Finite Group Databasebeta

← #14782318

Subgroups — #14782318

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077206C211yesmaximal, characteristic, complemented
2C2×#10622715C211yesmaximal, characteristic, complemented
3#13077136C211yesmaximal, characteristic
4C2×#10622726C211yesmaximal, characteristic
5C2×#10622745C211yesmaximal, characteristic
6#13069978C214yesmaximal, complemented
7#13069971C214yesmaximal, complemented
8#13068354C211yesmaximal, characteristic, complemented
9C22×C11×#108C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×C11×#108—24no—
18C2×C11×#108C2214yes—
19C2×#66888C2212yes—
20#10622746—22no—
21#10622745—24no—
22#10622744C2212yes—
23C2×#66887C2212yes—
24#10622734—22no—
25#10622734C2214yes—
26#10622733C2212yes—
27#10622726—22no—
28#10622726—22no—
29#10622726—22no—
30C2×#66885C2212yes—
31#10622719—22no—
32C2×#66880C2212yes—
33#10622715—22no—
34#10622715C2214yes—
35C2×Dic11⋊C8—22no—
36#10622192C2214yes—
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11—21no—
39C2×#4339—22no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339Q814yes—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22C2311yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16—22no—
52C2×C11×M16—21no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C2×C11×M16D414yes—
56C2×C11×M16C2312yes—
57C2×C11×M16C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11—21no—
60C22×C8×C11—22no—
61C22×C8×C11—21no—
62C22×C8×C11D412yes—
63C22×C8×C11D412yes—
64C22×C8×C11C2312yes—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67#66979—21no—
68#66979—21no—
69#66979—21no—
70#66979—21no—
71#66979—21no—
72#66979—21no—
73#66979D412yes—
74#66979C2312yes—
75C2×C4⋊Dic11D412yes—
76C2×C4⋊Dic11C2312yes—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×#4318—21no—
80C2×#4318—22no—
81C2×#4318—22no—
82C2×#4318C2312yes—
83C22×C11⋊C8—21no—
84C11×#108—28no—
85#66888—24no—
86#66887—24no—
87#66885—24no—
88#66885—24no—
89#66882—24no—
90#66881—24no—
91#66880—24no—
92#66880—24no—
93Dic11⋊C8—28no—
94#23601—111nomaximal, Sylow
95C24×C11#4111yescharacteristic
96C23×D11—21no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×Q812yes—
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—24no—
108C2×C22⋊D11—41no—
109C2×C22⋊D11—41no—
110C2×C22⋊D11—42no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114#4339—24no—
115#4339—24no—
116#4339—24no—
117#4339—24no—
118#4339—42no—
119#4339—42no—
120#4339—42no—
121#4339—42no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44C2×Q812yes—
128C2×C4×D11—24no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C2×C4×D11—42no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22C2×Q812yes—
138C11×M16—24no—
139C11×M16—22no—
140C11×M16—22no—
141C11×M16—22no—
142C11×M16—42no—
143C11×M16C2×D414yes—
144C2×C8×C11—24no—
145C2×C8×C11—24no—
146C2×C8×C11—24no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—42no—
152C2×C8×C11C2×D414yes—
153C22⋊Dic11—22no—
154C22⋊Dic11—22no—
155C22⋊Dic11—41no—
156C22⋊Dic11—41no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11C2×D414yes—
161C4×Dic11—22no—
162C4×Dic11—22no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165#4318—22no—
166#4318—22no—
167#4318—42no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170C22×#108D1111yescharacteristic, complemented
171#2911—111no—
172C2×#424—111no—
173#2896—111no—
174C2×#416—111no—
175C2×#413—111no—
176#2064—114no—
177#2063—114no—
178#1742—111no—
179C23×C11—42no—
180C23×C11#12111yescharacteristic
181C23×C11#12111yescharacteristic
182C23×C11C22⋊Q812yes—
183C23×C11#12612yes—
184C23×C11C2×#4111yescharacteristic
185C22×D11—22no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—82no—
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12112yes—
192C2×C4×C11#12112yes—
193C2×C4×C11#12112yes—
194C2×C4×C11#12112yes—
195C2×C4×C11C22⋊Q812yes—
196C2×C4×C11C22⋊Q812yes—
197C2×C4×C11C22⋊Q812yes—
198C2×C4×C11C22⋊Q812yes—
199C2×C4×C11C22⋊Q812yes—
200C2×C4×C11#12612yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×Q811yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C22⋊D11—44no—
208C22⋊D11—44no—
209C2×Dic11—24no—
210C2×Dic11—22no—
211C2×Dic11—44no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—82no—
216D44—22no—
217D44—22no—
218D44—41no—
219D44—41no—
220C4×D11—44no—
221C4×D11—44no—
222Dic22—22no—
223Dic22—22no—
224Dic22—41no—
225Dic22—41no—
226C8×C11—24no—
227C8×C11—24no—
228C8×C11—42no—
229C11⋊C8—42no—
230C22×#41—111no—
231C22×M16—111no—
232C22×M16C2×D1111yescharacteristic
233C22×M16C2×D1111yescharacteristic
234C23×C8C2×D1111yescharacteristic
235C2×#117—111no—
236C2×#117—111no—
237C2×#108—24no—
238C2×#108C2×D1114yes—
239#428—114no—
240#428—222no—
241#427—222no—
242#424—114no—
243#424—222no—
244C2×C4⋊C8—222no—
245#419—112no—
246#418—112no—
247#417—222no—
248#416—222no—
249#416—222no—
250#416—222no—
251C2×#103—112no—
252C2×#102—112no—
253#413—224no—
254C2×#101—112no—
255C2×#100—112no—
256#343—114no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11#39612yes—
263C22×C11#39612yes—
264C22×C11C2×#12111yescharacteristic
265C22×C11C2×C22⋊Q811yescharacteristic
266C22×C11C2×#12611yescharacteristic
267C2×D11—42no—
268C2×D11—82no—
269C2×D11—82no—
270C2×D11—82no—
271C4×C11#39612yes—
272C4×C11#39612yes—
273C4×C11C2×#12111yescharacteristic
274C4×C11C2×#12111yescharacteristic
275C4×C11C2×C22⋊Q811yescharacteristic
276C4×C11C2×C22⋊Q811yescharacteristic
277Dic11—42no—
278Dic11—44no—
279Dic11—82no—
280C2×#41—114no—
281C2×#41—222no—
282C2×#41—221no—
283C2×#41—221no—
284C2×#41—222no—
285C2×#41—221no—
286C2×#41—221no—
287C2×#41—222no—
288C22×Q8—111no—
289C22×D4—111no—
290C22×D4—221no—
291C23×C4—221no—
292C23×C4C22×D1111yescharacteristic
293C2×M16—21no—
294C2×M16—22no—
295C2×M16—21no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—112no—
299C2×M16—221no—
300C2×M16—222no—
301C2×M16—222no—
302C2×M16C22⋊D1114yes—
303C2×M16C22×D1112yes—
304C2×M16C22×D1112yes—
305C22×C8—22no—
306C22×C8—21no—
307C22×C8—22no—
308C22×C8—21no—
309C22×C8—221no—
310C22×C8D4412yes—
311C22×C8D4412yes—
312C22×C8C22×D1112yes—
313#117—112no—
314#117—112no—
315#117—221no—
316#117—221no—
317#117—221no—
318#117—221no—
319#117—221no—
320#117—221no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—112no—
323C2×C22⋊C4—221no—
324C2×C22⋊C4—221no—
325C2×C42—221no—
326C2×C42—221no—
327#108—28no—
328#107—224no—
329#106—224no—
330C4⋊C8—228no—
331#103—224no—
332#103—224no—
333#102—224no—
334#102—224no—
335#101—224no—
336#100—224no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—22no—
340C2×C11—22no—
341C2×C11C2×#39611yescharacteristic
342C2×C11#306712yes—
343D11—82no—
344C24—221no—
345C24#434311yescharacteristic
346#41—224no—
347#41—224no—
348#41—224no—
349#41—224no—
350#41—442no—
351#41—442no—
352#41—442no—
353#41—442no—
354C2×Q8—112no—
355C2×Q8—221no—
356C2×Q8—221no—
357C2×Q8—221no—
358C2×Q8—221no—
359C2×Q8—221no—
360C2×D4—112no—
361C2×D4—224no—
362C2×D4—221no—
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—442no—
370C22×C4—222no—
371C22×C4—221no—
372C22×C4—224no—
373C22×C4—222no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4—442no—
377C22×C4C2×D4411yescharacteristic
378C22×C4C2×D4411yescharacteristic
379C22×C4#433912yes—
380C22×C4D4×D1111yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4#434112yes—
383C22×C4Q8×D1112yes—
384C22×C4#434311yescharacteristic
385C22×C4C2×C22⋊D1112yes—
386C22×C4C23×D1111yescharacteristic
387M16—24no—
388M16—22no—
389M16—22no—
390M16—22no—
391M16—42no—
392M16—222no—
393M16—222no—
394M16—442no—
395M16C2×C22⋊D1114yes—
396C2×C8—24no—
397C2×C8—24no—
398C2×C8—24no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—42no—
404C2×C8—222no—
405C2×C8—442no—
406C2×C8C2×D4414yes—
407C4⋊C4—114no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C22⋊C4—222no—
412C22⋊C4—222no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C42—222no—
416C42—222no—
417C42—441no—
418C42—441no—
419C11#2360111yescharacteristic, complemented, Sylow
420C23—42no—
421C23—222no—
422C23—441no—
423C23—441no—
424C23—882no—
425C23#6694811yescharacteristic
426C23#6694811yescharacteristic
427C23#6695112yes—
428C23#6699912yes—
429C23C2×#434311yescharacteristic
430Q8—222no—
431Q8—222no—
432Q8—441no—
433Q8—441no—
434D4—222no—
435D4—222no—
436D4—444no—
437D4—444no—
438D4—441no—
439D4—441no—
440C2×C4—224no—
441C2×C4—222no—
442C2×C4—444no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—444no—
446C2×C4—444no—
447C2×C4—442no—
448C2×C4—882no—
449C2×C4#6694811yescharacteristic
450C2×C4#6694811yescharacteristic
451C2×C4#6694912yes—
452C2×C4#6694912yes—
453C2×C4#6695012yes—
454C2×C4#6695012yes—
455C2×C4#6695112yes—
456C2×C4#6698312yes—
457C2×C4#6698312yes—
458C2×C4#6699212yes—
459C2×C4#6699212yes—
460C2×C4#6699912yes—
461C2×C4C22×D4411yescharacteristic
462C2×C4C2×#433911yescharacteristic
463C2×C4C2×D4×D1111yescharacteristic
464C2×C4C2×#434111yescharacteristic
465C2×C4C2×Q8×D1111yescharacteristic
466C2×C4C22×C22⋊D1111yescharacteristic
467C8—24no—
468C8—24no—
469C8—42no—
470C8—442no—
471C22—22no—
472C22—22no—
473C22—22no—
474C22—42no—
475C22—42no—
476C22—442no—
477C22—882no—
478C22—882no—
479C22—882no—
480C22#1062260712yes—
481C22#1062260712yes—
482C22C2×#6694811yescharacteristic
483C22C2×#6695111yescharacteristic
484C22C2×#6699911yescharacteristic
485C4—444no—
486C4—442no—
487C4—882no—
488C4#1062260712yes—
489C4#1062260712yes—
490C4C2×#6694911yescharacteristic
491C4C2×#6695011yescharacteristic
492C4C2×#6698311yescharacteristic
493C4C2×#6699211yescharacteristic
494C2—21no—
495C2—21no—
496C2—22no—
497C2—22no—
498C2—882no—
499C2C2×#1062260711yescharacteristic
500C2#1307833712yes—
subgroupG/H
centerC2×C4#66948
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#108C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
hypercenterC22×#108D11
hypocenterC11#23601
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#108

Complements

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

NH ≅ G/Ntype
1. #13077206C2semidirect
2. C2×#10622715C2semidirect
6. #13069978C2semidirect
7. #13069971C2semidirect
8. #13068354C2semidirect
9. C22×C11×#108C2semidirect
170. C22×#108D11semidirect
419. C11#23601semidirect

Maximal subgroups

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

subgroupindex
#130772062
C2×#106227152
#130771362
C2×#106227262
C2×#106227452
#130699782
#130699712
#130683542
C22×C11×#1082
#2360111