Finite Group Databasebeta

← #14795242

Subgroups — #14795242

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C4×#67002C211yesmaximal, characteristic
3#13077282C211yesmaximal, characteristic, complemented
4#13070064C212yesmaximal, complemented
5#13069906C212yesmaximal
6#13069606C211yesmaximal, characteristic, complemented
7#13069393C212yesmaximal, complemented
8#13069389C211yesmaximal, characteristic, complemented
9#13069277C212yesmaximal, complemented
10#13068605C211yesmaximal, characteristic, complemented
11C11×#3079C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C4×C11×#41C2211yescharacteristic
14C2×#67002C2211yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C11×#477—21no—
17C11×#476—21no—
18C11×#475—21no—
19C11×#474—21no—
20C11×#428C2212yes—
21C11×#423C2211yescharacteristic
22C11×#417C2212yes—
23#10622847C2212yes—
24#10622845C2211yescharacteristic
25C2×#66887C2212yes—
26C2×#66886C2212yes—
27#10622697—21no—
28#10622697—21no—
29#10622697—22no—
30#10622639—21no—
31C4×#4325—21no—
32#10622627—21no—
33C4×#4323—21no—
34#10622614C2211yescharacteristic
35#10622613—22no—
36#10622610C2212yes—
37#10622608C2211yescharacteristic
38C2×#66873C2212yes—
39C2×#66872C2212yes—
40#10622539—21no—
41#10622538—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622196C2212yes—
46#10622192C2212yes—
47#10622168C2212yes—
48#10622168C2212yes—
49C2×C11×#41C2311yescharacteristic
50C22×Q8×C11—21no—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C2×C11×M16C2312yes—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C4×Q8×C11D411yescharacteristic
59C4×Q8×C11D411yescharacteristic
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11D411yescharacteristic
63C4×D4×C11D411yescharacteristic
64C11×#117—21no—
65C11×#117C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2312yes—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70#67002—22no—
71#67002—22no—
72C2×#4325—21no—
73C2×#4323—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×#4318C2312yes—
77C2×#4318C2311yescharacteristic
78C2×#4318C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C4×D44—21no—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44—21no—
84C11×#107—22no—
85C11×#106—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8—21no—
88C11×#103—22no—
89C11×#102—22no—
90#66899—21no—
91#66896—21no—
92C22⋊(C11⋊C8)—22no—
93C22⋊(C11⋊C8)—22no—
94#66887—24no—
95#66886—24no—
96#66873—21no—
97#66873—21no—
98#66873—22no—
99#66873—22no—
100#66872—21no—
101#66872—22no—
102#66872—22no—
103#66871—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)D411yescharacteristic
107C4⋊(C11⋊C8)D411yescharacteristic
108C4⋊(C11⋊C8)D412yes—
109#66867—21no—
110#66867—22no—
111C4×C11⋊C8—21no—
112C4×C11⋊C8—22no—
113#24721—111nomaximal, Sylow
114C23×D11—21no—
115C11×#41—21no—
116C11×#41—21no—
117C11×#41—21no—
118C11×#41—21no—
119C2×Q8×C11—41no—
120C2×Q8×C11—41no—
121C2×Q8×C11—82no—
122C2×Q8×C11C2×D411yescharacteristic
123C2×D4×C11—21no—
124C2×D4×C11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44#4112yes—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11—82no—
142C11×M16—22no—
143C11×M16—22no—
144C2×C8×C11—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4C2×D411yescharacteristic
152C11×C4⋊C4C2×D411yescharacteristic
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163#4325—24no—
164#4323—24no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169#4318—21no—
170#4318—22no—
171#4318—21no—
172#4318—21no—
173#4318—22no—
174#4318#4112yes—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8C2×D412yes—
181C2×C11⋊C8C2×D412yes—
182#3079D1111yescharacteristic, complemented
183C2×#476—111no—
184C4×AGL(1,ℤ/8)—111no—
185#2925—111no—
186#2079—112no—
187#2051—112no—
188#1997—111no—
189#1951—112no—
190#1950—111no—
191#1931—112no—
192#1800—111no—
193C23×C11—21no—
194C23×C11C2×#4111yescharacteristic
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—81no—
199C22×D11—81no—
200Q8×C11—21no—
201Q8×C11—21no—
202Q8×C11—82no—
203Q8×C11—82no—
204D4×C11—21no—
205D4×C11—21no—
206D4×C11—41no—
207D4×C11—41no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—81no—
218C2×C4×C11—82no—
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C112−1+411yescharacteristic
228C2×C4×C112−1+411yescharacteristic
229C2×Dic11—41no—
230C2×Dic11—81no—
231D44—22no—
232D44—22no—
233D44—41no—
234D44—41no—
235C4×D11—82no—
236C4×D11—82no—
237C8×C11—42no—
238C11⋊C8—22no—
239C11⋊C8—22no—
240C11⋊C8—22no—
241C11⋊C8—41no—
242C11⋊C8—42no—
243C2×AGL(1,ℤ/8)—111no—
244C2×C4⋊Q8C2×D1111yescharacteristic
245C4×#41C2×D1111yescharacteristic
246C2×C4×D4—111no—
247#477—21no—
248#476—21no—
249#476—221no—
250#476—221no—
251#476—222no—
252#475—21no—
253#474—21no—
254#442—221no—
255#440—221no—
256C4×SD16—221no—
257C4×D8—221no—
258#433—222no—
259#432—221no—
260#431—221no—
261C2×#108—112no—
262#428—111no—
263#428C2×D1112yes—
264C2×#106—112no—
265#423—111no—
266#423C2×D1111yescharacteristic
267C2×C4⋊C8—111no—
268#418—111no—
269#417—111no—
270#417C2×D1112yes—
271C2×#102—112no—
272C2×#100—112no—
273#408—112no—
274#405—112no—
275C4×M16—111no—
276#343—112no—
277#343—112no—
278#343—112no—
279#341—112no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11C2×#12111yescharacteristic
286C22×C11#55211yescharacteristic
287C22×C11#55611yescharacteristic
288C2×D11—42no—
289C2×D11—82no—
290C2×D11—81no—
291C2×D11—81no—
292C2×D11—82no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—82no—
300C4×C11#47112yes—
301C4×C11#52511yescharacteristic
302C4×C11#53611yescharacteristic
303C4×C11#54711yescharacteristic
304C4×C11#54811yescharacteristic
305Dic11—81no—
306C2×#41C22×D1111yescharacteristic
307C22×Q8—21no—
308C22×D4—111no—
309C23×C4—221no—
310AGL(1,ℤ/8)—222no—
311AGL(1,ℤ/8)—222no—
312C2×SD16—221no—
313C2×D8—221no—
314C2×M16—111no—
315C2×M16—111no—
316C2×M16—112no—
317C2×M16C22×D1112yes—
318C22×C8—112no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4×Q8C22⋊D1111yescharacteristic
324C4×Q8C22⋊D1111yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4—221no—
330C4×D4—221no—
331C4×D4C22⋊D1111yescharacteristic
332C4×D4C22⋊D1111yescharacteristic
333#117—21no—
334#117C22×D1111yescharacteristic
335C2×C4⋊C4—21no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4C22×D1112yes—
338C2×C22⋊C4—221no—
339C2×C42—21no—
340C2×C42C22×D1111yescharacteristic
341#108—224no—
342#107—22no—
343#107—221no—
344#106—22no—
345#106—222no—
346#106—222no—
347#106—221no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—111no—
351C4⋊C8—111no—
352C4⋊C8—112no—
353C4⋊C8—221no—
354C4⋊C8—221no—
355#103—22no—
356#103—221no—
357#102—22no—
358#102—222no—
359#102—222no—
360#102—221no—
361#102—221no—
362#102—221no—
363#100—224no—
364C22⋊C8—222no—
365C22⋊C8—222no—
366#97—222no—
367#97—221no—
368C4×C8—222no—
369C4×C8—221no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—81no—
373C2×C11#241511yescharacteristic
374C2×C11C2×#47111yescharacteristic
375C2×C11#306811yescharacteristic
376D11—82no—
377C24—221no—
378#41—21no—
379#41—21no—
380#41—21no—
381#41—21no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—82no—
385C2×Q8C2×C22⋊D1111yescharacteristic
386C2×D4—21no—
387C2×D4—112no—
388C2×D4—221no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—221no—
393C2×D4C2×C22⋊D1111yescharacteristic
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—221no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—882no—
402C22×C4#434111yescharacteristic
403C22×C4#434111yescharacteristic
404C22×C4C23×D1111yescharacteristic
405SD16—224no—
406D8—224no—
407M16—22no—
408M16—22no—
409M16—112no—
410M16—221no—
411M16—221no—
412M16—221no—
413M16—222no—
414M16—222no—
415C2×C8—22no—
416C2×C8—112no—
417C2×C8—112no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—221no—
421C2×C8—222no—
422C2×C8—221no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4C2×C22⋊D1111yescharacteristic
432C4⋊C4C2×C22⋊D1111yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C42—21no—
439C42—21no—
440C42—21no—
441C42D4×D1111yescharacteristic
442C42D4×D1111yescharacteristic
443C42C2×C22⋊D1111yescharacteristic
444C42C2×C22⋊D1111yescharacteristic
445C11#2472111yescharacteristic, complemented, Sylow
446C23—21no—
447C23—222no—
448C23—441no—
449C23—441no—
450C23—881no—
451C23—881no—
452C23C2×#434111yescharacteristic
453Q8—21no—
454Q8—21no—
455Q8—82no—
456Q8—82no—
457D4—21no—
458D4—21no—
459D4—41no—
460D4—41no—
461D4—222no—
462D4—222no—
463D4—441no—
464D4—441no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—81no—
475C2×C4—82no—
476C2×C4—441no—
477C2×C4—882no—
478C2×C4—882no—
479C2×C4—881no—
480C2×C4#6699211yescharacteristic
481C2×C4#6699211yescharacteristic
482C2×C4#6699211yescharacteristic
483C2×C4#6699211yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4#6704011yescharacteristic
486C2×C4#6704011yescharacteristic
487C2×C4#41×D1111yescharacteristic
488C2×C4#41×D1111yescharacteristic
489C2×C4C22×C22⋊D1111yescharacteristic
490C8—42no—
491C8—222no—
492C8—222no—
493C8—222no—
494C8—441no—
495C8—442no—
496C22—21no—
497C22—21no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—442no—
502C22—882no—
503C22—882no—
504C22—881no—
505C22—881no—
506C22#1062317011yescharacteristic
507C22#1062317211yescharacteristic
508C22C2×#6699211yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—82no—
516C4—881no—
517C4#1062281612yes—
518C4#1062316211yescharacteristic
519C4#1062316411yescharacteristic
520C4#1062334711yescharacteristic
521C4#1062335911yescharacteristic
522C2—21no—
523C2—21no—
524C2—81no—
525C2—882no—
526C2#1307204611yescharacteristic
527C2C2×#1062281611yescharacteristic
528C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3079C2
socleC22×C11C2×#121
prime radicalC2×#67002C22
hypercenter#3079D11
hypocenterC11#24721
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
3. #13077282C2semidirect
4. #13070064C2semidirect
6. #13069606C2semidirect
7. #13069393C2semidirect
8. #13069389C2semidirect
9. #13069277C2semidirect
10. #13068605C2semidirect
11. C11×#3079C2semidirect
182. #3079D11semidirect
445. C11#24721semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C4×#670022
#130772822
#130700642
#130699062
#130696062
#130693932
#130693892
#130692772
#130686052
C11×#30792
#2472111