Finite Group Databasebeta

← #14782680

Subgroups — #14782680

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622611C211yesmaximal, characteristic, complemented
2#13077136C211yesmaximal, characteristic
3#13077133C211yesmaximal, characteristic
4C2×#10622742C211yesmaximal, characteristic
5#13070065C214yesmaximal, complemented
6#13070060C214yesmaximal, complemented
7#13068354C211yesmaximal, characteristic, complemented
8C2×#10622196C211yesmaximal, characteristic, complemented
9C11×#1742C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17#10622746C2214yes—
18#10622744—21no—
19#10622742—22no—
20#10622742C2212yes—
21#10622742C2212yes—
22#10622733—21no—
23#10622726—22no—
24C2×(C2×D11)⋊C8—22no—
25#10622617—21no—
26#10622615—22no—
27#10622614—21no—
28#10622611—22no—
29#10622611—22no—
30#10622579C2214yes—
31C2×#66872C2212yescomplemented
32C2×#66871C2212yescomplemented
33C11×#343C2214yescomplemented
34#10622196C2212yescomplemented
35#10622196C2212yescomplemented
36#10622192C2214yescomplemented
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—22no—
42C2×#4339—22no—
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339D412yes—
46C2×#4339C2312yes—
47C22×D44D411yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22D411yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C2×C11×M16C2312yes—
57C2×C11×M16C2312yes—
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C11×#117—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117—21no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C22⋊Dic11—21no—
68#66979—21no—
69#66979—21no—
70#66979—21no—
71#66979—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4×Dic11—21no—
74C2×#4318—21no—
75C2×#4318—22no—
76C2×#4318—22no—
77C2×#4318C2312yes—
78C22×C11⋊C8—22no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—21no—
81C22×C11⋊C8D412yes—
82C22×C11⋊C8D412yes—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85#66885—24no—
86(C2×D11)⋊C8—24no—
87(C2×D11)⋊C8—24no—
88#66880—24no—
89#66874—24no—
90#66873—24no—
91#66872—24no—
92#66871—24no—
93#23646—111nomaximal, Sylow
94C24×C11#4111yescharacteristic
95C23×D11—21no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4112yes—
103C22×C4×C11#4112yes—
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—22no—
108C2×C22⋊D11—22no—
109C2×C22⋊D11—42no—
110C2×C22⋊D11—42no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113#4339—24no—
114#4339—24no—
115#4339—22no—
116#4339—22no—
117#4339—22no—
118#4339—22no—
119#4339—42no—
120#4339—42no—
121#4339—42no—
122#4339—42no—
123C2×D44—21no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44C2×D412yes—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×Dic22—21no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22C2×D412yes—
135C11×M16—22no—
136C11×M16—22no—
137C11×M16—22no—
138C11×M16—22no—
139C11×M16—42no—
140C11×M16—42no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—42no—
144C2×C8×C11—42no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C42×C11—41no—
150C42×C11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4×Dic11—41no—
156C4×Dic11—41no—
157#4318—22no—
158#4318—22no—
159#4318—42no—
160C2×C11⋊C8—24no—
161C2×C11⋊C8—24no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—42no—
168C2×C11⋊C8C2×D412yes—
169C2×C11⋊C8C2×D412yes—
170C2×#427—111no—
171#2896—111no—
172#2896—111no—
173C2×#408—111no—
174#2079—114no—
175#2078—114no—
176#1742—111no—
177#1742D1111yescharacteristic, complemented
178C2×#341—111no—
179C23×C11—42no—
180C23×C11#12111yescharacteristic
181C23×C11#12111yescharacteristic
182C23×C11#12612yes—
183C23×C11#12612yes—
184C23×C11C2×#4111yescharacteristic
185C22×D11—22no—
186C22×D11—44no—
187C22×D11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—82no—
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12312yes—
193C2×C4×C11#12312yes—
194C2×C4×C11#12312yes—
195C2×C4×C11#12312yes—
196C2×C4×C11#12312yes—
197C2×C4×C11#12312yes—
198C2×C4×C11#12412yes—
199C2×C4×C11#12412yes—
200C2×C4×C11#12612yes—
201C2×C4×C11#12612yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C22⋊D11—42no—
209C22⋊D11—42no—
210C22⋊D11—44no—
211C2×Dic11—22no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—82no—
215D44—22no—
216D44—22no—
217D44—42no—
218C4×D11—42no—
219C4×D11—42no—
220C4×D11—44no—
221Dic22—22no—
222Dic22—22no—
223Dic22—42no—
224C8×C11—42no—
225C8×C11—42no—
226C11⋊C8—22no—
227C11⋊C8—22no—
228C11⋊C8—42no—
229C22×#41—111no—
230C22×M16—111no—
231C22×M16C2×D1111yescharacteristic
232C22×M16C2×D1111yescharacteristic
233C23×C8—111no—
234C2×#117—111no—
235C2×#117C2×D1111yescharacteristic
236#427—222no—
237#427—222no—
238C2×#107—112no—
239C2×#106—112no—
240#419—221no—
241#419—221no—
242#418—221no—
243#418—221no—
244#417—114no—
245#417—114no—
246#416—222no—
247#416—222no—
248#408—112no—
249#408—112no—
250#408—222no—
251C2×C22⋊C8—222no—
252#343—114no—
253#343C2×D1114yescomplemented
254#341—112no—
255#341—112no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11#39712yes—
262C22×C11#39712yes—
263C22×C11C2×#12111yescharacteristic
264C22×C11C2×#12611yescharacteristic
265C22×C11C2×#12611yescharacteristic
266C2×D11—42no—
267C2×D11—44no—
268C2×D11—84no—
269C4×C11—82no—
270C4×C11#39712yes—
271C4×C11#39712yes—
272C4×C11C2×#12311yescharacteristic
273C4×C11C2×#12311yescharacteristic
274C4×C11C2×#12311yescharacteristic
275C4×C11C2×#12411yescharacteristic
276Dic11—42no—
277Dic11—82no—
278C2×#41—112no—
279C2×#41—112no—
280C2×#41—221no—
281C2×#41—221no—
282C2×#41—222no—
283C2×#41—222no—
284C2×#41—222no—
285C2×#41—222no—
286C22×Q8—111no—
287C22×D4—111no—
288C22×D4—221no—
289C23×C4—221no—
290C23×C4C22×D1111yescharacteristic
291C2×M16—21no—
292C2×M16—21no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—112no—
298C2×M16—221no—
299C2×M16—222no—
300C2×M16—222no—
301C2×M16C22×D1112yes—
302C2×M16C22×D1112yes—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—112no—
306C22×C8—112no—
307C22×C8—111no—
308C22×C8—111no—
309C22×C8—222no—
310C22×C8—222no—
311C22×C8—221no—
312#117—21no—
313#117—21no—
314#117—21no—
315#117—21no—
316#117—221no—
317#117—221no—
318#117—221no—
319#117—221no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4C22×D1112yes—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—221no—
324C2×C42—21no—
325C2×C42—221no—
326#107—224no—
327#106—224no—
328#103—224no—
329#103—224no—
330#102—224no—
331#102—224no—
332C22⋊C8—224no—
333C22⋊C8—224no—
334C2×C11—22no—
335C2×C11—21no—
336C2×C11—21no—
337C2×C11—22no—
338C2×C11C2×#39711yescharacteristic
339C2×C11#306712yes—
340D11—82no—
341C24—221no—
342C24#433911yescharacteristic
343#41—224no—
344#41—224no—
345#41—222no—
346#41—222no—
347#41—222no—
348#41—222no—
349#41—442no—
350#41—442no—
351#41—442no—
352#41—442no—
353C2×Q8—112no—
354C2×Q8—221no—
355C2×Q8—222no—
356C2×Q8—222no—
357C2×D4—112no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—221no—
362C2×D4—222no—
363C2×D4—442no—
364C2×D4—442no—
365C22×C4—22no—
366C22×C4—221no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4#433911yescharacteristic
373C22×C4#433912yes—
374C22×C4#433912yes—
375C22×C4D4×D1111yescharacteristic
376C22×C4D4×D1111yescharacteristic
377C22×C4D4×D1111yescharacteristic
378C22×C4D4×D1111yescharacteristic
379C22×C4#434112yes—
380C22×C4#434312yes—
381C22×C4C23×D1111yescharacteristic
382M16—22no—
383M16—22no—
384M16—22no—
385M16—22no—
386M16—42no—
387M16—42no—
388M16—222no—
389M16—222no—
390M16—442no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—42no—
394C2×C8—42no—
395C2×C8—112no—
396C2×C8—112no—
397C2×C8—224no—
398C2×C8—224no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—222no—
404C2×C8—442no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C42—41no—
414C42—41no—
415C42—441no—
416C42—441no—
417C11#2364611yescharacteristic, complemented, Sylow
418C23—42no—
419C23—222no—
420C23—444no—
421C23—442no—
422C23#6692912yes—
423C23#6693711yescharacteristic
424C23#6693711yescharacteristic
425C23#6695112yes—
426C23C2×#433911yescharacteristic
427Q8—222no—
428Q8—222no—
429Q8—442no—
430D4—222no—
431D4—222no—
432D4—442no—
433D4—442no—
434D4—444no—
435D4—442no—
436C2×C4—42no—
437C2×C4—82no—
438C2×C4—222no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—444no—
443C2×C4—442no—
444C2×C4—882no—
445C2×C4#6692912yes—
446C2×C4#6693612yes—
447C2×C4#6693612yes—
448C2×C4#6693711yescharacteristic
449C2×C4#6693711yescharacteristic
450C2×C4#6693812yes—
451C2×C4#6693812yes—
452C2×C4#6694712yes—
453C2×C4#6694712yes—
454C2×C4#6694712yes—
455C2×C4#6694712yes—
456C2×C4#6695112yes—
457C2×C4C2×#433911yescharacteristic
458C2×C4C2×#433911yescharacteristic
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4C2×#434311yescharacteristic
463C8—42no—
464C8—42no—
465C8—222no—
466C8—222no—
467C8—442no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—42no—
472C22—42no—
473C22—444no—
474C22—442no—
475C22—884no—
476C22#1062228812yes—
477C22#1062228812yes—
478C22C2×#6692911yescharacteristic
479C22C2×#6693711yescharacteristic
480C22C2×#6695111yescharacteristic
481C4—82no—
482C4—442no—
483C4—882no—
484C4#1062228812yes—
485C4#1062228812yes—
486C4C2×#6693611yescharacteristic
487C4C2×#6693811yescharacteristic
488C4C2×#6694711yescharacteristic
489C4C2×#6694711yescharacteristic
490C2—22no—
491C2—21no—
492C2—21no—
493C2—22no—
494C2—882no—
495C2C2×#1062228811yescharacteristic
496C2#1307833512yes—
subgroupG/H
centerC2×C4#66937
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1742C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
hypercenter#1742D11
hypocenterC11#23646
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
1. C2×#10622611C2semidirect
5. #13070065C2semidirect
6. #13070060C2semidirect
7. #13068354C2semidirect
8. C2×#10622196C2semidirect
9. C11×#1742C2semidirect
31. C2×#66872C22semidirect
32. C2×#66871C22semidirect
33. C11×#343C22semidirect
34. #10622196C22semidirect
35. #10622196C22semidirect
36. #10622192C22semidirect
177. #1742D11semidirect
253. #343C2×D11semidirect
417. C11#23646semidirect

Maximal subgroups

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

subgroupindex
C2×#106226112
#130771362
#130771332
C2×#106227422
#130700652
#130700602
#130683542
C2×#106221962
C11×#17422
#2364611