Finite Group Databasebeta

← #14770540

Subgroups — #14770540

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic
2M16×Dic22C211yesmaximal, characteristic, complemented
3#13077567C211yesmaximal, characteristic, complemented
4#13069464C212yesmaximal
5#13069464C212yesmaximal
6#13069461C211yesmaximal, characteristic, complemented
7#13068610C212yesmaximal, complemented
8#13068605C211yesmaximal, characteristic
9#101×Dic11C212yesmaximal, complemented
10C4×#66887C211yesmaximal, characteristic
11C11×#1966C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#67000C2212yes—
14C2×Q8×Dic11C2212yes—
15#10623263—21no—
16#10623263—21no—
17#10623263—22no—
18#10623263—22no—
19#10623263—21no—
20#10623263—21no—
21C2×#66951C414yes—
22C2×#66950C412yes—
23C2×#66945C412yes—
24C2×C4×D44C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C11×#423C2211yescharacteristic
27C2×C11×#101C2212yes—
28C2×C11×#101C2212yes—
29C4×C11×M16C2211yescharacteristic
30C2×#66900C2212yes—
31C2×#66900C2212yes—
32C2×#66887C2211yescharacteristic
33C2×#66887C2211yescharacteristic
34C2×#66887C2212yes—
35#10622731C2212yes—
36#10622731C2212yes—
37M16×Dic11C2212yes—
38M16×Dic11C2212yes—
39#10622537C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622444—21no—
42#10622443—21no—
43#10622441—22no—
44#10622314—22no—
45#10622292—21no—
46C8×Dic22—21no—
47#10622192C2212yes—
48#10622192C2211yescharacteristic
49#10622192C2211yescharacteristic
50C22×Q8×C11C2312yes—
51C22×D44C2311yescharacteristic
52C22×C4×D11C2×C412yes—
53C22×Dic22C2×C411yescharacteristic
54C2×C11×M16C2312yes—
55C2×C11×M16C2311yescharacteristic
56C2×C11×M16C2311yescharacteristic
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C2×C11×C4⋊C4C2×C412yes—
62C2×C11×C4⋊C4C2×C412yes—
63C2×C42×C11C2311yescharacteristic
64#67000—22no—
65#67000—22no—
66#67000—22no—
67#67000—22no—
68Q8×Dic11—22no—
69Q8×Dic11—22no—
70Q8×Dic11—22no—
71Q8×Dic11—22no—
72C2×(C2×D11)⋊C4C2×C412yes—
73C2×(C2×D11)⋊C4C2×C414yes—
74C2×(C2×D11)⋊C4C2×C414yes—
75C2×C4⋊Dic11C2×C414yes—
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4C2×C412yes—
79C2×C4×Dic11C2×C414yes—
80C2×C4×Dic11C2312yes—
81C2×#4318C2312yes—
82C2×#4318C2311yescharacteristic
83C2×#4318C2311yescharacteristic
84#66951—24no—
85#66951—24no—
86#66951—24no—
87#66951—24no—
88#66950—22no—
89#66950—22no—
90#66950—24no—
91#66945—24no—
92#66945—22no—
93#66945—22no—
94C4×D44—21no—
95C4×D44—21no—
96C4×D44—21no—
97C4×D44—21no—
98C4×Dic22D411yescharacteristic
99C4×Dic22D411yescharacteristic
100C4×Dic22D412yes—
101C4×Dic22D412yes—
102C4×Dic22D411yescharacteristic
103C4×Dic22D411yescharacteristic
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×#101—24no—
107C11×#101—42no—
108C11×#97—21no—
109C4×C8×C11—21no—
110#66900—24no—
111#66900—42no—
112#66887—22no—
113#66887—22no—
114#66887—42no—
115#66879—22no—
116#66879—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121C8×Dic11—22no—
122C8×Dic11—22no—
123C4⋊(C11⋊C8)—21no—
124C4⋊(C11⋊C8)—21no—
125#66867—21no—
126C4×C11⋊C8—21no—
127#22537—111nomaximal, Sylow
128C23×D11C22×C412yes—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11C22×C412yes—
140C22×Dic11C22×C412yes—
141C22×Dic11C22×C412yes—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—44no—
151C2×Dic22—42no—
152C2×Dic22C22⋊C411yescharacteristic
153C2×Dic22C22⋊C411yescharacteristic
154C2×Dic22C22⋊C412yes—
155C11×M16—21no—
156C11×M16—22no—
157C11×M16—22no—
158C11×M16—21no—
159C11×M16—21no—
160C11×M16#4112yes—
161C2×C8×C11—21no—
162C2×C8×C11—22no—
163C2×C8×C11—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—22no—
177(C2×D11)⋊C4—22no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22⋊C412yes—
183C4⋊Dic11C22⋊C411yescharacteristic
184C4⋊Dic11C22⋊C411yescharacteristic
185Dic11⋊C4C22⋊C412yes—
186Dic11⋊C4C22⋊C412yes—
187Dic11⋊C4C22⋊C412yes—
188Dic11⋊C4C22⋊C412yes—
189C4×Dic11—24no—
190C4×Dic11—24no—
191C4×Dic11C2×D412yes—
192C4×Dic11C2×D412yes—
193C4×Dic11C2×D412yes—
194C4×Dic11C2×D412yes—
195#4318—21no—
196#4318—22no—
197#4318—22no—
198#4318—21no—
199#4318—21no—
200#4318#4112yes—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—22no—
204C2×#556—111no—
205Q8×M16—111no—
206Q8×M16—111no—
207#1967—112no—
208#1967—112no—
209#1966—111no—
210#1966D1111yescharacteristic, complemented
211#1801—112no—
212#1800—111no—
213C4×#101—112no—
214C4×#100—111no—
215C23×C11C23×C411yescharacteristic
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—42no—
220C22×D11—42no—
221Q8×C11—42no—
222Q8×C11—42no—
223Q8×C11—42no—
224Q8×C11—42no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—41no—
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×C4×C11C2×C22⋊C411yescharacteristic
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11C2×C22⋊C412yes—
245C2×Dic11C2×C22⋊C412yes—
246C2×Dic11C2×C22⋊C412yes—
247C2×Dic11C2×C22⋊C412yes—
248D44—41no—
249D44—41no—
250D44—41no—
251D44—41no—
252C4×D11—44no—
253C4×D11—44no—
254Dic22—22no—
255Dic22—22no—
256Dic22—42no—
257C8×C11—22no—
258C8×C11—42no—
259C8×C11—41no—
260C11⋊C8—22no—
261C11⋊C8—41no—
262C11⋊C8—42no—
263#556—221no—
264#556—221no—
265#556—221no—
266#556—221no—
267#556—222no—
268#556—222no—
269C2×C4⋊Q8C2×D1111yescharacteristic
270C2×#126—114no—
271C2×#124—112no—
272C2×C22⋊Q8—112no—
273C2×C4×Q8—112no—
274C2×C4×Q8—111no—
275C2×C4×D4—111no—
276C2×#117—112no—
277#446—221no—
278#446—222no—
279#446—222no—
280#446—221no—
281C8×Q8—221no—
282C8×Q8—221no—
283#423—112no—
284#423—112no—
285#423—111no—
286#423C2×D1111yescharacteristic
287C2×#101—112no—
288C2×#101—112no—
289C2×#101C2×D1112yes—
290C2×#101C2×D1112yes—
291C2×#100—111no—
292C2×#100—111no—
293C2×#100—112no—
294C4×M16—112no—
295C4×M16—112no—
296C4×M16—111no—
297C4×M16C2×D1111yescharacteristic
298#343—112no—
299#343—111no—
300#343—111no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11C22×C22⋊C411yescharacteristic
304C22×C11C4×#4111yescharacteristic
305C22×C11#52011yescharacteristic
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—82no—
310C2×D11—82no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—44no—
315C4×C11#41312yes—
316C4×C11#54811yescharacteristic
317C4×C11#54811yescharacteristic
318C4×C11#55011yescharacteristic
319C4×C11#55011yescharacteristic
320Dic11—22no—
321Dic11—22no—
322Dic11—22no—
323Dic11—22no—
324Dic11—42no—
325C22×Q8—111no—
326C22×Q8C22×D1112yes—
327C22×D4—111no—
328C23×C4—112no—
329C2×M16—111no—
330C2×M16—111no—
331C2×M16—112no—
332C2×M16C22×D1112yes—
333C2×M16C22×D1111yescharacteristic
334C2×M16C22×D1111yescharacteristic
335C4⋊Q8—21no—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339#126—224no—
340#126—224no—
341#126—224no—
342#126—224no—
343#124—222no—
344#124—222no—
345#124—222no—
346#124—222no—
347C22⋊Q8—222no—
348C22⋊Q8—222no—
349C22⋊Q8—224no—
350C4×Q8—111no—
351C4×Q8—111no—
352C4×Q8—112no—
353C4×Q8—112no—
354C4×Q8—111no—
355C4×Q8—111no—
356C4×Q8—222no—
357C4×Q8—222no—
358C4×Q8—222no—
359C4×Q8—222no—
360C4×D4—221no—
361C4×D4—221no—
362C4×D4—221no—
363C4×D4—221no—
364#117—224no—
365#117—222no—
366#117—222no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4C4×D1112yes—
372C2×C4⋊C4C4×D1112yes—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—112no—
375C2×C22⋊C4—114no—
376C2×C42—112no—
377C2×C42—114no—
378C2×C42C22×D1111yescharacteristic
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—222no—
382C4⋊C8—222no—
383C4⋊C8—222no—
384C4⋊C8—222no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387#101—24no—
388#101—42no—
389#101—224no—
390#101—442no—
391#100—222no—
392#100—222no—
393#100—442no—
394#97—21no—
395#97—222no—
396#97—222no—
397#97—221no—
398C4×C8—21no—
399C4×C8—222no—
400C4×C8—222no—
401C4×C8—221no—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11#234111yescharacteristic
405C2×C11C2×#41311yescharacteristic
406C2×C11#288911yescharacteristic
407D11—82no—
408C24—112no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—111no—
416C2×Q8—111no—
417C2×Q8—112no—
418C2×Q8—442no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—221no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—444no—
431C22×C4C2×C4×D1114yes—
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435M16—21no—
436M16—22no—
437M16—22no—
438M16—21no—
439M16—21no—
440M16—112no—
441M16—221no—
442M16—221no—
443M16—222no—
444M16—221no—
445M16—222no—
446M16#434112yes—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—22no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—222no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—112no—
458C4⋊C4—111no—
459C4⋊C4—111no—
460C4⋊C4—112no—
461C4⋊C4—112no—
462C4⋊C4—112no—
463C4⋊C4—112no—
464C4⋊C4—224no—
465C4⋊C4—224no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C22⋊C4—224no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C22⋊C4—222no—
473C22⋊C4—222no—
474C42—112no—
475C42—112no—
476C42—112no—
477C42—112no—
478C42—224no—
479C42—224no—
480C42D4×D1111yescharacteristic
481C42D4×D1111yescharacteristic
482C42D4×D1111yescharacteristic
483C42D4×D1111yescharacteristic
484C11#2253711yescharacteristic, complemented, Sylow
485C23—222no—
486C23—222no—
487C23—222no—
488C23—442no—
489C23—442no—
490C23C22×C4×D1111yescharacteristic
491Q8—42no—
492Q8—42no—
493Q8—42no—
494Q8—42no—
495Q8—222no—
496Q8—222no—
497Q8—442no—
498D4—441no—
499D4—441no—
500D4—441no—
501D4—441no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—41no—
507C2×C4—112no—
508C2×C4—112no—
509C2×C4—112no—
510C2×C4—112no—
511C2×C4—222no—
512C2×C4—444no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—444no—
516C2×C4—442no—
517C2×C4C22⋊C4×D1111yescharacteristic
518C2×C4C22⋊C4×D1111yescharacteristic
519C2×C4C22⋊C4×D1111yescharacteristic
520C2×C4C22⋊C4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434111yescharacteristic
524C2×C4#6703711yescharacteristic
525C2×C4#41×D1111yescharacteristic
526C2×C4#6704311yescharacteristic
527C8—22no—
528C8—42no—
529C8—41no—
530C8—222no—
531C8—441no—
532C8—442no—
533C22—21no—
534C22—21no—
535C22—442no—
536C22—442no—
537C22—442no—
538C22—882no—
539C22—882no—
540C22C2×C22⋊C4×D1111yescharacteristic
541C22C4×#434111yescharacteristic
542C22#1062307711yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—44no—
547C4—222no—
548C4—222no—
549C4—222no—
550C4—222no—
551C4—442no—
552C4#1062236412yes—
553C4#1062312911yescharacteristic
554C4#1062313011yescharacteristic
555C4#1062320811yescharacteristic
556C4#1062324911yescharacteristic
557C2—21no—
558C2—21no—
559C2—882no—
560C2#1307145511yescharacteristic
561C2C2×#1062236411yescharacteristic
562C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1966C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1966D11
hypocenterC11#22537
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
2. M16×Dic22C2semidirect
3. #13077567C2semidirect
6. #13069461C2semidirect
7. #13068610C2semidirect
9. #101×Dic11C2semidirect
11. C11×#1966C2semidirect
210. #1966D11semidirect
484. C11#22537semidirect

Maximal subgroups

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

subgroupindex
C2×#106232632
M16×Dic222
#130775672
#130694642
#130694612
#130686102
#130686052
#101×Dic112
C4×#668872
C11×#19662
#2253711