C4#6699211yescharacteristic
471C2×C4#6699211yescharacteristic
472C2×C4#6700311yescharacteristic
473C2×C4C22×C22⋊D1111yescharacteristic
474C8—22no—
475C8—42no—
476C8—442no—
477C8#6699211yescharacteristic
478C8#6699211yescharacteristic
479C8C2×D4×D1111yescharacteristic
480C8C2×#434111yescharacteristic
481C22—22no—
482C22—41no—
483C22—42no—
484C22—81no—
485C22—161no—
486C22—881no—
487C22—1761no—
488C22#1062265111yescharacteristic
489C22#1062265111yescharacteristic
490C22C2×#6700311yescharacteristic
491C4—22no—
492C4—81no—
493C4—881no—
494C4#1062265111yescharacteristic
495C4#1062265111yescharacteristic
496C4C22×#432311yescharacteristic
497C4C2×#6699211yescharacteristic
498C2—21no—
499C2—21no—
500C2—21no—
501C2—42no—
502C2—161no—
503C2—1761no—
504C2C2×#1062265111yescharacteristic
subgroupG/H
centerC4#10622651
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3067C2
socleC2×C11C2×#466
hypercenter#3067D11
hypocenterC11#33617
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. C2×#10622807C2semidirect
2. C2×#10622753C2semidirect
3. #13078336C2semidirect
4. #13070748C2semidirect
5. #13070744C2semidirect
6. #13070739C2semidirect
7. #13070734C2semidirect
8. C2×#10622131C2semidirect
9. #13070365C2semidirect
10. #13070363C2semidirect
11. C11×#3067C2semidirect
26. C2×#66893C22semidirect
27. C2×#66892C22semidirect
28. C2×#66891C22semidirect
29. C2×#66890C22semidirect
43. #10622203C22semidirect
44. #10622201C22semidirect
45. #10622134C22semidirect
46. #10622133C22semidirect
47. #10622131C22semidirect
48. #10622131C22semidirect
188. #3067D11semidirect
436. C11#33617semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
C2×#106227532
#130783362
#130707482
#130707442
#130707392
#130707342
C2×#106221312
#130703652
#130703632
C11×#30672
#3361711