Finite Group Databasebeta

← #14803270

Subgroups — #14803270

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622443C211yesmaximal, characteristic, complemented
2#13073619C211yesmaximal, characteristic, complemented
3#13073538C211yesmaximal, characteristic, complemented
4#13070002C212yesmaximal, complemented
5#13069924C212yesmaximal, complemented
6#13069483C212yesmaximal, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13069375C211yesmaximal, characteristic, complemented
9#13069296C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#459C211yesmaximal, characteristic
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66989—21no—
16C2×#66977—21no—
17C2×C4×Dic22C2211yescharacteristic
18C11×#459—24no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2212yes—
21#10622835—22no—
22#10622834—21no—
23#10622834C2212yes—
24#10622834C2212yes—
25#10622834C2212yes—
26C2×#66896C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66896C2211yescharacteristic
29C2×#66896C2212yes—
30#10622825—21no—
31C2×#66882C2212yes—
32C2×Dic11⋊C8C2212yes—
33C2×C8×Dic11C2212yes—
34#10622586C2212yes—
35#10622561—22no—
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622443—24no—
40#10622189C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×Dic22D411yescharacteristic
49C2×C11×D8—24no—
50C2×C11×D8—24no—
51C2×C11×D8—42no—
52C22×C8×C11C2312yes—
53C11×#127—22no—
54C11×#127—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66#66989—44no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2312yes—
73#66977—44no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4D412yes—
76C2×C4×Dic11—21no—
77C2×C4×Dic11C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C4×Dic22—22no—
81C4×Dic22—22no—
82C11×C4⋊C8D414yes—
83C11×#102—24no—
84#66896—22no—
85#66896—22no—
86#66896—24no—
87#66896—42no—
88C11⋊#95—21no—
89C11⋊#95—22no—
90#66882—42no—
91Dic11⋊C8—24no—
92C8×Dic11—24no—
93C4×C11⋊C8—22no—
94#25292—111nomaximal, Sylow
95C24×C11—21no—
96C24×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—22no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—81no—
113C2×D4×C11—81no—
114C2×D4×C11#4112yes—
115C22×C4×C11—21no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11C2×D412yes—
126C22×Dic11C2×D412yes—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22D814yescomplemented
130C11×D8—48no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11C2×D414yes—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C22⋊C4—42no—
137C42×C11C2×D412yes—
138C42×C11#4112yes—
139C22⋊Dic11—44no—
140C22⋊Dic11—44no—
141C22⋊Dic11—44no—
142C22⋊Dic11—82no—
143C22⋊Dic11—82no—
144C22⋊Dic11—82no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—42no—
153C4⋊Dic11—81no—
154Dic11⋊C4—24no—
155Dic11⋊C4—44no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C4×Dic11—42no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8#4112yes—
165C2×#459D1111yescharacteristic
166C2×C8×Q8—111no—
167#2548—111no—
168#2538—111no—
169#2067—112no—
170#2054—112no—
171#1970—112no—
172#1957—111no—
173#1947—111no—
174#1934—112no—
175C4×#102—111no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11C22×D411yescharacteristic
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—42no—
194D4×C11—41no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—41no—
198D4×C11—42no—
199D4×C11—84no—
200D4×C11—84no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—84no—
207C2×C4×C11#12112yes—
208C2×C4×C11#12112yes—
209C2×C4×C11C2×D812yes—
210C2×C4×C11#13512yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11H(5,𝔽2)11yescharacteristic
216C2×C4×C112−1+411yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—42no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11C2×D814yes—
232Dic22—28no—
233C8×C11—24no—
234C11⋊C8—22no—
235C11⋊C8—41no—
236C22×D8C2×D1112yes—
237C2×#127C2×D1111yescharacteristic
238C2×#124—221no—
239C2×C22⋊Q8—221no—
240C2×C4×Q8—111no—
241C2×C4×D4C2×D1111yescharacteristic
242#459—24no—
243C8×Q8—224no—
244C2×#107—112no—
245C2×C4⋊C8—112no—
246C2×C4⋊C8C2×D1111yescharacteristic
247C2×#102—111no—
248C2×#102—112no—
249C2×#102—111no—
250C2×#102—112no—
251C2×#102C2×D1112yes—
252C2×C4×C8—112no—
253C2×C4×C8—111no—
254#396—222no—
255#394—222no—
256#390—112no—
257#390—112no—
258#390—112no—
259#390—221no—
260#389—112no—
261#384—111no—
262#380—221no—
263C4×C4⋊C4—111no—
264#340—112no—
265#340—111no—
266#340—111no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11C2×#12111yescharacteristic
282C22×C11#54811yescharacteristic
283C22×C11#55011yescharacteristic
284C22×C11C22×D811yescharacteristic
285C22×C11C2×#13511yescharacteristic
286C22×C11#57611yescharacteristic
287C22×C11#57711yescharacteristic
288C4×C11—22no—
289C4×C11—81no—
290C4×C11#46614yes—
291C4×C11#52911yescharacteristic
292C4×C11#54211yescharacteristic
293C4×C11#54611yescharacteristic
294C4×C11#54811yescharacteristic
295Dic11—24no—
296Dic11—42no—
297Dic11—81no—
298Dic11—81no—
299Dic11—82no—
300C22×Q8—111no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C22×D1112yes—
304C22×D4C22×D1111yescharacteristic
305C23×C4—21no—
306C2×D8—24no—
307C2×D8—24no—
308C2×D8—42no—
309C22×C8—111no—
310C22×C8—111no—
311C22×C8C22×D1112yes—
312#127—22no—
313#127—22no—
314#124—444no—
315C22⋊Q8—444no—
316C4×Q8—222no—
317C4×Q8—222no—
318C4×D4—22no—
319C4×D4—22no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—112no—
337C2×C42—221no—
338C2×C42C22×D1111yescharacteristic
339#107—442no—
340C4⋊C8—224no—
341C4⋊C8C22⋊D1114yes—
342#102—24no—
343#102—222no—
344#102—224no—
345#102—222no—
346#102—442no—
347C4×C8—224no—
348C4×C8—222no—
349#95—222no—
350#95—221no—
351C2×C11—82no—
352C2×C11—162no—
353C2×C11#242611yescharacteristic
354C2×C11C2×#46611yescharacteristic
355C2×C11#306211yescharacteristic
356C2×C11#335811yescharacteristic
357C2×C11#336111yescharacteristic
358C2×C11#339111yescharacteristic
359C2×C11#339411yescharacteristic
360C24—21no—
361C24—22no—
362C2×Q8—114no—
363C2×Q8—222no—
364C2×Q8—222no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—21no—
371C2×D4—22no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—81no—
381C2×D4—81no—
382C2×D4#434112yes—
383C22×C4—21no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—112no—
388C22×C4—112no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—222no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395D8—48no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—112no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8C2×C22⋊D1114yes—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—224no—
408C4⋊C4—222no—
409C4⋊C4—221no—
410C4⋊C4—222no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—221no—
415C4⋊C4—444no—
416C4⋊C4—442no—
417C4⋊C4—881no—
418C22⋊C4—42no—
419C22⋊C4—444no—
420C22⋊C4—444no—
421C22⋊C4—444no—
422C22⋊C4—882no—
423C22⋊C4—882no—
424C22⋊C4—882no—
425C42—222no—
426C42—222no—
427C42—442no—
428C42#434112yes—
429C42C2×C22⋊D1112yes—
430C11#2529211yescharacteristic, complemented, Sylow
431C23—22no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23C2×D4×D1111yescharacteristic
446Q8—228no—
447D4—22no—
448D4—22no—
449D4—42no—
450D4—41no—
451D4—42no—
452D4—42no—
453D4—41no—
454D4—42no—
455D4—84no—
456D4—84no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—84no—
463C2×C4—114no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—442no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—442no—
477C2×C4—441no—
478C2×C4D8×D1112yes—
479C2×C4#6696512yes—
480C2×C4#6699112yes—
481C2×C4#6699112yes—
482C2×C4C2×#434111yescharacteristic
483C2×C4C2×#434111yescharacteristic
484C2×C4#6703711yescharacteristic
485C2×C4#41×D1111yescharacteristic
486C2×C4#6704311yescharacteristic
487C2×C4C22×C22⋊D1111yescharacteristic
488C8—24no—
489C8—222no—
490C8—441no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—82no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22—82no—
504C22—82no—
505C22#1062312911yescharacteristic
506C22#1062313011yescharacteristic
507C22C2×D8×D1111yescharacteristic
508C22C2×#6696511yescharacteristic
509C22#1062330511yescharacteristic
510C22#1062330611yescharacteristic
511C22C2×#6699111yescharacteristic
512C4—22no—
513C4—81no—
514C4—224no—
515C4—442no—
516C4—881no—
517C4—881no—
518C4—882no—
519C4#1062277014yes—
520C4#1062313111yescharacteristic
521C4#1062313411yescharacteristic
522C4#1062333711yescharacteristic
523C4#1062336211yescharacteristic
524C2—82no—
525C2—162no—
526C2#1307217811yescharacteristic
527C2C2×#1062277011yescharacteristic
528C2#1307829011yescharacteristic
529C2#1308124611yescharacteristic
530C2#1308128011yescharacteristic
531C2#1308158711yescharacteristic
532C2#1308161611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11#25292
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10622443C2semidirect
2. #13073619C2semidirect
3. #13073538C2semidirect
4. #13070002C2semidirect
5. #13069924C2semidirect
6. #13069483C2semidirect
7. #13069423C2semidirect
8. #13069375C2semidirect
9. #13069296C2semidirect
10. C4×#66896C2semidirect
129. C2×Dic22D8semidirect
430. C11#25292semidirect

Maximal subgroups

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

subgroupindex
C2×#106224432
#130736192
#130735382
#130700022
#130699242
#130694832
#130694232
#130693752
#130692962
C4×#668962
C2×C11×#4592
#2529211